%! % The following defines procedures assumed and used by program "dvi2ps" % % $Header: tex.ps,v 1.15 88/01/21 23:44:40 van Exp $ % % Original By: Neal Holtz, Carleton University, Ottawa, Canada % % % June, 1985 % Seriously hacked by Van Jacobson, LBL % /TeXDict 200 dict def % define a working dictionary TeXDict begin % start using it. % units are in "dots" (300/inch) /Resolution 300 def /Inch {Resolution mul} def % converts inches to internal units /Mtrx 6 array def %%%%%%%%%%%%%%%%%%%%% Page setup (user) options %%%%%%%%%%%%%%%%%%%%%%%% % dvi2ps will output coordinates in the TeX system ([0,0] 1" down and in % from top left, with y +ive downward). The default PostScript system % is [0,0] at bottom left, y +ive up. The Many Matrix Machinations in % the following code are an attempt to reconcile that. The intent is to % specify the scaling as 1 and have only translations in the matrix to % properly position the text. Caution: the default device matrices are % *not* the same in all PostScript devices; that should not matter in most % of the code below (except for lanscape mode -- in that, rotations of % -90 degrees resulted in the the rotation matrix [ e 1 ] % [ 1 e ] % where the "e"s were almost exactly but not quite unlike zeros. /@letter { % letter initmatrix 72 Resolution div dup neg scale % set scaling to 1. 310 -3005 translate % move origin to top (these are not exactly 1" Mtrx currentmatrix pop % and -10" because margins aren't set exactly right) /@TeXSave save def } def % note mode is like letter, except it uses less VM /@note { note initmatrix 72 Resolution div dup neg scale % set scaling to 1. 310 -3005 translate % move origin to top Mtrx currentmatrix pop /@TeXSave save def } def /@landscape { % letter initmatrix 72 Resolution div dup neg scale % set scaling to 1. [0 -1 1 0 0 0] concat 300 310 translate % move origin to top Mtrx currentmatrix pop /@TeXSave save def } def /@legal { legal initmatrix 72 Resolution div dup neg scale % set scaling to 1. 295 -3880 translate % move origin to top Mtrx currentmatrix pop /@TeXSave save def } def /@manualfeed { statusdict /manualfeed true put } def /@duplex { statusdict begin /setduplexmode where { pop true setduplexmode } if end } def % n @copies - set number of copies /@copies { /#copies exch def } def %%%%%%%%%%%%%%%%%%%% Procedure Defintions %%%%%%%%%%%%%%%%%%%%%%%%%% % id @newfont - initialize a new font dictionary /@newfont { /newname exch def /xscale exch def % these two lines are added here for scaling /yscale xscale neg def newname 7 dict def % allocate new font dictionary newname load begin /FontType 3 def /FontMatrix [xscale 0 0 yscale 0 0] def /FontBBox [0 0 1 1] def /BitMaps 128 array def /BuildChar {CharBuilder} def /Encoding 128 array def 0 1 127 {Encoding exch /.undef put} for end newname newname load definefont pop } def % the following is the only character builder we need. it looks up the % char data in the BitMaps array, and paints the character if possible. % char data -- a bitmap descriptor -- is an array of length 6, of % which the various slots are: /ch-image {ch-data 0 get} def % the hex string image /ch-width {ch-data 1 get} def % the number of pixels across /ch-height {ch-data 2 get} def % the number of pixels tall /ch-xoff {ch-data 3 get} def % number of pixels below origin /ch-yoff {ch-data 4 get} def % number of pixels to left of origin /ch-tfmw {ch-data 5 get} def % spacing to next character % fontdict ch Charbuilder - -- image one character /CharBuilder { /ch-code exch def % save the char code /font-dict exch def % and the font dict. /ch-data font-dict /BitMaps get ch-code get def % get the bitmap ch-data null eq not { ch-tfmw 0 ch-xoff neg ch-yoff neg ch-width ch-xoff sub ch-height ch-yoff sub setcachedevice ch-width ch-height true [1 0 0 1 ch-xoff ch-yoff] {ch-image} imagemask } if } def % fontdict @sf - -- make that the current font /@sf { setfont } def % in the following, the font-cacheing mechanism requires that % a name unique in the particular font be generated % char-data ch @dc - -- define a new character bitmap in current font /@dc { /ch-code exch def dup 0 get length 2 lt { pop [ <00> 1 1 0 0 8.00 ] } % replace <> with null if /ch-data exch def currentfont /BitMaps get ch-code ch-data put % generate a unique name simply from the character code currentfont /Encoding get ch-code dup ( ) cvs cvn put } def /@DRAFTF { gsave initmatrix newpath /Helvetica-Bold findfont setfont (Draft) dup stringwidth pop 8.875 exch div dup 72 mul dup scale 52.3 rotate 2.5 exch div -.35 translate 0.95 setgray 0 0 moveto show grestore } def /@DRAFTM { gsave initmatrix newpath /Helvetica-Bold findfont 72 scalefont setfont 0.95 setgray 576 702 moveto (Draft) stringwidth exch neg exch neg rmoveto (Draft) show grestore } def % n @bop0 - -- begin the char def section of a new page /@bop0 { pop } def % n @bop1 - -- begin a brand new page /@bop1 { pop Mtrx setmatrix /SaveImage save def } def /@draft { /@bop1 { 1 le {@DRAFTF} {@DRAFTM} ifelse Mtrx setmatrix /SaveImage save def } def } def % - @eop - -- end a page /@eop { showpage SaveImage restore } def % - @start - -- start everything /@start { @letter /@TeXSave save def } def % - @end - -- done the whole shebang /@end { end } def % x y p - -- move to position /p { moveto } bind def % x r - -- move right /r { 0 rmoveto } bind def % string s - -- show the string /s { show } bind def % x string m - -- move right then show string /m { exch 0 rmoveto show } bind def % ch c - -- show the character (code given) /c { c-string dup 0 4 -1 roll put show } bind def /c-string ( ) def % dx dy ru - -- set a rule (rectangle) /ru { /dy exch neg def % because dy is height up from bottom /dx exch def /x currentpoint /y exch def def % remember current point newpath x y moveto dx 0 rlineto 0 dy rlineto dx neg 0 rlineto closepath fill x y moveto } bind def /@MacSetUp { userdict /md known % if md is defined { userdict /md get type /dicttype eq % and if it is a dictionary { md begin % then redefine some stuff /letter {} def /note {} def /legal {} def /od{txpose 1 0 mtx defaultmatrix dtransform exch atan/pa exch def newpath clippath mark {transform{itransform moveto}} {transform{itransform lineto}} { 6 -2 roll transform 6 -2 roll transform 6 -2 roll transform { itransform 6 2 roll itransform 6 2 roll itransform 6 2 roll curveto } } {{closepath}} pathforall newpath counttomark array astore /gc xdf pop ct 39 0 put 10 fz 0 fs 2 F/|______Courier fnt invertflag{PaintBlack}if }def /txpose{ pxs pys scale ppr aload pop por { noflips { pop exch neg exch translate pop 1 -1 scale }if xflip yflip and { pop exch neg exch translate 180 rotate 1 -1 scale ppr 3 get ppr 1 get neg sub neg ppr 2 get ppr 0 get neg sub neg translate }if xflip yflip not and { pop exch neg exch translate pop 180 rotate ppr 3 get ppr 1 get neg sub neg 0 translate }if yflip xflip not and { ppr 1 get neg ppr 0 get neg translate }if } { noflips { translate pop pop 270 rotate 1 -1 scale }if xflip yflip and { translate pop pop 90 rotate 1 -1 scale ppr 3 get ppr 1 get neg sub neg ppr 2 get ppr 0 get neg sub neg translate }if xflip yflip not and { translate pop pop 90 rotate ppr 3 get ppr 1 get neg sub neg 0 translate }if yflip xflip not and { translate pop pop 270 rotate ppr 2 get ppr 0 get neg sub neg 0 exch translate }if }ifelse scaleby96 { ppr aload pop 4 -1 roll add 2 div 3 1 roll add 2 div 2 copy translate .96 dup scale neg exch neg exch translate }if }def /cp {pop pop showpage pm restore}def end }if } if } def % All software, documentation, and related files in this distribution of % psfig/tex are Copyright (c) 1987 Trevor J. Darrell % % Permission is granted for use and non-profit distribution of psfig/tex % providing that this notice be clearly maintained, but the right to % distribute any portion of psfig/tex for profit or as part of any commercial % product is specifically reserved for the author. % % % psfigTeX PostScript Prolog % $Header: tex.ps,v 1.15 88/01/21 23:44:40 van Exp $ % /psf$TeXscale { 65536 div } def /DocumentInitState [ matrix currentmatrix currentlinewidth currentlinecap currentlinejoin currentdash currentgray currentmiterlimit ] cvx def % x y bb-llx bb-lly bb-urx bb-ury startFig - /startTexFig { /psf$SavedState save def userdict maxlength dict begin currentpoint transform DocumentInitState setmiterlimit setgray setdash setlinejoin setlinecap setlinewidth setmatrix itransform moveto /psf$ury exch psf$TeXscale def /psf$urx exch psf$TeXscale def /psf$lly exch psf$TeXscale def /psf$llx exch psf$TeXscale def /psf$y exch psf$TeXscale def /psf$x exch psf$TeXscale def currentpoint /psf$cy exch def /psf$cx exch def /psf$sx psf$x psf$urx psf$llx sub div def % scaling for x /psf$sy psf$y psf$ury psf$lly sub div def % scaling for y psf$sx psf$sy scale % scale by (sx,sy) psf$cx psf$sx div psf$llx sub psf$cy psf$sy div psf$ury sub translate /DefFigCTM matrix currentmatrix def /initmatrix { DefFigCTM setmatrix } def /defaultmatrix { DefFigCTM exch copy } def /initgraphics { DocumentInitState setmiterlimit setgray setdash setlinejoin setlinecap setlinewidth setmatrix DefFigCTM setmatrix } def /showpage { initgraphics } def /erasepage { } def /copypage { initgraphics } def @MacSetUp } def % llx lly urx ury doclip - (args in figure coordinates) /doclip { currentpoint 6 2 roll newpath 4 copy 4 2 roll moveto 6 -1 roll exch lineto exch lineto exch lineto closepath clip newpath moveto } def % - endTexFig - /endTexFig { end psf$SavedState restore } def %%%% Additions by LA Carr to reencode Adobe fonts as TeX fonts (almost) %%%% Based on routine in LaserWriter Cookbook /ReEncodeForTeX { /newfontname exch def /basefontname exch def /TeXstr 30 string def /basefontdict basefontname findfont def /newfont basefontdict maxlength dict def basefontdict { exch dup /FID ne { dup /Encoding eq { exch dup length array copy newfont 3 1 roll put } { exch newfont 3 1 roll put } ifelse } { pop pop } ifelse } forall basefontdict /MathFontName known not { /TeXvec basefontname TeXstr cvs (Courier) search { pop pop pop TeXcourvec } { pop TeXnormalvec } ifelse def TeXvec aload pop TeXvec length 2 idiv { newfont /Encoding get 3 1 roll put } repeat } if newfontname newfont definefont pop } def /TeXnormalvec [ 8#014 /fi 8#015 /fl 8#020 /dotlessi 8#022 /grave 8#023 /acute 8#024 /caron 8#025 /breve 8#026 /macron 8#027 /ring 8#030 /cedilla 8#031 /germandbls 8#032 /ae 8#033 /oe 8#034 /oslash 8#035 /AE 8#036 /OE 8#037 /Oslash 8#042 /quotedblright 8#074 /exclamdown 8#076 /questiondown 8#134 /quotedblleft 8#136 /circumflex 8#137 /dotaccent 8#173 /endash 8#174 /emdash 8#175 /hungarumlat 8#176 /tilde 8#177 /dieresis ] def /TeXcourvec [ 8#016 /exclamdown 8#017 /questiondown 8#020 /dotlessi 8#022 /grave 8#023 /acute 8#024 /caron 8#025 /breve 8#026 /macron 8#027 /ring 8#030 /cedilla 8#031 /germandbls 8#032 /ae 8#033 /oe 8#034 /oslash 8#035 /AE 8#036 /OE 8#037 /Oslash 8#074 /less 8#076 /greater 8#134 /backslash 8#136 /circumflex 8#137 /underscore 8#173 /braceleft 8#174 /bar 8#175 /braceright 8#177 /dieresis ] def /TeXPSmakefont { % defines a routine for generating PS fonts, fudged! /TeXsize exch def findfont [ TeXsize 0 0 TeXsize neg 0 0 ] makefont } def % fontname basefontname angle ObliqueFont - % Create a General Oblique font /ObliqueFont { /ObliqueAngle exch def /ObliqueBaseName exch def /ObliqueFontName exch def /ObliqueTransform [1 0 ObliqueAngle sin ObliqueAngle cos div 1 0 0] def /basefontdict ObliqueBaseName findfont ObliqueTransform makefont def /newfont basefontdict maxlength dict def basefontdict { exch dup /FID ne { dup /Encoding eq { exch dup length array copy newfont 3 1 roll put } { exch newfont 3 1 roll put } ifelse } { pop pop } ifelse } forall newfont /FontName ObliqueFontName put ObliqueFontName newfont definefont pop } def % Palatino-ItalicUnslanted? You must be joking! % fontname basename SmallCapsFont - Create a General SmallCaps font /SmallCapsFont { /SmallCapsBaseName exch def /SmallCapsFontName exch def /basefontdict SmallCapsBaseName findfont def /newfont basefontdict maxlength 10 add dict def newfont begin /FontName SmallCapsFontName def /FontBaseDict basefontdict 1000 scalefont def /FontSCDict FontBaseDict .8 scalefont def /FontType 3 def /BuildChar {SmallCapChar} def /FontMatrix dup basefontdict exch get def /FontBBox dup basefontdict exch get def /Encoding dup basefontdict exch get def end SmallCapsFontName newfont definefont pop } def % fontdict ch SmallCapChar - % It shouldn't be so damn hard to do this (make one font out % of two others) but I tried several dozen variations on this % theme until I found something that worked. -- vj /SmallCapChar { /achar (A) def achar exch 0 exch put begin achar 0 get dup 97 ge exch 122 le and { % handle 'a' through 'z' specially achar 0 achar 0 get 32 sub put FontSCDict } { FontBaseDict } ifelse setfont achar stringwidth FontBBox setcachedevice newpath 0 0 moveto achar show end } def /MathEncodingVec [ /Gamma /Delta /Theta /Lambda /Xi /Pi /Sigma /Upsilon1 /Phi /Psi /Omega /alpha /beta /gamma /delta /epsilon /zeta /nu /theta /iota /kappa /lambda /mu /nu /xi /pi /rho /sigma /tau /upsilon /phi /chi /psi /omega /epsilon /theta1 /omega1 /rho /sigma /phi1 /arrowleft /arrowleft /arrowright /arrowright /suchthat /congruent /proportional /angle /zero /one /two /three /four /five /six /seven /eight /nine /period /comma /less /slash /greater /asteriskmath /partialdiff /A /B /C /D /E /F /G /H /I /J /K /L /M /N /O /P /Q /R /S /T /U /V /W /X /Y /Z /registerserif /copyrightserif /trademarkserif /logicalor /logicaland /section /a /b /c /d /e /f /g /h /i /j /k /l /m /n /o /p /q /r /s /t /u /v /w /x /y /z /dotlessi /j /weierstrass /macron /breve ] def % the following gives the character codes of the above characters % in their font. I.e., this is the character we have to hand "show" % to image the characters above. /MathCharVec [ 71 68 81 76 88 80 83 161 70 89 87 97 98 103 100 101 122 110 113 105 107 108 109 110 120 112 114 115 116 117 102 99 121 119 101 74 118 114 115 106 172 172 174 174 39 64 181 208 48 49 50 51 52 53 54 55 56 57 46 44 60 47 62 42 182 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 210 211 212 218 217 167 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 245 106 195 197 198 ] def % this array tells which font dictionary holds each character above % (0 = basefont, 1 = symbol (maybe slanted), 2 = symbol (unslanted)). /MathDictVec [ 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 ] def % fontname basename symbolname symbolbase angle MathOblique - % Create a "math" font with the symbol font characters slanted % by "angle" /MathOblique { 3 copy ObliqueFont pop pop MathFont } def % fontname basename symbolname MathFont - Create a math italic font % % We build this font out of the base font & the symbol font % using an encoding vec as close as we can get to cmmi10 with % standard postscript characters. An array parallel to the % encoding vector tells which font dictionary to use for a % particular character. /MathFont { /MathSymName exch def /MathBaseName exch def /MathFontName exch def /basefontdict MathBaseName findfont def /newfont basefontdict maxlength 10 add dict def newfont begin /FontName MathFontName def /FontDictArray [ basefontdict 1000 scalefont MathSymName findfont 950 scalefont /Symbol findfont 950 scalefont ] def /FontType 3 def /BuildChar {MathFontChar} def /FontMatrix dup basefontdict exch get def /FontBBox dup basefontdict exch get def % the encoding vector is a copy of the original font's % encoding, modified "appropriately". /Encoding dup basefontdict exch get dup length array copy def /WhichFont MathDictVec def /WhichChar MathCharVec def MathEncodingVec Encoding copy pop /achar (A) def end MathFontName newfont definefont pop } def % fontdict ch MathFontChar - % (there's some serious magic going on here: see note on % SmallCapChar above -- vj). /MathFontChar { exch begin achar exch 0 exch put FontDictArray WhichFont achar 0 get get get setfont achar dup 0 get WhichChar exch get 0 exch put achar stringwidth FontBBox setcachedevice newpath 0 0 moveto achar show end } bind def /@flushfonts { @TeXSave restore /@TeXSave save def} def end % revert to previous dictionary TeXDict begin @start %%Title: guide.dvi %%Creator: dvi2ps %%EndProlog %%Page: 1 1 1 @bop0 1.000000 /cmss10.432 @newfont cmss10.432 @sf [ 32 42 -5 0 42.340] 78 @dc [ 8 42 -5 0 16.604] 73 @dc [<00FF800007FFE0001FFFF8007FFFFC00FF80FE00FC003F00F0001F0060000F8000000F80000007 C0000007C0000007C0000007C0000007C0000007C000000FC000001F8000001F8000007F800003 FF00003FFE0001FFFC0007FFF8000FFFF0001FFFC0003FFE00003FE000007F0000007E000000FC 000000FC000000F8000000F8000000F8000000F8000000780000007C0000007E0006003F000F00 1FC07F000FFFFF0007FFFE0001FFF800007FC000> 32 44 -3 1 33.208] 83 @dc [<0001F800000001F800000001F800000001F800000001F800000001F800000001F800000001F800 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1E03E03F03E03F03E03F07C03F0FC01FFF8007FC00> 24 20 -1 0 25.410] 97 @dc [<01F807FC0FCC0F860F860F860F860F860F800F800F800F800F800F800F800F800F800F80FFFCFF FC3F800F800780038003800380018001800180> 16 29 -1 0 20.328] 116 @dc [<03FF801FFFF03F01F87C007CF8003EF0001EF0001EF0001EF8003E7C00FE3FFFFC0FFFF81FFFF0 1FFFC01E00001C00001800001FFE001FFF801F8FC01F07C03E03E03E03E03E03E03E03E03E03E0 1F07DE1F8FDE0FFFFE03FE7C> 24 30 -1 10 26.136] 103 @dc [ 16 33 -2 0 14.520] 105 @dc cmr10.329 @sf [<001FF000007FFC6001FC1FE003E007E007C003E00F8001E01F0001E03E0001E03E0001E07C0001 E07C0001E07C0001E0F8007FFCF8007FFCF8000000F8000000F8000000F8000000F8000000F800 0000F80000607C0000607C0000607C0000E03E0000E03E0000E01F0001E00F8003E007C007E003 E00FE001F83CE0007FF860001FE060> 32 33 -3 1 35.668] 71 @dc [ 24 30 -2 0 22.727] 50 @dc [ 32 31 -2 0 30.934] 69 @dc [ 16 30 -4 0 22.727] 49 @dc [ 32 31 -2 0 32.196] 66 @dc 3 @bop1 cmcsc10.518 @sf 225 519 p (Abstra)s -1(ct)m cmr10.329 @sf 225 746 p (ODRP)s -3 r 65 c (CK)s 17(is)m 18 r 97 c 18(soft)m 119 c -2(are)m 16(pac)m 107 c -2(age)m 17(for)m cmti10.329 @sf 17(weighte)m -1 r 100 c 19(ortho)m -1(gonal)m 18(distanc)m -1 r 101 c 17 r 114 c -1 r 101 c -1(g)m -1 r 114 c -2(ess)m -1(ion)m cmr10.329 @sf 44 c 17(i.e.,)m 18(for)m 225 802 p (\014nding)s 16(the)m 16(parameters)m 15(that)m 15(minimize)m 15(the)m 15(sum)m 16(of)m 16(the)m 15(squared)m 16 r 119 c (eigh)s -1(ted)m 14(orthogonal)m 14(dis-)m 225 858 p (tances)s 14(from)m 13 r 97 c 14(set)m 13(of)m 14(observ)m -2(ations)m 12(to)m 13(the)m 15(curv)m 101 c 13(or)m 13(surface)m 14(determined)m 14 r 98 c 121 c 13(the)m 14(parameters.)m 225 915 p (It)s 17(can)m 17(also)m 16 r 98 c 1 r 101 c 18(used)m 18(to)m 16(solv)m 101 c 15(the)m 17(nonlinear)m 17(ordinary)m 16(least)m 16(squares)m 17(problem.)m 25(The)m 17(pro)m 1(ce-)m 225 971 p (dure)s 17(has)m 16(application)m 15(to)m 16(curv)m 101 c 15(and)m 17(surface)m 16(\014tting,)m 15(and)m 17(to)m 15(measuremen)m 116 c 15(error)m 16(mo)m 1(dels)m 16(in)m 225 1028 p (statistics.)s 18(ODRP)m -3 r 65 c (CK)s 13(can)m 15(handle)m 15 r 98 c 1(oth)m 15(explicit)m 14(and)m 14(implicit)m 14(mo)m 1(dels,)m 14(and)m 15(will)m 13(easily)m 14(ac-)m 225 1084 p (commo)s 1(date)m 10(complex)m 11(and)m 11(other)m 11 r 116 c (yp)s 1(es)m 10(of)m 10 r 109 c (ultiresp)s 1(onse)m 9(data.)m 18(The)m 11(algorithm)m 9(implemen)m (ted)s 225 1141 p (is)s 14(an)m 14(e\016cien)m 116 c 13(and)m 15(stable)m 14(trust)m 14(region)m 13(Lev)m (en)s 98 c 1(erg-Marquardt)m 12(pro)m 1(cedure)m 16(that)m 13(exploits)m 14(the)m 225 1197 p (structure)s 17(of)m 17(the)m 17(problem)m 17(so)m 17(that)m 16(the)m 17(computational)m 16(cost)m 16 r 112 c 1(er)m 18(iteration)m 15(is)m 17(equal)m 17(to)m 17(that)m 225 1254 p (for)s 13(the)m 14(same)m 14 r 116 c (yp)s 1 r 101 c 13(of)m 14(algorithm)m 12(applied)m 14(to)m 13(the)m 14(nonlinear)m 14(ordinary)m 13(least)m 13(squares)m 14(problem.)m 225 1310 p (The)s 12(pac)m 107 c -2(age)m 11(allo)m -1(ws)m 10 r 97 c 12(general)m 11 r 119 c (eigh)s -1(ting)m 10(sc)m (heme,)s 12(pro)m (vides)s 10(for)m 12(\014nite)m 12(di\013erence)m 12(deriv)m -2(ativ)m -1(es,)m 225 1367 p (and)s 15(con)m (tains)s 14(extensiv)m 101 c 14(error)m 14 r 99 c (hec)s (king)s 13(and)m 16(rep)m 1(ort)m 14(generating)m 15(facilities.)m cmbx10.329 @sf 239 1514 p (Keyw)s (ords)s -1 r 58 c cmr10.329 @sf 44(orthogonal)m 9(distance)m 11(regression;)m 11(measuremen)m 116 c 10(error)m 11(mo)m 1(dels;)m 12(errors)m 10(in)m 11 r 118 c -2(ari-)m 526 1570 p (ables;)s 14(nonlinear)m 15(least)m 14(squares.)m cmbx10.329 @sf 225 1705 p (Categories:)s cmr10.329 @sf 45(G2E,)m 14(I1B1)m 1069 2581 p (iii)s @eop %%Page: 4 6 4 @bop0 4 @bop1 cmr10.329 @sf 0 123 p (iv)s 1515(Abstract)m 0 134 p 1725 2 ru @eop %%Page: 5 7 5 @bop0 cmcsc10.518 @sf [<0000000001FC00FFFFF80007FF00FFFFF8001FC38003FE00003F80C001FC00007F00C001FC0000 FF006001FC0000FF006001FC0001FE006001FC0001FE006001FC0001FE000001FC0001FE000001 FC0001FE000001FC0001FE000001FC0001FC000001FC0001FC000001FC0001FC000001FC0001FC 000001FC0001FC000001FC0001F8000001FC0003F8000001FC0003F0000001FC0003F0000001FC 0007E0000001FC000F80000001FC007F00000001FFFFFC00000001FFFFFF00000001FC003FC000 0001FC0007F0000001FC0001F8000001FC0000FE000001FC00007F000001FC00007F000001FC00 003F800001FC00003F800001FC00003FC00001FC00003FC00001FC00003FC00001FC00003FC000 01FC00003FC00001FC00003F800001FC00003F800001FC00007F000001FC00007F000001FC0000 FE000001FC0001F8000001FC0007F0000003FE003FC00000FFFFFFFF000000FFFFFFF0000000> 56 50 -4 1 57.383] 82 @dc [ 40 37 -3 0 40.009] 101 @dc [<000018000000003C000000003C000000007E000000007E000000007E00000000FB00000000FB00 000001FB80000001F180000001F180000003E0C0000003E0C0000007E0E0000007C060000007C0 6000000F803000000F803000001F001800001F001800003F001C00003E000C00003E000C00007C 000600007C00060000FC00070000F800030000F800030001F000018001F000018003F00001C003 E00000C003E00000E007E00001F00FE00003F8FFFC0007FFFFFC0007FF> 40 37 -1 0 43.994] 118 @dc [ 16 37 -3 0 21.678] 105 @dc [<0001FE0000000FFFC000003F03F00000F8007C0001F0003E0003E0001F0007C0000F800F800007 C01F800007E01F000003E03F000003F03E000001F07E000001F87E000001F87C000000F8FC0000 00FCFC000000FCFC000000FCFC000000FCFC000000FCFC000000FCFC000000FCFC000000FCFC00 0000FC7C000000F87E000001F87E000001F83E000001F03E000001F01F000003E01F000003E00F 800007C007C0000F8003E0001F0001F0003E0000F8007C00003F03F000000FFFC0000001FE0000> 40 39 -3 1 45.588] 111 @dc [ 40 37 -3 0 43.994] 110 @dc [ 56 49 -4 0 58.379] 72 @dc [<0007FFF0000007FFF00000007F000000003E000000003E000000003E000000003E000000003E00 0000003E000000003E000000003E000000003E000000003E000000003E000000003E000000003E 000000007F00000000FF80000000F980000001F9C0000003F0C0000007E060000007E07000000F C03000001F801800001F801C00003F000C00007E000E00007E00070000FC00030001F800038001 F800018003F00001C007E00001E00FF00003F8FFFC0007FFFFFC0007FF> 40 37 -1 0 43.994] 121 @dc cmr10.329 @sf [<03F0000FFC001E1E001C0E00380700780780700380700380700380F003C0F003C0F003C0F003C0 F003C0F003C0F003C0F003C0F003C0F003C0F003C0F003C0F003C0700380700380700380780780 3807001C0E001E1E000FFC0003F000> 24 31 -2 1 22.727] 48 @dc [<00E001C003C0038007000E000E001C001C003800380030007000700070006000E000E000E000E0 00E000E000E000E000E000E000E000E000E000E00060007000700070003000380038001C001C00 0E000E000700038003C001C000E0> 16 46 -3 12 17.676] 40 @dc [<03F0000FFC001E1E003C0F003807807807807803C07003C07003C0F003C0F003C0F003C0F003C0 F003C0F80380F80780FC0780FE0F00F7FE00F3FC00F060007000007800007800003C07803C0780 1E07800F078007C78003FF0000FE00> 24 31 -2 1 22.727] 54 @dc [<0FC0003FF000787800783C00781E00780F007807000007800007800003800183C00FF3C01FFBC0 3C1FC0780FC07807C07007C0F003C0F003C0F003C0F003C0F003C0F00380F00380F00780780780 7807003C0F001E1E000FFC0003F000> 24 31 -2 1 22.727] 57 @dc [ 16 46 -3 12 17.676] 41 @dc 1.000000 /cmtt10.329 @newfont cmtt10.329 @sf [ 24 28 -1 0 23.863] 78 @dc [ 24 28 -1 0 23.863] 68 @dc [ 24 28 -3 0 23.863] 73 @dc [<01F9C007FDC00FFFC01F1FC03E0FC03C07C07803C07803C07003C0F001C0F01FF0E01FF0E01FF0 E00000E00000E00000E00000F00000F000007001C07801C07803C03C03C03E07C01F0FC00FFFC0 07FFC001F9C0> 24 28 -2 0 23.863] 71 @dc [<07FF0007FF0007FF00007000007000007000007000007000007000007000007000007000007000 007000007000007000007000007000007000007000007000E07038E07038E07038E07038FFFFF8 FFFFF8FFFFF8> 24 28 -1 0 23.863] 84 @dc cmr10.329 @sf [<0003800000038000000380000007C0000007C000000FE000000F6000000F6000001F7000001E30 00001E3000003C1800003C1800003C180000780C0000780C0000780C0000F0060000F0060000F0 060001E0030001E0030003E0038003C0018003C0018007C001C0078000C0078000C00F0000E00F 8001F0FFF007FEFFF007FE> 32 32 -1 1 34.090] 86 @dc [<381C7C3EFC7EFC7EF87CC060C060C060E07060307038381C3C1E180C> 16 14 -5 -18 22.727] 92 @dc [<000FC000003FF00000F8780000F01C0001E00C0003C00E0003C006000780070007800300078003 000780030007800300078003000780030007800300078003000780030007800300078003000780 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[<3F00FFC0F1E0F0E0F0F00070007000700070007000700070007000700070007000700070007000 700070007000700070007000F007F007F0007000000000000000000000000000E001F001F001F0 00E0> 16 40 2 9 13.889] 106 @dc 1.000000 /cmsy10.329 @newfont cmsy10.329 @sf [<07E01FF83FFC7FFE7FFEFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF7FFE7FFE3FFC1FF807E0> 16 18 -3 -2 22.727] 15 @dc cmtt10.329 @sf [<0E03800F07800F07800D05800D8D801D8DC01D8DC01D8DC01D8DC0198CC019DCC019DCC019DCC0 39DCE039DCE038F8E038F8E03800E03800E03800E03800E03800E0700070700070700070FE03F8 FE03F8FE03F8> 24 28 -1 0 23.863] 87 @dc [<0FF8003FFE007FFF00780F00700700F00780E00380E00380E00380E00380E00380E00380E00380 E00380E00380E00380E00380E00380E00380E00380E00380E00380F00780700700780F007FFF00 3FFE000FF800> 24 28 -3 0 23.863] 79 @dc [ 24 28 -1 0 23.863] 82 @dc [ 24 28 -1 0 23.863] 75 @dc 1.000000 /cmmi10.329 @newfont cmmi10.329 @sf [ 24 29 1 9 22.869] 112 @dc cmr10.329 @sf [<000600000006000000060000000600000006000000060000000600000006000000060000000600 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0700E00700E00700E00700E00700E0FFFFE0FFFFE00700E00700E00700E00700E00700E00700E0 0700E00781E003C1E001F1E000FFE0001FE0> 24 32 0 0 25.252] 13 @dc [<000E00070000000E00070000000E00070000001F000F8000001F000F8000001F000F8000003F00 0FC000003D801EC000003D801EC000003D801EC0000078C03C60000078C03C60000078C03C6000 00F0E07C300000F06078300000F06078300000F06078300001E030F0180001E030F0180001E030 F0180003C039E00C0003C019E00C0003C019E00C00078019E00E0007800FC0060007800FC00600 07800FC006000F00078003000F00078003001F000F800F80FFF07FF83FF0FFF07FF83FF0> 48 32 -1 1 46.716] 87 @dc 5 @bop1 cmcsc10.518 @sf 225 519 p (Revision)s 26(Histor)m -4 r 121 c cmr10.329 @sf 225 746 p (2.01)s 14(\(06-19-92\))m 21(ODRP)m -3 r 65 c (CK)s 9(2.01)m 10(corrects)m 10 r 116 c 119 c -1 r 111 c 8(minor)m 10(errors.)m 18(The)m 11(\014rst)m 10(a\013ected)m 11(the)m 11(deriv)m -2(a-)m 546 802 p (tiv)s 101 c 11 r 99 c (hec)s (king)s 12(pro)m 1(cedure,)m 14(and)m 14(the)m 13(second)m 14(a\013ected)m 13(the)m 14 r 118 c -2(alues)m 12(sp)m 1(eci\014ed)m 15 r 98 c 121 c cmtt10.329 @sf 546 858 p (NDIGIT)s cmr10.329 @sf 46 c 16(The)m 18(solutions)m 16(found)m 18 r 98 c 121 c 17(ODRP)m -3 r 65 c (CK)s 16(2.00)m 17 r 119 c (ere)s 16(not)m 18(a\013ected)m 17(in)m 546 915 p (an)s 121 c 14 r 119 c 97 c -1 r 121 c 13 r 98 c 121 c 15(the)m 16(\014rst)m 15(of)m 15(these)m 16(errors,)m 14(and)m 16 r 119 c (ere)s 14(not)m 15(seriously)m 15(a\013ected)m 15 r 98 c 121 c 546 971 p (the)s 15(second.)m 546 1046 p 86 c -3(ersion)m 17(2.01)m 17(also)m 18(encorp)m 1(orates)m 18(sev)m (eral)s 16(other)m 18(minor)m 18(mo)m 1(di\014cations)m 18(that)m 546 1103 p (further)s 17(impro)m 118 c -1 r 101 c 15(the)m 18(co)m 1(de.)m 27(The)m 17(most)m 17(signi\014can)m 116 c 15(of)m 17(these)m 18(mo)m 1(di\014cations)m 546 1159 p 99 c (hanges)s 18(ho)m 119 c 17(the)m 20(scale)m 18 r 118 c -2(alues)m 19(are)m 18(used)m 20(within)m 18(the)m 20(solution)m 17(pro)m 1(cedure.)m 546 1216 p (This)s 14 r 99 c (hange)s 14(should)m 14(increase)m 15(the)m 14(robustness)m 15(of)m 14(the)m 15(pro)m 1(cedure)m 15(for)m 14 r 112 c 1 r 111 c 1(orly)m 546 1272 p (scaled)s 18(problems,)m 19(and)m 19(will)m 17(result)m 18(in)m 18(sligh)m (tl)s -1 r 121 c 17(di\013eren)m 116 c 17(computed)m 19(results)m 546 1329 p (for)s 12(all)m 11(problems.)m 19(Another)m 13(of)m 12(these)m 13 r 99 c (hanges)s 12(is)m 12(to)m 12(the)m 13(rep)m 1(ort)m 12(generated)m 13 r 98 c 121 c 546 1385 p (the)s 18(deriv)m -2(ativ)m -1 r 101 c 17 r 99 c (hec)s (king)s 16(pro)m 1(cedure.)m 31(This)m 18(rep)m 1(ort)m 18(no)m 119 c 17(includes)m 18(the)m 19(user)m 546 1442 p (supplied)s 15(deriv)m -2(ativ)m -1 r 101 c 14 r 118 c -2(alue,)m 14(as)m 15 r 119 c (ell)s 13(as)m 15(the)m 15(relativ)m -1 r 101 c 14(di\013erence)m 15 r 98 c 1(et)m 119 c (een)s 14(the)m 546 1498 p (user)s 11(supplied)m 11 r 118 c -2(alue)m 10(and)m 11(the)m 12(\014nite)m 10(di\013erence)m 12 r 118 c -2(alue)m 10(it)m 10 r 119 c (as)s 9 r 99 c (hec)s 107 c -1(ed)m 10(against.)m 546 1555 p (This)s 21(should)m 21(help)m 22(users)m 22(assess)m 21(the)m 22 r 118 c -2(alidit)m -2 r 121 c 20(of)m 21(the)m 22 r 99 c (hec)s (king)s 19(pro)m 1(cedure)m 546 1611 p (results.)s 546 1686 p (The)s 16(\\ODRP)m -3 r 65 c (CK)s 14(2.01)m 15(User's)m 15(Reference)m 17(Guide")m 16(is)m 15(essen)m (tially)s 13(the)m 16(same)m 546 1743 p (as)s 16(the)m 17 r 118 c (ersion)s 15(2.00)m 15(Guide)m 17(\(NISTIR)m 17(89-4103,)m 15(Revised\).)m 25(The)m 17(ma)m 3(jor)m 15(dif-)m 546 1799 p (ferences)s 16(are)m 14(that)m cmsy10.329 @sf 546 1865 p 15 c cmr10.329 @sf 22(the)m 18(minim)m (um)s 16(length)m 18(of)m 18(arra)m 121 c cmtt10.329 @sf 16(WORK)m cmr10.329 @sf 17(has)m 18 r 98 c 1(een)m 19(increased)m 19 r 98 c 121 c 17 r 40 c cmmi10.329 @sf 112 c cmr10.329 @sf 11 r 43 c cmmi10.329 @sf 12 r 109 c cmr10.329 @sf 41 c cmmi10.329 @sf 113 c cmr10.329 @sf 591 1922 p (lo)s 1(cations,)m 14(and)m cmsy10.329 @sf 546 1988 p 15 c cmr10.329 @sf 22(the)m 13(sample)m 12(programs)m 11(and)m 13(output)m 13(sho)m (wn)s 11(in)m 12(Chapter)m 13(2,)m 12(and)m 13(the)m 13(discus-)m 591 2044 p (sion)s 10(of)m 10(the)m 11(deriv)m -2(ativ)m -1 r 101 c 9 r 99 c (hec)s (king)s 8(results)m 10(in)m 10(Chapter)m 11 r 53 c 10(ha)m 118 c -1 r 101 c 9 r 98 c 1(een)m 12(mo)m 1(di\014ed)m 591 2101 p (to)s 15(re\015ect)m 15(the)m 15(ab)m 1 r 111 c 118 c 101 c 13(men)m (tioned)s 14 r 99 c (hanges.)s 225 2195 p (2.00)s 14(\(03-04-92\))m 21(ODRP)m -3 r 65 c (CK)s 12(2.00)m 13(adds)m 14(sev)m (eral)s 12(new)m 15(features)m 13(to)m 13(those)m 14 r 97 c 118 c -2(ail)m -1(able)m 12(in)m 14 r 118 c (ersion)s 546 2251 p (1.8)s 14(and)m 15(earlier)m 14 r 118 c (ersions.)s cmsy10.329 @sf 546 2317 p 15 c cmr10.329 @sf 22(With)m 12 r 118 c (ersion)s 11(2.00,)m 11(ODRP)m -3 r 65 c (CK)s 11(can)m 13(no)m 119 c 11(easily)m 11(accommo)m 1(date)m 12(complex)m 591 2374 p (and)s 14(other)m 14 r 116 c (yp)s 1(es)m 13(of)m 14 r 109 c (ulti)s -1(resp)m 1(onse)m 13(data,)m 13(i.e.,)m 13(data)m 13(where)m 15(eac)m 104 c 13(observ)m -2(a-)m 591 2430 p (tion)s 15(is)m 14 r 109 c (ultidimensional)s -1 r 46 c 1075 2581 p 118 c @eop %%Page: 6 8 6 @bop0 cmr10.329 @sf [ 32 31 -2 0 34.090] 72 @dc cmti10.329 @sf [ 32 31 -3 0 31.994] 66 @dc [<03E1E007FBF00F3FB80E0F180E0F180E079C0E078C0E03800E03800F03C00703C00701C00781C0 E381E06381E063C0E071C0E03BC0F01F80F00F0070> 24 20 -3 0 24.393] 117 @dc [<7C00007F0000FF00007B800073800001C00001C00001C00001E00000E00000E00000E00000E000 00F000007000007000007000007000007800003800003800003800003800003C00001C00001C00 001C0001FFE001FFE0000E00000E00000E00000E00000E0000070000070000073C00073C0003BC 0001FC0000F8> 24 41 2 9 13.939] 102 @dc [ 8 14 -3 9 13.939] 44 @dc [<3803801E003C03C03F003C03C07B801C01C071C01C01C078C01E01E038C01E01E038E00E00E03C 000E00E01C000F00F01C000F00F01E000700700E000780780E00C780780E00E7C07C0F0063E03C 070063F07E0F0077F8778E003F1FF3FE001E0FE0FC00> 40 20 -3 0 37.171] 109 @dc [<01FC000007FF80000F83E0001E00F0003C003C0038001E0078000F007800070070000780F00003 C0F00001C0F00001E0F00000E0F00000F0F00000F0780000787800007878000078780000783C00 00383C0000381E0000381E0000380F000038070000380780007803C0007001E0007000F000E000 3801E0001F07C00007FF000001FC00> 32 33 -6 1 34.847] 79 @dc [ 32 31 -3 0 34.317] 68 @dc [<000007C0FFF81FE0FFF81E700F803C3807803C1807803C1807C03E0003C03E0003C01E0003C01E 0003E01E0001E01F0001E00F0001E01F0001F01E0000F03E0000FFFC0000FFFE0000F80F000078 03C0007801E0007800F0007C00F0003C0078003C0078003C0078003E0078001E0078001E00F000 1E01E001FFFFC001FFFF00> 32 32 -3 1 33.156] 82 @dc [ 32 31 -3 0 30.832] 80 @dc [ 32 32 -2 0 33.787] 65 @dc [<00FE000007FFC0000FC1F0001F0078003E001C003C000E00780007007800030070000380F00001 80F0000180F00001C0F0000000F0000000F80000007800000078000000780000007C0000003C00 00003C0000301E0000301E0000300F0000380F80003807C0003803C0003801F0007C00F8007C00 7E00FC001F83CC0007FF8E0001FE06> 32 33 -6 1 32.524] 67 @dc [ 40 31 -3 0 34.948] 75 @dc [ 24 31 -3 1 23.232] 50 @dc [ 8 5 -5 0 13.939] 46 @dc [<0FC0001FF000387800701C00700E00700F00F00700F00780F00380F003C07003C07801C07801E0 7801E07801E03C00F03C00F03C00F03C00F01E00701E00780E00780F00780F0078070078038038 03807001C07000F0F0003FE0000F80> 24 31 -4 1 23.232] 48 @dc [<1F003FC071E070F0E078E03CE03CE01EE01EF01F701F700F700F780F780F3C0F3E0E3F1E3FFC1C F81C001E001E000E000E000F000F00070007003F803F800780> 16 32 -5 0 20.908] 98 @dc [ 24 29 0 9 23.232] 112 @dc cmtt10.329 @sf [ 24 28 -2 0 23.863] 70 @dc [<01FC0007FF000FFF801F07C03E03E03C01E07800E07800E07000E0F00000F00000E00000E00000 E00000E00000E00000E00000F00000F000007000E07800E07801E03C01E03E03E01F07E00FFFE0 07FFE001FCE0> 24 28 -2 0 23.863] 67 @dc cmti10.329 @sf [<1F00007FC00071E000787000783800783C00101C00001E00000E0003EE0007FE000F3F000E0F00 0E0F000E07000E07800E03800E03800F03800703C00701C00781C0E381C06381E063C0E071C0E0 3BC0E01F80F00F0070> 24 29 -3 9 22.070] 121 @dc cmtt10.329 @sf [<007C0001FF0007FFC00FC7E00F01E01E00F01E00F01C00701C00701C00701C00701C00701C0070 1C00701C00701C00701C00701C00701C00701C00701C00701C00701C00701C00701C0070FF83FE FF83FEFF83FE> 24 28 0 0 23.863] 85 @dc [<1FE0007FF800FFFC00F03E00F01E00F00E00600E00000E00000E00000E00000E00000E00000E00 000E00000E00000E00000E00000E00000E00000E00000E00000E00000E00000E00000E0003FFC0 03FFC003FFC0> 24 28 -3 0 23.863] 74 @dc [ 24 28 -1 0 23.863] 65 @dc cmti10.329 @sf [<03F00007F8000F1C000E0E000E07000E03000E03000E01800E01800F01800701C00700C00780C0 E380C06380E063C1E071C3E03BC3E01F83E00F01C0> 24 20 -3 0 20.908] 118 @dc cmtt10.329 @sf [ 24 28 -1 0 23.863] 66 @dc [ 24 28 -1 0 23.863] 69 @dc cmr10.329 @sf [ 16 45 -3 11 22.727] 47 @dc [<180001E01C0003F80C0007380E000E1C07000E0C03001C0E03801C0601C01C0600C01C0600E01C 0600701C0600301C0600381C06001C1C0E000C0E0C000E0E1C00070738000303F8000381E00F81 80003FC1C00039C0E00070E0600070607000E0703800E0301800E0301C00E0300E00E0300600E0 300700E033FB80E07FFF80707E0FC070F801E039E000E03FC000700F800030> 32 37 -3 3 37.878] 37 @dc [<0FC0003FE00078F000E07800F87C00F83C00F83C00F83C00703C00003C00003C00003C00003C00 003C00003C00003C00003C00003C00003C00003C00003C00003C00003C00003C00003C00003C00 003C00003C00003C00003C000FFFC00FFFC0> 24 32 -2 1 23.358] 74 @dc [<07800007800007800007800007800007800007800007800003800003800003800003800003C000 01C00001C00000C00000E00000E000007000003000003800001C00000C00C00E00C00700C00300 6003807FFFC07FFFC07FFFC0600000> 24 31 -3 1 22.727] 55 @dc [ 40 32 -2 0 37.878] 1 @dc cmsy10.329 @sf [ 32 36 -4 7 35.353] 21 @dc cmtt10.329 @sf [ 24 28 -1 0 23.863] 88 @dc [<007000F003F007E00F800F001E003E003C007800780070007000F000F000E000E000E000E000E0 00E000F000F00070007000780078003C003E001E000F000F8007E003F000F00070> 16 36 -7 4 23.863] 40 @dc [ 16 28 -5 0 23.863] 49 @dc [ 8 12 -8 6 23.863] 44 @dc [ 16 36 -4 4 23.863] 41 @dc [ 24 28 -2 0 23.863] 83 @dc 6 @bop1 cmr10.329 @sf 0 114 p (vi)s 1357(Revision)m 15(History)m 0 134 p 1725 2 ru cmsy10.329 @sf 321 259 p 15 c cmr10.329 @sf 22(It)m 15(can)m 16(handle)m 15(implicit)m 14(as)m 15 r 119 c (ell)s 13(as)m 15(explicit)m 14(mo)m 1(dels.)m cmsy10.329 @sf 321 325 p 15 c cmr10.329 @sf 22(The)m 13 r 119 c (eigh)s -1(ting)m 10(sc)m (heme)s 13(has)m 12 r 98 c 1(een)m 14(enhanced)m 14(to)m 13(allo)m -1 r 119 c 11(for)m 12(instances)m 12(when)m 366 381 p (the)s 15(comp)m 1(onen)m (ts)s 15(of)m 14 r 97 c 15 r 109 c (ultidimensional)s 12(observ)m -2(ation)m 14(are)m 15(correlated.)m cmsy10.329 @sf 321 448 p 15 c cmr10.329 @sf 22 r 65 c 15(facilit)m -1 r 121 c 13(for)m 14(computing)m 14(cen)m (tral)s 13(\014nite)m 14(di\013erence)m 15(deriv)m -2(ativ)m -1(es)m 13(has)m 15 r 98 c 1(een)m 366 504 p (added.)s cmsy10.329 @sf 321 570 p 15 c cmr10.329 @sf 22(The)m 19(amoun)m 116 c 17(of)m 18 r 119 c (ork)s 16(space)m 19(required)m 19(for)m 17(the)m 19(computations)m 17(has)m 19 r 98 c 1(een)m 366 627 p (reduced)s 16(for)m 15(most)m 14(problems.)m cmti10.329 @sf 321 702 p (Be)s -1 r 99 c -2(ause)m 18(of)m 21(these)m 20(new)m 19(fe)m -1(atur)m -1(es,)m 19(the)m 21(ar)m -1(gument)m 19(lists)m 19(for)m 21(the)m 20(ODRP)m -2 r 65 c -1(CK)m 321 758 p (2.00)s 22(user)m 22 r 99 c -1(al)m 2(lable)m 19(subr)m -1(outines,)m 22(including)m 20(the)m 22(user)m 22(supplie)m -1 r 100 c 20(subr)m -1(outine)m cmtt10.329 @sf 321 815 p (FCN)s cmti10.329 @sf 18(that)m 19(now)m 19 r 99 c -1(omprises)m 17(the)m 19(functionality)m 18(of)m 19(subr)m -1(outines)m cmtt10.329 @sf 17(FUN)m cmti10.329 @sf 19(and)m cmtt10.329 @sf 18(JAC)m cmti10.329 @sf 44 c 321 871 p (ar)s -1 r 101 c 18(not)m 18(the)m 19(same)m 19(as)m 19(for)m 19 r 101 c -1(arlier)m 18(versions.)m cmr10.329 @sf 27(The)m 18(in)m (terpretatio)s -1(ns)m 17(of)m 17(some)m 321 928 p (argumen)s (ts)s 20(ha)m 118 c 101 c 20 r 99 c (hanged,)s 24(and)m 22(new)m 23(argumen)m (ts)s 20(ha)m 118 c 101 c 20 r 98 c 1(een)m 24(added.)m 42(In)m 321 984 p (addition,)s 18(the)m 19(argumen)m (ts)s 16(ha)m 118 c 101 c 17 r 98 c 1(een)m 20(reordered,)m 19(with)m 18(argumen)m (ts)s 17(ha)m (ving)s 321 1041 p (similar)s 14(purp)m 1(ose)m 16(no)m 119 c 14(group)m 1(ed)m 17(together.)m 21(Those)m 15(who)m 16(ha)m 118 c -1 r 101 c 14 r 98 c 1(een)m 17(using)m 16(an)m 321 1097 p (earlier)s 19(release)m 19(of)m 20(ODRP)m -3 r 65 c (CK)s 18(should)m 20 r 98 c 1 r 101 c 21(esp)m 1(ecially)m 19(careful)m 20(to)m 19(examine)m 321 1153 p (the)s 13(new)m 13(calling)m 12(sequences,)m 15(and)m 13(the)m 13(de\014nitions)m 13(for)m 13(subroutine)m 13(argumen)m (ts)s cmtt10.329 @sf 321 1210 p (FCN)s cmr10.329 @sf 44 c cmtt10.329 @sf 14(JOB)m cmr10.329 @sf 44 c cmtt10.329 @sf 14(WE)m cmr10.329 @sf 15(and)m cmtt10.329 @sf 16(WD)m cmr10.329 @sf 46 c 0 1304 p (1.80)s 14(\(12-18-90\))m 21(ODRP)m -3 r 65 c (CK)s 17(1.80,)m 19 r 97 c 19(test)m 18(release)m 19(with)m 19(only)m 18(limited)m 18(distribution,)m 19(di\013ers)m 321 1360 p (from)s 14(prior)m 15(releases)m 14(in)m 15(sev)m (eral)s 14(resp)m 1(ects.)m cmsy10.329 @sf 321 1426 p 15 c cmr10.329 @sf 22(The)m 15 r 110 c (um)s 98 c 1(er)m 13(of)m 14(function)m 14(ev)m -2(aluations)m 13(required)m 14(to)m 14(\014nd)m 15(the)m 15(solution)m 13(has)m 366 1483 p 98 c 1(een)m 18(reduced,)m 17(and)m 16(the)m 16(\\restart")m 15(facilit)m -1 r 121 c 14(has)m 16 r 98 c 1(een)m 18(mo)m 1(di\014ed)m 16(to)m 16 r 98 c 1(etter)m 366 1539 p (accommo)s 1(date)m 16(cases)m 15(where)m 17(the)m 16(user)m 16(supplied)m 16(subroutines)m cmtt10.329 @sf 16(FUN)m cmr10.329 @sf 15(and/or)m cmtt10.329 @sf 366 1596 p (JAC)s cmr10.329 @sf 15(are)m 15 r 118 c (ery)s 14(time)m 14(consuming.)m cmsy10.329 @sf 321 1662 p 15 c cmr10.329 @sf 22(The)m 13(prin)m (ted)s 11(rep)m 1(orts)m 13(ha)m 118 c -1 r 101 c 11 r 98 c 1(een)m 14(redesigned)m 13(to)m 12(iden)m (tify)s 11(parameters)m 12(that)m 366 1718 p (induce)s 18(rank)m 16(de\014ciency)m -3 r 44 c 18(and)m 17(to)m 16(include)m 17 r 97 c 17(95%)m 16(con\014dence)m 19(in)m (terv)s -3(al)m 15(for)m 366 1775 p (the)s 15(estimated)m 15(parameters.)m cmsy10.329 @sf 321 1841 p 15 c cmr10.329 @sf 22(Sev)m (eral)s 10(enhancemen)m (ts)s 11(ha)m 118 c 101 c 9 r 98 c 1(een)m 13(added)m 12(to)m 11(the)m 12(co)m 118 c -2(ar)m -1(iance)m 10(matrix)m 10(com-)m 366 1898 p (putations,)s 12(including)m 13(the)m 14(option)m 12(of)m 13(constructing)m 12(the)m 13(co)m 118 c -2(aria)m -1(nce)m 12(matrix)m 366 1954 p (without)s 14(incurring)m 15(an)m 121 c 14(additional)m 14(deriv)m -2(ativ)m -1 r 101 c 13(ev)m -2(aluations.)m cmsy10.329 @sf 321 2020 p 15 c cmr10.329 @sf 22(The)m 15(\014nite)m 15(di\013erence)m 15(appro)m (ximati)s -1(on)m 13(to)m 15(the)m 15(Jacobian)m 14(matrix)m 14(has)m 15 r 98 c 1(een)m 366 2077 p (impro)s 118 c -1(ed.)m 0 2171 p (1.71)s 14(\(07-27-89\))m 21(ODRP)m -3 r 65 c (CK)s 11(1.71)m 11(corrects)m 11(an)m 13(error)m 11(in)m 12(the)m 13(co)m 1(de)m 13(that)m 11 r 112 c 1(erforms)m 12(the)m 12(compu-)m 321 2227 p (tation)s 13(of)m 14(\014nite)m 15(di\013erence)m 15(deriv)m -2(ativ)m -1(es)m 12(with)m 14(resp)m 1(ect)m 15(to)m 14(the)m 15(errors)m 14 r 1 c 14(when)m cmmi10.329 @sf 321 2283 p 109 c cmsy10.329 @sf 12 r 21 c cmr10.329 @sf 13 r 50 c 15(and)m 15(the)m 15(default)m 14 r 118 c -2(alue)m 14(of)m cmtt10.329 @sf 15(IFIXX)m cmr10.329 @sf 14(is)m 14(in)m 118 c -1(ok)m -1(ed.)m 18(\(The)m 15(default)m 14 r 118 c -2(alue)m 14(of)m cmtt10.329 @sf 321 2340 p (IFIXX)s cmr10.329 @sf 16(is)m 16(in)m 118 c (o)s -1 r 107 c -1(ed)m 15(when)m cmtt10.329 @sf 18(IFIXX\(1,1\))m cmr10.329 @sf 15(is)m 17(set)m 16(to)m 16 r 97 c 17(negativ)m 101 c 15 r 118 c -2(alue)m 16(or)m 16(when)m 321 2396 p (ODRP)s -3 r 65 c (CK)s 15(routines)m cmtt10.329 @sf 16(DODR)m cmr10.329 @sf 16(or)m cmtt10.329 @sf 16(SODR)m cmr10.329 @sf 17(are)m 16(called.\))m 24(This)m 16(error)m 16(could)m 16(result)m 321 2453 p (in)s 19(incorrect)m 19(\\\014xing")m 19(of)m 19(the)m 19(explanatory)m 19 r 118 c -2(ariables,)m 18(whic)m 104 c 19 r 119 c (ould)s 18(a\013ect)m @eop %%Page: 7 9 7 @bop0 7 @bop1 cmr10.329 @sf 225 114 p (Revision)s 15(History)m 1344(vii)m 225 134 p 1725 2 ru 546 259 p (the)s 20(\014nal)m 20(solution.)m 34(Suc)m 104 c 20(\\\014xing")m 19(could)m 20 r 98 c 1 r 101 c 21(detected)m 21 r 98 c 121 c 19(observing)m 20(the)m 546 315 p (presence)s 16(of)m 16(estimated)m 15 r 118 c -2(alues)m 15(for)m 15 r 1 c 15(that)m 15(are)m 16(iden)m (ticall)s -1 r 121 c 14(zero.)m 22(The)m 16(error)m 546 372 p (could)s 17(go)m 16(undetected)m 18 r 98 c 121 c 16(the)m 16(user,)m 17(ho)m 119 c (ev)s -1(er,)m 14(if)m 17(the)m 17 r 118 c -2(alues)m 16(of)m 16 r 1 c 17 r 119 c (ere)s 15(not)m 546 428 p (examined)s 15(after)m 14(the)m 16(\014t.)m @eop %%Page: 8 10 8 @bop0 8 @bop1 cmr10.329 @sf 0 114 p (viii)s 1331(Revision)m 15(History)m 0 134 p 1725 2 ru @eop %%Page: 9 11 9 @bop0 cmcsc10.518 @sf [ 48 49 -4 0 53.199] 80 @dc [ 32 37 -3 0 38.415] 102 @dc cmr10.329 @sf [ 32 31 -2 0 29.671] 70 @dc [ 8 45 -4 11 12.626] 91 @dc [ 8 45 -1 11 12.626] 93 @dc 9 @bop1 cmcsc10.518 @sf 225 519 p (Pref)s -5 r 97 c -1(ce)m cmr10.329 @sf 225 746 p (ODRP)s -3 r 65 c (CK)s 14(is)m 15 r 97 c 15 r 112 c 1(ortable)m 15(collection)m 14(of)m 15(ANSI)m 16 r 70 c -3(ortran)m 14(77)m 14(subroutines)m 16(for)m 14(\014tting)m 15 r 97 c 15(mo)m 1(del)m 225 802 p (to)s 15(data.)m 19(It)m 15(is)m 15(designed)m 15(primarily)m 14(for)m 14(instances)m 15(when)m 16(all)m 14(of)m 14(the)m 16 r 118 c -2(ariables)m 13(ha)m 118 c 101 c 13(signi\014can)m 116 c 225 858 p (errors)s 13(\(see,)m 13(e.g.,)m 13([F)m -3(uller,)m 11(1987])m 12(and)m 14([Boggs)m 12(and)m 14(Rogers,)m 13(1990]\),)m 11(implemen)m (ting)s 12 r 97 c 13(highly)m 13(ef-)m 225 915 p (\014cien)s 116 c 11(algorithm)m 10(for)m 12(solving)m 11(the)m 12 r 119 c (eigh)s -1(ted)m 10(orthogonal)m 11(distance)m 12(regression)m 11(problem)m 12([Boggs)m cmti10.329 @sf 225 971 p (et)s 13(al.)m cmr10.329 @sf 44 c 12(1987)m 11(and)m 12(1989],)m 11(i.e.,)m 11(for)m 12(minimizing)m 10(the)m 13(sum)m 12(of)m 11(the)m 12(squares)m 12(of)m 12(the)m 12 r 119 c (eigh)s -1(t)m -1(ed)m 11(orthog-)m 225 1028 p (onal)s 13(distances)m 14 r 98 c 1(et)m 119 c -1(een)m 13(eac)m 104 c 13(data)m 13 r 112 c 1(oin)m 116 c 12(and)m 15(the)m 14(curv)m 101 c 13(describ)m 1(ed)m 14 r 98 c 121 c 13(the)m 14(mo)m 1(del)m 14(equation.)m 225 1084 p (It)s 17(can)m 17(also)m 15 r 98 c 1 r 101 c 18(used)m 17(to)m 16(solv)m 101 c 15(the)m 17(ordinary)m 15(least)m 16(squares)m 17(problem)m 16(where)m 17(all)m 16(of)m 16(the)m 17(errors)m 225 1141 p (are)s 15(attributed)m 14(to)m 15(the)m 15(observ)m -2(ations)m 13(of)m 15(the)m 16(dep)m 1(enden)m 116 c 15 r 118 c -2(ariable.)m 225 1217 p (ODRP)s -3 r 65 c (CK)s 14(is)m 16(designed)m 16(to)m 15(handle)m 16(man)m 121 c 15(lev)m (els)s 14(of)m 15(user)m 16(sophistication)m 14(and)m 16(problem)m 16(di\016-)m 225 1273 p (cult)s 121 c -3 r 46 c cmsy10.329 @sf 316 1352 p 15 c cmr10.329 @sf 22(It)m 19(is)m 18(easy)m 19(to)m 18(use,)m 20(pro)m (viding)s 16 r 116 c 119 c -1 r 111 c 17(lev)m (els)s 17(of)m 18(user)m 19(con)m (trol)s 16(of)m 19(the)m 18(computations,)m 19(ex-)m 361 1408 p (tensiv)s 101 c 13(error)m 13(handling)m 13(facilities,)m 12(optional)m 12(prin)m (ted)s 13(rep)m 1(orts,)m 13(and)m 14(no)m 14(size)m 14(restrictions)m 361 1465 p (other)s 15(than)m 15(e\013ectiv)m 101 c 14(mac)m (hine)s 14(size.)m cmsy10.329 @sf 316 1531 p 15 c cmr10.329 @sf 22(It)m 20(can)m 21(handle)m 20(implicit)m 18(as)m 20 r 119 c (ell)s 18(as)m 19(explicit)m 20(mo)m 1(dels,)m 20(and)m 20(can)m 21(accommo)m 1(date)m 19(com-)m 361 1587 p (plex)s 17(and)m 16(other)m 16 r 116 c (yp)s 1(es)m 15(of)m 16 r 109 c (ulti)s -1(resp)m 1(onse)m 15(data,)m 16(i.e.,)m 15(data)m 15(where)m 17(eac)m 104 c 15(observ)m -2(ation)m 14(is)m 361 1644 p 109 c (ultidimensional)s -1 r 46 c cmsy10.329 @sf 316 1710 p 15 c cmr10.329 @sf 22(The)m 19(necessary)m 18(deriv)m -2(ativ)m -1(es)m 17(\(Jacobian)m 17(matrices\))m 17(are)m 18(appro)m (ximated)s 16 r 110 c (umerically)s 16(if)m 361 1767 p (they)s 13(are)m 11(not)m 12(supplied)m 13 r 98 c 121 c 11(the)m 12(user,)m 13(and)m 12(the)m 12(correctness)m 12(of)m 12(user)m 12(supplied)m 13(deriv)m -2(ativ)m -1(es)m 361 1823 p (can)s 16 r 98 c 1 r 101 c 16 r 118 c (eri\014ed)s 14 r 98 c 121 c 14(the)m 15(deriv)m -2(ativ)m -1 r 101 c 14 r 99 c (hec)s (king)s 13(pro)m 1(cedure)m 16(pro)m (vided.)s cmsy10.329 @sf 316 1889 p 15 c cmr10.329 @sf 22(Both)m 15 r 119 c (eigh)s -1(ted)m 14(and)m 15(un)m 119 c (eig)s -1 r 104 c -1(ted)m 14(analysis)m 14(can)m 15 r 98 c 1 r 101 c 16 r 112 c 1(erformed.)m cmsy10.329 @sf 316 1956 p 15 c cmr10.329 @sf 22(Subsets)m 15(of)m 13(the)m 14(unkno)m (wns)s 13(can)m 14 r 98 c 1 r 101 c 14(treated)m 14(as)m 13(constan)m (ts)s 12(with)m 13(their)m 13 r 118 c -2(alues)m 13(held)m 14(\014xed)m 361 2012 p (at)s 16(their)m 16(input)m 16 r 118 c -2(alues,)m 15(allo)m -1(wing)m 14(the)m 16(user)m 16(to)m 16(examine)m 16(the)m 16(results)m 15(obtained)m 16 r 98 c 121 c 15(esti-)m 361 2068 p (mating)s 14(subsets)m 14(of)m 14(the)m 15(unkno)m (wns)s 13(of)m 15 r 97 c 14(general)m 14(mo)m 1(del)m 14(without)m 13(rewriting)m 13(the)m 15(mo)m 1(del)m 361 2125 p (subroutine.)s cmsy10.329 @sf 316 2191 p 15 c cmr10.329 @sf 22(The)m 12(co)m 118 c -2(a)m -1(riance)m 9(matrix)m 10(and)m 11(the)m 11(standard)m 11(errors)m 10(of)m 11(the)m 11(mo)m 1(del)m 11(parameter)m 10(estimators)m 361 2248 p (are)s 15(optionally)m 14(pro)m (vided.)s cmsy10.329 @sf 316 2314 p 15 c cmr10.329 @sf 22(The)m 17(ODRP)m -3 r 65 c (CK)s 15(scaling)m 15(algorithm)m 15(automaticall)m -1 r 121 c 15(comp)m 1(ensates)m 16(for)m 16 r 112 c 1 r 111 c 1(orly)m 16(scaled)m 361 2370 p (problems,)s 17(i.e.,)m 17(problems)m 17(with)m 16(mo)m 1(del)m 17(parameters,)m 17(and/or)m 17(unkno)m (wn)s 16(errors)m 17(in)m 17(the)m 361 2427 p (explanatory)s 14 r 118 c -2(ariables)m 14(that)m 14 r 118 c -2(ary)m 15(widely)m 14(in)m 15(magnitude.)m 1069 2581 p (ix)s @eop %%Page: 10 12 10 @bop0 cmmi10.329 @sf [<0F801FC03CE0387038303C303C381C001C001E001E000E000E000F000F00070007000780FFF8FF F8038003C003C001C001C001E001E000E0> 16 28 -1 0 16.414] 116 @dc cmr10.329 @sf [ 8 8 -9 -24 22.727] 19 @dc 10 @bop1 cmr10.329 @sf 0 123 p 120 c 1555(Preface)m 0 134 p 1725 2 ru cmsy10.329 @sf 91 259 p 15 c cmr10.329 @sf 22(The)m 20(trust)m 18(region)m 19(Lev)m (en)s 98 c 1(erg-Marquardt)m 17(algorithm)m 17(implemen)m (ted)s 18 r 98 c 121 c 18(ODRP)m -3 r 65 c (CK)s 136 315 p ([Boggs)s cmti10.329 @sf 16(et)m 18(al.)m cmr10.329 @sf 44 c 17(1987)m 16(and)m 17(1989])m 15(has)m 17 r 97 c 16(computational)m 16(e\013ort)m 15 r 112 c 1(er)m 18(step)m 17(that)m 16(is)m 16(of)m 17(the)m 136 372 p (same)s 12(order)m 11(as)m 11(that)m 11(required)m 11(for)m 11(ordinary)m 11(least)m 10(squares,)m 12(ev)m (en)s 11(though)m 11(the)m 12 r 110 c (um)s -1 r 98 c 1(er)m 10(of)m 136 428 p (unkno)s (wns)s 12(estimated)m 11(in)m 13(the)m 12(orthogonal)m 11(distance)m 12(regression)m 11(problem)m 12(is)m 12(the)m 13 r 110 c (um)s -1 r 98 c 1(er)m 136 484 p (of)s 10(unkno)m (wn)s 10(mo)m 1(del)m 10(parameters)m 9(plus)m 11(the)m 10 r 110 c (um)s 98 c 1(er)m 9(of)m 10(explanatory)m 9 r 118 c -2(ariables,)m 9(while)m 10(the)m 136 541 p 110 c (um)s 98 c 1(er)m 15(of)m 17(unkno)m (wns)s 16(estimated)m 15(in)m 17(the)m 17(ordinary)m 16(least)m 16(squares)m 16(problem)m 16(is)m 17(simply)m 136 597 p (the)s 16 r 110 c (um)s -1 r 98 c 1(er)m 14(of)m 15(unkno)m (wn)s 14(mo)m 1(del)m 15(parameters.)m cmsy10.329 @sf 91 664 p 15 c cmr10.329 @sf 22(The)m 16(co)m 1(de)m 16(is)m 14 r 112 c 1(ortable)m 15(and)m 15(is)m 15(easily)m 14(used)m 16(with)m 15(other)m 14 r 70 c -3(ortran)m 13(subroutine)m 16(libraries.)m 0 752 p (Computer)s 15(facilities)m 13(for)m 14(the)m 16(ODRP)m -3 r 65 c (CK)s 13(pro)m 3(ject)m 15(ha)m 118 c -1 r 101 c 13 r 98 c 1(een)m 17(pro)m (vided)s 13 r 98 c 121 c 14(the)m 16(National)m 13(In-)m 0 808 p (stitute)s 13(of)m 13(Standards)m 14(and)m 13 r 84 c -3(ec)m (hnology)s 12(\(NIST\),)m 13(Applied)m 14(and)m 14(Computational)m 11(Mathematics)m 0 865 p (Division,)s 17(and)m 18 r 119 c 101 c 17(gratefully)m 16(ac)m (kno)s -1(wledge)m 16(their)m 18(supp)m 1(ort.)m 28(Mac)m (hine)s 16(dep)m 1(enden)m 1 r 116 c 18(constan)m (ts)s 0 921 p (are)s 10(supplied)m 12(using)m 10(subroutines)m 11(based)m 11(on)m 11(the)m 11(Bell)m 10(Lab)m 1(oratories)m 10(\\F)m -3(ramew)m -2(ork)m 9(for)m 10 r 97 c 10 r 80 c (ortable)s 0 978 p (Library")s 15([F)m -3 r 111 c -1 r 120 c cmti10.329 @sf 13(et)m 16(al.)m cmr10.329 @sf 44 c 15(1978a].)m 18 r 87 c -3 r 101 c 15(ha)m 118 c -1 r 101 c 14(also)m 14(used)m 16(subroutines)m 15(from)m 15(LINP)m -3 r 65 c (CK)s 14([Dongarra)m cmti10.329 @sf 0 1034 p (et)s 22(al.)m cmr10.329 @sf 44 c 23(1979],)m 22(and)m 22(from)m 21(the)m 22(\\Basic)m 22(Linear)m 22(Algebra)m 21(Subprograms)m 21(for)m 22 r 70 c -3(ortra)m -1 r 110 c 21(Usage")m 0 1091 p ([La)s (wson)s cmti10.329 @sf 17(et)m 20(al.)m cmr10.329 @sf 44 c 20(1979].)m 29(The)m 20(co)m 1(de)m 19(that)m 19(computes)m 19(the)m cmmi10.329 @sf 19 r 116 c cmr10.329 @sf (-v)s -2(alues)m 19(used)m 20(in)m 18(constructing)m 19(the)m 0 1147 p (con\014dence)s 18(in)m (terv)s -2(al)m -1 r 115 c 15(is)m 16(from)m 16 r 68 c 65 c -3 r 84 c -4(AP)m -4 r 65 c -1 r 67 c 15([Fillib)m 1(en,)m 15(1977],)m 16(and)m 17(the)m 16(co)m 1(de)m 18(that)m 16 r 99 c (hec)s (ks)s 15(user)m 0 1204 p (supplied)s 18(deriv)m -2(ativ)m -1(es)m 16 r 119 c (as)s 16(adapted)m 18(from)m 17(ST)m -3(ARP)m -3 r 65 c 67 c 16([Donaldson)m 16(and)m 18 r 84 c -3(ry)m (on,)s 16(1986])m 16(using)m 0 1260 p (algorithms)s 13(describ)m 1(ed)m 16(in)m 15([Sc)m (hnab)s 1(el,)m 14(1982].)m 0 1336 p 87 c -3 r 101 c 11(appreciate)m 12(the)m 11(commen)m (ts)s 11(and)m 12(suggestions)m 11 r 119 c 101 c 10(ha)m 118 c 101 c 10(receiv)m (ed)s 11(regarding)m 11(earlier)m 11 r 118 c (ersions)s 0 1393 p (of)s 14(ODRP)m -3 r 65 c (CK)s 13(and)m 15(its)m 14(do)m 1(cumen)m (tation.)s 18(In)m 15(particular,)m 13(man)m 121 c 14(of)m 14(the)m 14(impro)m 118 c -1(emen)m -1(ts)m 13(in)m 14 r 118 c (er-)s 0 1449 p (sion)s 11(2.01)m 9(are)m 11(the)m 11(result)m 11(of)m 10(the)m 11(authors')m 10(collab)m 1(oration)m 9(with)m 11 r 80 c (aul)s 9(D.)m 10(Domic)m (h,)s 10(NIST)m 12(Applied)m 0 1506 p (and)s 12(Computational)m 10(Mathematics)m 11(Division,)m 11(and)m 12(with)m 12(Da)m (vid)s 10(A.)m 12 r 86 c -3(orp,)m 11(Univ)m (ersit)s -1 r 121 c 10(of)m 12(Pitts-)m 0 1562 p (burgh)s 17(Departmen)m 116 c 14(of)m 17(Surgery)m -3 r 46 c 23 r 87 c -3 r 101 c 15(wish)m 17(to)m 16(esp)m 1(ecially)m 16(thank)m 16 r 80 c (aul)s 15(D.)m 16(Domic)m 104 c 14(for)m 16(man)m 121 c 0 1618 p (pro)s 1(ductiv)m 101 c 11(discussions.)m 19(While)m 11(it)m 12(is)m 12(not)m 12 r 112 c 1(ossible)m 12(to)m 12(list)m 11(ev)m (ery)s -1(one)m 11(else)m 12(who)m 12(has)m 12(con)m (tributed)s 0 1675 p (to)s 13(ODRP)m -3 r 65 c (CK,)s 12 r 119 c 101 c 13 r 119 c (ould)s 12(lik)m 101 c 12(to)m 13(thank)m 13(Vincen)m 116 c 13(D.)m 13(Arp)m 14(\(formerly)m 12(of)m 14(the)m 13(NIST)m 15(Chemical)m 0 1731 p (Engineering)s 17(Science)m 19(Division\),)m 16(Hariharan)m 17(K.)m 17(Iy)m (er)s 17(\(Colorado)m 16(State)m 17(Univ)m (ersit)s -1(y\))m -1 r 44 c 16(Susan-)m 0 1788 p (nah)s 20(B.)m 20(Sc)m (hiller)s 19(\(NIST)m 20(Statistical)m 18(Engineering)m 20(Division\),)m 19(Bernard)m 20(Thiesse)m 20(\(Ecole)m 20(Na-)m 0 1844 p (tionale)s 17(Sup)m 19 c -21(erieure)m 16(d'Electrtec)m (hnique,)s 17(d'Electronique)m 18(d'Informatique)m 17(et)m 18(d'Hydraulique,)m 0 1901 p 84 c -3(oulouse,)m 20 r 70 c -3(rance\),)m 20(and)m 20(Eric)m 20(J.)m 20 r 86 c -3(anzura)m 20(\(NIST)m 20(Electromagnetic)m 19(Fields)m 19(Division\),)m 20(for)m 0 1957 p (pro)s (viding)s 13(us)m 15(with)m 15(data)m 15(sets)m 14(that)m 15 r 119 c (ere)s 14(in)m 118 c -2(al)m -1(uable)m 13(in)m 16(testing)m 14(the)m 15(new)m 15(release.)m 1310 2147 p 80 c (aul)s 13(T.)m 15(Boggs)m 1310 2204 p (Ric)s (hard)s 14(H.)m 15(Byrd)m 1310 2260 p (Janet)s 15(E.)m 15(Rogers)m 1310 2317 p (Rob)s 1(ert)m 15(B.)m 15(Sc)m (hnab)s 1(el)m 1310 2430 p (June)s 16(1992)m @eop %%Page: 11 13 11 @bop0 cmcsc10.518 @sf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dc cmbx10.329 @sf [ 40 31 -2 0 39.519] 65 @dc [<183FC01CFFF01FE1F81F80FC1F007E1F003E1F003F1F003F1F003F1F003F1F003F1F003F1F003F 1F003F1F003E1F007E1F807C1FE1F81FFFF01F1FC01F00001F00001F00001F00001F00001F0000 1F00001F00001F00001F0000FF0000FF0000> 24 32 -2 0 29.040] 98 @dc [<03FE000FFF801FC3C03F00E07E00607E0000FC0000FC0000FC0000FC0000FC0000FC0000FC0000 FC07807C0FC07E0FC03F0FC01F8FC00FFF8003FE00> 24 20 -2 0 23.232] 99 @dc [ 40 31 -2 0 39.203] 82 @dc [<001C0000001C0000003E0000003E0000007F0000007F000000FF800000F9800001F9C00001F0C0 0001F0C00003E0600003E0600007C0300007C030000F8018000F8018001F001C00FFE07F80FFE0 7F80> 32 20 -1 0 27.588] 118 @dc [ 24 20 -3 0 29.040] 110 @dc [ 40 31 -2 0 40.908] 72 @dc [ 32 31 -2 0 35.731] 80 @dc [<3FFC003FFC0007C00007C00007C00007C00007C00007C00007C00007C00007C00007C00007C000 07C00007C00007C00007C00007C000FFFC00FFFC0007C00007C00007C00007C00007C00007C3C0 07C7E007E7E003E7E001FFE000FFC0003F80> 24 32 -1 0 15.972] 102 @dc [ 32 20 -1 0 27.588] 120 @dc [ 24 29 -4 0 26.136] 49 @dc [<000FFC0600007FFF3E0001FF07FE0003F801FE000FE000FE001FC000FE001F8000FE003F8000FE 007F0000FE007F0000FE007F0000FE00FE0000FE00FE007FFFE0FE007FFFE0FE00000000FE0000 0000FE00000000FE00000000FE00000000FE000006007F000006007F00000E007F00000E003F80 000E001F80001E001FC0003E000FE0007E0003F800FE0001FE03DE00007FFF8E00000FFC0600> 40 31 -3 0 41.097] 71 @dc [ 24 31 -3 0 29.040] 83 @dc cmmi10.329 @sf [<70F8F8F870> 8 5 -4 0 12.626] 58 @dc cmbx10.329 @sf [ 24 29 -3 0 26.136] 50 @dc [<0003FE0000001FFF8000007F03E00000FC00F00001F800300003F800380003F000180007F0001C 0007F0000C0007F0000C0007F0000C0007F0000C0007F0000C0007F0000C0007F0000C0007F000 0C0007F0000C0007F0000C0007F0000C0007F0000C0007F0000C0007F0000C0007F0000C0007F0 000C0007F0000C0007F0000C0007F0000C0007F0000C0007F0000C00FFFF81FFE0FFFF81FFE0> 40 31 -2 0 40.213] 85 @dc [<001FF80000FFFF0001F81F8007E007E00FC003F01F8001F83F8001FC3F0000FC7F0000FE7F0000 FE7E00007EFE00007FFE00007FFE00007FFE00007FFE00007FFE00007FFE00007FFE00007FFE00 007F7E00007E7E00007E7F0000FE3F0000FC1F0000F81F8001F80FC003F007E007E001F81F8000 FFFF00001FF800> 32 31 -3 0 39.267] 79 @dc [ 40 31 -2 0 40.087] 68 @dc [<01E00003F00003F00003F00003F00003F00003F00003F00003F00001F00001F00001F00000F000 00F00000F000007800007800003800001C00C00C00C00E00C00700E00380FFFFC07FFFE07FFFE0 7FFFF07FFFF87FFFF8600000> 24 30 -3 0 26.136] 55 @dc 11 @bop1 cmcsc10.518 @sf 225 500 p (Contents)s cmbx10.329 @sf 225 752 p (Abstract)s 1481(iii)m 225 854 p (Revision)s 16(History)m 1311 r 118 c 225 956 p (Preface)s 1513(ix)m 225 1058 p 49 c 42(Getting)m 18(Started)m 1269 r 49 c cmr10.329 @sf 293 1114 p (1.A)s 35(Notation)m 13(and)m 16(Problem)m 14(De\014nition)m cmmi10.329 @sf 29 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c cmr10.329 @sf 87 r 50 c 398 1170 p (1.A.i)s 49(Explicit)m 14(Orthogonal)m 14(Distance)m 15(Regression)m cmmi10.329 @sf 16 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c cmr10.329 @sf 87 r 52 c 398 1227 p (1.A.ii)s 36(Implicit)m 15(Orthogonal)m 14(Distance)m 14(Regression)m cmmi10.329 @sf 17 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c cmr10.329 @sf 87 r 53 c 398 1283 p (1.A.iii)s 23(Orthogonal)m 14(Distance)m 15(Regression)m 15(for)m 14(Multidimensional)m 13(Data)m cmmi10.329 @sf 33 r 58 c 22 r 58 c 22 r 58 c cmr10.329 @sf 87 r 53 c 293 1340 p (1.B)s 37(Algorithm)m cmmi10.329 @sf 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c cmr10.329 @sf 87 r 56 c 293 1396 p (1.C)s 36(Sp)m 1(ecifying)m 15(the)m 15 r 84 c -3(ask)m cmmi10.329 @sf 13 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c cmr10.329 @sf 87 r 56 c 293 1453 p (1.D)s 34(ODRP)m -3 r 65 c (CK)s 14(Generated)m 15(Results)m cmmi10.329 @sf 39 r 58 c 23 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c cmr10.329 @sf 87 r 57 c 398 1509 p (1.D.i)s 48(Error)m 14(Rep)m 1(orts)m cmmi10.329 @sf 16 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c cmr10.329 @sf 65(10)m 398 1566 p (1.D.ii)s 35(Computation)m 14(Rep)m 1(orts)m cmmi10.329 @sf 37 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c cmr10.329 @sf 65(10)m 543 1622 p (1.D.ii.a)s 41(Initial)m 14(Rep)m 1(orts)m cmmi10.329 @sf 28 r 58 c 23 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c cmr10.329 @sf 65(11)m 543 1679 p (1.D.ii.b)s 39(Iteration)m 14(Rep)m 1(orts)m cmmi10.329 @sf 46 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c cmr10.329 @sf 65(12)m 543 1735 p (1.D.ii.c)s 44(Final)m 14(Rep)m 1(orts)m cmmi10.329 @sf 45 r 58 c 23 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c cmr10.329 @sf 65(12)m 293 1791 p (1.E)s 38(Starting)m 14 r 86 c -3(alues)m cmmi10.329 @sf 26 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c cmr10.329 @sf 65(13)m 293 1848 p (1.F)s 39 r 87 c -3(eigh)m -1(ts)m cmmi10.329 @sf 32 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c cmr10.329 @sf 65(14)m 293 1904 p (1.G)s 33(Default)m 14 r 86 c -3(alues)m 14(and)m 16(Structured)m 15(Argumen)m (ts)s cmmi10.329 @sf 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c cmr10.329 @sf 65(15)m 398 1961 p (1.G.i)s 47(Default)m 14 r 86 c -3(alues)m cmmi10.329 @sf 38 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c cmr10.329 @sf 65(15)m 398 2017 p (1.G.ii)s 34(Structured)m 16(Argumen)m (ts)s cmmi10.329 @sf 24 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c cmr10.329 @sf 65(16)m cmbx10.329 @sf 225 2119 p 50 c 42(Using)m 17(ODRP)m -3 r 65 c -1(CK)m 1188(17)m cmr10.329 @sf 293 2176 p (2.A)s 35(Subroutine)m 15(Declaration)m 14(and)m 15(Call)m 14(Statemen)m (ts)s cmmi10.329 @sf 15 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c cmr10.329 @sf 65(17)m 293 2232 p (2.B)s 37(Subroutine)m 15(Argumen)m 116 c 14(Descriptions)m cmmi10.329 @sf 29 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c cmr10.329 @sf 65(22)m 398 2289 p (2.B.i)s 51(Synopsis)m cmmi10.329 @sf 17 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c cmr10.329 @sf 65(22)m 398 2345 p (2.B.ii)s 38(ODRP)m -3 r 65 c (CK)s 14(Subroutine)m 15(Argumen)m 116 c 14(De\014nitions)m cmmi10.329 @sf 22 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c cmr10.329 @sf 65(23)m 293 2401 p (2.C)s 36(Examples)m cmmi10.329 @sf 35 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c cmr10.329 @sf 65(39)m 398 2458 p (2.C.i)s 50(Example)m 15(Problem)m 15(for)m 14(an)m 15(Explicit)m 14(Mo)m 1(del)m cmmi10.329 @sf 26 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c cmr10.329 @sf 65(39)m 1069 2581 p (xi)s @eop %%Page: 12 14 12 @bop0 cmtt10.329 @sf [<03E3F80FFBF83FFFF83E3F80781F80780F80F00780F00780E00380E00380E00380E00380F00380 F007807807807C0F803E1F801FFF800FFF8003F380000380000380000380000380000380003F80 003F80003F80> 24 28 -2 0 23.863] 100 @dc [<0FE1F03FFFF07FFFF0F83F00F00F00E00700E00700F00700F807007F07003FFF000FFF0001FF00 000700000F00780F00783E007FFE007FF8001FE000> 24 20 -3 0 23.863] 97 @dc [<007E0000FF8001FFC003E3E003C1E00380E00380E0038040038000038000038000038000038000 038000038000038000038000FFFFC0FFFFC0FFFFC0038000038000038000038000038000> 24 25 -1 0 23.863] 116 @dc [ 24 20 -1 0 23.863] 114 @dc [<01FC000FFF001FFF803F07C07C03C07801C0F00000F00000FFFFC0FFFFC0FFFFC0E001C0F003C0 F003C07803807C07803E1F801FFF000FFE0003F000> 24 20 -3 0 23.863] 101 @dc [ 24 30 0 10 23.863] 112 @dc [<01F0000FFE001FFF003E0F803C07807803C07001C0F001E0E000E0E000E0E000E0E000E0E000E0 7001C07001C03803803E0F801FFF000FFE0001F000> 24 20 -2 0 23.863] 111 @dc [ 24 28 -2 0 23.863] 50 @dc [<07F8001FFE007FFF80FC0FC0F003C0F001E0F001E0F000E00000E00000E00001E00001E00003C0 000FC003FF8003FE0003FF00000F800007C00003C00001C07801C07801C07803C07C0FC07FFF80 1FFE0007F800> 24 28 -2 0 23.863] 51 @dc cmbx10.329 @sf [<03FE001FFF803E0FE07E07E0FF07F0FF03F8FF03F8FF03F8FF03F87E03F83C03F80003F00007F0 0007E0001F8001FE0001FE00003F00001F801F0FC03F8FE03F8FE03F87E03F87E03F87E01F0FE0 1F1FC00FFF8003FC00> 24 29 -2 0 26.136] 51 @dc [<000180003000000001C0007000000003C0007800000003E000F800000007E000FC00000007E000 FC00000007F001FC0000000FF001FE0000000FF803FE0000001FF803FF0000001FD803FB000000 1FCC07F30000003FCC07F18000003F8E0FF18000003F860FE18000007F060FE0C000007F031FE0 C00000FF031FC0E00000FE031FC0600000FE01BF80600001FC01BF80300001FC01FF80300003FC 00FF00380003F800FF00180003F800FE00180007F800FE000C0007F001FE000C0007F001FC000C 000FE001FC000E00FFFF1FFFC0FFE0FFFF1FFFC0FFE0> 56 31 -1 0 54.039] 87 @dc [ 24 32 -3 0 29.040] 104 @dc [ 48 31 -2 0 49.620] 77 @dc [ 16 32 -2 0 14.520] 108 @dc [ 24 31 -1 0 19.823] 73 @dc [<000070000000007000000000F800000000F800000001FC00000001FC00000003FE00000003FE00 000003FE00000007FB00000007F30000000FF18000000FE18000001FE1C000001FC0C000003FC0 E000003F806000003F806000007F003000007F00300000FF00180000FE00180001FE000C0001FC 000C0003FC000E0003F800060007F800070007F000030007F0000380FFFF003FF8FFFF003FF8> 40 31 -1 0 39.519] 86 @dc [<07FFFFC007FFFFC0000FE000000FE000000FE000000FE000000FE000000FE000000FE000000FE0 00000FE000000FE000000FE000000FE000000FE000000FE000000FE000000FE000000FE000C00F E006C00FE006C00FE006C00FE006E00FE00E600FE00C600FE00C700FE01C7C0FE07C7FFFFFFC7F FFFFFC> 32 30 -2 0 36.363] 84 @dc [ 40 20 -3 0 43.559] 109 @dc [<03FCFF0FFEFF1F87F81F03F81F01F81F00F81F00F81F00F81F00F81F00F81F00F81F00F81F00F8 1F00F81F00F81F00F81F00F81F00F8FF07F8FF07F8> 24 20 -3 0 29.040] 117 @dc [<01FE0007FF801F87C01F03E03E01F07C01F87C01F87C01F8FC01F8FC01F8FC01F8FC01F8FE01F8 FE01F0FF03F0FF83E0FFFFC0FCFF80FC10007C00007C01E07E03F03E03F03E03F01F03F00F81F0 07E0E001FFC0007F80> 24 29 -2 0 26.136] 54 @dc [<01FFFE01FFFE000FC0000FC0000FC0000FC0000FC0000FC0FFFFFEFFFFFEE007C07007C03807C0 1807C00C07C00E07C00707C00387C00187C000C7C00067C00077C0003FC0001FC0000FC00007C0 0007C00003C00001C0> 24 29 -1 0 26.136] 52 @dc [ 24 29 -2 9 29.040] 112 @dc cmmi10.329 @sf [ 32 41 0 9 25.710] 12 @dc cmbx10.329 @sf [<0FF0001FFE003C3F00701F80FC0FC0FE0FC0FE0FE0FE0FE0FE0FE07C0FE0000FE0000FE0000FE0 300FC0381FC03E3F803FFE0033F8003000003000003000003000003F80003FF8003FFC003FFF00 3FFF803FFF80380380> 24 29 -3 0 26.136] 53 @dc [ 24 32 -2 0 27.588] 107 @dc [<03FE001FFF803F03E07C00E0F800F0F80078F00078F000F8F000F8F003F8F80FF87C3FF83E7FF0 1FFFF00FFFE00FFFC01FFF801FFF803FFFC03FE3C03F81E03F01E03E01E03C01E01C03E01E03C0 0F0FC007FF8001FE00> 24 29 -2 0 26.136] 56 @dc [ 32 31 -2 0 37.183] 66 @dc [<07F0001FFE003C3F007C0F807E07C07E03E07E03E07E03F03C01F00001F00041F80FF9F81FFFF8 3E0FF87E07F87C03F8FC03F8FC01F8FC01F8FC01F8FC01F8FC01F0FC01F07C01F07C03E03E03E0 1F0FC00FFF0003FC00> 24 29 -2 0 26.136] 57 @dc 12 @bop1 cmr10.329 @sf 0 123 p (xii)s 1498(Con)m (ten)s -1(ts)m 0 134 p 1725 2 ru 318 259 p (2.C.i.a)s 56(User)m 15(Supplied)m 16(Co)m 1(de)m cmmi10.329 @sf 32 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c cmr10.329 @sf 65(40)m 318 315 p (2.C.i.b)s 54(User)m 15(Supplied)m 16(Data)m 14(\(\014le)m cmtt10.329 @sf 14(data1)m cmr10.329 @sf 41 c cmmi10.329 @sf 40 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c cmr10.329 @sf 65(45)m 318 372 p (2.C.i.c)s 59(Rep)m 1(ort)m 15(Generated)m 15 r 98 c 121 c 14(ODRP)m -3 r 65 c (CK)s 14(\(\014le)m cmtt10.329 @sf 15(report1)m cmr10.329 @sf 41 c cmmi10.329 @sf 31 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c cmr10.329 @sf 65(46)m 173 428 p (2.C.ii)s 37(Example)m 15(Problem)m 15(for)m 14(an)m 15(Implicit)m 15(Mo)m 1(del)m cmmi10.329 @sf 26 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c cmr10.329 @sf 65(49)m 318 484 p (2.C.ii.a)s 43(User)m 15(Supplied)m 16(Co)m 1(de)m cmmi10.329 @sf 32 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c cmr10.329 @sf 65(49)m 318 541 p (2.C.ii.b)s 41(User)m 15(Supplied)m 16(Data)m 14(\(\014le)m cmtt10.329 @sf 14(data2)m cmr10.329 @sf 41 c cmmi10.329 @sf 40 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c cmr10.329 @sf 65(53)m 318 597 p (2.C.ii.c)s 46(Rep)m 1(ort)m 15(Generated)m 15 r 98 c 121 c 14(ODRP)m -3 r 65 c (CK)s 14(\(\014le)m cmtt10.329 @sf 15(report2)m cmr10.329 @sf 41 c cmmi10.329 @sf 31 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c cmr10.329 @sf 65(54)m 173 654 p (2.C.iii)s 24(Example)m 15(Problem)m 15(for)m 14(an)m 15(Explicit)m 14(Mo)m 1(del)m 15(with)m 15(Multiresp)m 1(onse)m 14(Data)m 52(56)m 318 710 p (2.C.iii.)s -1 r 97 c 31(User)m 15(Supplied)m 16(Co)m 1(de)m cmmi10.329 @sf 32 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c cmr10.329 @sf 65(57)m 318 767 p (2.C.iii.)s -1 r 98 c 29(User)m 15(Supplied)m 16(Data)m 14(\(\014le)m cmtt10.329 @sf 14(data3)m cmr10.329 @sf 41 c cmmi10.329 @sf 40 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c cmr10.329 @sf 65(63)m 318 823 p (2.C.iii.)s -1 r 99 c 34(Rep)m 1(ort)m 15(Generated)m 15 r 98 c 121 c 14(ODRP)m -3 r 65 c (CK)s 14(\(\014le)m cmtt10.329 @sf 15(report3)m cmr10.329 @sf 41 c cmmi10.329 @sf 31 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c cmr10.329 @sf 65(64)m cmbx10.329 @sf 0 925 p 51 c 42(When)m 18(the)m 17(Mo)m 1(del)m 18(Is)m 16 r 86 c -3(ery)m 15(Time)m 17(Consuming)m 622(67)m 0 1027 p 52 c 42(Computational)m 18(Details)m 1086(71)m cmr10.329 @sf 68 1083 p (4.A)s 35(Computing)m 14(the)m 15(Jacobian)m 15(Matrices)m cmmi10.329 @sf 45 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c cmr10.329 @sf 65(71)m 173 1140 p (4.A.i)s 49(\\Hand)m 15(Co)m 1(ded")m 16(Deriv)m -2(ativ)m -2(es)m cmmi10.329 @sf 44 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c cmr10.329 @sf 65(71)m 173 1196 p (4.A.ii)s 36(Automatic)m 14(Di\013eren)m (tia)s -1(tio)m -1 r 110 c cmmi10.329 @sf 27 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c cmr10.329 @sf 65(72)m 173 1253 p (4.A.iii)s 23(Finite)m 14(Di\013erence)m 15(Deriv)m -2(ativ)m -1(es)m cmmi10.329 @sf 44 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c cmr10.329 @sf 65(73)m 318 1309 p (4.A.iii.a)s 29 r 70 c -3(orw)m -1(a)m -1(rd)m 13(Finite)m 15(Di\013erence)m 15(Deriv)m -2(ati)m -1 r 118 c -1(es)m cmmi10.329 @sf 32 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c cmr10.329 @sf 65(73)m 318 1366 p (4.A.iii.b)s 27(Cen)m (tral)s 13(Finite)m 14(Di\013erence)m 15(Deriv)m -2(ati)m -1 r 118 c -1(es)m cmmi10.329 @sf 13 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c cmr10.329 @sf 65(74)m 68 1422 p (4.B)s 37(Co)m 118 c -3(aria)m -1(nce)m 14(Matrix)m cmmi10.329 @sf 34 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c cmr10.329 @sf 65(74)m 68 1479 p (4.C)s 36(Condition)m 14(Num)m 98 c 1(er)m cmmi10.329 @sf 31 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c cmr10.329 @sf 65(77)m 68 1535 p (4.D)s 34(Scaling)m 14(Algorithms)m cmmi10.329 @sf 25 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c cmr10.329 @sf 65(78)m 173 1591 p (4.D.i)s 48(Scaling)m cmmi10.329 @sf 15 r 12 c 41 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c cmr10.329 @sf 65(80)m 173 1648 p (4.D.ii)s 35(Scaling)m 15 r 1 c cmmi10.329 @sf 29 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c cmr10.329 @sf 65(81)m cmbx10.329 @sf 0 1750 p 53 c 42 r 87 c -3(ork)m 16 r 86 c -3(ectors)m 1289(83)m cmr10.329 @sf 68 1806 p (5.A)s 35(Extracting)m 13(Information)m 15(from)m 14 r 86 c -3(ector)m cmtt10.329 @sf 14(WORK)m cmmi10.329 @sf 40 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c cmr10.329 @sf 65(83)m 68 1863 p (5.B)s 37(Extracting)m 13(Information)m 15(from)m 14 r 86 c -3(ector)m cmtt10.329 @sf 14(IWORK)m cmmi10.329 @sf 16 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 23 r 58 c 22 r 58 c 22 r 58 c cmr10.329 @sf 65(91)m cmbx10.329 @sf 0 1965 p (Bibliograph)s 121 c 1377(97)m @eop %%Page: 1 15 1 @bop0 cmcsc10.518 @sf [<7FFFFF807FFFFF8000FFC000003F0000003F0000003F0000003F0000003F0000003F0000003F00 00003F0000003F0000003F0000003F0000003F0000003F0000003F0000003F0000003F0000003F 0000003F0000003F0000003F0000003F0000003F0000003F0000003F0000003F0000003F000000 3F0000003F0000003F0000003F0000003F0000003F0000003F0000003F0000003F0000003F0000 003F0000E03F0000FF3F00001FFF000000FF0000001F0000000F000000070000> 32 47 -7 0 39.650] 49 @dc [<3C7EFFFFFFFF7E3C> 8 8 -7 0 22.913] 46 @dc [<000007FE00000000003FFFE004000001FE00F81C000007F0001C3C00000FC0000E7C00003F0000 03FC00007E000003FC0000FC000001FC0001F8000001FC0003F0000001FC0007F0000001FC000F E0000001FC000FC0000001FC001FC0000001FC001FC0000001FC003F80000001FC003F80000001 FC007F80000001FC007F80000001FC007F00000007FE007F000003FFFFE0FF000003FFFFE0FF00 0000000000FF000000000000FF000000000000FF000000000000FF000000000000FF0000000000 00FF000000000000FF0000000000007F0000000000007F000000000C007F800000000C007F8000 00000C003F800000000C003F800000001C001FC00000001C001FC00000001C000FC00000003C00 0FE00000003C0007E00000007C0003F00000007C0001F8000000FC0000FC000001FC00007E0000 03FC00003F0000067C00000FC0000C3C000007F000383C000001FE01F01C0000003FFFC00C0000 0007FE000400> 56 51 -5 1 61.069] 71 @dc [<0000FF8000000FFFF020003F807860007E000CE001F80007E003E00003E007C00003E00F800003 E00F800003E01F000003E03F000003E03E000003E07E000003E07E000003E07C000007F0FC0001 FFFEFC0001FFFEFC00000000FC00000000FC00000000FC00000000FC00000000FC00000000FC00 0000607C000000607E000000607E000000E03E000000E03F000000E01F000001E00F800001E00F 800003E007C00003E003E00007E001F0000DE0007C0038E0003F80F0E0000FFFC0600000FF0020> 40 39 -3 1 45.986] 103 @dc [<8007FC0000C03FFF8000E0F803C000F3C000F000F700007800FC00003C00F800001C00F000001E 00F000001F00E000000F00E000000F00E000000F80C000000F80C000000F80C000000F80C00000 1F800000001F800000003F800000003F800000007F00000001FF00000007FE0000007FFE00000F FFFC00007FFFF80001FFFFF00003FFFFE0000FFFFFC0001FFFFF00001FFFF000003FFF0000007F F00000007F800000007F00000000FE00000000FC00000600FC00000600F800000600F800000E00 F800000E00F800000E007800001E007800001E003C00003E003C00003E001E00007E000F0001DE 000780039E0003E01F0E0000FFFC0600001FE00200> 40 51 -5 1 43.834] 83 @dc [ 40 37 -3 0 44.791] 100 @dc cmsy10.329 @sf [<0F801FE038F07070707870387038003800380078007000F001E007C01FE03CF078707078F038E0 38E038E038E078F07070F079E03FC01F003C0078007000F000E000E000E070E070F070707078E0 3FC00F80> 16 41 -3 9 20.202] 120 @dc 1 @bop1 cmcsc10.518 @sf 225 519 p (1.)s 35(Getting)m 28(St)m -4(ar)m -4(ted)m cmr10.329 @sf 225 746 p (ODRP)s -3 r 65 c (CK)s 14(is)m 15 r 97 c 15 r 112 c 1(ortable)m 15(collection)m 14(of)m 15(ANSI)m 16 r 70 c -3(ortran)m 14(77)m 14(subroutines)m 16(for)m 14(\014tting)m 15 r 97 c 15(mo)m 1(del)m 225 802 p (to)s 15(data.)m 19(It)m 15(is)m 15(designed)m 15(primarily)m 14(for)m 14(instances)m 15(when)m 16(all)m 14(of)m 14(the)m 16 r 118 c -2(ariables)m 13(ha)m 118 c 101 c 13(signi\014can)m 116 c 225 858 p (errors)s 13(\(see,)m 13(e.g.,)m 13([F)m -3(uller,)m 11(1987])m 12(and)m 14([Boggs)m 12(and)m 14(Rogers,)m 13(1990]\),)m 11(implemen)m (ting)s 12 r 97 c 13(highly)m 13(ef-)m 225 915 p (\014cien)s 116 c 11(algorithm)m 10(for)m 12(solving)m 11(the)m 12 r 119 c (eigh)s -1(ted)m 10(orthogonal)m 11(distance)m 12(regression)m 11(problem)m 12([Boggs)m cmti10.329 @sf 225 971 p (et)s 17(al.)m cmr10.329 @sf 44 c 15(1987)m 14(and)m 16(1989].)m 19(It)m 15(can)m 16(also)m 15 r 98 c 1 r 101 c 16(used)m 16(to)m 15(solv)m 101 c 13(the)m 16(ordinary)m 15(least)m 14(squares)m 16(problem,)m 225 1028 p (ho)s 119 c -1(ev)m -1(er,)m 17(where)m 18(all)m 18(of)m 18(the)m 18(errors)m 18(are)m 18(attributed)m 17(to)m 18(the)m 18(observ)m -2(ations)m 17(of)m 18(only)m 17(one)m 19(of)m 18(the)m 225 1084 p 118 c -2(ariables.)m 225 1160 p 87 c -3 r 101 c 13(suggest)m 12(that)m 13(\014rst)m 13(time)m 13(users)m 14(of)m 13(ODRP)m -3 r 65 c (CK)s 12 r 98 c 1(egin)m 13 r 98 c 121 c 13(at)m 13(least)m 12(skimming)m 13(this)m 12 r 99 c (hapter,)s 225 1217 p (and)s 17(then)m 17(pro)m 1(ceed)m 17(to)m 17(the)m 16(sample)m 17(programs)m 15(giv)m (en)s 15(in)m cmsy10.329 @sf 17 r 120 c cmr10.329 @sf (2.C,)s 16(mo)m 1(difying)m 16(them)m 16(as)m 17(necessary)m 225 1273 p (to)s 20(solv)m 101 c 19(their)m 21(particular)m 20(problem.)m 37(The)m 21(sample)m 20(programs)m 20(are)m 21(distributed)m 20(in)m 21(mac)m (hine)s 225 1330 p (readable)s 21(form)m 20(with)m 20(the)m 22(ODRP)m -3 r 65 c (CK)s 19(release,)m 22(and)m 21(th)m (us)s 20(should)m 21 r 98 c 1 r 101 c 22 r 97 c 118 c -2(a)m -1(ila)m -1(ble)m 20(for)m 20(use)m 21(as)m 225 1386 p (templates)s 17(without)m 18(requiring)m 17(that)m 18(the)m 19(user)m 18(en)m (ter)s 17(the)m 19(co)m 1(de.)m 30(The)m 18(subroutine)m 19(argumen)m (ts)s 225 1443 p (used)s 16(in)m 15(these)m 15(examples)m 15(are)m 15(de\014ned)m 17(in)m 15(detail)m 14(in)m cmsy10.329 @sf 15 r 120 c cmr10.329 @sf (2.B.ii.)s 225 1519 p (Chapter)s 14 r 49 c 14(presen)m (ts)s 13(information)m 12(that)m 13(is)m 14(esp)m 1(ecially)m 14(imp)m 1(ortan)m 116 c 12(to)m 13(\014rst)m 14(time)m 13(users)m 15(of)m 13(ODR-)m 225 1575 p 80 c -3 r 65 c (CK.)s 18(Users)m 21(are)m 20(directed)m 21(to)m cmsy10.329 @sf 20 r 120 c cmr10.329 @sf (1.A)s 20(for)m 20 r 97 c 21(brief)m 20(description)m 20(of)m 20(the)m 21(orthogonal)m 19(distance)m 225 1631 p (regression)s 13(problem.)m 19(This)m 13(section)m 13(in)m (tro)s (duces)s 13(notation)m 12(and)m 13(pro)m (vides)s 12(bac)m (kground)s 13(material)m 225 1688 p (for)s 11(understanding)m 12(the)m 11(remainder)m 12(of)m 11(the)m 12(do)m 1(cumen)m (tation.)s 17(The)m 12(algorithm)m 9(itself)m 11(is)m 11(describ)m 1(ed)m 225 1744 p (brie\015y)s 19(in)m cmsy10.329 @sf 18 r 120 c cmr10.329 @sf (1.B,)s 19(and)m 18(in)m 19(greater)m 17(detail)m 18(in)m 18([Boggs)m cmti10.329 @sf 17(et)m 20(al.)m cmr10.329 @sf 44 c 18(1987)m 18(and)m 18(1989].)m 29(Options)m 18 r 97 c 118 c -2(ai)m -1(l-)m 225 1801 p (able)s 17(for)m 16(sp)m 1(ecifying)m 17(the)m 17(problem)m 17(are)m 16(brie\015y)m 17(discussed)m 18(in)m cmsy10.329 @sf 17 r 120 c cmr10.329 @sf (1.C,)s 16(and)m 17(ODRP)m -3 r 65 c (CK's)s 15(rep)m 1(ort)m 225 1857 p (generation)s 16(facilit)m 121 c 15(is)m 17(discussed)m 18(in)m cmsy10.329 @sf 17 r 120 c cmr10.329 @sf (1.D.)s 25(The)m 18(need)m 18(for)m 17(go)m 1 r 111 c 1 r 100 c 17(starting)m 16 r 118 c -2(alues)m 16(for)m 17(the)m 17(un-)m 225 1914 p (kno)s (wn)s 18(parameters)m 17(of)m 19(the)m 19(mo)m 1(del)m 18(is)m 19(explained)m 18(in)m cmsy10.329 @sf 19 r 120 c cmr10.329 @sf (1.E,)s 19(and)m 19(the)m 19(use)m 19(of)m 18 r 119 c (eigh)s -1(ts)m 16(in)m cmsy10.329 @sf 19 r 120 c cmr10.329 @sf (1.F.)s 225 1970 p (Finally)s -3 r 44 c cmsy10.329 @sf 12 r 120 c cmr10.329 @sf (1.G)s 13(describ)m 1(es)m 15 r 116 c 119 c -1 r 111 c 12(features)m 14(of)m 13(ODRP)m -3 r 65 c (CK)s 13(that)m 14(simplify)m 13(the)m 14(user)m 14(in)m (terface)s 13(with)m 225 2027 p (the)s 15(pac)m 107 c -2(age.)m 225 2103 p (Chapter)s 16 r 50 c 16(describ)m 1(es)m 17(the)m 16(use)m 17(of)m 16(ODRP)m -3 r 65 c (CK)s 15(in)m 16(detail.)m 22(Most)m 15(exp)m 1(erienced)m 18(users)m 16(of)m 16(ODR-)m 225 2159 p 80 c -3 r 65 c (CK)s 15(will)m 16(only)m 17(need)m 18(the)m 18(information)m 15(in)m 17(this)m 17 r 99 c (hapter.)s 25(The)m 18(declaration)m 16(and)m 17(call)m 17(state-)m 225 2216 p (men)s (ts)s 17(for)m 17(eac)m 104 c 17(user)m 18(callable)m 17(ODRP)m -3 r 65 c (CK)s 17(subroutine)m 18(are)m 18(giv)m (en)s 16(in)m cmsy10.329 @sf 18 r 120 c cmr10.329 @sf (2.A,)s 18(the)m 18(subroutine)m 225 2272 p (argumen)s (ts)s 13(are)m 15(de\014ned)m 17(in)m cmsy10.329 @sf 15 r 120 c cmr10.329 @sf (2.B,)s 14(and)m 16(sample)m 14(programs)m 14(are)m 15(sho)m (wn)s 14(in)m cmsy10.329 @sf 15 r 120 c cmr10.329 @sf (2.C.)s 225 2348 p (The)s 10(last)m 9(three)m 11 r 99 c (hapters)s 9(pro)m (vide)s 8(auxiliary)m 9(information.)m 16(Chapter)m 10 r 51 c 10(is)m 10(generally)m 9(only)m 10(needed)m 225 2404 p 98 c 121 c 12(users)m 13(with)m 12 r 118 c (ery)s 12(time)m 13(consuming)m 12(functions;)m 13(it)m 13(explains)m 12(ho)m 119 c 12(ODRP)m -3 r 65 c (CK's)s 11(features)m 13(can)m 225 2461 p 98 c 1 r 101 c 19(exploited)m 18(in)m 18(order)m 19(to)m 17(minimize)m 18(cost,)m 18(and)m 19(to)m 18(reduce)m 19(the)m 19 r 112 c 1(ossibilit)m -1 r 121 c 16(of)m 18(losing)m 18(results)m 1076 2581 p 49 c @eop %%Page: 2 16 2 @bop0 1.000000 /cmbx12.300 @newfont cmbx12.300 @sf [<7FFFE07FFFE001F80001F80001F80001F80001F80001F80001F80001F80001F80001F80001F800 01F80001F80001F80001F80001F80001F80001F80001F80001F80001F80001F80001F80001F800 01F800FFF800FFF80001F800007800001800> 24 32 -4 0 28.019] 49 @dc [<7CFEFEFEFEFE7C> 8 7 -4 0 15.566] 46 @dc [ 40 34 -2 0 42.317] 65 @dc [ 40 34 -2 0 43.816] 78 @dc [<00FE0007FFC00F83E01F01F03E00F87C007C7C007CFC007EFC007EFC007EFC007EFC007EFC007E FC007E7C007C7C007C7C007C3E00F81E00F00F83E007FFC000FE00> 24 22 -2 0 28.019] 111 @dc [<00FC0003FF0007E7000FE3800FC1800FC1800FC1800FC1800FC1800FC0000FC0000FC0000FC000 0FC0000FC0000FC0000FC0000FC0000FC0000FC000FFFF00FFFF001FC0000FC00007C00003C000 01C00001C00000C00000C00000C00000C000> 24 32 -1 0 21.793] 116 @dc [<0FF0FF3FFDFF7F1FF8FE0FF0FC07F0FC03F0FC03F0FE03F07E03F07F03F03FE3F00FFFF001FFF0 0003F00003F01E03F03F03F03F07F03F07E03F0FC01FFF8007FE00> 24 22 -2 0 27.241] 97 @dc [ 16 36 -1 0 15.566] 105 @dc [ 32 22 -2 0 31.133] 110 @dc [<01FC7FC00FFF7FC01F83FE003F01FE003E00FE007E007E007C007E00FC007E00FC007E00FC007E 00FC007E00FC007E00FC007E00FC007E00FC007E007C007E007E007E003E007E003F00FE001FC3 FE0007FFFE0001FE7E0000007E0000007E0000007E0000007E0000007E0000007E0000007E0000 007E0000007E0000007E0000007E000003FE000003FE00> 32 35 -2 0 31.133] 100 @dc [ 32 34 -2 0 38.281] 80 @dc [ 24 22 -2 0 22.888] 114 @dc [<1C1FE0001E7FF8001FF0FE001FC03F001F801F001F801F801F800F801F800FC01F800FC01F800F C01F800FC01F800FC01F800FC01F800FC01F800FC01F800F801F801F801F801F801FC03F001FF0 7E001FBFFC001F8FE0001F8000001F8000001F8000001F8000001F8000001F8000001F8000001F 8000001F8000001F8000001F800000FF800000FF800000> 32 35 -2 0 31.133] 98 @dc [ 16 35 -1 0 15.566] 108 @dc [<00FF8007FFE00FE0F01F80383F00187E00007E0000FC0000FC0000FC0000FC0000FFFFF8FFFFF8 FC00F8FC00F87C00F87E00F03E01F03F03E01F87E007FF8001FE00> 24 22 -2 0 25.569] 101 @dc [ 48 22 -2 0 46.699] 109 @dc [ 40 34 -2 0 42.951] 68 @dc [<7FF0FFE07FF0FFE00FC03F000FC03F000FC03F000FC03F000FC03F000FC03F000FC03F000FC03F 000FC03F000FC03F000FC03F000FC03F000FC03F000FC03F000FC03F000FC03F000FC03F000FC0 3F00FFFFFF00FFFFFF000FC000000FC000000FC000000FC000000FC00C000FC03F000FC03F000F E03F0007E03F0003F01F0001FC1E00007FFC00000FF800> 32 35 -1 0 31.133] 12 @dc cmsy10.329 @sf [<007FF801FFF807C0000F00001C0000380000300000700000600000600000E00000C00000C00000 FFFFF8FFFFF8C00000C00000E000006000006000007000003000003800001C00000F000007C000 01FFF8007FF8> 24 28 -4 3 30.302] 50 @dc [<0F8007C01FC00FE038E01F7070F01E38E0703E10F0783C0070783E0000783E0000783C0000783C 0000783C0000783C003C7C3C007C7C3C006E7C3C00667C3C00667C3C00067FFE00067FFFC0067C 03E00E7C00F80E7C007C1C78007C3C7800F8387801F8707801F0607803E0607803E060FC07C070 FE07C039E78F803FC3FF001F01FF0000003E00> 32 34 -2 1 32.828] 60 @dc 1.000000 /cmmi8.300 @newfont cmmi8.300 @sf [ 24 20 1 6 17.761] 112 @dc cmmi10.329 @sf [<7E00007F0000FB80007B800071C00001C00001E00000E00000E00000E00000F000007000007000 007000007000007800003800003800003800003800003800003C00001C00001C00001C00001C00 001E0001FFF000FFF0000E00000E00000F0000070000070000070000070000079E00039E0003DE 0001FE0000FC> 24 41 -2 9 22.253] 102 @dc cmti10.329 @sf [<7C7C00FFFF00EFC780F7C180F381C0F3C0C073C0E001C00001C00001E00001E00000E00000E000 E0E1C060F1E07071E07079E03CFCE01FFFC007C780> 24 20 -3 0 21.085] 120 @dc cmmi10.329 @sf [<3C3E007FFF80E7E3C0F3E0C0F1C0E0F1E06071E07000E00000E00000F00000F000007000007000 E070E06078F07038F0307CF03C7E701FFFE007C3C0> 24 20 -2 0 25.978] 120 @dc [<60F07038181C0C0C0C7CFCFCF870> 8 14 -4 9 12.626] 59 @dc [<1F80003FE00038F0003C78003C3C003C1E00080E00000F0000070001F70003FF00079F80070780 0707800703800703C00701C00701C00781C00381E00380E003C0E0E1C0E061C0F061E07070E070 39E0701FC0780F8038> 24 29 -1 9 22.285] 121 @dc cmsy10.329 @sf [<80003F008000FFC0C003FFE0C007E1E0E01F8070787E00307FFC00303FF000100FC00010000000 000000000080003F008000FFC0C003FFE0C007E1E0E01F8070787E00307FFC00303FF000100FC0 0010> 32 20 -3 -2 35.353] 25 @dc cmti10.329 @sf [<0FFE000FFE0000F0000070000070000070000078000038000038001F38003FFC0078FC00707C00 F03C00F01E00F01E00F00E00F00E00F80F007807007807007807003C07803C07801E07800F0F80 078FC003FDC000F8C0> 24 29 -4 9 20.908] 113 @dc cmbx10.329 @sf [ 32 31 -2 0 34.342] 69 @dc cmmi8.300 @sf [<1F003F8039C03DC01CC01C001E000E000F00E700670077003F001E000000000000000000000000 00018001C001C0> 16 23 0 0 12.013] 105 @dc cmsy10.329 @sf [ 32 20 -3 -1 35.353] 17 @dc 1.000000 /cmtt9.300 @newfont cmtt9.300 @sf [ 16 23 -4 0 19.613] 49 @dc [ 16 23 -2 0 19.613] 50 @dc cmmi10.329 @sf [<0FE01FFC3C3E780F7003F000F000F000F000F8007FE07FF8783E7C0E3C071E030F0307C703FE00 FC> 16 20 -2 0 21.164] 101 @dc cmmi8.300 @sf [ 24 29 0 6 19.798] 12 @dc cmtt9.300 @sf [<0FE03FF07FF8F07CF01EF00E600E000E000E001C007C07F807F007F80078003C001C781C781C78 7C7FF83FF00FE0> 16 23 -2 0 19.613] 51 @dc cmmi8.300 @sf [<7CF800FFFE00E78E00E38700E3830003C00003C00001C00001C000E1C30061E38071F3803FFF80 1F9F00> 24 14 -1 0 19.862] 120 @dc 1.000000 /cmmi6.300 @newfont cmmi6.300 @sf [<3C3E3733381818DCEC7C3C00000000060F07> 8 18 -1 0 11.098] 105 @dc cmsy10.329 @sf [ 32 2 -4 -10 35.353] 0 @dc cmmi10.329 @sf [<0F801FC01CE01C701C301C301E380E000F000700070007800380E3C061C061C071C039C01FC00F 80000000000000000000000000000000F000F000F00070> 16 31 -1 0 15.659] 105 @dc cmr10.329 @sf [ 32 12 -3 -5 35.353] 61 @dc cmmi10.329 @sf [<1C00F8001E01FC001E03CE000E0387000E03C3000F01C3000F01C3800701E0000700E0000780E0 000780F0000380700003C07000E3C0700063E0780061E0380071F0780033FC70003F9FF0001F07 E000> 32 20 -1 0 27.283] 110 @dc 2 @bop1 cmr10.329 @sf 0 114 p 50 c 1388(Getting)m 14(Started)m 0 134 p 1725 2 ru 0 259 p 98 c 1(ecause)m 20(limits)m 17(imp)m 1(osed)m 19 r 98 c 121 c 17(their)m 18(computer)m 19(system)m 18 r 119 c (ere)s 18(reac)m (hed.)s 30(Chapter)m 18 r 52 c 18(describ)m 1(es)m 0 315 p (the)s 16(details)m 14(of)m 16(certain)m 15(ODRP)m -3 r 65 c (CK)s 14(computations,)m 14(and)m 16(Chapter)m 15 r 53 c 16(describ)m 1(es)m 16(ho)m 119 c 14(the)m 16(user)m 0 372 p (can)s 15(extract)m 15(computed)m 15(results)m 15(from)m 14(the)m 16 r 119 c (ork)s 13 r 118 c (ectors.)s cmbx12.300 @sf 0 516 p (1.A.)s 18(Notation)m 18(and)m 19(Problem)m 18(De\014nition)m cmr10.329 @sf 0 637 p (The)s 18(metho)m 1 r 100 c 19(of)m 17(least)m 17(squares)m 18(is)m 18(often)m 17(used)m 19(to)m 17(\014nd)m 19(the)m 18(parameters)m cmmi10.329 @sf 17 r 12 c cmsy10.329 @sf 15 r 50 c 13 r 60 c cmmi8.300 @sf 1453 622 p 112 c cmr10.329 @sf 1491 637 p (of)s 17 r 97 c 18(mathe-)m 0 694 p (matical)s 15(mo)m 1(del)m 16(that)m 16(de\014nes)m 18 r 97 c 16(relationship)m 15 r 98 c 1(et)m 119 c (een)s 15 r 118 c -2(ariables)m 15(that)m 16(are)m 16(sub)m 3(ject)m 16(to)m 16(errors.)m 0 750 p (When)s 20(errors)m 19 r 111 c 1(ccur)m 21(in)m 20(more)m 19(than)m 20(one)m 20(of)m 20(the)m 20 r 118 c -2(ariables,)m 19(then)m 20(the)m 20(relationship)m 19 r 98 c 1(et)m 119 c -1(een)m 0 807 p (the)s 20 r 118 c -2(ariables)m 19(is)m 19(frequen)m (tly)s 19(referred)m 20(to)m 20(as)m 20 r 97 c cmti10.329 @sf 20(me)m -1(asur)m -2(ement)m 19(err)m -1(or)m 20(mo)m -1(del)m cmr10.329 @sf 19(or)m 20(an)m cmti10.329 @sf 20(err)m -1(ors)m 19(in)m 0 863 p (variables)s 18(pr)m -1(oblem)m cmr10.329 @sf 46 c 28(The)m 18(computational)m 17(problem)m 18(asso)m 1(ciated)m 17(with)m 17(\014nding)m 19(the)m 18(maxim)m (um)s 0 919 p (lik)s (eli)s -1(ho)m 1 r 111 c 1 r 100 c 14(estimators)m 13(of)m 15(the)m 15(parameters)m 14(of)m 14(suc)m 104 c 15(mo)m 1(dels)m 15(is)m 14(kno)m (wn)s 14(as)m cmti10.329 @sf 15(ortho)m -1(gonal)m 15(distanc)m -1 r 101 c 0 976 p 114 c -1 r 101 c -2(gr)m -2(ess)m -1(ion)m cmr10.329 @sf 46 c 27(These)m 19(mo)m 1(dels)m 18(are)m 18(discussed)m 18(in)m 19([F)m -3(uller,)m 16(1987],)m 17(and)m 19([Seb)m 1(er)m 19(and)m 18(Wild,)m 18(1989].)m 0 1032 p (The)s 18(orthogonal)m 15(distance)m 17(regression)m 17(pro)m 1(cedure)m 18(implemen)m (ted)s 16(in)m 17(ODRP)m -3 r 65 c (CK)s 16(is)m 17(review)m (ed)s 0 1089 p (in)s 18([Boggs)m 17(and)m 18(Rogers,)m 19(1990].)m 27(That)m 17(publication)m 18(also)m 17(summarizes)m 17(the)m 19(results)m 17(of)m 18(sev)m (eral)s 0 1145 p (sim)s (ulat)s -1(ion)m 10(studies)m 11(that)m 11(compare)m 12(orthogonal)m 10(distance)m 12(regression)m 10(results)m 12(to)m 11(those)m 11(obtained)m 0 1202 p (using)s 16(ordinary)m 15(least)m 16(squares,)m 16(where)m 16(the)m 17(errors)m 15(are)m 16(assumed)m 16(to)m 16 r 111 c 1(ccur)m 17(in)m 16(only)m 16(one)m 16(of)m 16(the)m 0 1258 p 118 c -2(ariables.)m 18(\(See)m 16(also)m 14([Boggs)m cmti10.329 @sf 14(et)m 16(al.)m cmr10.329 @sf 44 c 15(1988].\))m 0 1334 p (The)s 15(mo)m 1(del)m cmmi10.329 @sf 15 r 102 c cmr10.329 @sf 20(that)m 14(de\014nes)m 16(the)m 16(relationship)m 13 r 98 c 1(et)m 119 c (een)s 13(the)m 16 r 118 c -2(ariables)m 13(can)m 15 r 98 c 1 r 101 c 16(either)m 14(linear)m 14(or)m 0 1391 p (nonlinear)s 14(in)m 14(its)m 13(parameters)m cmmi10.329 @sf 14 r 12 c cmr10.329 @sf 2 r 46 c 19(Sometimes)m 14(one)m 14(of)m 14(the)m 15(observ)m (ed)s 13 r 118 c -2(ariables)m 13(is)m 13(distinguished)m 0 1447 p (as)s 11 r 98 c 1(eing)m 13 r 97 c cmti10.329 @sf 11 r 114 c -1(esp)m -2(onse)m cmr10.329 @sf 9(that)m 11(is)m cmti10.329 @sf 12(dep)m -1(endent)m cmr10.329 @sf 10(up)m 1(on)m 12(the)m 12(remaining)m 11 r 118 c -2(ariables,)m 11(whic)m 104 c 10(are)m 12(commonly)m 0 1504 p (called)s 16(the)m cmti10.329 @sf 16(explanatory)m cmr10.329 @sf 44 c cmti10.329 @sf 17 r 114 c -1 r 101 c -2(gr)m -2(es)m -1(sor)m cmr10.329 @sf 14(or)m cmti10.329 @sf 16(indep)m -1(endent)m cmr10.329 @sf 14 r 118 c -2(ariables.)m 21(In)m 17(these)m 17(cases,)m 16(the)m 16(explana-)m 0 1560 p (tory)s 15 r 118 c -2(ariables)m 14(are)m 15(often)m 16(used)m 16(to)m 15(predict)m 16(the)m 16 r 98 c 1(eha)m (vior)s 14(of)m 15(the)m 16(resp)m 1(onse)m 16 r 118 c -2(ariable.)m 20(In)m 16(other)m 0 1616 p (cases,)s 15(ho)m 119 c -1(ev)m -1(er,)m 13(there)m 15(is)m 15(no)m 15(suc)m 104 c 14(distinction)m 14(among)m 15(the)m 15 r 118 c -2(ariables.)m 0 1693 p 87 c -3 r 101 c 14(sa)m 121 c 14(that)m 14(there)m 16(is)m 14(an)m cmbx10.329 @sf 15(explicit)m cmr10.329 @sf 14(relationship)m cmmi10.329 @sf 14 r 102 c cmr10.329 @sf 20 r 98 c 1(et)m 119 c (een)s 14(the)m 15 r 118 c -2(ariables)m 14 r 40 c cmmi10.329 @sf (x;)s 8 r 121 c cmr10.329 @sf 2 r 41 c 13(if)m cmmi10.329 @sf 738 1785 p 121 c cmsy10.329 @sf 14 r 25 c cmmi10.329 @sf 13 r 102 c cmr10.329 @sf 5 r 40 c cmmi10.329 @sf 120 c cmr10.329 @sf 59 c cmmi10.329 @sf 8 r 12 c cmr10.329 @sf 2 r 41 c cmmi10.329 @sf 14 r 59 c cmr10.329 @sf 645(\(1)m cmmi10.329 @sf 58 c cmr10.329 @sf (1\))s 0 1877 p (where)s cmmi10.329 @sf 19 r 121 c cmr10.329 @sf 21(denotes)m 19(the)m 20(resp)m 1(onse)m 19 r 118 c -2(ariable,)m cmmi10.329 @sf 18 r 120 c cmr10.329 @sf 19(denotes)m 19(the)m 19(explanatory)m 18 r 118 c -2(ariables,)m 18(and)m cmmi10.329 @sf 20 r 121 c cmr10.329 @sf 20(is)m 0 1934 p (assumed)s 16(to)m 15 r 98 c 1 r 101 c 17(only)m 16(appro)m (xima)s -1(tely)m 14(equal)m 15(to)m cmmi10.329 @sf 16 r 102 c cmr10.329 @sf 5 r 40 c cmmi10.329 @sf 120 c cmr10.329 @sf 59 c cmmi10.329 @sf 8 r 12 c cmr10.329 @sf 2 r 41 c 14 r 98 c 1(ecause)m 17(of)m 16(the)m 16(measuremen)m 116 c 15(errors)m 0 1990 p (in)s cmmi10.329 @sf 16 r 121 c cmr10.329 @sf 17(and)m 16 r 112 c 1(ossibly)m cmmi10.329 @sf 15 r 120 c cmr10.329 @sf 46 c 22(When)m 16 r 98 c 1(oth)m cmmi10.329 @sf 16 r 120 c cmr10.329 @sf 15(and)m cmmi10.329 @sf 16 r 121 c cmr10.329 @sf 18(are)m 15(observ)m (ed)s 15(with)m 15(error,)m 15(then)m 16(the)m 16(parameters)m cmmi10.329 @sf 0 2047 p 12 c cmr10.329 @sf 18(can)m 17 r 98 c 1 r 101 c 16(found)m 17 r 98 c 121 c cmti10.329 @sf 15(ortho)m -1(gonal)m 16(distanc)m -1 r 101 c 16 r 114 c -1 r 101 c -2(gr)m -2(es)m -1(sion)m cmr10.329 @sf 46 c 21(If)m 16(only)m cmmi10.329 @sf 16 r 121 c cmr10.329 @sf 18(is)m 16(sub)m 3(ject)m 16(to)m 15(measuremen)m 116 c 0 2103 p (error,)s 17(and)m cmmi10.329 @sf 17 r 120 c cmr10.329 @sf 17(is)m 17(observ)m (ed)s 17(without)m 16(error,)m 16(then)m 18(the)m 17(parameters)m 17(of)m 17(suc)m 104 c 16(an)m 18(explicit)m 16(mo)m 1(del)m 0 2160 p (can)s 15 r 98 c 1 r 101 c 16(obtained)m 15(using)m cmti10.329 @sf 15(or)m -1(dinary)m 16(le)m -1(ast)m 14(squar)m -1(es)m cmr10.329 @sf 14(pro)m 1(cedures.)m cmbx10.329 @sf 136 2226 p (Example:)s cmr10.329 @sf 19(The)m 16(mo)m 1(del)m 15(sho)m (wn)s 14(in)m cmsy10.329 @sf 15 r 120 c cmr10.329 @sf (2.C.i,)s cmmi10.329 @sf 528 2318 p 121 c cmmi8.300 @sf 550 2325 p 105 c cmsy10.329 @sf 606 2318 p 25 c cmmi10.329 @sf 42 r 102 c cmmi8.300 @sf 705 2325 p 105 c cmr10.329 @sf 719 2318 p 40 c cmmi10.329 @sf 120 c cmmi8.300 @sf 763 2325 p 105 c cmr10.329 @sf 777 2318 p 59 c cmmi10.329 @sf 8 r 12 c cmr10.329 @sf 2 r 41 c cmsy10.329 @sf 41 r 17 c cmmi10.329 @sf 42 r 12 c cmtt9.300 @sf 988 2325 p 49 c cmr10.329 @sf 1019 2318 p 43 c cmmi10.329 @sf 11 r 12 c cmtt9.300 @sf 1091 2325 p 50 c cmr10.329 @sf 1112 2318 p 91 c cmmi10.329 @sf 101 c cmmi8.300 @sf 1146 2303 p 12 c cmtt9.300 @sf 1166 2314 p 51 c cmmi8.300 @sf 1187 2303 p 120 c cmmi6.300 @sf 1207 2308 p 105 c cmsy10.329 @sf 1232 2318 p 0 c cmr10.329 @sf 11(1])m cmr8.300 @sf 1314 2303 p 50 c cmr10.329 @sf 136 2411 p (for)s cmmi10.329 @sf 20 r 105 c cmr10.329 @sf 20 r 61 c 22 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 7 r 58 c 5 r 59 c 8 r 110 c cmr10.329 @sf 44 c 21(whic)m 104 c 19(is)m 19(example)m 20(3.2.2)m 19(on)m 20(pages)m 20(230-238)m 18(of)m 20([F)m -3(uller,)m 19(1987],)m 19(is)m 136 2467 p (an)s 18(explicit)m 16(orthogonal)m 16(distance)m 17(regression)m 17(mo)m 1(del.)m 26(In)m 18(this)m 17(case,)m cmmi10.329 @sf 18 r 120 c cmr10.329 @sf 17(is)m 17(the)m 17 r 112 c 1(ercen)m 116 c @eop %%Page: 3 17 3 @bop0 1.000000 /lasy10.329 @newfont lasy10.329 @sf [ 32 25 -4 -3 33.964] 50 @dc cmmi10.329 @sf [<01F80003FC00078E000707000703000701800701800701C00700C00780C00380E003806003C060 E1C06061C07061E0F070E1F039E1F01FC1E00F80E0> 24 20 -1 0 22.032] 118 @dc [ 24 32 -2 0 26.188] 104 @dc cmr8.300 @sf [<7FF07FF0070007000700070007000700070007000700070007000700070007000700F700FF000F 000300> 16 21 -2 0 17.642] 49 @dc cmmi10.329 @sf [ 24 20 -2 0 21.138] 122 @dc 1.000000 /cmex10.300 @newfont cmex10.300 @sf [<000E001E001C0038007000E000E001C003800380070007000E000E000E001C001C001C00380038 0038003800700070007000700070007000E000E000E000E000E000E000E000E000E000E000E000 E000E000E000E000E000E000E00070007000700070007000700038003800380038001C001C001C 000E000E000E00070007000380038001C000E000E000700038001C001E000E> 16 74 -8 72 24.791] 16 @dc cmmi10.329 @sf [<7E007F80FBC079C071E000E000F000F0007000700078007800380038003C003C001C001C001E00 1E000E000E070F030F0307038701CF00FE007C> 16 29 1 9 17.455] 124 @dc [<0E01800F03C00703C007038003838003838003830001C30001C30000C30000E30000E300006300 E063806073807031803C31801FFFFF0FFFFF07FFFF> 24 20 0 0 25.910] 25 @dc 1.000000 /cmsy8.300 @newfont cmsy8.300 @sf [ 24 2 -3 -7 27.443] 0 @dc 1.000000 /cmr6.300 @newfont cmr6.300 @sf [<3F007FC0F1C0F0E0F0E060E000E001C00F800F8003C071C079C071C07F801F00> 16 16 -1 0 15.220] 51 @dc [<1FE01FE0030003000300FFE0FFE0E300630033003B001B001F000F0007000700> 16 16 -1 0 15.220] 52 @dc cmex10.300 @sf [ 16 74 -1 72 24.791] 17 @dc cmr6.300 @sf [<3F00FFC0E1C0E0E0E0E000E070E079E07FC06F80600060007C007F007F806180> 16 16 -1 0 15.220] 53 @dc 3 @bop1 cmr10.329 @sf 225 114 p (Getting)s 14(Started)m 1388 r 51 c 225 134 p 1725 2 ru 361 259 p (saturation)s 14(of)m 14(nitrogen)m 14(gas)m 15(in)m 14 r 97 c 15(brine)m 15(solution)m 14(forced)m 15(in)m (to)s 13(the)m 15 r 112 c 1(ores)m 15(of)m 14(sandstone,)m 361 315 p (and)s cmmi10.329 @sf 11 r 121 c cmr10.329 @sf 12(is)m 11(the)m 10(observ)m (ed)s 10(compressional)m 9 r 119 c 97 c -1 r 118 c -1 r 101 c 9 r 118 c (elo)s 1(cit)m -2 r 121 c 9(of)m 10(ultrasonic)m 9(signals)m 10(propagated)m 361 372 p (through)s 11(the)m 12(sandstone.)m 18(Here,)m 12(as)m 11(in)m 11(most)m 10(explicit)m 11(mo)m 1(dels,)m 11(the)m 11(explanatory)m 11 r 118 c -2(ariable)m cmmi10.329 @sf 361 428 p 120 c cmr10.329 @sf 15(is)m 15(used)m 16(primarily)m 13(to)m 15(predict)m 15(the)m 15 r 98 c 1(eha)m (vior)s 14(of)m 15(the)m 15(resp)m 1(onse)m 16 r 118 c -2(ariable)m cmmi10.329 @sf 14 r 121 c cmr10.329 @sf 2 r 46 c lasy10.329 @sf 170 r 50 c cmr10.329 @sf 225 504 p (If)s 15(the)m 16(relationship)m 14 r 98 c 1(et)m 119 c -1(een)m 14(the)m 15 r 118 c -2(ariables)m 14(is)m 15(expressed)m cmbx10.329 @sf 15(implicitly)m cmr10.329 @sf 44 c 13(then)m cmmi10.329 @sf 964 606 p 102 c cmr10.329 @sf 5 r 40 c cmmi10.329 @sf 120 c cmr10.329 @sf 59 c cmmi10.329 @sf 8 r 12 c cmr10.329 @sf 2 r 41 c cmsy10.329 @sf 11 r 25 c cmr10.329 @sf 13 r 48 c cmmi10.329 @sf 15 r 59 c cmr10.329 @sf 225 708 p (where)s 19(here)m 18 r 119 c 101 c 17(denote)m cmti10.329 @sf 19(al)m 2 r 108 c cmr10.329 @sf 18(of)m 18(the)m 18 r 118 c -2(ariables)m 17 r 98 c 121 c cmmi10.329 @sf 17 r 120 c cmr10.329 @sf 46 c 29(Although)m 18(one)m 19(of)m 17(these)m 19 r 118 c -2(ariables)m 17(ma)m 121 c 225 765 p (still)s 11 r 98 c 1 r 101 c 14(dep)m 1(enden)m 116 c 14(on)m 13(the)m 13(others,)m 12(when)m 14(the)m 13(mo)m 1(del)m 13(is)m 13(implicit)m 11 r 119 c 101 c 12(do)m 13(not)m 12(assume)m 13(that)m 13(suc)m 104 c 225 821 p 97 c 15(dep)m 1(enden)m 1 r 116 c 16 r 118 c -2(ariable)m 14(can)m 15 r 98 c 1 r 101 c 17(expressed)m 16(as)m 16(an)m 15(explicit)m 15(function)m 16(of)m 15(the)m 16(other)m 15(explanatory)m 225 878 p 118 c -2(ariables)m 16(as)m 18(in)m 18(\(1.1\).)m 27(Th)m (us,)s 17(in)m 18(the)m 18(implicit)m 17(case)m 18(the)m 18(distinction)m 17 r 98 c 1(et)m 119 c -1(een)m 17(resp)m 1(onse)m 19(and)m 225 934 p (regressor)s 9 r 118 c -2(ariables)m 9(is)m 9(unnecessary)m -3 r 46 c 18(When)m 11(the)m 10(relationship)m 9(is)m 10(implicit,)m 9(then)m 11(the)m 10(parameters)m cmmi10.329 @sf 225 990 p 12 c cmr10.329 @sf 15(cannot)m 13 r 98 c 1 r 101 c 14(estimated)m 13 r 98 c 121 c 12(most)m 13(ordinary)m 12(least)m 13(squares)m 13(pro)m 1(cedures,)m 14(but)m 13(can)m 14 r 98 c 1 r 101 c 14(estimated)m 225 1047 p 98 c 121 c 14(orthogonal)m 14(distance)m 15(regression)m 14(pro)m 1(cedures)m 16(suc)m 104 c 14(as)m 15(ODRP)m -3 r 65 c (CK.)s cmbx10.329 @sf 361 1113 p (Example:)s cmr10.329 @sf 24(One)m 18(of)m 17(the)m 17(simplist)m 16(examples)m 17(of)m 17(an)m 17(implicit)m 16(mo)m 1(del)m 17(is)m 17(that)m 17(of)m 17(\014tting)m 361 1170 p 97 c 16(circle)m 17(or)m 15(ellipse)m 16(in)m 17 r 97 c 16(plane,)m 16(as)m 16(is)m 16(done)m 17(in)m 16(example)m 16(3.2.4)m 15(on)m 16(page)m 17(244)m 15(of)m 16([F)m -3(uller,)m 361 1226 p (1987].)s 18(In)m 14(this)m 12(example,)m 13(sho)m (wn)s 12(in)m cmsy10.329 @sf 13 r 120 c cmr10.329 @sf (2.C.ii,)s 11(the)m 14(data)m 12(are)m 13(observ)m -2(ations)m 11(digitized)m 13(from)m 361 1283 p (the)s 12(x-ra)m 121 c 11(image)m 11(of)m 11 r 97 c 12(hip)m 12(prosthesis,)m 11(where)m 12(the)m 12 r 118 c -2(ariables)m cmmi10.329 @sf 10 r 120 c cmmi8.300 @sf 1471 1290 p 105 c cmr10.329 @sf 1498 1283 p 61 c 13 r 40 c cmmi10.329 @sf 118 c cmmi8.300 @sf 1586 1290 p 105 c cmmi10.329 @sf 1600 1283 p 59 c 8 r 104 c cmmi8.300 @sf 1647 1290 p 105 c cmr10.329 @sf 1660 1283 p 41 c cmmi10.329 @sf 59 c 19 r 105 c cmr10.329 @sf 12 r 61 c 13 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 8 r 58 c 5 r 59 c 8(n;)m cmr10.329 @sf 361 1339 p (are)s 19(the)m 19 r 118 c (ertical)s 16(and)m 19(horizon)m (ta)s -1 r 108 c 17(distances)m 18(from)m 18(the)m 19(origin,)m 18(resp)m 1(ectiv)m (ely)s -3 r 44 c 17(and)m 19(the)m 361 1395 p (implicit)s 14(mo)m 1(del)m 15(is)m 15(that)m 14(of)m 15(the)m 15(ellipse)m cmmi10.329 @sf 442 1498 p 102 c cmmi8.300 @sf 464 1505 p 105 c cmr10.329 @sf 478 1498 p 40 c cmmi10.329 @sf 120 c cmmi8.300 @sf 522 1505 p 105 c cmr10.329 @sf 536 1498 p 59 c cmmi10.329 @sf 8 r 12 c cmr10.329 @sf 2 r 41 c cmsy10.329 @sf 41 r 17 c cmmi10.329 @sf 41 r 12 c cmr8.300 @sf 746 1505 p 51 c cmr10.329 @sf 766 1498 p 40 c cmmi10.329 @sf 118 c cmmi8.300 @sf 806 1505 p 105 c cmsy10.329 @sf 830 1498 p 0 c cmmi10.329 @sf 10 r 12 c cmr8.300 @sf 901 1505 p 49 c cmr10.329 @sf 921 1498 p 41 c cmr8.300 @sf 939 1483 p 50 c cmr10.329 @sf 968 1498 p 43 c 11 r 50 c cmmi10.329 @sf 12 c cmr8.300 @sf 1063 1505 p 52 c cmr10.329 @sf 1082 1498 p 40 c cmmi10.329 @sf 118 c cmmi8.300 @sf 1122 1505 p 105 c cmsy10.329 @sf 1146 1498 p 0 c cmmi10.329 @sf 10 r 12 c cmr8.300 @sf 1217 1505 p 49 c cmr10.329 @sf 1237 1498 p (\)\()s cmmi10.329 @sf 104 c cmmi8.300 @sf 1299 1505 p 105 c cmsy10.329 @sf 1322 1498 p 0 c cmmi10.329 @sf 11 r 12 c cmr8.300 @sf 1394 1505 p 50 c cmr10.329 @sf 1413 1498 p 41 c 10 r 43 c cmmi10.329 @sf 10 r 12 c cmr8.300 @sf 1512 1505 p 53 c cmr10.329 @sf 1532 1498 p 40 c cmmi10.329 @sf 104 c cmmi8.300 @sf 1576 1505 p 105 c cmsy10.329 @sf 1600 1498 p 0 c cmmi10.329 @sf 10 r 12 c cmr8.300 @sf 1671 1505 p 50 c cmr10.329 @sf 1691 1498 p 41 c cmr8.300 @sf 1709 1483 p 50 c cmsy10.329 @sf 1770 1498 p 25 c cmr10.329 @sf 42 r 48 c 361 1600 p (for)s cmmi10.329 @sf 15 r 105 c cmr10.329 @sf 12 r 61 c 13 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 8 r 58 c 5 r 59 c 8 r 110 c cmr10.329 @sf 46 c lasy10.329 @sf 1244 r 50 c cmr10.329 @sf 225 1676 p (Finally)s -3 r 44 c 19(sometimes)m 20(the)m 20(observ)m -2(ations)m 19(are)m cmbx10.329 @sf 20 r 109 c (ultir)s -1(esp)m 1(onse)m cmr10.329 @sf 18(and)m 21(th)m (us)s 19 r 109 c (ust)s 19(satisfy)m 19(more)m 225 1732 p (than)s 13(one)m 13(relationship)m cmmi10.329 @sf 12 r 102 c cmr10.329 @sf 5 r 46 c 19(This)m 12(most)m 12(commonly)m 13(arises)m 12(when)m 13(the)m 13(observ)m -2(ations)m 11(are)m 13(complex)m 225 1789 p 118 c -2(ariables,)m 13(although)m 15(it)m 14(can)m 15 r 111 c 1(ccur)m 16(in)m 15(other)m 15(cases)m 15(as)m 15 r 119 c (ell.)s cmbx10.329 @sf 361 1855 p (Example:)s cmr10.329 @sf 24(The)m 17(problem)m 17(sho)m (wn)s 16(in)m cmsy10.329 @sf 17 r 120 c cmr10.329 @sf (2.C.iii)s 15(is)m 17(an)m 17(example)m 17(of)m 17 r 109 c (ultiresp)s 1(onse)m 16(data)m 361 1911 p (that)s 19(originates)m 18 r 98 c 1(ecause)m 21(the)m 20(underlying)m 19(data)m 19(are)m 20(complex.)m 33(The)m 20(problem)m 19(is)m 19(de-)m 361 1968 p (scrib)s 1(ed)m 16(in)m 16(Chapter)m 15(4,)m 15(and)m 16(on)m 15(pages)m 15(280-281,)m 14(of)m 15([Bates)m 15(and)m 16 r 87 c -3(atts,)m 13(1988].)m 19(In)m 16(this)m 361 2024 p (case,)s 17(the)m 17(resp)m 1(onse)m 17 r 118 c -2(ariable)m 15(is)m 16(the)m 17(pair)m 16(of)m 16 r 118 c -2(alues)m 16(represen)m (ting)s 15(the)m 17(real)m 16(and)m 17(imag-)m 361 2081 p (inary)s 19(parts)m 18(of)m 19(complex-v)m -2(alued)m 18(imp)m 1(edance)m 20(measuremen)m (ts,)s cmmi10.329 @sf 18 r 122 c cmmi8.300 @sf 1546 2088 p 105 c cmmi10.329 @sf 1561 2081 p 59 c 26 r 105 c cmr10.329 @sf 19 r 61 c 19 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 7 r 58 c 5 r 59 c 8(n;)m cmr10.329 @sf 19(of)m 18 r 97 c 361 2137 p 112 c 1(olymer,)m 16(and)m 16(the)m 16(explanatory)m 15 r 118 c -2(ariable,)m cmmi10.329 @sf 14 r 120 c cmmi8.300 @sf 1181 2144 p 105 c cmmi10.329 @sf 1195 2137 p 59 c 23 r 105 c cmr10.329 @sf 14 r 61 c 14 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 8 r 58 c 5 r 59 c 8 r 110 c cmr10.329 @sf 44 c 15(is)m 16(the)m 16(\(real-v)m -2(alued\))m 14(fre-)m 361 2194 p (quency)s -3 r 46 c 19(The)m 13(function)m 13(is)m 12(explicit,)m 12(represen)m (ting)s 12(the)m 12(dielectric)m 12(constan)m 116 c 11 r 98 c 121 c 12 r 97 c 12(general)m 361 2250 p (mo)s 1(del)m 15(prop)m 1(osed)m 16(in)m 15([Ha)m (vril)s -1(iak)m 13(and)m 15(Negami,)m 14(1967],)m cmmi10.329 @sf 834 2374 p 122 c cmmi8.300 @sf 855 2381 p 105 c cmsy10.329 @sf 882 2374 p 25 c cmmi10.329 @sf 13 r 12 c cmr8.300 @sf 956 2381 p 50 c cmr10.329 @sf 985 2374 p 43 c cmmi10.329 @sf 1181 2343 p 12 c cmr8.300 @sf 1207 2350 p 49 c cmsy10.329 @sf 1236 2343 p 0 c cmmi10.329 @sf 11 r 12 c cmr8.300 @sf 1308 2350 p 50 c 1036 2363 p 438 2 ru cmex10.300 @sf 1036 2380 p 16 c cmr10.329 @sf 1060 2427 p 49 c 10 r 43 c 11 r 40 c cmmi10.329 @sf -1 r 124 c cmr10.329 @sf 50 c cmmi10.329 @sf 25 c 2 r 120 c cmmi8.300 @sf 1250 2434 p 105 c cmmi10.329 @sf 1264 2427 p 101 c cmsy8.300 @sf 1285 2415 p 0 c cmmi8.300 @sf 12 c cmr6.300 @sf 1332 2420 p 51 c cmr10.329 @sf 1352 2427 p 41 c cmmi8.300 @sf 1369 2405 p 12 c cmr6.300 @sf 1389 2410 p 52 c cmex10.300 @sf 1409 2380 p 17 c cmmi8.300 @sf 1433 2391 p 12 c cmr6.300 @sf 1453 2396 p 53 c @eop %%Page: 4 18 4 @bop0 cmsy10.329 @sf [<0006000000000E000000000F000000001F000000001F800000003F800000003DC00000007CC000 00007CE00000007860000000F870000000F030000001F038000001E018000003E01C000003C00C 000007C00E00000780060000EF80070000FF000300007F000380001E000180000E0001C0000200 00C000000000E000000000600000000070000000003000000000380000000018000000001C0000 00000C000000000E000000000600000000070000000003000000000380000000018000000001C0 00000000C000000000E000000000600000000070000000003000000000380000000018> 40 46 -2 44 37.878] 112 @dc [<001FF000007EFC0000F83E0001F01F0003E00F800FC007803F800780FF000F80FC000F0000001F 0000003E0000007C00000078000000780003C078000FC078301E00787038007CF070003FE06000 0F80E0000000C0000000C0000000C0000FC0C0003FF0E000FC706001F0307003E0003807C0001E 1F80000FFE000003F80000> 32 32 -3 0 32.828] 61 @dc cmbx10.329 @sf [<7CFEFEFEFEFE7C> 8 7 -4 0 14.520] 46 @dc cmmi10.329 @sf [<0200001FC0003FE000787000703000F03800F01800F01C00F00C00F00C00F80C00780E00780600 7806003C06003C0E001E0E000F1E0007FE0003FC0000FC0001F80003E00003C000038000038000 03800003800003800001C0C000F1C0007F80003F00> 24 33 -2 1 20.202] 14 @dc cmsy8.300 @sf [<070007000700E738FFF87FF01FC01FC07FF0FFF8E738070007000700> 16 14 -2 -1 17.642] 3 @dc cmmi10.329 @sf [<07E01FF83E3C780078007000F000F000F000F8007FF87FF878007C003C001E000F0007C003FE00 FE> 16 20 -2 0 18.450] 15 @dc cmsy10.329 @sf [<018001C001800180C183E187F99F7DBE1FF807E007E01FF87DBEF99FE187C1830180018001C001 80> 16 20 -3 -1 22.727] 3 @dc cmmi8.300 @sf [ 8 10 -3 6 9.801] 59 @dc [<02001FC03FC070E07070E030F03070387018701838383C381F7807F803F007E007800700070007 00070003C601FE00FC> 16 24 0 1 15.613] 14 @dc [<1FC03FE07870F000E000E000E000FFC0FFC0F00078003C001FF007F0> 16 14 -1 0 14.263] 15 @dc [<3807C03C0FE03C0E701C0F701C07301E07001E07800E03800F0380CF8380EF83806FE3807FFF80 3E3F00> 24 14 0 0 21.409] 110 @dc cmex10.300 @sf [ 56 58 -2 58 59.959] 88 @dc cmr8.300 @sf [ 24 10 -2 -3 27.443] 61 @dc 4 @bop1 cmr10.329 @sf 0 114 p 52 c 1388(Getting)m 14(Started)m 0 134 p 1725 2 ru 136 259 p (for)s cmmi10.329 @sf 21 r 105 c cmr10.329 @sf 21 r 61 c 22 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 8 r 58 c 5 r 59 c 8 r 110 c cmr10.329 @sf 44 c 21(where)m cmmi10.329 @sf 21 r 124 c cmr10.329 @sf 22 r 61 c cmsy10.329 @sf 726 223 p 112 c 59 2 ru 764 259 p 0 c cmr10.329 @sf 49 c 46 c 36 r 70 c -3(or)m 19(ODRP)m -3 r 65 c (CK,)s 19(this)m 21 r 109 c (ust)s 19 r 98 c 1 r 101 c 21(enco)m 1(ded)m 22(as)m 136 315 p 97 c 18 r 116 c 119 c -1(o-t)m -1(erm)m 16 r 109 c (ultiresp)s 1(onse)m 16(problem)m 18(with)m cmmi10.329 @sf 17 r 121 c cmmi8.300 @sf 973 322 p 105 c cmsy10.329 @sf 1000 315 p 50 c 13 r 60 c cmr8.300 @sf 1076 300 p 50 c cmr10.329 @sf 1114 315 p (represen)s (ting)s 16(the)m 18(pair)m 17(of)m 18 r 118 c -2(alues)m 136 372 p 91 c cmsy10.329 @sf 60 c cmr10.329 @sf 40 c cmmi10.329 @sf 122 c cmmi8.300 @sf 221 379 p 105 c cmr10.329 @sf 235 372 p 41 c cmmi10.329 @sf 59 c cmsy10.329 @sf 8 r 61 c cmr10.329 @sf 40 c cmmi10.329 @sf 122 c cmmi8.300 @sf 346 379 p 105 c cmr10.329 @sf 358 372 p (\)])s cmmi10.329 @sf 59 c 22 r 105 c cmr10.329 @sf 12 r 61 c 13 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 8 r 58 c 5 r 59 c 8 r 110 c cmr10.329 @sf 46 c lasy10.329 @sf 1026 r 50 c cmr10.329 @sf 0 448 p (The)s 17(explicit,)m 17(implicit)m 16(and)m 17 r 109 c (ultiresp)s 1(onse)m 15(problem)m 17 r 116 c (yp)s 1(es)m 17(are)m 16(describ)m 1(ed)m 19(in)m 17(greater)m 16(detail)m 0 504 p (in)s 17(the)m 17(follo)m (wi)s -1(ng)m 15(sections.)m 26(They)m 17(are)m 17(eac)m 104 c 16(easily)m 17(solv)m (ed)s 15(using)m 17(ODRP)m -3 r 65 c (CK.)s 16(The)m 17(solution)m 0 560 p (pro)s 1(cedures)m 12(required)m 11(for)m 11(single)m 10(and)m 11 r 109 c (ultiresp)s 1(onse)m 10(data)m 10(are)m 11(essen)m (tially)s 9(the)m 11(same,)m 11(although,)m 0 617 p (as)s 15(noted)m 16 r 98 c 1(elo)m (w,)s 14(ODRP)m -3 r 65 c (CK)s 14(do)m 1(es)m 16(need)m 17(to)m 15(kno)m 119 c 14(that)m 15(the)m 15(data)m 15(are)m 16 r 109 c (ulti)s -1(resp)m 1(onse)m 14(rather)m 0 673 p (than)s 22(single)m 21(resp)m 1(onse)m 22(in)m 21(order)m 22(to)m 21(\014nd)m 22(the)m 22(correct)m 21(solution.)m 39(The)m 22(solution)m 20(pro)m 1(cedures)m 0 730 p (required)s 21(for)m 20(explicit)m 20(and)m 21(implicit)m 19(functions,)m 21(ho)m 119 c (ev)s -1(er,)m 19(are)m 21(di\013eren)m (t,)s 20(with)m 20(the)m 20(implicit)m 0 786 p (relationships)s 17(generally)m 18(costing)m 18(more)m 19(to)m 18(solv)m (e.)s 29(\(See)m cmsy10.329 @sf 19 r 120 c cmr10.329 @sf (1.B.\))s 30(Th)m (us,)s 19(it)m 18(is)m 18(imp)m 1(ortan)m 116 c 17(that)m 0 843 p (users)s 20 r 98 c 1 r 101 c 21 r 97 c 119 c -1(are)m 19(of)m 19(the)m 21(di\013erences)m 20 r 98 c 1(et)m 119 c (een)s 19(explicit)m 20(and)m 20(implicit)m 19(mo)m 1(dels,)m 21(and)m 21 r 98 c 1(et)m 119 c -1(een)m 0 899 p (single)s 12(and)m 13 r 109 c (ultir)s -1(esp)m 1(onse)m 12(data,)m 12(and)m 13(in)m 118 c -1(ok)m -1 r 101 c 10(ODRP)m -3 r 65 c (CK)s 12(appropriately)m 11(for)m 12(their)m 12(particular)m 0 956 p (mo)s 1(del)m 15(and)m 15(data)m 15 r 116 c (yp)s 1(e.)m cmbx10.329 @sf 0 1095 p (1.A.i.)s 15(Explicit)m 17(Orthogonal)m 18(Distance)m 17(Regression)m cmr10.329 @sf 0 1201 p 87 c -3 r 101 c 10(de\014ne)m 12(the)m 11(explicit)m 10(orthogonal)m 9(distance)m 10(regression)m 10(problem)m 11(as)m 10(follo)m -1(ws.)m 16(Let)m 11 r 40 c cmmi10.329 @sf 120 c cmmi8.300 @sf 1542 1208 p 105 c cmmi10.329 @sf 1556 1201 p 59 c 8 r 121 c cmmi8.300 @sf 1599 1208 p 105 c cmr10.329 @sf 1613 1201 p 41 c cmmi10.329 @sf 59 c 17 r 105 c cmr10.329 @sf 13 r 61 c 0 1257 p 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 7 r 58 c 6 r 59 c 8(n;)m cmr10.329 @sf 14 r 98 c 1 r 101 c 17(an)m 15(observ)m (ed)s 15(set)m 15(of)m 15(data,)m 15(where,)m 16(for)m 15(simplicit)m -1 r 121 c -4 r 44 c 13 r 119 c 101 c 15(assume)m 15(that)m cmmi10.329 @sf 15 r 120 c cmmi8.300 @sf 1514 1264 p 105 c cmsy10.329 @sf 1541 1257 p 50 c 13 r 60 c cmr8.300 @sf 1617 1242 p 49 c cmr10.329 @sf 1652 1257 p (and)s cmmi10.329 @sf 0 1314 p 121 c cmmi8.300 @sf 22 1321 p 105 c cmsy10.329 @sf 49 1314 p 50 c 13 r 60 c cmr8.300 @sf 125 1299 p 49 c cmr10.329 @sf 144 1314 p 46 c 39(\(F)m -3(or)m 20 r 97 c 21(discussion)m 21(of)m 22(the)m 21(orthogonal)m 20(distance)m 21(regression)m 21(problem)m 21(for)m 21(higher)m 0 1370 p (dimensional)s 16(data,)m 17(see)m cmsy10.329 @sf 17 r 120 c cmr10.329 @sf (1.A.iii.\))s 23(Supp)m 1(ose)m 18(that)m 16(the)m 17 r 118 c -2(alues)m 17(of)m cmmi10.329 @sf 16 r 121 c cmmi8.300 @sf 1215 1377 p 105 c cmr10.329 @sf 1247 1370 p (are)s 16 r 97 c 17 r 112 c 1(ossibly)m 16(nonlinear)m 0 1426 p (function)s 13(of)m cmmi10.329 @sf 13 r 120 c cmmi8.300 @sf 252 1433 p 105 c cmr10.329 @sf 280 1426 p (and)s 14 r 97 c 13(set)m 13(of)m 13(unkno)m (wn)s 13(parameters)m cmmi10.329 @sf 12 r 12 c cmsy10.329 @sf 15 r 50 c 13 r 60 c cmmi8.300 @sf 1065 1411 p 112 c cmr10.329 @sf 1085 1426 p 44 c 13(but)m 14(that)m 13 r 98 c 1(oth)m 13(the)m cmmi10.329 @sf 14 r 120 c cmmi8.300 @sf 1498 1433 p 105 c cmr10.329 @sf 1525 1426 p (and)s 14(the)m cmmi10.329 @sf 14 r 121 c cmmi8.300 @sf 1711 1433 p 105 c cmr10.329 @sf 0 1483 p (con)s (tain)s 15(actual)m 16(but)m 18(unkno)m (wn)s 16(errors)m cmmi10.329 @sf 16 r 14 c cmsy8.300 @sf 735 1468 p 3 c cmmi8.300 @sf 733 1495 p 105 c cmsy10.329 @sf 767 1483 p 50 c 13 r 60 c cmr8.300 @sf 843 1468 p 49 c cmr10.329 @sf 880 1483 p (and)s cmmi10.329 @sf 17 r 15 c cmsy8.300 @sf 988 1468 p 3 c cmmi8.300 @sf 988 1495 p 105 c cmsy10.329 @sf 1021 1483 p 50 c 13 r 60 c cmr8.300 @sf 1097 1468 p 49 c cmmi10.329 @sf 1116 1483 p 59 c cmr10.329 @sf 17(resp)m 1(ectiv)m (ely)s -3 r 44 c 15(where)m 17(here,)m 18(and)m 0 1539 p (in)s 15(the)m 16(remainder)m 15(of)m 16(this)m 15(do)m 1(cumen)m (t,)s 14 r 119 c 101 c 15(use)m 16 r 97 c 15(sup)m 1(erscript)m 16 r 92 c cmsy10.329 @sf 3 c cmr10.329 @sf 34 c 14(to)m 15(denote)m 16(suc)m 104 c 15(actual)m 15(but)m 0 1596 p (unkno)s (wn)s 14(quan)m (tities.)s 18(Then)m 16(the)m 15(observ)m (ed)s 14 r 118 c -2(alue)m 15(of)m cmmi10.329 @sf 14 r 121 c cmmi8.300 @sf 997 1603 p 105 c cmr10.329 @sf 1027 1596 p (satis\014es)s cmmi10.329 @sf 463 1698 p 121 c cmmi8.300 @sf 485 1705 p 105 c cmr10.329 @sf 512 1698 p 61 c cmmi10.329 @sf 13 r 102 c cmmi8.300 @sf 582 1705 p 105 c cmr10.329 @sf 597 1698 p 40 c cmmi10.329 @sf 120 c cmmi8.300 @sf 641 1705 p 105 c cmr10.329 @sf 664 1698 p 43 c cmmi10.329 @sf 11 r 14 c cmsy8.300 @sf 732 1680 p 3 c cmmi8.300 @sf 730 1709 p 105 c cmr10.329 @sf 751 1698 p 59 c cmmi10.329 @sf 8 r 12 c cmsy8.300 @sf 800 1680 p 3 c cmr10.329 @sf 820 1698 p 41 c cmsy10.329 @sf 9 r 0 c cmmi10.329 @sf 11 r 15 c cmsy8.300 @sf 911 1680 p 3 c cmmi8.300 @sf 911 1709 p 105 c cmmi10.329 @sf 1022 1698 p 105 c cmr10.329 @sf 12 r 61 c 13 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 7 r 58 c 6 r 59 c 8(n;)m cmr10.329 @sf 0 1800 p (for)s 15(some)m 14(actual)m 15(but)m 15(again)m 14(unkno)m (wn)s 15 r 118 c -2(alue)m cmmi10.329 @sf 14 r 12 c cmsy8.300 @sf 864 1785 p 3 c cmmi10.329 @sf 884 1800 p 58 c cmr10.329 @sf 0 1876 p (The)s 13(explicit)m 13(orthogonal)m 11(distance)m 13(regression)m 12(problem)m 13(is)m 12(to)m 13(appro)m (ximat)s -1 r 101 c cmmi10.329 @sf 12 r 12 c cmsy8.300 @sf 1419 1861 p 3 c cmr10.329 @sf 1451 1876 p 98 c 121 c 12(\014nding)m 14(the)m cmmi10.329 @sf 0 1933 p 12 c cmr10.329 @sf 16(for)m 13(whic)m 104 c 13(the)m 14(sum)m 13(of)m 14(the)m 14(squares)m 13(of)m 14(the)m cmmi10.329 @sf 14 r 110 c cmr10.329 @sf 14(orthogonal)m 12(distances)m 13(from)m 13(the)m 14(curv)m 101 c cmmi10.329 @sf 13 r 102 c cmr10.329 @sf 5 r 40 c cmmi10.329 @sf 120 c cmr10.329 @sf 59 c cmmi10.329 @sf 8 r 12 c cmr10.329 @sf 2 r 41 c 0 1989 p (to)s 15(the)m cmmi10.329 @sf 15 r 110 c cmr10.329 @sf 15(data)m 15 r 112 c 1(oin)m (ts)s 13(is)m 15(minimized.)m 19(This)m 15(is)m 15(accomplished)m 15 r 98 c 121 c 14(the)m 15(minimization)m 14(problem)m 709 2119 p (min)s cmmi8.300 @sf 712 2149 p 12 c 2(;\016)m (;\017)s 812 2066 p 110 c cmex10.300 @sf 793 2079 p 88 c cmmi8.300 @sf 794 2170 p 105 c cmr8.300 @sf (=1)s cmr10.329 @sf 853 2119 p 40 c cmmi10.329 @sf 15 c cmr8.300 @sf 889 2101 p 50 c cmmi8.300 @sf 889 2130 p 105 c cmr10.329 @sf 918 2119 p 43 c cmmi10.329 @sf 11 r 14 c cmr8.300 @sf 986 2101 p 50 c cmmi8.300 @sf 984 2130 p 105 c cmr10.329 @sf 1006 2119 p 41 c 608(\(1)m cmmi10.329 @sf 58 c cmr10.329 @sf (2\))s 0 2255 p (sub)s 3(ject)m 15(to)m 15(the)m 15(constrain)m (ts)s cmmi10.329 @sf 480 2357 p 121 c cmmi8.300 @sf 502 2364 p 105 c cmr10.329 @sf 529 2357 p 61 c cmmi10.329 @sf 13 r 102 c cmmi8.300 @sf 599 2364 p 105 c cmr10.329 @sf 613 2357 p 40 c cmmi10.329 @sf 120 c cmmi8.300 @sf 657 2364 p 105 c cmr10.329 @sf 681 2357 p 43 c cmmi10.329 @sf 10 r 14 c cmmi8.300 @sf 746 2364 p 105 c cmr10.329 @sf 760 2357 p 59 c cmmi10.329 @sf 8 r 12 c cmr10.329 @sf 2 r 41 c cmsy10.329 @sf 10 r 0 c cmmi10.329 @sf 10 r 15 c cmmi8.300 @sf 900 2364 p 105 c cmmi10.329 @sf 1005 2357 p 105 c cmr10.329 @sf 13 r 61 c 13 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 7 r 58 c 5 r 59 c 8(n:)m cmr10.329 @sf 386(\(1)m cmmi10.329 @sf 58 c cmr10.329 @sf (3\))s 0 2459 p (Since)s 16(the)m 15(constrain)m (ts)s 13(\(1.3\))m 14(are)m 15(linear)m 14(in)m cmmi10.329 @sf 15 r 15 c cmmi8.300 @sf 811 2466 p 105 c cmmi10.329 @sf 826 2459 p 59 c cmr10.329 @sf 15 r 119 c 101 c 14(can)m 15(eliminate)m 15(them)m 15(and)m 15(th)m (us)s 14(the)m cmmi10.329 @sf 16 r 15 c cmmi8.300 @sf 1603 2466 p 105 c cmr10.329 @sf 1633 2459 p (from)s @eop %%Page: 5 19 5 @bop0 cmmi10.329 @sf [<00F87E0003FEFF00078FE3800707C1C00703C0E00703C0600701C0600701C0300701C0300781E0 300381E0380380E01803C0E018E1C0E01861C0F01C61E0703C70E0707C39E0707C1FC078780F80 3838> 32 20 -1 0 32.541] 119 @dc 5 @bop1 cmr10.329 @sf 225 114 p (Getting)s 14(Started)m 1388 r 53 c 225 134 p 1725 2 ru 225 259 p (\(1.2\),)s 13(thereb)m 121 c 14(obtaining)m 731 391 p (min)s cmmi8.300 @sf 745 421 p 12 c 2(;\016)m 834 338 p 110 c cmex10.300 @sf 815 350 p 88 c cmmi8.300 @sf 816 442 p 105 c cmr8.300 @sf (=1)s cmex10.300 @sf 882 344 p 16 c cmr10.329 @sf 907 391 p 91 c cmmi10.329 @sf 102 c cmmi8.300 @sf 942 398 p 105 c cmr10.329 @sf 956 391 p 40 c cmmi10.329 @sf 120 c cmmi8.300 @sf 1000 398 p 105 c cmr10.329 @sf 1024 391 p 43 c cmmi10.329 @sf 10 r 14 c cmmi8.300 @sf 1089 398 p 105 c cmr10.329 @sf 1104 391 p 59 c cmmi10.329 @sf 8 r 12 c cmr10.329 @sf 2 r 41 c cmsy10.329 @sf 9 r 0 c cmmi10.329 @sf 10 r 121 c cmmi8.300 @sf 1247 398 p 105 c cmr10.329 @sf 1261 391 p 93 c cmr8.300 @sf 1274 373 p 50 c cmr10.329 @sf 1304 391 p 43 c cmmi10.329 @sf 10 r 14 c cmr8.300 @sf 1371 373 p 50 c cmmi8.300 @sf 1369 402 p 105 c cmex10.300 @sf 1391 344 p 17 c cmmi10.329 @sf 1439 391 p 58 c cmr10.329 @sf 405(\(1)m cmmi10.329 @sf 58 c cmr10.329 @sf (4\))s 225 549 p 87 c -3 r 101 c 12(then)m 13(generalize)m 12(\(1.4\))m 11(to)m 12(the)m 12 r 119 c (eigh)s -1(ted)m 11(orthogonal)m 11(distance)m 12(regression)m 12(\(ODR\))m 12(problem)m 688 681 p (min)s cmmi8.300 @sf 702 711 p 12 c 2(;\016)m 791 628 p 110 c cmex10.300 @sf 772 641 p 88 c cmmi8.300 @sf 773 732 p 105 c cmr8.300 @sf (=1)s cmex10.300 @sf 839 634 p 16 c cmmi10.329 @sf 864 681 p 119 c cmmi8.300 @sf 892 688 p 15 c cmmi6.300 @sf 906 693 p 105 c cmr10.329 @sf 928 681 p 91 c cmmi10.329 @sf -1 r 102 c cmmi8.300 @sf 962 688 p 105 c cmr10.329 @sf 977 681 p 40 c cmmi10.329 @sf 120 c cmmi8.300 @sf 1021 688 p 105 c cmr10.329 @sf 1045 681 p 43 c cmmi10.329 @sf 10 r 14 c cmmi8.300 @sf 1110 688 p 105 c cmr10.329 @sf 1124 681 p 59 c cmmi10.329 @sf 8 r 12 c cmr10.329 @sf 2 r 41 c cmsy10.329 @sf 9 r 0 c cmmi10.329 @sf 11 r 121 c cmmi8.300 @sf 1268 688 p 105 c cmr10.329 @sf 1282 681 p 93 c cmr8.300 @sf 1295 661 p 50 c cmr10.329 @sf 1325 681 p 43 c cmmi10.329 @sf 10 r 119 c cmmi8.300 @sf 1398 688 p 14 c cmmi6.300 @sf 1414 693 p 105 c cmmi10.329 @sf 1428 681 p 14 c cmr8.300 @sf 1450 663 p 50 c cmmi8.300 @sf 1448 693 p 105 c cmex10.300 @sf 1469 634 p 17 c cmr10.329 @sf 1857 681 p (\(1)s cmmi10.329 @sf 58 c cmr10.329 @sf (5\))s 225 824 p 98 c 121 c 16(in)m (tro)s 1(ducing)m 15(the)m 17 r 119 c (eigh)s -1(ts)m cmmi10.329 @sf 15 r 119 c cmmi8.300 @sf 806 831 p 15 c cmmi6.300 @sf 820 836 p 105 c cmsy10.329 @sf 847 824 p 50 c 13 r 60 c cmr8.300 @sf 923 809 p 49 c cmr10.329 @sf 959 824 p (and)s cmmi10.329 @sf 17 r 119 c cmmi8.300 @sf 1077 831 p 14 c cmmi6.300 @sf 1093 836 p 105 c cmsy10.329 @sf 1120 824 p 50 c 12 r 60 c cmr8.300 @sf 1195 809 p 49 c cmr10.329 @sf 1215 824 p 44 c cmmi10.329 @sf 17 r 105 c cmr10.329 @sf 15 r 61 c 16 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 8 r 58 c 5 r 59 c 8(n;)m cmr10.329 @sf 16(whic)m 104 c 16(are)m 16(sets)m 17(of)m 17(non-)m 225 880 p (negativ)s 101 c 10 r 110 c (um)s 98 c 1(ers.)m 17(The)m 12 r 119 c (eigh)s -1(ts)m cmmi10.329 @sf 10 r 119 c cmmi8.300 @sf 878 887 p 15 c cmmi6.300 @sf 892 892 p 105 c cmr10.329 @sf 918 880 p (and)s cmmi10.329 @sf 12 r 119 c cmmi8.300 @sf 1031 887 p 14 c cmmi6.300 @sf 1047 892 p 105 c cmr10.329 @sf 1072 880 p (can)s 13(th)m (us)s 10 r 98 c 1 r 101 c 13(used)m 12(to)m 12(comp)m 1(ensate)m 12(for)m 11(instances)m 225 937 p (when)s 16(the)m cmmi10.329 @sf 15 r 121 c cmmi8.300 @sf 444 944 p 105 c cmr10.329 @sf 474 937 p (and)s cmmi10.329 @sf 15 r 120 c cmmi8.300 @sf 588 944 p 105 c cmr10.329 @sf 618 937 p (ha)s 118 c -1 r 101 c 14(unequal)m 15(precision,)m 15(or)m 15(when)m 15(there)m 16(are)m 15(observ)m -2(ations)m 13(that)m 15(should)m 225 993 p 98 c 1 r 101 c 16(eliminated)m 14(from)m 15(the)m 15(analysis.)m 18(\(See)m cmsy10.329 @sf 16 r 120 c cmr10.329 @sf (1.F.\))s cmbx10.329 @sf 225 1133 p (1.A.ii.)s 15(Implicit)m 16(Orthogonal)m 18(Distance)m 17(Regression)m cmr10.329 @sf 225 1238 p (The)s 14(univ)m -2(ariate)m 12(implicit)m 13(orthogonal)m 12(distance)m 14(regression)m 13(problem)m 13(arises)m 14(from)m 13(the)m 14(assump-)m 225 1294 p (tion)s 14(that)m 15(there)m 15(is)m 15(no)m 15(distinguished)m 15 r 118 c -2(ariable)m cmmi10.329 @sf 13 r 121 c cmr10.329 @sf 17(and)m 16(th)m (us)s 14(that)m 14(the)m 16(data)m 14 r 109 c (ust)s 14(satisfy)m cmmi10.329 @sf 742 1396 p 102 c cmmi8.300 @sf 764 1403 p 105 c cmr10.329 @sf 778 1396 p 40 c cmmi10.329 @sf 120 c cmmi8.300 @sf 822 1403 p 105 c cmr10.329 @sf 846 1396 p 43 c cmmi10.329 @sf 11 r 14 c cmsy8.300 @sf 914 1378 p 3 c cmmi8.300 @sf 912 1408 p 105 c cmr10.329 @sf 933 1396 p 59 c cmmi10.329 @sf 8 r 12 c cmsy8.300 @sf 982 1378 p 3 c cmr10.329 @sf 1001 1396 p 41 c 13 r 61 c 12 r 48 c cmmi10.329 @sf 91 r 105 c cmr10.329 @sf 12 r 61 c 13 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 8 r 58 c 5 r 59 c 8(n:)m cmr10.329 @sf 225 1498 p 70 c -3(or)m cmmi10.329 @sf 14 r 120 c cmmi8.300 @sf 333 1505 p 105 c cmsy10.329 @sf 359 1498 p 50 c 13 r 60 c cmr8.300 @sf 435 1483 p 49 c cmr10.329 @sf 455 1498 p 44 c 15(this)m 14(yields)m 15(the)m 15(minimization)m 13(problem)m 942 1628 p (min)s cmmi8.300 @sf 956 1658 p 12 c 2(;\016)m 1044 1575 p 110 c cmex10.300 @sf 1025 1588 p 88 c cmmi8.300 @sf 1027 1679 p 105 c cmr8.300 @sf (=1)s cmmi10.329 @sf 1093 1628 p 119 c cmmi8.300 @sf 1121 1635 p 14 c cmmi6.300 @sf 1137 1640 p 105 c cmmi10.329 @sf 1150 1628 p 14 c cmr8.300 @sf 1172 1610 p 50 c cmmi8.300 @sf 1170 1639 p 105 c cmr10.329 @sf 660 1835 p (sub)s 3(ject)m 15(to)m cmmi10.329 @sf 41 r 102 c cmmi8.300 @sf 922 1842 p 105 c cmr10.329 @sf 936 1835 p 40 c cmmi10.329 @sf 120 c cmmi8.300 @sf 980 1842 p 105 c cmr10.329 @sf 1004 1835 p 43 c cmmi10.329 @sf 11 r 14 c cmmi8.300 @sf 1070 1842 p 105 c cmr10.329 @sf 1084 1835 p 59 c cmmi10.329 @sf 8 r 12 c cmr10.329 @sf 2 r 41 c 12 r 61 c 13 r 48 c cmmi10.329 @sf 41 r 105 c cmr10.329 @sf 12 r 61 c 13 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 7 r 58 c 6 r 59 c 8(n;)m cmr10.329 @sf 1857 1716 p (\(1)s cmmi10.329 @sf 58 c cmr10.329 @sf (6\))s 225 1940 p (where)s cmmi10.329 @sf 13 r 119 c cmmi8.300 @sf 382 1947 p 14 c cmmi6.300 @sf 398 1952 p 105 c cmsy10.329 @sf 424 1940 p 50 c 13 r 60 c cmr8.300 @sf 500 1925 p 49 c cmr10.329 @sf 520 1940 p 44 c cmmi10.329 @sf 13 r 105 c cmr10.329 @sf 12 r 61 c 13 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 7 r 58 c 5 r 59 c 8(n;)m cmr10.329 @sf 12(again)m 12(denotes)m 13 r 97 c 13(set)m 12(of)m 12 r 112 c 1(ositiv)m 101 c 11 r 110 c (um)s 98 c 1(ers)m 11(used)m 14(for)m 12 r 119 c (eigh)s -1(ti)m -1(ng.)m 225 1996 p (\(See)s cmsy10.329 @sf 18 r 120 c cmr10.329 @sf (1.F.\))s 26(The)m 18(constrain)m (t)s -1 r 115 c 16(in)m 17(\(1.6\))m 16(are)m 18(not)m 17(assumed)m 18(to)m 17 r 98 c 1 r 101 c 18(linear)m 17(in)m cmmi10.329 @sf 17 r 14 c cmmi8.300 @sf 1638 2003 p 105 c cmr10.329 @sf 1653 1996 p 44 c 17(and)m 18(therefore)m 225 2053 p (cannot)s 15 r 98 c 1 r 101 c 15(eliminated)m 15(to)m 14(create)m 15(an)m 15(unconstrained)m 15(problem)m 14(as)m 15 r 119 c (as)s 13(done)m 16(ab)m 1 r 111 c 118 c -1 r 101 c 13(to)m 15(sp)m 1(ecify)m 225 2109 p (the)s 18(explicit)m 17(problem)m 18(\(1.4\).)m 27(The)m 18(implicit)m 17(orthogonal)m 16(distance)m 18(regression)m 17(problem)m 17 r 109 c (ust)s 225 2166 p (therefore)s 15 r 98 c 1 r 101 c 16(solv)m (ed)s 13(di\013eren)m (tly)s 13(than)m 15(the)m 16(explicit)m 14(problem.)m 20(\(See)m cmsy10.329 @sf 15 r 120 c cmr10.329 @sf (1.B.\))s cmbx10.329 @sf 225 2305 p (1.A.iii)s -1 r 46 c 15(Orthogonal)m 18(Distance)m 18(Regression)m 16(for)m 17(Multidimensi)m -1(onal)m 16(Data)m cmr10.329 @sf 225 2411 p 70 c -3(or)m 15(simplicit)m -1 r 121 c -4 r 44 c 15(the)m 17(preceding)m 17 r 116 c 119 c -1 r 111 c 15(sections)m 16(dev)m (elop)s 1(ed)m 16(the)m 17(explicit)m 16(and)m 17(implicit)m 15(orthogo-)m 225 2467 p (nal)s 17(distance)m 18(regression)m 16(problem)m 18(for)m 17(univ)m -2(ariate)m 16(data,)m 17(i.e.,)m 17(for)m cmmi10.329 @sf 17 r 120 c cmmi8.300 @sf 1469 2474 p 105 c cmsy10.329 @sf 1496 2467 p 50 c 13 r 60 c cmr8.300 @sf 1572 2452 p 49 c cmr10.329 @sf 1609 2467 p (and)s cmmi10.329 @sf 18 r 121 c cmmi8.300 @sf 1722 2474 p 105 c cmsy10.329 @sf 1749 2467 p 50 c 12 r 60 c cmr8.300 @sf 1824 2452 p 49 c cmr10.329 @sf 1862 2467 p (with)s @eop %%Page: 6 20 6 @bop0 cmr10.329 @sf [<70F8F8F8700000000000000000000070F8F8F870> 8 20 -4 0 12.626] 58 @dc cmr8.300 @sf [<003000003000003000003000003000003000003000003000003000003000003000FFFFFCFFFFFC 003000003000003000003000003000003000003000003000003000003000003000> 24 24 -2 4 27.443] 43 @dc cmsy10.329 @sf [<000000060000000007000000000300000000038000000001C000000000E00000000070FFFFFFFF FCFFFFFFFFFC000000007000000000E000000001C0000000038000000003000000000700000000 0600> 40 16 -3 -3 45.454] 33 @dc cmmi8.300 @sf [<380E03E03C0F07F03C0F07381C0707B81C0703981E0783801E0783C00E0381C00F03C1C0CF83C1 C0EF83E1C06FE3F1C07FFFBFC03E3F1F80> 32 14 0 0 31.210] 109 @dc [<0FF80FF801C001E000E000E03EE07FF0F3F0E0F0C070E078E038E038E038703C783C3C7C1FFC07 CC> 16 20 -1 6 15.753] 113 @dc cmsy8.300 @sf [ 16 18 -5 1 27.443] 2 @dc cmmi10.329 @sf [ 40 31 -1 0 37.657] 88 @dc [<3FFF00001FFF000001F0000000F0000000F0000000F00000007000000078000000780000007800 0000380000003C0000003C0000003E0000007F0000007F00000079800000F8C00000F0600000F0 700001F0380001E0180003E00C0003E0060003C0070007C0038007C001C0078000E00F8001F8FF F803FFFFF803FF> 32 31 -1 0 26.388] 89 @dc [ 32 31 -2 0 33.554] 69 @dc cmr10.329 @sf [ 16 6 -6 -25 22.727] 94 @dc cmti10.329 @sf [ 16 3 -3 -8 16.262] 45 @dc cmr6.300 @sf [<0FFE000FFE0000E00000E00000E00000E00000E00000E00000E00000E000C0E0C0C0E0C0C0E0C0 60E18070E3807FFF807FFF80> 24 17 -1 0 21.677] 84 @dc cmex10.300 @sf [<007C007C007C007C007C007C007C007C007C007C007C007C007C007C007C007C007C007C007C00 7C007C007C007C00F800F800F801F001F003E003E007C00F801F003E007C00F800E000> 16 37 -7 38 36.898] 57 @dc [ 8 14 -16 13 36.898] 62 @dc [ 16 77 -16 76 36.898] 61 @dc [ 16 37 -7 36 36.898] 59 @dc cmmi10.329 @sf [<3C007E00F700E300E300F380F1807000700078007800380038003C003C001C001C001E001E000E 000E000F000F000700070007800780038003801FC01FC003C0> 16 32 -2 0 13.562] 108 @dc cmmi8.300 @sf [<78FCEEE6E6F0F07070787838383C3C1C1C1E1E0E0E3F3F> 8 23 -1 0 10.531] 108 @dc cmr6.300 @sf [ 16 16 -2 0 15.220] 49 @dc 1.000000 /cmr9.300 @newfont cmr9.300 @sf [<03FFF00003FFF000001E0000001E0000001E0000001E0000001E0000001E0000001E0000001E00 00001E0000001E0000001E0000001E0000001E0000001E0000001E0000C01E0180C01E0180C01E 0180E01E0380601E0300601E0300781E0F007FFFFF007FFFFF00> 32 26 -1 0 27.731] 84 @dc [ 24 26 -1 0 21.331] 104 @dc [<07E01FF83E1C780C7000F000E000E000E000FFFCFFFC701C701C3C781FF007E0> 16 16 -1 0 17.080] 101 @dc [ 32 16 -1 0 31.997] 109 @dc [<3F3C7FFEF1F3E0F3E073E070F07078703FF01FF000F06070F0F0F1F0FFE07F80> 16 16 -2 0 19.198] 97 @dc [<07800FC01EE01C601C601C601C601C001C001C001C001C001C001C00FFC0FFC03C001C001C000C 000C000C000C00> 16 23 -1 0 14.932] 116 @dc [ 16 16 -1 0 15.018] 114 @dc [ 16 26 0 0 10.666] 105 @dc [ 24 16 0 0 20.265] 120 @dc 1.000000 /cmmi9.300 @newfont cmmi9.300 @sf [ 32 26 -1 0 28.792] 65 @dc cmr9.300 @sf [ 16 16 -1 0 15.145] 115 @dc 1.000000 /cmti9.300 @newfont cmti9.300 @sf [ 24 23 0 7 19.602] 112 @dc [<1F807FE070F0E078E03CE01CE01EE00EE00EF00E700E780E3C0E1E1C0FFC03F0> 16 16 -4 0 19.602] 111 @dc [<3F00FF80E3C0E1E0E0E040E001E00FE01FE01FC01E001C701C701E700FF003E0> 16 16 -3 0 15.682] 115 @dc [<3E003F0073007B80398039803C001C001C001E00CE00CE00EF0067007E003E0000000000000000 0000000000038003800380> 16 25 -3 0 11.761] 105 @dc [<7C00FE00E700E380E180F18070007000700078003800380038003C00FFC0FFC01C001E000E000E 000E000E000600> 16 23 -4 0 12.741] 116 @dc [<0FC01FE01E703C3038183C181C1C1C0C1C0C1E0CCE0ECE06EF0E670E7E0E3E0E> 16 16 -3 0 17.642] 118 @dc [<1F803FE070F0E038E018E000E000E000FFC0FFF07078783838181E380FF803F0> 16 16 -4 0 17.642] 101 @dc [<3E3C007FFE00F3F700E0F300E07300E07B00E07800E03800E03800F03C00703C00781C00383C00 1E7E000FFE0003EE00000E00000F00000F00000700000700000780000780000380001F80001F80> 24 26 -4 0 19.602] 100 @dc [ 24 33 1 7 21.562] 12 @dc [<700F80780FC0781CC0381EE0380E603C0E603C0F001C07001C07001E0700DE0780CF0380CF8380 EFC7807EFF003C7E00> 24 16 -3 0 21.562] 110 @dc cmr9.300 @sf [<7FE07FE00E000E000E000E000E000E000E000E000E000E000E000E00FFC0FFC00E000E000E000E 000E000E3C0F3C07BC03FC00F8> 16 26 0 0 11.732] 102 @dc [ 24 16 -1 0 21.331] 110 @dc [<0FCFC01FFFC03C3E00781E00700E00E00E00E00E00E00E00E00E00E00E00E00E00700E00781E00 3C3E001FFE000FEE00000E00000E00000E00000E00000E00000E00000E00000E00007E00007E00> 24 26 -1 0 21.331] 100 @dc [<07E01FF83C3C700E700EE007E007E007E007E007E0076006700E381C1FF807E0> 16 16 -1 0 19.198] 111 @dc [ 16 26 0 0 10.666] 108 @dc [<780000FE0000C70000F3000061800001800001800001C00001C00001C00003E00003E00007F000 0730000730000E38000E18000E18001C0C001C0C003C0E00FF3F80FF3F80> 24 23 -1 7 20.265] 121 @dc [ 32 10 -2 -4 29.864] 61 @dc [ 8 11 -3 7 10.666] 44 @dc cmmi9.300 @sf [<3E7C7FFEE3E6E1E3C0E3E0F3E0F0E070E070F0787078703838781C7C0FFC07DC> 16 16 -2 0 20.341] 97 @dc [ 24 24 -3 3 29.864] 62 @dc cmr9.300 @sf [<07801FE03870703870386018E01CE01CE01CE01CE01CE01CE01CE01CE01CE01CE01CE01C601870 38303038701FE00780> 16 24 -2 0 19.198] 48 @dc [ 16 16 -1 0 17.065] 122 @dc [<01C00001C00001C00003E00003E00007F0000730000730000E38000E18000E18001C0C001C0C00 3C0E00FF3F80FF3F80> 24 16 -1 0 20.265] 118 @dc [<07E01FF83E1C780C7000F000E000E000E000E000E0007018783C3C3C1FFC07F8> 16 16 -1 0 17.065] 99 @dc [ 8 4 -3 0 10.666] 46 @dc [ 16 26 -1 0 13.860] 73 @dc cmti9.300 @sf [<701C07C0781E07E0781E0E60380E0F70380E07303C0F07303C0F07801C0703801C0703801E0783 80DE0783C0CF03C1C0CF83E1C0EFC7F3C07EFF7F803C7E1F00> 32 16 -3 0 31.364] 109 @dc 1.000000 /cmsy9.300 @newfont cmsy9.300 @sf [ 24 31 -3 7 29.864] 21 @dc cmr9.300 @sf [<003000C000003801C000007801E000007801E000007C03E000007C03E00000FC03F00000F607B0 0000F607B00001E607980001E70F980001E30F180003C30F0C0003C30F0C0003C19E0C0007819E 0E0007819E06000780FC06000780FC06000F00FC03000F007803000F007803001E007803801E00 F803C0FFC7FF1FF0FFC7FF1FF0> 40 26 -1 0 39.457] 87 @dc [ 24 23 -1 7 21.331] 112 @dc [<7F0FE07F0FE00E07000E07000E07000E07000E07000E07000E07000E07000E07000E07000E0700 0E0700FFFF00FFFF000E00000E00000E00000E00000E0F000F0F00070F0007CF0001FE00007E00> 24 26 0 0 21.331] 12 @dc [<07EFC00FFFC01E3E001C1E001C0E001C0E001C0E001C0E001C0E001C0E001C0E001C0E001C0E00 1C0E00FC7E00FC7E00> 24 16 -1 0 21.331] 117 @dc [<0FF03FFC7C3EF00FE007E007E00FF01F7FFE3FFC7FF8700070007FC03FE0387070387038703870 38703838771FFF0FDF> 16 24 -1 8 19.198] 103 @dc cmmi9.300 @sf [<1F80003FE000787800F01C00E00C00E00600E00700E00300E00300F00380F00380700180700180 7801807801C03800C03800C03C00C03C00E01C00601C00601E00601E00700E0078FFE3FFFFE3FF> 24 26 -3 0 26.116] 85 @dc cmr9.300 @sf [<007F000001FFC00007C1F0000F0078001E003C003C001E0038000E0078000F0078000F00F00007 80F0000780F0000780F0000780F0000780F0000780F0000780F00007807000070078000F003800 0E003C001E001E003C000F00780007C1F00001FFC000007F0000> 32 26 -2 0 29.864] 79 @dc [ 32 26 -1 0 29.328] 68 @dc [ 32 26 -1 0 28.261] 82 @dc [ 24 26 -1 0 26.128] 80 @dc [ 32 26 -1 0 28.792] 65 @dc [<007F8001FFE007E0F00F80381E001C3C000C3C000E780006780006F00006F00000F00000F00000 F00000F00000F00000F0000678000678000E3C000E3C001E1E001E0F803E07E0FE01FFE6007F06> 24 26 -2 0 27.731] 67 @dc [ 32 26 -1 0 29.858] 75 @dc [ 24 26 -1 0 20.265] 107 @dc [<01C00380070007000E001C001C00380038007000700070006000E000E000E000E000E000E000E0 00E000E000E000E000E0006000700070007000380038001C001C000E0007000700038001C0> 16 38 -2 10 14.932] 40 @dc [ 16 38 -2 10 14.932] 41 @dc [<19F8001BFE001F0F001E07801C03801C01C01C01C01C01C01C01C01C01C01C01C01C03801E0780 1F0F001FFE001CFC001C00001C00001C00001C00001C00001C00001C00001C0000FC0000FC0000> 24 26 -1 0 21.331] 98 @dc 6 @bop1 cmr10.329 @sf 0 114 p 54 c 1388(Getting)m 14(Started)m 0 134 p 1725 2 ru cmmi10.329 @sf 0 259 p 102 c cmmi8.300 @sf 22 266 p 105 c cmr10.329 @sf 49 259 p 58 c cmsy10.329 @sf 12 r 60 c cmmi8.300 @sf 107 244 p 112 c cmr8.300 @sf (+1)s cmsy10.329 @sf 185 259 p 33 c 13 r 60 c cmr8.300 @sf 276 244 p 49 c cmr10.329 @sf 295 259 p 46 c 21(In)m 22(this)m 20(section,)m 22 r 119 c 101 c 20(generalize)m 21(these)m 21(problems)m 21(to)m 20(allo)m 119 c 19(for)m 20 r 109 c (ultiv)s -2(a)m -1(ri-)m 0 315 p (ate)s 16(explanatory)m 15(data)m cmmi10.329 @sf 16 r 120 c cmmi8.300 @sf 459 322 p 105 c cmsy10.329 @sf 485 315 p 50 c 13 r 60 c cmmi8.300 @sf 561 300 p 109 c cmr10.329 @sf 594 315 p 44 c cmmi10.329 @sf 16 r 109 c cmsy10.329 @sf 15 r 21 c cmr10.329 @sf 14(1,)m 16(and)m 17 r 109 c (ulti)s -1(resp)m 1(onse)m 15(dep)m 1(enden)m 116 c 17 r 118 c -2(ariables)m cmmi10.329 @sf 15 r 121 c cmmi8.300 @sf 1591 322 p 105 c cmsy10.329 @sf 1618 315 p 50 c 12 r 60 c cmmi8.300 @sf 1693 300 p 113 c cmr10.329 @sf 1712 315 p 44 c cmmi10.329 @sf 0 372 p 113 c cmsy10.329 @sf 18 r 21 c cmr10.329 @sf 16(1,)m 18(whic)m 104 c 16(are)m 17(mo)m 1(deled)m 17 r 98 c 121 c cmmi10.329 @sf 16 r 102 c cmmi8.300 @sf 622 379 p 105 c cmr10.329 @sf 653 372 p 58 c cmsy10.329 @sf 16 r 60 c cmmi8.300 @sf 715 357 p 112 c cmr8.300 @sf 43 c cmmi8.300 @sf 109 c cmsy10.329 @sf 809 372 p 33 c 17 r 60 c cmmi8.300 @sf 904 357 p 113 c cmr10.329 @sf 922 372 p 46 c 26 r 70 c -3(or)m 16(suc)m 104 c 17(higher)m 17(dimensional)m 16(data,)m 17(the)m 0 428 p (errors)s cmmi10.329 @sf 20 r 14 c cmmi8.300 @sf 155 435 p 105 c cmsy10.329 @sf 182 428 p 50 c 13 r 60 c cmmi8.300 @sf 258 413 p 109 c cmr10.329 @sf 311 428 p (asso)s 1(ciated)m 20(with)m cmmi10.329 @sf 20 r 120 c cmmi8.300 @sf 668 435 p 105 c cmr10.329 @sf 682 428 p 44 c 21(and)m 21(the)m 20(errors)m cmmi10.329 @sf 20 r 15 c cmmi8.300 @sf 1046 435 p 105 c cmsy10.329 @sf 1073 428 p 50 c 13 r 60 c cmmi8.300 @sf 1149 413 p 113 c cmr10.329 @sf 1188 428 p (asso)s 1(ciated)m 20(with)m cmmi10.329 @sf 20 r 121 c cmmi8.300 @sf 1541 435 p 105 c cmr10.329 @sf 1555 428 p 44 c 22(can)m 20 r 98 c 1 r 101 c 0 484 p 119 c (eigh)s -1(ted)m 15 r 98 c 121 c cmmi10.329 @sf 15 r 119 c cmmi8.300 @sf 283 491 p 14 c cmmi6.300 @sf 299 496 p 105 c cmsy10.329 @sf 326 484 p 50 c 13 r 60 c cmmi8.300 @sf 402 469 p 109 c cmsy8.300 @sf 2 c cmmi8.300 @sf 109 c cmr10.329 @sf 510 484 p (and)s cmmi10.329 @sf 17 r 119 c cmmi8.300 @sf 628 491 p 15 c cmmi6.300 @sf 642 496 p 105 c cmsy10.329 @sf 669 484 p 50 c 13 r 60 c cmmi8.300 @sf 745 469 p 113 c cmsy8.300 @sf 1 r 2 c cmmi8.300 @sf 113 c cmr10.329 @sf 808 484 p 44 c cmmi10.329 @sf 16 r 105 c cmr10.329 @sf 15 r 61 c 16 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 7 r 58 c 5 r 59 c 8(n;)m cmr10.329 @sf 16(resp)m 1(ectiv)m (ely)s -3 r 44 c 14(where)m 17(the)m cmmi10.329 @sf 17 r 119 c cmmi8.300 @sf 1598 491 p 14 c cmmi6.300 @sf 1614 496 p 105 c cmr10.329 @sf 1627 484 p 109 c (ust)s 0 541 p 98 c 1 r 101 c 16 r 112 c 1(ositiv)m 101 c 13(de\014nite)m 16(matrices)m 14(and)m 15(the)m cmmi10.329 @sf 16 r 119 c cmmi8.300 @sf 769 548 p 15 c cmmi6.300 @sf 783 553 p 105 c cmr10.329 @sf 797 541 p 109 c (ust)s 13 r 98 c 1 r 101 c 16 r 112 c 1(ositiv)m 101 c 13(semide\014nite)m 16(matrices.)m cmr8.300 @sf 1571 526 p 49 c cmr10.329 @sf 0 617 p 70 c -3(or)m 16(the)m 17(explicit)m 17(problem,)m 17 r 119 c 101 c 17(assume)m 17(that)m 17(the)m cmmi10.329 @sf 17 r 113 c cmr10.329 @sf 20(resp)m 1(onses)m 18(of)m 17(the)m 17(observ)m (ed)s 17 r 118 c -2(alues)m 17(of)m cmmi10.329 @sf 17 r 121 c cmmi8.300 @sf 1711 624 p 105 c cmr10.329 @sf 0 673 p (satis\014es)s cmmi10.329 @sf 463 730 p 121 c cmmi8.300 @sf 485 737 p 105 c cmr10.329 @sf 512 730 p 61 c cmmi10.329 @sf 13 r 102 c cmmi8.300 @sf 582 737 p 105 c cmr10.329 @sf 597 730 p 40 c cmmi10.329 @sf 120 c cmmi8.300 @sf 641 737 p 105 c cmr10.329 @sf 664 730 p 43 c cmmi10.329 @sf 11 r 14 c cmsy8.300 @sf 732 712 p 3 c cmmi8.300 @sf 730 741 p 105 c cmr10.329 @sf 751 730 p 59 c cmmi10.329 @sf 8 r 12 c cmsy8.300 @sf 800 712 p 3 c cmr10.329 @sf 820 730 p 41 c cmsy10.329 @sf 9 r 0 c cmmi10.329 @sf 11 r 15 c cmsy8.300 @sf 911 712 p 3 c cmmi8.300 @sf 911 741 p 105 c cmmi10.329 @sf 1022 730 p 105 c cmr10.329 @sf 12 r 61 c 13 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 7 r 58 c 6 r 59 c 8(n;)m cmr10.329 @sf 0 810 p (for)s 12(some)m 12(actual,)m 12(but)m 13(unkno)m (wn)s 12 r 118 c -2(alue)m cmmi10.329 @sf 12 r 12 c cmsy8.300 @sf 741 795 p 3 c cmmi10.329 @sf 761 810 p 58 c cmr10.329 @sf 12(Th)m (us,)s 12(if)m 12 r 119 c 101 c 11(let)m cmmi10.329 @sf 12 r 88 c cmsy10.329 @sf 16 r 50 c 13 r 60 c cmmi8.300 @sf 1208 795 p 110 c cmsy8.300 @sf 2 c cmmi8.300 @sf 109 c cmr10.329 @sf 1302 810 p (and)s cmmi10.329 @sf 13 r 89 c cmsy10.329 @sf 23 r 50 c 13 r 60 c cmmi8.300 @sf 1513 795 p 110 c cmsy8.300 @sf 2 c cmmi8.300 @sf 113 c cmr10.329 @sf 1594 810 p (denote)s 0 866 p (the)s 18(arra)m (ys)s 16(with)m cmmi10.329 @sf 18 r 105 c cmr10.329 @sf (th)s 18(ro)m 119 c cmmi10.329 @sf 16 r 120 c cmmi8.300 @sf 521 873 p 105 c cmr10.329 @sf 553 866 p (and)s cmmi10.329 @sf 19 r 121 c cmmi8.300 @sf 667 873 p 105 c cmr10.329 @sf 681 866 p 44 c 19(resp)m 1(ectiv)m (ely)s -3 r 44 c 16(and)m 19 r 1 c cmsy10.329 @sf 12 r 50 c 13 r 60 c cmmi8.300 @sf 1191 851 p 110 c cmsy8.300 @sf 2 c cmmi8.300 @sf 109 c cmr10.329 @sf 1292 866 p (and)s cmmi10.329 @sf 18 r 69 c cmsy10.329 @sf 15 r 50 c 13 r 60 c cmmi8.300 @sf 1508 851 p 110 c cmsy8.300 @sf 2 c cmmi8.300 @sf 113 c cmr10.329 @sf 1594 866 p (denote)s 0 923 p (the)s 15(arra)m (ys)s 13(with)m cmmi10.329 @sf 14 r 105 c cmr10.329 @sf (th)s 15(ro)m 119 c cmmi10.329 @sf 13 r 14 c cmmi8.300 @sf 499 930 p 105 c cmr10.329 @sf 528 923 p (and)s cmmi10.329 @sf 15 r 15 c cmmi8.300 @sf 634 930 p 105 c cmr10.329 @sf 649 923 p 44 c 15(resp)m 1(ectiv)m (ely)s -3 r 44 c 12 r 119 c 101 c 14(are)m 15(then)m 15(assuming)m 14(that)m 15(the)m 15(observ)m (ed)s 0 979 p 118 c -2(alues)m cmmi10.329 @sf 14 r 88 c cmr10.329 @sf 19(and)m cmmi10.329 @sf 15 r 89 c cmr10.329 @sf 26(satisfy)m cmmi10.329 @sf 693 1074 p 88 c cmr10.329 @sf 44 r 61 c cmmi10.329 @sf 42 r 88 c cmsy8.300 @sf 894 1056 p 3 c cmsy10.329 @sf 923 1074 p 0 c cmr10.329 @sf 11 r 1 c cmsy8.300 @sf 1007 1056 p 3 c cmmi10.329 @sf 697 1143 p 89 c cmr10.329 @sf 52 r 61 c cmmi10.329 @sf 42 r 89 c cmsy8.300 @sf 889 1125 p 3 c cmsy10.329 @sf 918 1143 p 0 c cmmi10.329 @sf 11 r 69 c cmsy8.300 @sf 1001 1125 p 3 c cmmi10.329 @sf 1020 1143 p 59 c cmr10.329 @sf 0 1238 p (and)s 15(that)m 15(the)m 15(estimated)m 14 r 118 c -2(alues,)m 14(whic)m 104 c 14 r 119 c 101 c 14(denote)m 16 r 98 c 121 c 14 r 97 c 15(\\hat,")m 14(will)m 14(satisfy)m 718 1323 p 94 c cmmi10.329 @sf 705 1334 p 88 c cmr10.329 @sf 787 1333 p 61 c cmmi10.329 @sf 42 r 88 c cmr10.329 @sf 14 r 43 c 969 1323 p 94 c 961 1334 p 1 c 716 1392 p 94 c cmmi10.329 @sf 709 1403 p 89 c cmr10.329 @sf 787 1402 p 61 c cmmi10.329 @sf 42 r 89 c cmr10.329 @sf 21 r 43 c 967 1392 p 94 c cmmi10.329 @sf 956 1403 p 69 c 1008 1402 p 58 c cmr10.329 @sf 0 1517 p (Generalizing)s 13(the)m 15(problem)m 14(presen)m (ted)s 14(in)m cmsy10.329 @sf 15 r 120 c cmr10.329 @sf (1.A.i,)s 13(the)m cmti10.329 @sf 14(explicit)m 16(multir)m -1(esp)m -2(onse)m 13(ortho)m -1(gonal)m 15(dis-)m 0 1573 p (tanc)s -1 r 101 c 15 r 114 c -1 r 101 c -2(gr)m -2(es)m -1(sion)m 14(pr)m -1(oblem)m 15(for)m 17(multivariate)m 17(explanatory)m 16(data)m cmr10.329 @sf 16(is)m 15(de\014ned)m 17(as)m 554 1696 p (min)s cmmi8.300 @sf 557 1726 p 12 c 2(;\016)m (;\017)s 656 1643 p 110 c cmex10.300 @sf 637 1656 p 88 c cmmi8.300 @sf 639 1747 p 105 c cmr8.300 @sf (=1)s cmr10.329 @sf 705 1696 p 40 c -1 r 91 c cmmi10.329 @sf 15 c cmr6.300 @sf 753 1678 p 84 c cmmi8.300 @sf 753 1708 p 105 c cmmi10.329 @sf 777 1696 p 119 c cmmi8.300 @sf 805 1703 p 15 c cmmi6.300 @sf 819 1708 p 105 c cmmi10.329 @sf 833 1696 p 15 c cmmi8.300 @sf 851 1703 p 105 c cmr10.329 @sf 866 1696 p 93 c 10 r 43 c 10 r 91 c cmmi10.329 @sf 14 c cmr6.300 @sf 969 1678 p 84 c cmmi8.300 @sf 967 1708 p 105 c cmmi10.329 @sf 992 1696 p 119 c cmmi8.300 @sf 1020 1703 p 14 c cmmi6.300 @sf 1036 1708 p 105 c cmmi10.329 @sf 1050 1696 p 14 c cmmi8.300 @sf 1070 1703 p 105 c cmr10.329 @sf 1084 1696 p 93 c 41 c 299 2000 p (sub)s 3(ject)m 15(to)m cmmi10.329 @sf 565 1904 p 89 c cmmi8.300 @sf 591 1911 p 105 c cmr8.300 @sf 49 c cmr10.329 @sf 635 1904 p 61 c cmmi10.329 @sf 13 r 102 c cmmi8.300 @sf 705 1911 p 105 c cmr8.300 @sf 49 c cmr10.329 @sf 737 1904 p 40 c cmmi10.329 @sf 120 c cmmi8.300 @sf 781 1911 p 105 c cmr10.329 @sf 805 1904 p 43 c cmmi10.329 @sf 11 r 14 c cmmi8.300 @sf 871 1911 p 105 c cmr10.329 @sf 885 1904 p 59 c cmmi10.329 @sf 8 r 12 c cmr10.329 @sf 2 r 41 c cmsy10.329 @sf 9 r 0 c cmmi10.329 @sf 11 r 69 c cmmi8.300 @sf 1041 1911 p 105 c cmr8.300 @sf 49 c cmmi10.329 @sf 565 1960 p 89 c cmmi8.300 @sf 591 1967 p 105 c cmr8.300 @sf 50 c cmr10.329 @sf 635 1960 p 61 c cmmi10.329 @sf 13 r 102 c cmmi8.300 @sf 705 1967 p 105 c cmr8.300 @sf 50 c cmr10.329 @sf 737 1960 p 40 c cmmi10.329 @sf 120 c cmmi8.300 @sf 781 1967 p 105 c cmr10.329 @sf 805 1960 p 43 c cmmi10.329 @sf 11 r 14 c cmmi8.300 @sf 871 1967 p 105 c cmr10.329 @sf 885 1960 p 59 c cmmi10.329 @sf 8 r 12 c cmr10.329 @sf 2 r 41 c cmsy10.329 @sf 9 r 0 c cmmi10.329 @sf 11 r 69 c cmmi8.300 @sf 1041 1967 p 105 c cmr8.300 @sf 50 c cmr10.329 @sf 565 2007 p 46 c 565 2024 p 46 c 565 2041 p 46 c cmmi10.329 @sf 565 2096 p 89 c cmmi8.300 @sf 591 2103 p (iq)s cmr10.329 @sf 635 2096 p 61 c cmmi10.329 @sf 13 r 102 c cmmi8.300 @sf 705 2103 p (iq)s cmr10.329 @sf 736 2096 p 40 c cmmi10.329 @sf 120 c cmmi8.300 @sf 780 2103 p 105 c cmr10.329 @sf 804 2096 p 43 c cmmi10.329 @sf 10 r 14 c cmmi8.300 @sf 869 2103 p 105 c cmr10.329 @sf 884 2096 p 59 c cmmi10.329 @sf 8 r 12 c cmr10.329 @sf 2 r 41 c cmsy10.329 @sf 9 r 0 c cmmi10.329 @sf 10 r 69 c cmmi8.300 @sf 1039 2103 p (iq)s cmex10.300 @sf 1093 1864 p 57 c 1093 1902 p 62 c 1093 1914 p 62 c 1093 1926 p 62 c 1093 1938 p 62 c 1093 1950 p 61 c 1093 2026 p 62 c 1093 2038 p 62 c 1093 2050 p 62 c 1093 2062 p 62 c 1093 2074 p 59 c cmmi10.329 @sf 1171 2000 p 105 c cmr10.329 @sf 12 r 61 c 13 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 8 r 58 c 5 r 59 c 8 r 110 c 14 r 59 c cmr10.329 @sf 1632 1880 p (\(1)s cmmi10.329 @sf 58 c cmr10.329 @sf (7\))s 0 2190 p (where)s 10(subscript)m cmmi10.329 @sf 11(il)m cmr10.329 @sf 10(denotes)m 10(the)m 10 r 40 c cmmi10.329 @sf (i;)s 8 r 108 c cmr10.329 @sf 1(\)th)m 8(elemen)m 116 c 9(of)m 10(the)m 10(corresp)m 1(onding)m 10(arra)m 121 c -4 r 44 c 9(e.g.,)m cmmi10.329 @sf 10 r 89 c cmmi8.300 @sf 1540 2197 p (il)s cmr10.329 @sf 1576 2190 p (denotes)s 0 2247 p (the)s cmmi10.329 @sf 14 r 108 c cmr10.329 @sf 1(th)m 14(resp)m 1(onse)m 15(of)m 14(the)m cmmi10.329 @sf 14 r 105 c cmr10.329 @sf (th)s 14(observ)m -2(ation,)m 13(and)m cmmi10.329 @sf 14 r 102 c cmmi8.300 @sf 896 2254 p (il)s cmr10.329 @sf 922 2247 p 40 c cmmi10.329 @sf 120 c cmmi8.300 @sf 966 2254 p 105 c cmr10.329 @sf 988 2247 p 43 c cmmi10.329 @sf 9 r 14 c cmmi8.300 @sf 1052 2254 p 105 c cmr10.329 @sf 1066 2247 p 59 c cmmi10.329 @sf 8 r 12 c cmr10.329 @sf 2 r 41 c 13(denotes)m 15(the)m 14(mo)m 1(del)m 14(for)m 14(the)m cmmi10.329 @sf 15 r 108 c cmr10.329 @sf 1(th)m 0 2286 p 690 2 ru cmr6.300 @sf 52 2315 p 49 c cmr9.300 @sf 69 2330 p (The)s 11(matrix)m cmmi9.300 @sf 11 r 65 c cmr9.300 @sf 10(is)m cmti9.300 @sf 10 r 112 c -1(ositiv)m -1 r 101 c 10(de\014nite)m cmr9.300 @sf 8(if)m 10(and)m 11(only)m 11(if)m cmmi9.300 @sf 10 r 65 c cmr6.300 @sf 863 2315 p 84 c cmr9.300 @sf 898 2330 p 61 c cmmi9.300 @sf 10 r 65 c cmr9.300 @sf 44 c 11(and)m cmmi9.300 @sf 11 r 97 c cmr6.300 @sf 1081 2315 p 84 c cmmi9.300 @sf 1105 2330 p (Aa)s 11 r 62 c cmr9.300 @sf 11 r 48 c 10(for)m 11(all)m 10(nonzero)m 12 r 118 c (ectors)s cmmi9.300 @sf 10 r 97 c cmr9.300 @sf 46 c 17(It)m 10(is)m cmti9.300 @sf 0 2376 p 112 c -1(osit)m -1(ive)m 11(semide\014n)m -1(ite)m cmr9.300 @sf 10(if)m 11(and)m 13(only)m 13(if)m cmmi9.300 @sf 12 r 65 c cmr6.300 @sf 605 2361 p 84 c cmr9.300 @sf 639 2376 p 61 c cmmi9.300 @sf 10 r 65 c cmr9.300 @sf 44 c 12(and)m cmmi9.300 @sf 13 r 97 c cmr6.300 @sf 825 2361 p 84 c cmmi9.300 @sf 849 2376 p (Aa)s cmsy9.300 @sf 11 r 21 c cmr9.300 @sf 11 r 48 c 12(for)m 12(all)m 12 r 118 c (ectors)s cmmi9.300 @sf 12 r 97 c cmr9.300 @sf 46 c 16(When)m cmmi9.300 @sf 14 r 65 c cmr9.300 @sf 12(is)m 12 r 112 c 1(ositiv)m 101 c 11(de\014nite)m 0 2421 p (or)s 14 r 112 c 1(ositiv)m 101 c 13(semide\014nite,)m 15(then)m 14(there)m 15(is)m 13(an)m 15(upp)m 1(er)m 15(triangular)m 14(matrix)m cmmi9.300 @sf 14 r 85 c cmr9.300 @sf 18(suc)m 104 c 14(that)m cmmi9.300 @sf 14 r 65 c cmr9.300 @sf 13 r 61 c cmmi9.300 @sf 12 r 85 c cmr6.300 @sf 1444 2406 p 84 c cmmi9.300 @sf 1468 2421 p 85 c cmr9.300 @sf 4 r 46 c 20(ODRP)m -2 r 65 c (CK)s 0 2467 p 99 c (hec)s (ks)s 12(for)m 12 r 112 c 1(ositiv)m 101 c 12(\(semi\)de\014niteness)m 14 r 98 c 121 c 13(attempting)m 13(to)m 13(form)m cmmi9.300 @sf 13 r 85 c cmr9.300 @sf 4 r 46 c @eop %%Page: 7 21 7 @bop0 cmmi10.329 @sf [ 32 33 -3 1 27.872] 83 @dc [<80000000E0000000F80000003E0000000F80000003E0000000F80000003E0000000F80000003E0 000000F80000003E0000000F80000003C0000003C000000F8000003E000000F8000003E000000F 8000003E000000F8000003E000000F8000003E000000F8000000E000000080000000> 32 28 -4 3 35.353] 62 @dc cmtt10.329 @sf [<000700000700000F00000E00001E00001C000FFC003FFE007FFF00787F0070F700F0E780E1E380 E1E380E00380E00380E00380E00380E00380E00380E00380E00380E00380E00380E00380E00380 E00380E00380F00780700700780F007FFF003FFE000FF800> 24 34 -3 6 23.863] 81 @dc 7 @bop1 cmr10.329 @sf 225 114 p (Getting)s 14(Started)m 1388 r 55 c 225 134 p 1725 2 ru 225 259 p (resp)s 1(onse)m 23(of)m 22(observ)m -2(ation)m cmmi10.329 @sf 20 r 105 c cmr10.329 @sf 46 c 41(Because)m 23(the)m 23(constrain)m -1(ts)m 20(in)m 22(\(1.7\))m 21(are)m 22(linear)m 22(in)m cmmi10.329 @sf 22 r 69 c cmr10.329 @sf 3 r 44 c 23(this)m 21(is)m 225 315 p (equiv)s -2(alen)m 116 c 13(to)m 14(the)m 16(problem)m 294 437 p (min)s cmmi8.300 @sf 308 467 p 12 c 2(;\016)m 397 384 p 110 c cmex10.300 @sf 377 397 p 88 c cmmi8.300 @sf 379 488 p 105 c cmr8.300 @sf (=1)s cmr10.329 @sf 445 437 p 40 c 91 c cmmi10.329 @sf 102 c cmmi8.300 @sf 498 444 p 105 c cmr10.329 @sf 511 437 p 40 c cmmi10.329 @sf 120 c cmmi8.300 @sf 555 444 p 105 c cmr10.329 @sf 579 437 p 43 c cmmi10.329 @sf 11 r 14 c cmmi8.300 @sf 645 444 p 105 c cmr10.329 @sf 659 437 p 59 c cmmi10.329 @sf 8 r 12 c cmr10.329 @sf 2 r 41 c cmsy10.329 @sf 9 r 0 c cmmi10.329 @sf 11 r 121 c cmmi8.300 @sf 803 444 p 105 c cmr10.329 @sf 817 437 p 93 c cmr6.300 @sf 830 419 p 84 c cmmi10.329 @sf 853 437 p 119 c cmmi8.300 @sf 881 444 p 15 c cmmi6.300 @sf 895 449 p 105 c cmr10.329 @sf 910 437 p 91 c cmmi10.329 @sf 102 c cmmi8.300 @sf 945 444 p 105 c cmr10.329 @sf 958 437 p 40 c cmmi10.329 @sf 120 c cmmi8.300 @sf 1002 444 p 105 c cmr10.329 @sf 1026 437 p 43 c cmmi10.329 @sf 11 r 14 c cmmi8.300 @sf 1092 444 p 105 c cmr10.329 @sf 1106 437 p 59 c cmmi10.329 @sf 8 r 12 c cmr10.329 @sf 2 r 41 c cmsy10.329 @sf 9 r 0 c cmmi10.329 @sf 11 r 121 c cmmi8.300 @sf 1250 444 p 105 c cmr10.329 @sf 1264 437 p 93 c 10 r 43 c cmmi10.329 @sf 10 r 14 c cmr6.300 @sf 1354 419 p 84 c cmmi8.300 @sf 1352 448 p 105 c cmmi10.329 @sf 1378 437 p 119 c cmmi8.300 @sf 1406 444 p 14 c cmmi6.300 @sf 1422 449 p 105 c cmmi10.329 @sf 1435 437 p 14 c cmmi8.300 @sf 1455 444 p 105 c cmr10.329 @sf 1470 437 p 41 c 12 r 61 c 13(min)m cmmi8.300 @sf 1562 467 p 12 c 2(;\016)m cmmi10.329 @sf 1631 437 p 83 c cmr10.329 @sf 3 r 40 c cmmi10.329 @sf 12 c 2 r 59 c 8 r 14 c cmr10.329 @sf 2 r 41 c cmmi10.329 @sf 13 r 59 c cmr10.329 @sf 62(\(1)m cmmi10.329 @sf 58 c cmr10.329 @sf (8\))s 225 568 p (where)s 15 r 119 c 101 c 14(de\014ne)m 17(the)m cmti10.329 @sf 15(weighte)m -1 r 100 c 15(sum)m 17(of)m 16(squar)m -1(es)m cmmi10.329 @sf 14 r 83 c cmr10.329 @sf 3 r 40 c cmmi10.329 @sf 12 c 2 r 59 c 8 r 14 c cmr10.329 @sf 2 r 41 c 13 r 98 c 121 c cmmi10.329 @sf 810 663 p 83 c cmr10.329 @sf 3 r 40 c cmmi10.329 @sf 12 c 2 r 59 c 8 r 14 c cmr10.329 @sf 2 r 41 c cmsy10.329 @sf 11 r 17 c cmmi10.329 @sf 13 r 83 c cmmi8.300 @sf 1035 670 p 15 c cmr10.329 @sf 1051 663 p 40 c cmmi10.329 @sf 12 c 2 r 59 c 8 r 14 c cmr10.329 @sf 2 r 41 c 9 r 43 c cmmi10.329 @sf 10 r 83 c cmmi8.300 @sf 1240 670 p 14 c cmr10.329 @sf 1259 663 p 40 c cmmi10.329 @sf 12 c 2 r 59 c 8 r 14 c cmr10.329 @sf 2 r 41 c 225 757 p (with)s cmmi10.329 @sf 524 832 p 83 c cmmi8.300 @sf 552 839 p 15 c cmr10.329 @sf 568 832 p 40 c cmmi10.329 @sf 12 c 2 r 59 c 8 r 14 c cmr10.329 @sf 2 r 41 c cmsy10.329 @sf 11 r 17 c cmmi8.300 @sf 753 779 p 110 c cmex10.300 @sf 734 792 p 88 c cmmi8.300 @sf 736 883 p 105 c cmr8.300 @sf (=1)s cmr10.329 @sf 802 832 p 40 c -1 r 91 c cmmi10.329 @sf 102 c cmmi8.300 @sf 854 839 p 105 c cmr10.329 @sf 868 832 p 40 c cmmi10.329 @sf 120 c cmmi8.300 @sf 912 839 p 105 c cmr10.329 @sf 936 832 p 43 c cmmi10.329 @sf 11 r 14 c cmmi8.300 @sf 1002 839 p 105 c cmr10.329 @sf 1016 832 p 59 c cmmi10.329 @sf 8 r 12 c cmr10.329 @sf 2 r 41 c cmsy10.329 @sf 9 r 0 c cmmi10.329 @sf 10 r 121 c cmmi8.300 @sf 1159 839 p 105 c cmr10.329 @sf 1174 832 p 93 c cmr6.300 @sf 1187 814 p 84 c cmmi10.329 @sf 1210 832 p 119 c cmmi8.300 @sf 1238 839 p 15 c cmmi6.300 @sf 1252 844 p 105 c cmr10.329 @sf 1266 832 p 91 c cmmi10.329 @sf 102 c cmmi8.300 @sf 1301 839 p 105 c cmr10.329 @sf 1315 832 p 40 c cmmi10.329 @sf 120 c cmmi8.300 @sf 1359 839 p 105 c cmr10.329 @sf 1383 832 p 43 c cmmi10.329 @sf 11 r 14 c cmmi8.300 @sf 1449 839 p 105 c cmr10.329 @sf 1463 832 p 59 c cmmi10.329 @sf 8 r 12 c cmr10.329 @sf 2 r 41 c cmsy10.329 @sf 9 r 0 c cmmi10.329 @sf 10 r 121 c cmmi8.300 @sf 1606 839 p 105 c cmr10.329 @sf 1621 832 p 93 c 41 c 225 946 p (and)s cmmi10.329 @sf 851 1021 p 83 c cmmi8.300 @sf 879 1028 p 14 c cmr10.329 @sf 897 1021 p 40 c cmmi10.329 @sf 12 c 2 r 59 c 8 r 14 c cmr10.329 @sf 2 r 41 c cmsy10.329 @sf 12 r 17 c cmmi8.300 @sf 1083 969 p 110 c cmex10.300 @sf 1064 981 p 88 c cmmi8.300 @sf 1065 1072 p 105 c cmr8.300 @sf (=1)s cmr10.329 @sf 1124 1021 p 40 c cmmi10.329 @sf 14 c cmr6.300 @sf 1164 1003 p 84 c cmmi8.300 @sf 1162 1033 p 105 c cmmi10.329 @sf 1187 1021 p 119 c cmmi8.300 @sf 1215 1028 p 14 c cmmi6.300 @sf 1231 1033 p 105 c cmmi10.329 @sf 1245 1021 p 14 c cmmi8.300 @sf 1265 1028 p 105 c cmr10.329 @sf 1279 1021 p 41 c cmmi10.329 @sf 15 r 58 c cmr10.329 @sf 225 1155 p (The)s cmti10.329 @sf 18(implicit)m 18(multir)m -1(esp)m -2(ons)m -1 r 101 c 16(ortho)m -1(gonal)m 18(distanc)m -1 r 101 c 16 r 114 c -1 r 101 c -1(g)m -1 r 114 c -2(ess)m -1(ion)m 16(pr)m -1(oblem)m 17(for)m 19(multivariate)m 19(ex-)m 225 1211 p (planatory)s 17(data)m cmr10.329 @sf 16(is)m 758 1333 p (min)s cmmi8.300 @sf 772 1363 p 12 c 2(;\016)m 861 1281 p 110 c cmex10.300 @sf 841 1293 p 88 c cmmi8.300 @sf 843 1384 p 105 c cmr8.300 @sf (=1)s cmr10.329 @sf 901 1333 p 91 c cmmi10.329 @sf 14 c cmr6.300 @sf 936 1315 p 84 c cmmi8.300 @sf 934 1345 p 105 c cmmi10.329 @sf 960 1333 p 119 c cmmi8.300 @sf 988 1340 p 14 c cmmi6.300 @sf 1004 1345 p 105 c cmmi10.329 @sf 1017 1333 p 14 c cmmi8.300 @sf 1037 1340 p 105 c cmr10.329 @sf 1051 1333 p 93 c 13 r 61 c 13(min)m cmmi8.300 @sf 1138 1363 p 12 c 2(;\016)m cmmi10.329 @sf 1208 1333 p 83 c cmmi8.300 @sf 1236 1340 p 14 c cmr10.329 @sf 1255 1333 p 40 c cmmi10.329 @sf 12 c 2 r 59 c 8 r 14 c cmr10.329 @sf 2 r 41 c 518 1637 p (sub)s 3(ject)m 15(to)m cmmi10.329 @sf 868 1541 p 102 c cmmi8.300 @sf 890 1548 p 105 c cmr8.300 @sf 49 c cmr10.329 @sf 922 1541 p 40 c cmmi10.329 @sf 120 c cmmi8.300 @sf 966 1548 p 105 c cmr10.329 @sf 990 1541 p 43 c cmmi10.329 @sf 10 r 14 c cmmi8.300 @sf 1055 1548 p 105 c cmr10.329 @sf 1069 1541 p 59 c cmmi10.329 @sf 8 r 12 c cmr10.329 @sf 2 r 41 c 12 r 61 c 13 r 48 c cmmi10.329 @sf 868 1597 p 102 c cmmi8.300 @sf 890 1604 p 105 c cmr8.300 @sf 50 c cmr10.329 @sf 922 1597 p 40 c cmmi10.329 @sf 120 c cmmi8.300 @sf 966 1604 p 105 c cmr10.329 @sf 990 1597 p 43 c cmmi10.329 @sf 10 r 14 c cmmi8.300 @sf 1055 1604 p 105 c cmr10.329 @sf 1069 1597 p 59 c cmmi10.329 @sf 8 r 12 c cmr10.329 @sf 2 r 41 c 12 r 61 c 13 r 48 c 868 1644 p 46 c 868 1661 p 46 c 868 1678 p 46 c cmmi10.329 @sf 868 1733 p 102 c cmmi8.300 @sf 890 1740 p (iq)s cmr10.329 @sf 921 1733 p 40 c cmmi10.329 @sf 120 c cmmi8.300 @sf 965 1740 p 105 c cmr10.329 @sf 989 1733 p 43 c cmmi10.329 @sf 10 r 14 c cmmi8.300 @sf 1054 1740 p 105 c cmr10.329 @sf 1069 1733 p 59 c cmmi10.329 @sf 8 r 12 c cmr10.329 @sf 2 r 41 c 11 r 61 c 13 r 48 c cmex10.300 @sf 1239 1501 p 57 c 1239 1539 p 62 c 1239 1551 p 62 c 1239 1563 p 62 c 1239 1575 p 62 c 1239 1587 p 61 c 1239 1663 p 62 c 1239 1675 p 62 c 1239 1687 p 62 c 1239 1699 p 62 c 1239 1711 p 59 c cmmi10.329 @sf 1402 1637 p 105 c cmr10.329 @sf 12 r 61 c 13 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 7 r 58 c 6 r 59 c 8 r 110 c 14 r 58 c cmr10.329 @sf 1857 1518 p (\(1)s cmmi10.329 @sf 58 c cmr10.329 @sf (9\))s 225 1826 p (As)s 17 r 119 c (as)s 15(the)m 18(case)m 17(in)m cmsy10.329 @sf 17 r 120 c cmr10.329 @sf (1.A.ii,)s 15(the)m 18(constrain)m (t)s -1 r 115 c 15(in)m 17(\(1.9\))m 16(are)m 17(not)m 16(assumed)m 17(to)m 17 r 98 c 1 r 101 c 18(linear)m 16(in)m cmmi10.329 @sf 17 r 14 c cmmi8.300 @sf 1923 1833 p 105 c cmr10.329 @sf 1937 1826 p 44 c 225 1883 p (and)s 20(therefore)m 19(cannot)m 20 r 98 c 1 r 101 c 20(eliminated)m 19(to)m 18(create)m 20(an)m 19(unconstrained)m 20(problem)m 19(as)m 20 r 119 c (as)s 18(done)m 225 1939 p (ab)s 1 r 111 c 118 c -1 r 101 c 13(to)m 13(sp)m 1(ecify)m 15(the)m 14(explicit)m 13(problem)m 14(\(1.8\).)m 18(The)m 14(implicit)m 13(orthogonal)m 12(distance)m 14(regression)m 225 1996 p (problem)s 15 r 109 c (ust)s 14(therefore)m 14 r 98 c 1 r 101 c 16(solv)m (ed)s 14(di\013eren)m (tly)s 13(than)m 15(the)m 15(explicit)m 15(problem.)m 19(\(See)m cmsy10.329 @sf 16 r 120 c cmr10.329 @sf (1.B.\))s 225 2072 p (Note)s 15(that)m 15(when)m cmmi10.329 @sf 16 r 113 c 16 r 62 c cmr10.329 @sf 14(1,)m 15(the)m 16(resp)m 1(onses)m 16(of)m 15 r 97 c 15 r 109 c (ultiresp)s 1(onse)m 14(orthogonal)m 14(distance)m 16(regression)m 225 2128 p (problem)s 12(cannot)m 12(simply)m 11 r 98 c 1 r 101 c 13(treated)m 11(as)m cmmi10.329 @sf 12 r 113 c cmr10.329 @sf 14(separate)m 11(observ)m -2(ations)m 10(as)m 12(can)m 12 r 98 c 1 r 101 c 13(done)m 12(for)m 12(ordinary)m 225 2185 p (least)s 13(squares)m 13(when)m 15(the)m cmmi10.329 @sf 13 r 113 c cmr10.329 @sf 16(resp)m 1(onses)m 14(are)m 14(uncorrelated.)m 19(This)m 13(is)m 13 r 98 c 1(ecause)m 15(ODRP)m -3 r 65 c (CK)s 13 r 119 c (ould)s 225 2241 p (then)s 14(treat)m 14(the)m 14 r 118 c -2(ariables)m 12(asso)m 1(ciated)m 13(with)m 14(these)m cmmi10.329 @sf 14 r 113 c cmr10.329 @sf 16(observ)m -2(ations)m 13(as)m 13(unrelated,)m 14(and)m 14(th)m (us)s 13(not)m 225 2298 p (constrain)s 19(the)m 20(errors)m cmmi10.329 @sf 19 r 14 c cmmi8.300 @sf 664 2305 p 105 c cmr10.329 @sf 697 2298 p (in)s cmmi10.329 @sf 20 r 120 c cmmi8.300 @sf 781 2305 p 105 c cmr10.329 @sf 815 2298 p (to)s 19 r 98 c 1 r 101 c 20(the)m 20(same)m 19(for)m 19(eac)m 104 c 19(of)m 19(the)m cmmi10.329 @sf 20 r 113 c cmr10.329 @sf 22 r 111 c 1(ccurrences)m 20(of)m 20(the)m cmmi10.329 @sf 19 r 105 c cmr10.329 @sf (th)s 225 2354 p (observ)s -2(ation.)m 32(The)m 21(user)m 20 r 109 c (ust)s 18(therefore)m 20(indicate)m 19(to)m 20(ODRP)m -3 r 65 c (CK)s 18(when)m 21(the)m 20(observ)m -2(ations)m 225 2411 p (are)s 19 r 109 c (ultiresp)s 1(onse,)m 18(so)m 19(that)m 19(ODRP)m -3 r 65 c (CK)s 18(can)m 20(mak)m 101 c 17(the)m 20(appropriate)m 18(adjustmen)m (ts)s 18(to)m 19(the)m 225 2467 p (estimation)s 13(pro)m 1(cedure.)m 21(\(See)m cmsy10.329 @sf 16 r 120 c cmr10.329 @sf (2.B.ii,)s 13(subroutine)m 15(argumen)m 116 c cmtt10.329 @sf 14(NQ)m cmr10.329 @sf -1(.\))m @eop %%Page: 8 22 8 @bop0 cmbx12.300 @sf [ 40 34 -2 0 39.838] 66 @dc [<01FFC0000FFFF8003F80FE007E003F00FC001F80F8000F80F8000F80F8000F80FC001F807E007F 803FFFFF000FFFFF001FFFFE001FFFFC001FFFE0001E0000001C000000180000001DFE00001FFF 80000F87C0001F03E0003E01F0003E01F0003E01F0003E01F0003E01F0003E01F0003E01F3001F 03E7800F87F78007FFFF8001FE1F00> 32 33 -1 11 28.019] 103 @dc [ 32 35 -2 0 31.133] 104 @dc cmmi10.329 @sf [ 32 31 -2 0 29.182] 80 @dc [<1C00001E00001E00000E00000E00000F00000F0000070000070000078000078000038000038000 E3C38063C3C061E3C071F3C033F9C03FBF801F0F00> 24 20 -1 0 20.507] 114 @dc cmmi8.300 @sf [ 16 23 -1 0 18.372] 107 @dc cmex10.300 @sf [<00E001E001C0038007000F000E001C001C001C003800380078007000700070007000E000E000E0 00E000E000E000E000E000E000E000E000E000E000E000E0007000700070007000780038003800 1C001C001C000E000F000700038001C001E000E0> 16 49 -6 47 19.026] 0 @dc [ 16 49 -1 47 19.026] 1 @dc cmsy10.329 @sf [<07F0003F800FFC00FFC01E3E03FFE0380F07F0F070078FC0386003CF8018E001FF001CC000FF00 0CC000FE000CC0007C000CC000F8000CC001FC000CC003FC000CE003FE001C6007CF0018700FC7 80383C3F83C0701FFF01F1E00FFC00FFC007F0003F80> 40 20 -3 0 45.454] 49 @dc cmbx12.300 @sf [<0007FF0000003FFFC00000FF01F00003FC00380007F0001C000FE0000E001FC00007001F800003 003F800003807F000001807F000001807F00000180FE00000000FE00000000FE00000000FE0000 0000FE00000000FE00000000FE00000000FE00000000FE00000000FE000001807F000001807F00 0003807F000003803F800003801F800007801FC0000F800FE0000F8007F0001F8003FC007F8000 FF01E780003FFFC3800007FE0180> 40 34 -3 0 40.472] 67 @dc [ 24 34 -3 0 31.133] 83 @dc [ 32 32 -2 10 31.133] 112 @dc [<01FF0007FFC01FE1E03F80703F00307E00007E0000FC0000FC0000FC0000FC0000FC0000FC0000 FC0000FC00007C01E07E03F03E03F03F03F01FC3F007FFE001FF80> 24 22 -2 0 24.906] 99 @dc [<7FFC007FFC000FC0000FC0000FC0000FC0000FC0000FC0000FC0000FC0000FC0000FC0000FC000 0FC0000FC0000FC0000FC0000FC0000FC0000FC000FFFC00FFFC000FC0000FC0000FC0000FC000 0FC0000FC0000FC3C00FC7E007E7E007E7E003F7E001FFC0003F80> 24 35 -1 0 17.123] 102 @dc [<1F0000007F80000069C00000FC600000FC300000FC3800007818000000180000000C0000000C00 00000E0000000E0000001F0000001F0000003F8000003F8000007FC000007EC000007EC00000FC 600000FC600001F8300001F8300003F8180003F0180007F01C0007E00C000FE00E000FC006000F C00700FFF01FE0FFF01FE0> 32 32 -1 10 29.576] 121 @dc [<03FFFFF80003FFFFF8000003F800000003F800000003F800000003F800000003F800000003F800 000003F800000003F800000003F800000003F800000003F800000003F800000003F800000003F8 00000003F800000003F800000003F800000003F800000003F800000003F80000C003F800C0C003 F800C0C003F800C0C003F800C0E003F801C0E003F801C06003F801807003F803807803F807807E 03F80F807FFFFFFF807FFFFFFF80> 40 34 -2 0 38.973] 84 @dc [ 24 22 -2 0 22.104] 115 @dc [ 32 35 -2 0 29.576] 107 @dc 8 @bop1 cmr10.329 @sf 0 114 p 56 c 1388(Getting)m 14(Started)m 0 134 p 1725 2 ru cmbx12.300 @sf 0 259 p (1.B.)s 18(Algorithm)m cmr10.329 @sf 0 380 p (The)s 24(algorithm)m 21(implemen)m (ted)s 23(in)m 23(ODRP)m -3 r 65 c (CK)s 22(is)m 23(describ)m 1(ed)m 25(in)m 23([Boggs)m cmti10.329 @sf 22(et)m 24(al.)m cmr10.329 @sf 44 c 25(1987)m 23(and)m 0 436 p (1989].)s 17(Brie\015y)m -3 r 44 c 10(the)m 11(solution)m 10(is)m 10(found)m 11(iterativ)m -1(ely)m 9(using)m 10 r 97 c 11(trust)m 10(region)m 10(Lev)m (en)s 98 c 1(erg-Marquardt)m 0 493 p (metho)s 1(d,)m 19(with)m 18(scaling)m 18(used)m 19(to)m 18(accommo)m 1(date)m 18(problems)m 18(in)m 18(whic)m 104 c 18(estimated)m 18 r 118 c -2(alues)m 17(ha)m 118 c 101 c 0 549 p (widely)s 19 r 118 c -2(arying)m 18(magnitudes.)m 32(The)m 20(Jacobian)m 20(matrices,)m 19(i.e.,)m 19(the)m 20(matrices)m 18(of)m 19(\014rst)m 20(partial)m 0 605 p (deriv)s -2(ativ)m -1(es)m 16(of)m cmmi10.329 @sf 18 r 102 c cmmi8.300 @sf 306 612 p (il)s cmr10.329 @sf 331 605 p 40 c cmmi10.329 @sf 120 c cmmi8.300 @sf 375 612 p 105 c cmr10.329 @sf 401 605 p 43 c cmmi10.329 @sf 13 r 14 c cmmi8.300 @sf 469 612 p 105 c cmr10.329 @sf 483 605 p 59 c cmmi10.329 @sf 8 r 12 c cmr10.329 @sf 2 r 41 c cmmi10.329 @sf 59 c 17 r 105 c cmr10.329 @sf 17 r 61 c 18 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 7 r 58 c 5 r 59 c 8(n;)m cmr10.329 @sf 17(and)m cmmi10.329 @sf 19 r 108 c cmr10.329 @sf 18 r 61 c 18 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 7 r 58 c 5 r 59 c 8 r 113 c 2 r 59 c cmr10.329 @sf 17(with)m 18(resp)m 1(ect)m 18(to)m 18(eac)m 104 c 17(com-)m 0 662 p 112 c 1(onen)m 116 c 15(of)m cmmi10.329 @sf 15 r 12 c cmr10.329 @sf 18(and)m 16(\001,)m 15(are)m 15(computed)m 17(at)m 15(ev)m (ery)s 14(iteration)m 14(either)m 15 r 98 c 121 c 15(\014nite)m 16(di\013erences)m 15(or)m 16 r 98 c 121 c 14 r 97 c 0 718 p (user)s 14(supplied)m 14(subroutine,)m 14(as)m 13(sp)m 1(eci\014ed)m 15 r 98 c 121 c 13(subroutine)m 14(argumen)m 116 c cmtt10.329 @sf 12(JOB)m cmr10.329 @sf 14(\(see)m cmsy10.329 @sf 14 r 120 c cmr10.329 @sf (2.B.ii,)s 12(and)m 14(also)m cmsy10.329 @sf 0 775 p 120 c cmr10.329 @sf (4.A\).)s 18(The)m 14(iterations)m 11(are)m 13(stopp)m 1(ed)m 13(when)m 14(an)m 121 c 12(one)m 13(of)m 13(three)m 13(stopping)m 12(criteria)m 12(are)m 13(met.)m 19(Tw)m 111 c 0 831 p (of)s 15(these)m 16(indicate)m 15(the)m 15(iterations)m 14(ha)m 118 c 101 c 13(con)m 118 c (erged)s 13(to)m 15 r 97 c 16(solution.)m 19(These)m 16(are)m cmti10.329 @sf 15(sum)m 17(of)m 17(squar)m -1(es)m 0 888 p 99 c -1(onver)m -2(gen)m -1 r 99 c -2 r 101 c cmr10.329 @sf 44 c 16(whic)m 104 c 17(indicates)m 18(that)m 17(the)m 19 r 99 c (hange)s 17(in)m 18(the)m 18 r 119 c (eigh)s -1(ted)m 16(sum)m 19(of)m 17(the)m 19(squared)m 18(ob-)m 0 944 p (serv)s -2(ation)m 19(errors)m 19(is)m 20(su\016cien)m (tly)s 18(small,)m 20(and)m cmti10.329 @sf 20 r 112 c -1(ar)m -1(ameter)m 19 r 99 c -1(onver)m -2(genc)m -3 r 101 c cmr10.329 @sf 44 c 19(whic)m 104 c 19(indicates)m 20(the)m 0 1001 p 99 c (hange)s 19(in)m 20(the)m 20(estimated)m 19 r 118 c -2(alues)m 20(of)m cmmi10.329 @sf 19 r 12 c cmr10.329 @sf 22(and)m 21 r 1 c 19(is)m 20(su\016cien)m (tly)s 18(small.)m 34(The)m 20(third)m 20(stopping)m 0 1057 p (criterion)s 14(is)m 15 r 97 c 15(limit)m 13(on)m 15(the)m 16 r 110 c (um)s 98 c 1(er)m 13(of)m 15(iterations.)m 0 1133 p (ODRP)s -3 r 65 c (CK)s 20(\014nds)m 22(the)m 21(solution)m 20(of)m 21(an)m 21(implicit)m 20(orthogonal)m 20(distance)m 21(regression)m 20(problem)m 0 1190 p (using)s 15(the)m 15(classic)m 15(quadratic)m 14 r 112 c 1(enalt)m 121 c 14(function)m 15(metho)m 1(d.)m 20(The)m cmti10.329 @sf 15 r 112 c -1(enalty)m 15(function)m cmr10.329 @sf 15(is)m cmmi10.329 @sf 235 1313 p 80 c cmr10.329 @sf 6 r 40 c cmmi10.329 @sf 12 c 2 r 59 c 8 r 14 c cmr10.329 @sf 2 r 59 c cmmi10.329 @sf 8 r 114 c cmmi8.300 @sf 401 1320 p 107 c cmr10.329 @sf 421 1313 p 41 c 12 r 61 c cmmi8.300 @sf 518 1260 p 110 c cmex10.300 @sf 499 1273 p 88 c cmmi8.300 @sf 501 1364 p 105 c cmr8.300 @sf (=1)s cmex10.300 @sf 567 1278 p 0 c cmmi10.329 @sf 586 1313 p 114 c cmmi8.300 @sf 607 1320 p 107 c cmr10.329 @sf 635 1313 p 91 c cmmi10.329 @sf 102 c cmmi8.300 @sf 670 1320 p 105 c cmr10.329 @sf 684 1313 p 40 c cmmi10.329 @sf 120 c cmmi8.300 @sf 728 1320 p 105 c cmr10.329 @sf 752 1313 p 43 c cmmi10.329 @sf 10 r 14 c cmmi8.300 @sf 817 1320 p 105 c cmr10.329 @sf 832 1313 p 59 c cmmi10.329 @sf 8 r 12 c cmr10.329 @sf 2 r 41 c 93 c cmr6.300 @sf 910 1293 p 84 c cmr10.329 @sf 942 1313 p 91 c cmmi10.329 @sf -1 r 102 c cmmi8.300 @sf 976 1320 p 105 c cmr10.329 @sf 991 1313 p 40 c cmmi10.329 @sf 120 c cmmi8.300 @sf 1035 1320 p 105 c cmr10.329 @sf 1058 1313 p 43 c cmmi10.329 @sf 11 r 14 c cmmi8.300 @sf 1124 1320 p 105 c cmr10.329 @sf 1138 1313 p 59 c cmmi10.329 @sf 8 r 12 c cmr10.329 @sf 2 r 41 c 93 c 9 r 43 c 10 r 91 c cmmi10.329 @sf 14 c cmr6.300 @sf 1307 1295 p 84 c cmmi8.300 @sf 1305 1324 p 105 c cmmi10.329 @sf 1331 1313 p 119 c cmmi8.300 @sf 1359 1320 p 14 c cmmi6.300 @sf 1375 1325 p 105 c cmmi10.329 @sf 1388 1313 p 14 c cmmi8.300 @sf 1408 1320 p 105 c cmr10.329 @sf 1422 1313 p 93 c cmex10.300 @sf 1435 1278 p 1 c cmmi10.329 @sf 1477 1313 p 59 c cmr10.329 @sf 119(\(1)m cmmi10.329 @sf 58 c cmr10.329 @sf (10\))s 0 1443 p (with)s cmti10.329 @sf 15 r 112 c -1(enalty)m 14(term)m cmmi8.300 @sf 532 1474 p 110 c cmex10.300 @sf 513 1487 p 88 c cmmi8.300 @sf 515 1578 p 105 c cmr8.300 @sf (=1)s cmmi10.329 @sf 581 1527 p 114 c cmmi8.300 @sf 602 1534 p 107 c cmr10.329 @sf 630 1527 p 91 c cmmi10.329 @sf 102 c cmmi8.300 @sf 665 1534 p 105 c cmr10.329 @sf 679 1527 p 40 c cmmi10.329 @sf 120 c cmmi8.300 @sf 723 1534 p 105 c cmr10.329 @sf 747 1527 p 43 c cmmi10.329 @sf 10 r 14 c cmmi8.300 @sf 812 1534 p 105 c cmr10.329 @sf 827 1527 p 59 c cmmi10.329 @sf 8 r 12 c cmr10.329 @sf 2 r 41 c 93 c cmr6.300 @sf 905 1507 p 84 c cmr10.329 @sf 937 1527 p 91 c cmmi10.329 @sf -1 r 102 c cmmi8.300 @sf 971 1534 p 105 c cmr10.329 @sf 986 1527 p 40 c cmmi10.329 @sf 120 c cmmi8.300 @sf 1030 1534 p 105 c cmr10.329 @sf 1053 1527 p 43 c cmmi10.329 @sf 11 r 14 c cmmi8.300 @sf 1119 1534 p 105 c cmr10.329 @sf 1133 1527 p 59 c cmmi10.329 @sf 8 r 12 c cmr10.329 @sf 2 r 41 c 93 c 0 1641 p (and)s cmti10.329 @sf 15 r 112 c -1(enalty)m 15 r 112 c -1(ar)m -1(ameter)m cmmi10.329 @sf 14 r 114 c cmmi8.300 @sf 478 1648 p 107 c cmr10.329 @sf 498 1641 p 46 c 20 r 65 c 16(sequence)m 16(of)m 15(unconstrained)m 15(minimization)m 13(problems)m 719 1737 p (min)s cmmi8.300 @sf 733 1767 p 12 c 2(;\016)m cmmi10.329 @sf 803 1737 p 80 c cmr10.329 @sf 6 r 40 c cmmi10.329 @sf 12 c 2 r 59 c 8 r 14 c cmr10.329 @sf 2 r 59 c cmmi10.329 @sf 8 r 114 c cmmi8.300 @sf 969 1744 p 107 c cmr10.329 @sf 988 1737 p 41 c 0 1852 p (is)s 22(then)m 23(solv)m (ed)s 21(for)m 22 r 97 c 22(sequence)m 24(of)m 22 r 118 c -2(alues)m 22(of)m 22(the)m 23 r 112 c 1(enalt)m 121 c 21(parameter)m cmmi10.329 @sf 22 r 114 c cmmi8.300 @sf 1389 1859 p 107 c cmr10.329 @sf 1432 1852 p (tending)s 23(to)m cmsy10.329 @sf 22 r 49 c cmmi10.329 @sf 58 c cmr10.329 @sf 0 1909 p (These)s 21(problems)m 20(are)m 20(equiv)m -2(alen)m 116 c 18(to)m 19(an)m 21(explicit)m 19(orthogonal)m 19(distance)m 20(regression)m 19(problem)m 0 1965 p (with)s cmmi10.329 @sf 16 r 15 c cmmi8.300 @sf 123 1972 p 105 c cmsy10.329 @sf 154 1965 p 17 c cmmi10.329 @sf 16 r 102 c cmmi8.300 @sf 227 1972 p 105 c cmr10.329 @sf 241 1965 p 40 c cmmi10.329 @sf 120 c cmmi8.300 @sf 285 1972 p 105 c cmr10.329 @sf 310 1965 p 43 c cmmi10.329 @sf 12 r 14 c cmmi8.300 @sf 377 1972 p 105 c cmr10.329 @sf 391 1965 p 59 c cmmi10.329 @sf 8 r 12 c cmr10.329 @sf 2 r 41 c 16 r 46 c 25(As)m cmmi10.329 @sf 17 r 114 c cmmi8.300 @sf 602 1972 p 107 c cmsy10.329 @sf 639 1965 p 33 c 16 r 49 c cmmi10.329 @sf 59 c 17 r 15 c cmmi8.300 @sf 793 1972 p 105 c cmsy10.329 @sf 823 1965 p 33 c cmr10.329 @sf 16 r 48 c cmmi10.329 @sf 59 c 24 r 105 c cmr10.329 @sf 15 r 61 c 16 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 8 r 58 c 5 r 59 c 8 r 110 c cmr10.329 @sf 44 c 16(and)m 18(the)m 17(solution)m 15(to)m 17(\(1.10\))m 0 2022 p (will)s 14(approac)m 104 c 14(that)m 15(of)m 14(the)m 16(implicit)m 14(problem)m 15(de\014ned)m 16 r 98 c 121 c 15(\(1.9\).)m 18(See,)m 16(e.g.,)m 14([Gill)m cmti10.329 @sf 13(et)m 17(al.)m cmr10.329 @sf 44 c 14(1981])m 0 2078 p (for)s 15(further)m 15(discussion)m 14(of)m 15 r 112 c 1(enalt)m 121 c 14(function)m 15(metho)m 1(ds.)m cmbx12.300 @sf 0 2223 p (1.C.)s 18(Sp)m 2(ecifying)m 17(the)m 18 r 84 c -4(ask)m cmr10.329 @sf 0 2344 p (The)s 15(user)m 16(has)m 15(the)m 15(option)m 15(of)m 14(sp)m 1(ecifying)m 15(sev)m (eral)s 14(di\013eren)m 116 c 13(asp)m 1(ects)m 16(of)m 14(the)m 16(problem:)m 78 2411 p (1.)s 22(whether)m 16(the)m 15(\014t)m 15(is)m 15(to)m 15 r 98 c 1 r 101 c 16 r 98 c 121 c 14(explicit)m 14(or)m 15(implicit)m 14(orthogonal)m 13(distance)m 15(regression,)m 14(or)m 136 2467 p 98 c 121 c 14(ordinary)m 15(least)m 14(squares)m 15(\(see)m cmsy10.329 @sf 15 r 120 c cmr10.329 @sf (1.A\);)s @eop %%Page: 9 23 9 @bop0 cmmi10.329 @sf [<01C0000001C0000001E0000001E0000001F0000001F8000001F8000003EC000003CC000003C600 0003C3000003C3000003C1800003C1800003C0C00003C0600007C0600007803000078030000780 180007800C0007800C00078006000780060007800300078001800F8001800F0000C00F0000E00F 8001F8FFF807FFFFF807FF> 32 32 -2 1 26.515] 86 @dc [<0FC0003FF000787800701C00E00E00E00F00E00700E00380E00380F003807003C07001C07801C0 3801C03C01C01E03800F878007FFFE03FFFE00FFFE> 24 20 -2 0 25.973] 27 @dc cmtt10.329 @sf [ 24 28 -1 0 23.863] 76 @dc cmbx12.300 @sf [<0007FC0000003FFF800000FC07E00003F001F80007E000FC000FC0007E001F80003F003F80003F 803F00001F807F00001FC07F00001FC07E00000FC0FE00000FE0FE00000FE0FE00000FE0FE0000 0FE0FE00000FE0FE00000FE0FE00000FE0FE00000FE0FE00000FE07E00000FC07E00000FC07F00 001FC03F00001F803F00001F801F80003F001F80003F000FC0007E0007E000FC0003F001F80000 FC07E000003FFF80000007FC0000> 40 34 -3 0 42.087] 79 @dc [ 40 34 -2 0 41.798] 82 @dc [ 40 34 -2 0 43.874] 75 @dc [<0003FF00C0003FFFE3C000FF80FFC001FC003FC007F0003FC00FE0001FC01FC0001FC01F80001F C03F80001FC07F00001FC07F00001FC07F00001FC0FE000FFFFCFE000FFFFCFE00000000FE0000 0000FE00000000FE00000000FE00000000FE00000000FE00000000FE000000C07F000000C07F00 0001C07F000001C03F800001C01F800003C01FC00007C00FE0000FC007F0001FC001FC003FC000 FF80F3C0003FFFE1C00003FF00C0> 40 34 -3 0 44.047] 71 @dc [<03FC7FC00FFF7FC00FC3FE001F81FE001F80FE001F80FE001F807E001F807E001F807E001F807E 001F807E001F807E001F807E001F807E001F807E001F807E001F807E001F807E001F807E001F80 7E00FF83FE00FF83FE00> 32 22 -2 0 31.133] 117 @dc 9 @bop1 cmr10.329 @sf 225 114 p (Getting)s 14(Started)m 1388 r 57 c 225 134 p 1725 2 ru 303 259 p (2.)s 22(whether)m 13(the)m 12(necessary)m 13(Jacobian)m 12(matrices)m 11(should)m 12 r 98 c 1 r 101 c 13(appro)m (ximat)s -1(ed)m 11 r 98 c 121 c 11(ODRP)m -3 r 65 c (CK)s 361 315 p (using)s 17(forw)m (a)s -1(rd)m 15(or)m 16(cen)m (tral)s 15(\014nite)m 17(di\013erences,)m 17(or)m 16(whether)m 17(the)m 16(user)m 17(has)m 17(supplied)m 17(the)m 361 372 p (co)s 1(de)m 15(to)m 13(compute)m 14(them,)m 13(and,)m 14(if)m 13(suc)m 104 c 13(co)m 1(de)m 15(has)m 13 r 98 c 1(een)m 15(pro)m (vided)s 13 r 98 c 121 c 12(the)m 14(user,)m 14(whether)m 361 428 p (it)s 15(should)m 15 r 98 c 1 r 101 c 16 r 99 c (hec)s 107 c -1(ed)m 14(\(see)m cmsy10.329 @sf 15 r 120 c cmr10.329 @sf (4.A\);)s 303 494 p (3.)s 22(whether)m 20(the)m 19(co)m 118 c -2(a)m -1(riance)m 17(matrix)m cmmi10.329 @sf 18 r 86 c cmmi8.300 @sf 1024 501 p 12 c cmr10.329 @sf 1066 494 p (and)s 19(standard)m 19(deviations)m cmmi10.329 @sf 18 r 27 c cmmi8.300 @sf 1598 501 p 12 c cmr10.329 @sf 1640 494 p (should)s 19 r 98 c 1 r 101 c 20(com-)m 361 551 p (puted)s 23(for)m 21(the)m 22(estimators)m 19(of)m cmmi10.329 @sf 22 r 12 c cmr10.329 @sf 2 r 44 c 23(and)m 22(whether)m 21(the)m 22(Jacobian)m 22(matrices)m 21(should)m 21 r 98 c 1 r 101 c 361 607 p (recalculated)s 15(at)m 15(the)m 15(solution)m 14(for)m 14(this)m 15(computation)m 14(\(see)m cmsy10.329 @sf 15 r 120 c cmr10.329 @sf 1(4.B\);)m 303 673 p (4.)s 22(whether)m 20(the)m 20(errors)m 19 r 1 c 20(ha)m 118 c 101 c 18 r 98 c 1(een)m 21(initiali)m -1(zed)m 19 r 98 c 121 c 19(the)m 20(user)m 20(\(see)m cmsy10.329 @sf 20 r 120 c cmr10.329 @sf (1.E,)s 20(and)m cmsy10.329 @sf 20 r 120 c cmr10.329 @sf (2.B.ii,)s 361 730 p (subroutine)s 15(argumen)m (ts)s cmtt10.329 @sf 14(JOB)m cmr10.329 @sf 15(and)m cmtt10.329 @sf 15(WORK)m cmr10.329 @sf -1(\);)m 303 796 p (5.)s 22(whether)m 15(the)m 15(\014t)m 15(is)m 14 r 97 c 15(\\restart,")m 12(i.e.,)m 14(whether)m 15(the)m 15(\014t)m 14(will)m 14(use)m 15(information)m 13(preserv)m (ed)s 361 852 p (in)s 17(the)m 16 r 118 c (ectors)s cmtt10.329 @sf 14(BETA)m cmr10.329 @sf 44 c cmtt10.329 @sf 16(WORK)m cmr10.329 @sf 16(and)m cmtt10.329 @sf 16(IWORK)m cmr10.329 @sf 16(to)m 16(con)m (tin)s -1(ue)m 15(from)m 15 r 97 c 16(previously)m 16(found)m 16 r 112 c 1(oin)m 116 c 361 909 p (\(see)s 16(Chapter)m 14(3\);)m 303 975 p (6.)s 22(whether)m 16(the)m 15(data)m 15(are)m 14 r 109 c (ultiresp)s 1(onse)m 14(or)m 15(not;)m 303 1041 p (7.)s 22(whether)m 17(subsets)m 17(of)m 17(the)m 17(unkno)m (wns)s cmmi10.329 @sf 16 r 12 c cmr10.329 @sf 19(and)m 17 r 1 c 16(should)m 17 r 98 c 1 r 101 c 18(treated)m 16(as)m 17(constan)m (ts)s 15(with)m 361 1098 p (their)s 18 r 118 c -2(alues)m 17(held)m 18(\\\014xed,")m 19(allo)m -1(wing)m 16(the)m 18(user)m 18(to)m 17(examine)m 18(the)m 18(results)m 17(obtained)m 18 r 98 c 121 c 361 1154 p (estimating)s 17(subsets)m 19(of)m 17(the)m 19(parameters)m 17(of)m 18 r 97 c 18(general)m 18(mo)m 1(del)m 19(without)m 17(rewriting)m 17(the)m 361 1211 p (mo)s 1(del)m 17(subroutine,)m 16(and)m 16(allo)m -1(wing)m 14(the)m 16(user)m 17(to)m 16(sp)m 1(ecify)m 16(that)m 16(some)m 16(comp)m 1(onen)m (ts)s 15(of)m cmmi10.329 @sf 16 r 88 c cmr10.329 @sf 361 1267 p (are)s 15(to)m 15 r 98 c 1 r 101 c 16(treated)m 14(as)m 15(if)m 15(they)m 15(are)m 15(kno)m (wn)s 14(exactly;)m 303 1333 p (8.)s 22(whether)m 16 r 119 c (eigh)s -1(ted)m 13(or)m 15(un)m 119 c (ei)s -1(gh)m -1(ted)m 13(analysis)m 14(should)m 16 r 98 c 1 r 101 c 15 r 112 c 1(erformed)m 16(\(see)m cmsy10.329 @sf 15 r 120 c cmr10.329 @sf (1.F\);)s 14(and)m 303 1400 p (9.)s 22(whether)m 15(the)m 16(unkno)m (wns)s cmmi10.329 @sf 14 r 12 c cmr10.329 @sf 17(and)m 15 r 1 c 15(should)m 14 r 98 c 1 r 101 c 16(scaled)m 15(to)m 14(comp)m 1(ensate)m 15(for)m 15(cases)m 15(where)m 361 1456 p (their)s 15 r 118 c -2(alues)m 14 r 118 c -2(ary)m 15(widely)m 14(in)m 15(magnitude)m 15(\(see)m cmsy10.329 @sf 15 r 120 c cmr10.329 @sf (4.D\).)s 225 1532 p (The)s 14(\014rst)m 14 r 53 c 14(of)m 13(these)m 15(options)m 13(are)m 14(sp)m 1(eci\014ed)m 15 r 98 c 121 c 13(ODRP)m -3 r 65 c (CK)s 12(subroutine)m 14(argumen)m 116 c cmtt10.329 @sf 13(JOB)m cmr10.329 @sf -1 r 59 c 14 r 109 c (ul-)s 225 1589 p (tiresp)s 1(onse)m 12(data)m 11(are)m 12(indicated)m 12 r 98 c 121 c 10(subroutine)m 12(argumen)m 116 c cmtt10.329 @sf 11(NQ)m cmr10.329 @sf -1 r 59 c 13(parameter)m 11(\\\014xing")m 11(is)m 12(sp)m 1(eci\014ed)m 225 1645 p 98 c 121 c 11(subroutine)m 12(argumen)m (ts)s cmtt10.329 @sf 10(IFIXB)m cmr10.329 @sf 12(and)m cmtt10.329 @sf 12(IFIXX)m cmr10.329 @sf -1 r 59 c 13 r 119 c (eigh)s -1(ti)m -1(ng)m 10(is)m 12(con)m (troll)s -1(ed)m 11 r 98 c 121 c 11(argumen)m (ts)s cmtt10.329 @sf 10(WE)m cmr10.329 @sf 12(and)m cmtt10.329 @sf 225 1702 p (WD)s cmr10.329 @sf 59 c 13(and)m 13(scaling)m 12(is)m 13(con)m (trol)s -1(led)m 11 r 98 c 121 c 12(argumen)m (ts)s cmtt10.329 @sf 11(SCLB)m cmr10.329 @sf 13(and)m cmtt10.329 @sf 13(SCLD)m cmr10.329 @sf -1 r 46 c 19 r 65 c 13(detailed)m 13(discussion)m 12(of)m 13(eac)m 104 c 225 1758 p (of)s 15(these)m 15(subroutine)m 15(argumen)m (ts)s 14(can)m 15 r 98 c 1 r 101 c 16(found)m 15(in)m cmsy10.329 @sf 15 r 120 c cmr10.329 @sf 1(2.B.ii.)m cmbx12.300 @sf 225 1904 p (1.D.)s 18(ODRP)m -4 r 65 c -1(CK)m 18(Generated)m 18(Results)m cmr10.329 @sf 225 2025 p (Results)s 15(generated)m 15 r 98 c 121 c 15(ODRP)m -3 r 65 c (CK)s 13(are)m 15(returned)m 16(to)m 14(the)m 16(user)m 15(in)m 15(four)m 15 r 119 c 97 c -1(ys:)m cmsy10.329 @sf 316 2091 p 15 c cmr10.329 @sf 22(the)m 16(estimated)m 14(parameter)m 14 r 118 c -2(alues)m 1006 2080 p 94 c cmmi10.329 @sf 1000 2092 p 12 c cmr10.329 @sf 1043 2091 p (are)s 15(returned)m 15(in)m 15(subroutine)m 16(argumen)m 116 c cmtt10.329 @sf 13(BETA)m cmr10.329 @sf -1 r 59 c cmsy10.329 @sf 316 2158 p 15 c cmr10.329 @sf 22(the)m 16(stopping)m 14(condition)m 15(is)m 14(returned)m 16(in)m 15(subroutine)m 15(argumen)m 116 c cmtt10.329 @sf 14(INFO)m cmr10.329 @sf -1 r 59 c cmsy10.329 @sf 316 2224 p 15 c cmr10.329 @sf 22(the)m 18(computed)m 18(results)m 17 r 97 c 118 c -3(ail)m -1(able)m 16(at)m 16(the)m 18(time)m 17(the)m 17(job)m 18(stopp)m 1(ed)m 18(are)m 17(returned)m 18(in)m 17(the)m 361 2280 p 118 c (ectors)s 14(sp)m 1(eci\014ed)m 16 r 98 c 121 c 14(subroutine)m 15(argumen)m (ts)s cmtt10.329 @sf 14(WORK)m cmr10.329 @sf 14(and)m cmtt10.329 @sf 16(IWORK)m cmr10.329 @sf -1 r 59 c 15(and)m cmsy10.329 @sf 316 2347 p 15 c cmr10.329 @sf 22(selected)m 16(results)m 14(are)m 15(summarized)m 15(in)m 15(automatically)m 13(generated)m 15(rep)m 1(orts.)m @eop %%Page: 10 24 10 @bop0 cmtt10.329 @sf [ 24 28 -1 0 23.863] 80 @dc 10 @bop1 cmr10.329 @sf 0 114 p (10)s 1365(Getting)m 14(Started)m 0 134 p 1725 2 ru 0 259 p (Argumen)s (ts)s cmtt10.329 @sf 10(BETA)m cmr10.329 @sf -1 r 44 c cmtt10.329 @sf 12(INFO)m cmr10.329 @sf 44 c cmtt10.329 @sf 11(WORK)m cmr10.329 @sf 11(and)m cmtt10.329 @sf 12(IWORK)m cmr10.329 @sf 10(are)m 11(discussed)m 12(in)m 12(detail)m 10(in)m cmsy10.329 @sf 11 r 120 c cmr10.329 @sf 1(2.B.ii.)m 17(The)m 11(remainder)m 0 315 p (of)s 15(this)m 14(section)m 15(describ)m 1(es)m 16(ODRP)m -3 r 65 c (CK's)s 13(automatically)m 13(generated)m 15(rep)m 1(orts.)m 0 391 p (ODRP)s -3 r 65 c (CK)s 12(can)m 13(generate)m 13 r 116 c 119 c -1 r 111 c 11(di\013eren)m 116 c 11 r 116 c (yp)s 1(es)m 12(of)m 13(rep)m 1(orts.)m 19(The)m 13(\014rst)m 13(is)m 13(an)m cmti10.329 @sf 13(err)m -1(or)m 13 r 114 c -1(ep)m -1(ort)m cmr10.329 @sf 44 c 12(and)m 0 448 p (the)s 17(second)m 17(is)m 16 r 97 c cmti10.329 @sf 16 r 99 c -1(omputation)m 17 r 114 c -1(ep)m -1(ort)m cmr10.329 @sf 46 c 22(These)m 17(are)m 16(written)m 16(to)m 16(the)m 16(logical)m 15(units)m 16(sp)m 1(eci\014ed)m 18 r 98 c 121 c 0 504 p (subroutine)s 18(argumen)m (ts)s cmtt10.329 @sf 16(LUNERR)m cmr10.329 @sf 17(and)m cmtt10.329 @sf 18(LUNRPT)m cmr10.329 @sf -1 r 44 c 19(resp)m 1(ectiv)m (ely)s -4 r 46 c 26(The)m 19(user)m 18(can)m 18(asso)m 1(ciate)m 17(these)m 0 560 p (units)s 18(with)m 17 r 97 c 18(\014le)m 18(using)m 18 r 97 c 17 r 70 c -3(ortran)m cmtt10.329 @sf 16(OPEN)m cmr10.329 @sf 18(statemen)m (t)s -1 r 46 c 27(If)m 18(the)m 18(user)m 18(sets)m 18(one)m 18(or)m 18(the)m 18(other)m 17(of)m 0 617 p (these)s 14(units)m 14(to)m 13 r 97 c 13(negativ)m 101 c 12 r 118 c -2(alue,)m 13(then)m 14(the)m 14(corresp)m 1(onding)m 14(rep)m 1(ort)m 14(will)m 12 r 98 c 1 r 101 c 15(generated)m 13(on)m 14(unit)m 0 673 p (6.)s 27(On)m 18(most)m 16(systems,)m 18(unit)m 17 r 54 c 17(is)m 17(\\standard)m 17(output,")m 17(whic)m 104 c 17(for)m 17(an)m 17(\\in)m (teracti)s -1 r 118 c -1(e")m 15(run)m 18(will)m 0 730 p 98 c 1 r 101 c 18(the)m 17(screen.)m 25(If)m 17(the)m 17(user)m 17(sets)m 17(one)m 17(or)m 16(the)m 17(other)m 17(of)m 16(these)m 18(units)m 16(to)m 16(0,)m 17(then)m 17(generation)m 16(of)m 0 786 p (the)s 15(corresp)m 1(onding)m 15(rep)m 1(ort)m 15(is)m 15(suppressed.)m 0 862 p (ODRP)s -3 r 65 c (CK's)s 11(computation)m 13(rep)m 1(orts)m 12(\(see)m cmsy10.329 @sf 14 r 120 c cmr10.329 @sf (1.D.ii)s 11 r 98 c 1(elo)m (w\))s 11(can,)m 14(at)m 12(the)m 14(user's)m 13(option,)m 12 r 98 c 1 r 101 c 14(writ-)m 0 919 p (ten)s 15(sim)m (ulta)s -1(neously)m 13(to)m 15 r 98 c 1(oth)m 15(the)m 15(\014le)m 15(asso)m 1(ciated)m 14(with)m 14(the)m 15(unit)m 15(sp)m 1(eci\014ed)m 16 r 98 c 121 c cmtt10.329 @sf 13(LUNRPT)m cmr10.329 @sf 14(and)m 16(to)m 0 975 p (unit)s 15 r 54 c 14(\(assuming)m cmtt10.329 @sf 14(LUNRPT)m cmr10.329 @sf 14(do)m 1(es)m 15(not)m 15(sp)m 1(ecify)m 15(unit)m 15(6\).)m 19(This)m 14(option,)m 14(in)m 118 c (o)s -1 r 107 c -1(ed)m 13 r 98 c 121 c 14(ODRP)m -3 r 65 c (CK)s 0 1032 p (subroutine)s 15(argumen)m 116 c cmtt10.329 @sf 14(IPRINT)m cmr10.329 @sf -1 r 44 c 15(enables)m 16(the)m 15(user)m 16(to)m 14(monitor)m 14(ODRP)m -3 r 65 c (CK's)s 14(progress)m 15(in)m (ter-)s 0 1088 p (activ)s (ely)s 17(while)m 19(still)m 17(preserving)m 19(the)m 20(results)m 18(in)m 20 r 97 c 18(\014le)m 20(for)m 18(future)m 20(reference.)m 32(The)m 20(option)m 18(is)m 0 1145 p (esp)s 1(ecially)m 15(useful)m 16(when)m 15(the)m 16(user's)m 15(mo)m 1(del)m 15(is)m 15(time)m 15(consuming)m 15(and)m 16(the)m 15(user)m 16(is)m 15(in)m (teracti)s -1 r 118 c -1(ely)m 0 1201 p (exp)s 1(erimen)m (ting)s 18(with)m 19(starting)m 17 r 118 c -2(alues)m 19(and)m 19(other)m 19(ODRP)m -3 r 65 c (CK)s 18(options:)m 28(results)m 18(prin)m (ted)s 19(to)m 0 1257 p (the)s 14(screen)m 14(can)m 13 r 98 c 1 r 101 c 15(used)m 14(to)m 13(terminate)m 12(ine\013ectiv)m 101 c 12(or)m 13(incorrect)m 13(runs,)m 14(while)m 13(results)m 13(stored)m 13(on)m 0 1314 p (the)s 14(logical)m 13(unit)m 13(sp)m 1(eci\014ed)m 16 r 98 c 121 c cmtt10.329 @sf 13(LUNRPT)m cmr10.329 @sf 13(can)m 14 r 98 c 1 r 101 c 15(used)m 15(to)m 13(preserv)m 101 c 14(the)m 14(successful)m 14(exp)m 1(erimen)m (ts.)s cmbx10.329 @sf 0 1454 p (1.D.i.)s 16(Error)m 16(Rep)m 1(orts)m cmr10.329 @sf 0 1559 p (Error)s 18(rep)m 1(orts)m 19(iden)m (tify)s 17(incorrect)m 19(user)m 19(supplied)m 20(information)m 17(passed)m 19(to)m 19(ODRP)m -3 r 65 c (CK)s 18(that)m 0 1615 p (prev)s (en)s (ts)s 15(the)m 18(computations)m 16(from)m 17 r 98 c 1(eginning.)m 27 r 70 c -3(or)m 16(example,)m 18(an)m 17(error)m 17(rep)m 1(ort)m 17(will)m 16 r 98 c 1 r 101 c 19(gen-)m 0 1672 p (erated)s 17(if)m 16(the)m 17(user)m 17(sp)m 1(eci\014es)m 18(the)m 17 r 110 c (um)s -1 r 98 c 1(er)m 16(of)m 16(observ)m -2(ations)m 15(to)m 17 r 98 c 1 r 101 c 17(an)m 17(ob)m (viously)s 15(meaningless)m 0 1728 p 110 c (um)s 98 c 1(er,)m 15(suc)m 104 c 16(as)m 17 r 97 c 16(negativ)m 101 c 15 r 118 c -2(alue.)m 25(Error)m 15(rep)m 1(orts)m 17(are)m 16(self)m 17(explanatory)m -3 r 44 c 15(and)m 17(are)m 17(not)m 16(dis-)m 0 1785 p (cussed)s 18(further)m 17(here.)m 26(The)m 18(information)m 15(written)m 17(in)m 17(the)m 17(error)m 16(rep)m 1(orts)m 17(is)m 17(also)m 16(enco)m 1(ded)m 19(and)m 0 1841 p (returned)s 16(to)m 14(the)m 15(user)m 16(in)m 15(subroutine)m 15(argumen)m 116 c cmtt10.329 @sf 13(INFO)m cmr10.329 @sf 46 c 20(\(See)m cmsy10.329 @sf 15 r 120 c cmr10.329 @sf (2.B.ii.\))s cmbx10.329 @sf 0 1981 p (1.D.ii.)s 15(Computation)m 18(Rep)m 1(orts)m cmr10.329 @sf 0 2086 p (Computation)s 14(rep)m 1(orts)m 15(are)m 14(divided)m 16(in)m (to)s 13(three)m 15(sections:)m cmbx10.329 @sf 74 2152 p (a.)s cmr10.329 @sf 22(the)m 16(initial)m 13(rep)m 1(ort,)m cmbx10.329 @sf 70 2219 p (b.)s cmr10.329 @sf 22(the)m 16(iteration)m 13(rep)m 1(ort,)m 15(and)m cmbx10.329 @sf 76 2285 p (c.)s cmr10.329 @sf 22(the)m 16(\014nal)m 15(rep)m 1(ort.)m 0 2361 p (Eac)s 104 c 14(of)m 15(these)m 15(can)m 16 r 98 c 1 r 101 c 15(either)m 15(\\short")m 14(or)m 15(\\long".)m @eop %%Page: 11 25 11 @bop0 cmr10.329 @sf [<40E0E3F07FF83F1C1C08> 16 5 -4 -25 22.727] 126 @dc cmtt10.329 @sf [ 24 28 -1 0 23.863] 77 @dc cmmi10.329 @sf [ 24 32 -2 0 23.663] 107 @dc cmsy10.329 @sf [<07E01FF83C3C700E6006E007C003C003C003C003C003C003E0076006700E3C3C1FF807E0> 16 18 -3 -2 22.727] 14 @dc 11 @bop1 cmr10.329 @sf 225 114 p (Getting)s 14(Started)m 1365(11)m 225 134 p 1725 2 ru cmbx10.329 @sf 225 259 p (1.D.ii.a.)s 15(Initial)m 17(Rep)m 1(orts)m cmr10.329 @sf 225 364 p (ODRP)s -3 r 65 c (CK's)s 11(initial)m 11(rep)m 1(ort)m 13(iden)m (ti\014es)s 12(the)m 13(output)m 13(for)m 12(future)m 13(reference,)m 14(and)m 13(pro)m (vides)s 12(infor-)m 225 420 p (mation)s 14(that)m 15(should)m 15(enable)m 15(the)m 15(user)m 16(to)m 14 r 118 c (erify)s 14(that)m 14(the)m 15(problem)m 15 r 119 c (as)s 14(sp)m 1(eci\014ed)m 16(correctly)m -3 r 46 c 225 496 p (The)s cmti10.329 @sf 15(short)m 17(initial)m 16 r 114 c -1(ep)m -2(ort)m cmr10.329 @sf 14(is)m 15(sho)m (wn)s 13(in)m cmsy10.329 @sf 16 r 120 c cmr10.329 @sf (2.C.i.c.)s 18(It)m 15(includes)m cmsy10.329 @sf 316 563 p 15 c cmr10.329 @sf 22(the)m 19 r 118 c -2(alues)m cmmi10.329 @sf 17 r 110 c cmr10.329 @sf 44 c cmmi10.329 @sf 19 r 109 c cmr10.329 @sf 44 c cmmi10.329 @sf 19 r 112 c cmr10.329 @sf 18(and)m cmmi10.329 @sf 19 r 113 c cmr10.329 @sf 2 r 44 c 18(the)m 19 r 110 c (um)s 98 c 1(er)m 19 r 126 c cmmi10.329 @sf -26 r 110 c cmr10.329 @sf 19(of)m 18(observ)m -2(ations)m 16(with)m 18(nonzero)m 19 r 119 c (eigh)s -1(t)m -1(s,)m 361 619 p (and)s 16(the)m 15 r 110 c (um)s 98 c 1(er)m 17 r 126 c cmmi10.329 @sf -26 r 112 c cmr10.329 @sf 15(of)m 14(parameters)m cmmi10.329 @sf 15 r 12 c cmr10.329 @sf 17(actually)m 14 r 98 c 1(eing)m 15(estimated;)m cmsy10.329 @sf 316 685 p 15 c cmr10.329 @sf 22(the)m 17 r 118 c -2(alues)m 15(sp)m 1(eci\014ed)m 17 r 98 c 121 c 15(ODRP)m -3 r 65 c (CK)s 15(subroutine)m 16(argumen)m (ts)s cmtt10.329 @sf 14(JOB)m cmr10.329 @sf 44 c cmtt10.329 @sf 16(NDIGIT)m cmr10.329 @sf -1 r 44 c cmtt10.329 @sf 16(TAUFAC)m cmr10.329 @sf -1 r 44 c cmtt10.329 @sf 361 742 p (SSTOL)s cmr10.329 @sf 44 c cmtt10.329 @sf 19(PARTOL)m cmr10.329 @sf -1 r 44 c 19(and)m cmtt10.329 @sf 19(MAXIT)m cmr10.329 @sf -1 r 44 c 20(that)m 18(indicate,)m 18(resp)m 1(ectiv)m (ely)s -3 r 44 c 17(the)m 19(requested)m 19(task,)m 19(the)m 361 798 p 110 c (um)s 98 c 1(er)m 16(of)m 16(\\go)m 1 r 111 c 1(d")m 17(digits)m 16(in)m 17(the)m 17(user's)m 17(function)m 17(results,)m 16(the)m 17(stopping)m 17(criteria)m 16(for)m 361 855 p (testing)s 17(for)m 16(sum)m 18(of)m 17(squares)m 17(con)m 118 c -1(ergence,)m 16(the)m 18(stopping)m 16(criteria)m 16(for)m 17(testing)m 16(for)m 17(pa-)m 361 911 p (rameter)s 15(con)m 118 c -1(ergence,)m 14(and)m 15(the)m 15(maxim)m (um)s 14 r 110 c (um)s -1 r 98 c 1(er)m 14(of)m 15(iterations)m 13 r 112 c 1(ermitted;)m 15(and)m cmsy10.329 @sf 316 977 p 15 c cmr10.329 @sf 22(the)m 17 r 119 c (eigh)s -1(t)m -1(ed)m 15(sum)m 16(of)m 16(the)m 16(squared)m 17(errors)m cmmi10.329 @sf 15 r 83 c cmr10.329 @sf 3 r 40 c cmmi10.329 @sf 12 c 2 r 59 c 8 r 14 c cmr10.329 @sf 2(\),)m cmmi10.329 @sf 14 r 83 c cmmi8.300 @sf 1353 984 p 14 c cmr10.329 @sf 1372 977 p 40 c cmmi10.329 @sf 12 c 2 r 59 c 8 r 14 c cmr10.329 @sf 2 r 41 c 15(and)m cmmi10.329 @sf 16 r 83 c cmmi8.300 @sf 1611 984 p 15 c cmr10.329 @sf 1627 977 p 40 c cmmi10.329 @sf 12 c 2 r 59 c 8 r 14 c cmr10.329 @sf 2(\),)m 15(ev)m -2(aluated)m 361 1034 p (at)s 15(the)m 15(initial)m 14 r 118 c -2(alues)m 14(of)m cmmi10.329 @sf 15 r 12 c cmr10.329 @sf 17(and)m 15(\001.)m 225 1110 p (The)s cmti10.329 @sf 16(long)m 15(initial)m 16 r 114 c -1(ep)m -1(ort)m cmr10.329 @sf 44 c 14(sho)m (wn)s 14(in)m cmsy10.329 @sf 15 r 120 c cmr10.329 @sf (2.C.ii.c)s 13(and)m cmsy10.329 @sf 16 r 120 c cmr10.329 @sf (2.C.iii.c,)s 13(includes)m 16(all)m 14(the)m 15(information)m 14(in)m 225 1166 p (the)s 18(short)m 17(initial)m 17(rep)m 1(ort)m 17(and,)m 19(in)m 18(addition,)m 17(includes)m 18 r 97 c 18(brief)m 18(summary)m 17(of)m 18(the)m 18(information)m 225 1223 p (sp)s 1(eci\014ed)m 19(for)m 17(the)m 17(function)m 18(parameters)m cmmi10.329 @sf 17 r 12 c cmr10.329 @sf 2 r 44 c 18(and)m 17(also)m 17(information)m 16(ab)m 1(out)m 17(the)m 18(user)m 18(supplied)m 225 1279 p 118 c -2(alues)m 14(for)m 15(the)m cmmi10.329 @sf 15 r 88 c cmr10.329 @sf 19(and)m cmmi10.329 @sf 15 r 89 c cmr10.329 @sf 26(data.)m 19(This)m 15(information)m 13(includes)m cmsy10.329 @sf 316 1346 p 15 c cmr10.329 @sf 22(the)m 16(starting)m 13(parameter)m 14 r 118 c -2(alues)m cmmi10.329 @sf 15 r 12 c cmmi8.300 @sf 988 1353 p 107 c cmmi10.329 @sf 1009 1346 p 59 c 8 r 107 c cmr10.329 @sf 13 r 61 c 13 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 7 r 58 c 5 r 59 c 8 r 112 c cmr10.329 @sf 44 c 14(whether)m 15(or)m 15(not)m 15(eac)m 104 c 14(parameter)m 14(is)m 361 1402 p (to)s 15 r 98 c 1 r 101 c 17(treated)m 15(as)m 15(\\\014xed",)m 16(what)m 15(\\scale")m 15 r 118 c -2(alue)m 15(will)m 14 r 98 c 1 r 101 c 17(used,)m 16(and,)m 16(when)m 16(the)m 16(deriv)m -2(a-)m 361 1458 p (tiv)s (es)s 10(are)m 12(constructed)m 12(using)m 12(\014nite)m 12(di\013erences)m 12(the)m 12(step)m 12(size)m 12(used)m 13(in)m 11(that)m 12(calculation,)m 361 1515 p (or)s 14(when)m 15(the)m 14(user)m 15(supplied)m 14(deriv)m -2(ativ)m -1(es)m 13 r 119 c (ere)s 13 r 99 c (hec)s 107 c -1(ed)m 12(what)m 14(deriv)m -2(ativ)m -1(es)m 12 r 119 c (ere)s 13(iden)m (ti-)s 361 1571 p (\014ed)s 16(as)m 15(questionable;)m cmsy10.329 @sf 316 1638 p 15 c cmr10.329 @sf 22(the)m 21 r 118 c -2(alue)m 21(of)m 20(the)m 21(\014rst)m 21(and)m 21(last)m 20(observ)m -2(ation)m 19(of)m 21(eac)m 104 c 20(column)m 20(of)m 21(the)m 21(explanatory)m 361 1694 p 118 c -2(ariable)m cmmi10.329 @sf 9 r 88 c cmr10.329 @sf 4 r 44 c 11(and)m 11(when)m 11(the)m 10(solution)m 10(is)m 10(found)m 11 r 98 c 121 c 10(orthogonal)m 9(distance)m 10(regression,)m cmsy10.329 @sf 361 1760 p 14 c cmr10.329 @sf 23(the)m 15(starting)m 14(errors)m 14 r 1 c 15(for)m 15(eac)m 104 c 14(of)m 15(these)m 15(observ)m -2(ations,)m cmsy10.329 @sf 361 1827 p 14 c cmr10.329 @sf 23(whether)m 15(or)m 15(not)m 15(these)m 15 r 118 c -2(alues)m 14(will)m 14 r 98 c 1 r 101 c 16(held)m 16(\014xed)m 15(at)m 15(their)m 15(input)m 15 r 118 c -2(alues,)m cmsy10.329 @sf 361 1893 p 14 c cmr10.329 @sf 23(the)m 15(scale)m 15 r 118 c -2(alues,)m cmsy10.329 @sf 361 1959 p 14 c cmr10.329 @sf 23(the)m 17(diagonal)m 16(elemen)m (ts)s 16(of)m 16(the)m 17 r 119 c (eigh)s (t)s -1 r 115 c cmmi10.329 @sf 15 r 119 c cmmi8.300 @sf 1184 1966 p 14 c cmmi6.300 @sf 1200 1971 p 105 c cmr10.329 @sf 1231 1959 p (asso)s 1(ciated)m 16(with)m 17(eac)m 104 c 16(of)m 17(these)m 17(obser-)m 407 2015 p 118 c -2(ations,)m 13(and)m cmsy10.329 @sf 361 2082 p 14 c cmr10.329 @sf 23(when)m 15(the)m 14(deriv)m -2(ativ)m (es)s 12(are)m 14(constructed)m 15(using)m 14(\014nite)m 15(di\013erences)m 15(the)m 14(step)m 15(size)m 14(used)m 407 2138 p (in)s 17(that)m 17(calculation,)m 16(or)m 17(when)m 17(the)m 18(user)m 17(supplied)m 18(deriv)m -2(ativ)m -1(es)m 16 r 119 c (ere)s 16 r 99 c (hec)s 107 c -1(ed)m 15(what)m 407 2195 p (deriv)s -2(ativ)m -1(es)m 13 r 119 c (ere)s 14(iden)m (ti\014ed)s 14(as)m 15(questionable;)m cmsy10.329 @sf 316 2261 p 15 c cmr10.329 @sf 22(the)m 19 r 118 c -2(alue)m 18(of)m 19(the)m 19(\014rst)m 18(and)m 20(last)m 17(observ)m -2(ation)m 18(of)m 18(the)m 19(resp)m 1(onse)m 20 r 118 c -2(ariable)m cmmi10.329 @sf 17 r 89 c cmr10.329 @sf 10 r 44 c 20(and)m 19(the)m 361 2317 p 118 c -2(alue)m 15(of)m 15(the)m 15(corresp)m 1(onding)m 15(diagonal)m 14(en)m (tries)s 13(of)m 15(the)m 15(error)m 15 r 119 c (eigh)s -1(ts)m cmmi10.329 @sf 13 r 119 c cmmi8.300 @sf 1660 2324 p 15 c cmmi6.300 @sf 1674 2329 p 105 c cmr10.329 @sf 1688 2317 p 46 c @eop %%Page: 12 26 12 @bop0 cmti10.329 @sf [<7E0000007F000000FF8000007B80000071C0000001C0000001C0000001E0000000E0000000E003 C000E007E000F00F7000700E3000700E3000700E3800700F180078070000380700003807000038 078000380380003C0380001C0380001C03C0001C01C0001C01C0001C01C000FFFFE000FFFFE000 0E0000000E0000000E0000000F000000070000000700000007007000038078000380780001E038 0000FFF800003FE0> 32 41 2 9 25.555] 12 @dc cmsy10.329 @sf [ 16 46 -8 12 20.202] 100 @dc cmmi10.329 @sf [ 16 45 -3 11 22.727] 61 @dc cmsy10.329 @sf [<006000600060006000600060006000600060006000600060006000600060006000600060006000 600060006000600060006000600060006000600060006000600060006000600060006000600060 00600060006000600060FFE0FFE0> 16 46 0 12 20.202] 101 @dc cmbx10.329 @sf [ 32 31 -2 0 32.890] 70 @dc 12 @bop1 cmr10.329 @sf 0 114 p (12)s 1365(Getting)m 14(Started)m 0 134 p 1725 2 ru cmbx10.329 @sf 0 259 p (1.D.ii.b.)s 15(Iteration)m 17(Rep)m 1(orts)m cmr10.329 @sf 0 364 p (The)s 15(ODRP)m -3 r 65 c (CK)s 13(iteration)m 13(rep)m 1(orts)m 15(enable)m 15(the)m 14(user)m 15(to)m 14(monitor)m 14(the)m 15(progress)m 14(of)m 14(the)m 15(\014tting)m 0 420 p (pro)s 1(cedure,)m 16(where)m 15(the)m 15(user)m 16(con)m (trols)s 13(at)m 14(whic)m 104 c 14(iterations)m 14(these)m 15(rep)m 1(orts)m 15(will)m 14 r 98 c 1 r 101 c 16(generated.)m 0 496 p (ODRP)s -3 r 65 c (CK)s 15(iteration)m 14(rep)m 1(orts)m 16(are)m 16(of)m 16(the)m 16(greatest)m 15(use)m 17(in)m 16(cases)m 16(when)m 17(ODRP)m -3 r 65 c (CK)s 15(fails)m 15(to)m 0 553 p (\014nd)s 12 r 97 c 11(satisfactory)m 9(solution.)m 17(In)m 12(cases)m 11(when)m 11(ODRP)m -3 r 65 c (CK)s 10(do)m 1(es)m 12(reac)m 104 c 10 r 97 c 11(satisfactor)m -1 r 121 c 10(solution,)m 0 609 p (the)s cmti10.329 @sf 15(\014nal)m 16 r 114 c -1(ep)m -2(ort)m cmr10.329 @sf 14(discussed)m 16 r 98 c 1(elo)m 119 c 13(summarizes)m 15(the)m 15(most)m 15(useful)m 15(information.)m 0 685 p (The)s cmti10.329 @sf 22(short)m 23(iter)m -1(ation)m 22 r 114 c -1(ep)m -2(ort)m cmr10.329 @sf 44 c 22(sho)m (wn)s 21(in)m cmsy10.329 @sf 22 r 120 c cmr10.329 @sf (2.C.i.c,)s 22(is)m 22 r 97 c 21(one)m 23(line)m 21(summary)m 22(of)m 22(the)m 22(results,)m 0 742 p (listing)s cmsy10.329 @sf 91 808 p 15 c cmr10.329 @sf 22(the)m 16(iteration)m 13 r 110 c (um)s 98 c 1(er;)m cmsy10.329 @sf 91 874 p 15 c cmr10.329 @sf 22(the)m 21(cum)m (ulativ)s -1 r 101 c 18 r 110 c (um)s 98 c 1(er)m 19(of)m 20(function)m 20(ev)m -2(aluations)m 19(made)m 20 r 98 c 121 c 20(the)m 20(end)m 21(of)m 20(the)m 21(listed)m 136 931 p (iteration;)s cmsy10.329 @sf 91 997 p 15 c cmr10.329 @sf 22(the)m 15 r 119 c (eigh)s -1(ted)m 13(sum)m 15(of)m 15(the)m 15(squared)m 15(observ)m -2(ation)m 13(errors)m cmmi10.329 @sf 14 r 83 c cmr10.329 @sf 3 r 40 c cmmi10.329 @sf 12 c 2 r 59 c 8 r 14 c cmr10.329 @sf 2 r 41 c 13(at)m 14(the)m 15(curren)m 116 c 14 r 112 c 1(oin)m (t;)s cmsy10.329 @sf 91 1063 p 15 c cmr10.329 @sf 22(the)m 17(actual)m 16(relativ)m 101 c 15(reduction)m 17(in)m cmmi10.329 @sf 16 r 83 c cmr10.329 @sf 3 r 40 c cmmi10.329 @sf 12 c 2 r 59 c 8 r 14 c cmr10.329 @sf 2 r 41 c 15(at)m 17(the)m 17(most)m 16(recen)m (tly)s 15(tried)m 17(step)m 16(\(used)m 18(to)m 136 1120 p 99 c (hec)s 107 c 14(for)m 14(sum)m 16(of)m 14(squares)m 15(con)m 118 c (ergence\);)s cmsy10.329 @sf 91 1186 p 15 c cmr10.329 @sf 22(the)m 17(predicted)m 17(relativ)m -1 r 101 c 15(reduction)m 16(in)m cmmi10.329 @sf 16 r 83 c cmr10.329 @sf 3 r 40 c cmmi10.329 @sf 12 c 2 r 59 c 8 r 14 c cmr10.329 @sf 2 r 41 c 15(at)m 15(the)m 17(most)m 15(recen)m (tly)s 15(tried)m 16(step)m 17(\(used)m 136 1242 p (to)s 15 r 99 c (hec)s 107 c 13(for)m 15(sum)m 15(of)m 15(squares)m 15(con)m 118 c (erg)s -1(ence\);)m cmsy10.329 @sf 91 1309 p 15 c cmr10.329 @sf 22(the)m 17(ratio)m 16(of)m 16(the)m 17(trust)m 16(region)m 16(radius)m 16(to)m 16(the)m 17(scaled)m 17(norm)m 16(of)m cmmi10.329 @sf 17 r 12 c cmr10.329 @sf 18(and)m 17(\001,)m 17(whic)m 104 c 16(is)m 16(an)m 136 1365 p (upp)s 1(er)m 16 r 98 c 1(ound)m 17(on)m 15(the)m 15(relativ)m -1 r 101 c 13 r 99 c (hange)s 15(in)m 15(the)m 15(estimated)m 14 r 118 c -2(alues)m 14 r 112 c 1(ossible)m 15(at)m 15(the)m 15(next)m 136 1422 p (step)s 16(\(used)m 15(to)m 15 r 99 c (hec)s 107 c 13(for)m 15(parameter)m 14(con)m 118 c (erg)s -1(ence\);)m 14(and)m cmsy10.329 @sf 91 1488 p 15 c cmr10.329 @sf 22(whether)m 16(the)m 15(step)m 15 r 119 c (as)s 14 r 97 c 14(Gauss-Newton)m 15(step.)m 0 1564 p (The)s cmti10.329 @sf 21(long)m 21(iter)m -1(ation)m 21(summary)m cmr10.329 @sf 21(lists)m 20(all)m 20(of)m 21(the)m 21(information)m 19(found)m 21(in)m 21(the)m 21(short)m 21(iteration)m 0 1620 p (summary)s 15(and,)m 15(in)m 15(addition,)m 14(includes)m cmsy10.329 @sf 91 1686 p 15 c cmr10.329 @sf 22(the)m 11 r 118 c -2(alues)m 9(of)m cmmi10.329 @sf 10 r 12 c cmr10.329 @sf 13(at)m 9(the)m 11(end)m 11(of)m 10(the)m 10(curren)m 116 c 9(iteration.)m 17(\(A)m 116 c 8(the)m 11(last)m 9(iteration,)m 9(the)m 11 r 118 c -2(alues)m 136 1743 p (listed)s 18(will)m 17 r 98 c 1 r 101 c 19(those)m 18(that)m 18(pro)m 1(duced)m 19(the)m 18(actual)m 18(and)m 18(predicted)m 19(relativ)m 101 c 16(reductions)m 136 1799 p (sho)s (wn)s 14(only)m 14(if)m 14(the)m 14(most)m 14(recen)m (tly)s 13(tried)m 14(step)m 15(did)m 15(in)m 14(fact)m 14(mak)m 101 c 13(the)m 15(\014t)m 14 r 98 c 1(etter.)m 20(If)m 15(not,)m 136 1856 p (then)s 16(the)m 15 r 118 c -2(alues)m 15(of)m cmmi10.329 @sf 14 r 12 c cmr10.329 @sf 18(listed)m 14(are)m 15(those)m 15(that)m 14(pro)m 1(duced)m 17(the)m 15 r 98 c 1(est)m 15(\014t.\))m 0 1932 p (The)s 15(long)m 15(iteration)m 13(rep)m 1(ort)m 15(requires)m 15(125)m 15(columns,)m 14(and)m 16(uses)m cmsy10.329 @sf 15 r 100 c cmmi10.329 @sf (p=)s cmr10.329 @sf 51 c cmsy10.329 @sf 101 c cmr10.329 @sf 15(lines)m 15 r 112 c 1(er)m 15(iteration.)m cmbx10.329 @sf 0 2072 p (1.D.ii.c.)s 15(Final)m 17(Rep)m 1(orts)m cmr10.329 @sf 0 2177 p (The)s 17(\014nal)m 17(rep)m 1(ort)m 17(pro)m (vides)s 16(information)m 15(that)m 16(allo)m (ws)s 15(the)m 17(user)m 17(to)m 17(assess)m 16(the)m 17(qualit)m 121 c 15(of)m 17(the)m 0 2233 p (solution)s 14(found)m 15 r 98 c 121 c 15(ODRP)m -3 r 65 c (CK.)s 0 2309 p (The)s cmti10.329 @sf 15(short)m 17(\014nal)m 15 r 114 c -1(ep)m -1(ort)m cmr10.329 @sf 44 c 13(sho)m (wn)s 14(in)m cmsy10.329 @sf 15 r 120 c cmr10.329 @sf (2.C.ii.c)s 13(and)m cmsy10.329 @sf 16 r 120 c cmr10.329 @sf (2.C.iii.)s -1(c,)m 13(includes)m cmsy10.329 @sf 91 2376 p 15 c cmr10.329 @sf 22(the)m 16(reason)m 14(the)m 16(computations)m 14(stopp)m 1(ed;)m cmsy10.329 @sf 91 2442 p 15 c cmr10.329 @sf 22(the)m 16 r 110 c (um)s -1 r 98 c 1(er)m 14(of)m 15(iterations;)m @eop %%Page: 13 27 13 @bop0 cmmi8.300 @sf [<7C00FF00E780E38003C001C001C001E001E000E000E000F000F0007000701C780C780E7807F803 F0000000000000000000000000001C001C001C> 16 29 0 6 14.269] 106 @dc cmmi10.329 @sf [<7E00007F8000FBC00079E00070F000007000007800007800003800003800003C00003C00001C00 001C00001E00001E00000E00000E00000F00000F0000070000070007078003078003838001C380 01E78000FF00003E000000000000000000000000000000000000000000000001C00001E00001E0 0001E0> 24 40 1 9 18.718] 106 @dc cmbx12.300 @sf [ 32 34 -2 0 36.782] 69 @dc [<0000380000000038000000007C000000007C00000000FE00000000FE00000000FE00000001FF00 000001FF00000003FD80000003F980000007F9C0000007F0C0000007F0C000000FF06000000FE0 6000001FE03000001FC03000003FC03800003F801800003F801800007F800C00007F000C0000FF 00060000FE00060001FE00070001FC00030001FC00030003F800018003F800018007F80000C007 F00000C0FFFF800FFEFFFF800FFE> 40 34 -1 0 42.317] 86 @dc cmr8.300 @sf [<07C01FF03838701C701C600CE00EE00EE00EE00EE00EE00EE00EE00EE00E600C600C701C38381F F007C0> 16 21 -1 0 17.642] 48 @dc 13 @bop1 cmr10.329 @sf 225 114 p (Getting)s 14(Started)m 1365(13)m 225 134 p 1725 2 ru cmsy10.329 @sf 316 259 p 15 c cmr10.329 @sf 22(the)m 13 r 110 c (um)s 98 c 1(er)m 11(of)m 12(function)m 12(ev)m -2(aluations)m 11(and,)m 13(if)m 12(the)m 12(Jacobian)m 13 r 119 c (as)s 10(supplied)m 13 r 98 c 121 c 12(the)m 12(user,)m 361 315 p (the)s 16 r 110 c (um)s -1 r 98 c 1(er)m 14(of)m 15(Jacobian)m 15(ev)m -2(aluations;)m cmsy10.329 @sf 316 381 p 15 c cmr10.329 @sf 22(the)m 16(rank)m 15(de\014ciency)m 16(of)m 15(the)m 15(mo)m 1(del)m 15(at)m 15(the)m 15(time)m 14(the)m 16(computations)m 14(stopp)m 1(ed;)m cmsy10.329 @sf 316 448 p 15 c cmr10.329 @sf 22(the)m 14(in)m 118 c -1(erse)m 11(of)m 13(the)m 13(condition)m 13 r 110 c (um)s 98 c 1(er)m 11(of)m 13(the)m 13(problem)m 13(at)m 13(the)m 13(time)m 13(the)m 13(computations)m 361 504 p (stopp)s 1(ed)m 16(\(see)m cmsy10.329 @sf 15 r 120 c cmr10.329 @sf (4.C\);)s cmsy10.329 @sf 316 570 p 15 c cmr10.329 @sf 22(the)m 16 r 119 c (eigh)s -1(t)m -1(ed)m 14(sum)m 15(of)m 15(the)m 15(squared)m 15(errors,)m cmmi10.329 @sf 14 r 83 c cmr10.329 @sf 3 r 40 c cmmi10.329 @sf 12 c 2 r 59 c 8 r 14 c cmr10.329 @sf 2(\),)m cmmi10.329 @sf 13 r 83 c cmmi8.300 @sf 1357 577 p 14 c cmr10.329 @sf 1375 570 p 40 c cmmi10.329 @sf 12 c 2 r 59 c 8 r 14 c cmr10.329 @sf 2 r 41 c 14(and)m cmmi10.329 @sf 15 r 83 c cmmi8.300 @sf 1612 577 p 15 c cmr10.329 @sf 1629 570 p 40 c cmmi10.329 @sf 12 c 2 r 59 c 8 r 14 c cmr10.329 @sf 2(\),)m 13(ev)m -2(aluated)m 361 627 p (at)s 20(the)m 20(\014nal)m 20 r 118 c -2(alues)m 758 616 p 94 c cmmi10.329 @sf 752 628 p 12 c cmr10.329 @sf 800 627 p (and)s 901 617 p 94 c 893 628 p 1 c 931 627 p 44 c 21(and)m 20(if)m 20(the)m 20(co)m 118 c -2(aria)m -1(nce)m 19(matrix)m 19 r 119 c (as)s 18(computed,)m 22(the)m 361 683 p (estimated)s 15(residual)m 14 r 118 c -2(ariance)m 14(of)m 15(the)m 15(\014t)m 16(and)m 15(its)m 14(asso)m 1(ciated)m 15(degrees)m 15(of)m 15(freedom;)m 15(and)m cmsy10.329 @sf 316 749 p 15 c cmr10.329 @sf 22(the)m 20(\014nal)m 19 r 118 c -2(alues)m 696 738 p 94 c cmmi10.329 @sf 689 750 p 12 c cmr10.329 @sf 717 749 p 44 c 20(whether)m 20(eac)m 104 c 19 r 118 c -2(alue)m 19 r 119 c (as)s 17(\\\014xed")m 20(using)m 19(subroutine)m 20(argumen)m 116 c cmtt10.329 @sf 361 806 p (IFIXB)s cmr10.329 @sf 11(or)m 11(\\dropp)m 1(ed")m 11 r 98 c 121 c 10(ODRP)m -3 r 65 c (CK)s 10 r 98 c 1(ecause)m 13(it)m 10(induced)m 12(rank)m 11(de\014ciency)m -3 r 44 c 12(and,)m 12(if)m 11(the)m 361 862 p (co)s 118 c -2(aria)m -1(nce)m 16(matrix)m 739 852 p 94 c cmmi10.329 @sf 732 863 p 86 c cmmi8.300 @sf 759 870 p 12 c cmr10.329 @sf 799 862 p (and)s 17(standard)m 17(deviations)m 18 r 94 c cmmi10.329 @sf -26 r 27 c cmmi8.300 @sf 1324 869 p 12 c cmr10.329 @sf 1365 862 p 119 c (ere)s 15(computed,)m 17(the)m 17(standard)m 361 919 p (errors)s 15(and)m 15(95%)m 15(con\014dence)m 16(in)m (terv)s -2(al)m -1 r 115 c 14(for)m 14(the)m 15(estimators)m 14(of)m cmmi10.329 @sf 14 r 12 c cmr10.329 @sf 2 r 46 c 20(\(See)m cmsy10.329 @sf 16 r 120 c cmr10.329 @sf (4.B\).)s 225 995 p (The)s cmti10.329 @sf 14(long)m 15(\014nal)m 15 r 114 c -1(ep)m -2(ort)m cmr10.329 @sf 13(is)m 14(sho)m (wn)s 13(in)m cmsy10.329 @sf 14 r 120 c cmr10.329 @sf (2.C.i.c.)s 18(It)m 14(includes)m 15(the)m 14(same)m 14(information)m 12(as)m 14(the)m 15(short)m 225 1051 p (\014nal)s 16(rep)m 1(ort,)m 17(and,)m 17(in)m 16(addition,)m 16(pro)m (vides)s 15(the)m 17 r 118 c -2(alues)m 15(for)m 16(all)m 1375 1041 p 94 c cmmi10.329 @sf 1364 1052 p 69 c cmmi8.300 @sf 1398 1059 p (il)s cmmi10.329 @sf 1423 1051 p 59 c 8 r 105 c cmr10.329 @sf 14 r 61 c 15 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 7 r 58 c 5 r 59 c 8(n;)m 24 r 108 c cmr10.329 @sf 15 r 61 c 16 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 7 r 58 c 5 r 59 c 8 r 113 c 2 r 59 c cmr10.329 @sf 225 1108 p (and)s 321 1098 p 94 c 313 1109 p 1 c cmmi8.300 @sf 351 1116 p (ij)s cmmi10.329 @sf 382 1108 p 59 c 8 r 105 c cmr10.329 @sf 11 r 61 c 13 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 7 r 58 c 6 r 59 c 8(n;)m 21 r 106 c cmr10.329 @sf 15 r 61 c 13 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 8 r 58 c 5 r 59 c 8 r 109 c cmr10.329 @sf 46 c cmbx12.300 @sf 225 1254 p (1.E.)s 18(Starting)m 18 r 86 c -4(alues)m cmr10.329 @sf 225 1375 p (The)s 15(user)m 15 r 109 c (ust)s 14(supply)m 15(starting)m 14 r 118 c -2(alues)m 14(for)m 14(the)m 15(unkno)m (wns)s 14 r 98 c 1(eing)m 16(estimated,)m 14(i.e.,)m 13(for)m cmmi10.329 @sf 15 r 12 c cmr10.329 @sf 17(and)m 225 1431 p (\001.)s 19(Users)m 12(familiar)m 11(with)m 12(the)m 13(nonlinear)m 12(ordinary)m 12(least)m 11(squares)m 13(problem)m 12(are)m 12(generally)m 12 r 97 c 119 c -1(are)m 225 1488 p (of)s 14(the)m 15(imp)m 1(ortance)m 14(of)m 15(obtaining)m 13(go)m 1 r 111 c 1 r 100 c 15(starting)m 13 r 118 c -2(alues)m 14(for)m cmmi10.329 @sf 14 r 12 c cmr10.329 @sf 2 r 46 c 20(It)m 14(is)m 15(equally)m 14(imp)m 1(ortan)m 116 c 12(here.)m 225 1544 p (Go)s 1 r 111 c 1 r 100 c 12(initial)m 11(appro)m (xima)s -1(tio)m -1(ns)m 11(can)m 12(signi\014can)m (tly)s 10(decrease)m 13(the)m 13 r 110 c (um)s 98 c 1(er)m 10(of)m 12(iterations)m 11(required)m 225 1601 p (to)s 14(\014nd)m 15 r 97 c 14(solution;)m 13 r 97 c 14 r 112 c 1 r 111 c 1(or)m 14(initial)m 12(appro)m (ximati)s -1(on)m 13(ma)m 121 c 12(ev)m (en)s 14(prev)m (en)s 116 c 12 r 97 c 14(solution)m 13(from)m 14 r 98 c 1(eing)m 225 1657 p (found.)s 23(Reasonable)m 16(initial)m 15(appro)m (xima)s -1(tio)m -1(ns)m 15(are)m 15(often)m 16 r 97 c 118 c -2(ail)m -1(able)m 14(from)m 16(previous)m 16(analysis)m 14(or)m 225 1714 p (exp)s 1(erimen)m (ts.)s 26(When)m 18(go)m 1 r 111 c 1 r 100 c 18(starting)m 16 r 118 c -2(alues)m 17(are)m 17(not)m 17(readily)m 17 r 97 c 118 c -2(ai)m -1(lable,)m 16(the)m 18(user)m 17(ma)m 121 c 16(ha)m 118 c 101 c 225 1770 p (to)s 14(do)m 15(some)m 14(preliminary)m 14(analysis)m 13(to)m 14(obtain)m 14(them.)m 20(\(See,)m 15(e.g.,)m 13([Bates)m 14(and)m 15 r 87 c -3(atts,)m 12(1988],)m 13(or)m 225 1827 p ([Himmelblau,)s 14(1970].\))m 225 1903 p (Users)s 15(who)m 16(do)m 15(not)m 15(pro)m (vide)s 14(scale)m 15(information)m 14(are)m 15(strongly)m 14(encouraged)m 16(not)m 15(to)m 15(use)m 16(zero)m 15(as)m 225 1959 p (an)s 19(initial)m 16(appro)m (ximati)s -1(on)m 17(for)m 18(an)m 121 c 18(of)m 18(the)m 19(parameters)m cmmi10.329 @sf 18 r 12 c cmr10.329 @sf 20(since)m 19 r 97 c 19(zero)m 18 r 118 c -2(alue)m 18(can)m 19(result)m 18(in)m 225 2015 p (incorrect)s 11(scaling.)m 18(\(See)m cmsy10.329 @sf 13 r 120 c cmr10.329 @sf (4.D\).)s 17(Setting)m 12(the)m 12(initial)m 10(appro)m (ximati)s -1(on)m 10(to)m 12(the)m 12(largest)m 10(magnitude)m 225 2072 p (that,)s 12(for)m 11(the)m 12(user's)m 12(problem,)m 12(is)m 11(e\013ectiv)m (ely)s 10(zero,)m 12(rather)m 12(than)m 11(to)m 12(zero,)m 12(will)m 11(help)m 12(to)m 11(eliminate)m 225 2128 p (scaling)s 12(problems)m 12(and)m 14 r 112 c 1(ossibly)m 12(pro)m 1(duce)m 14(faster)m 12(con)m 118 c (erg)s -1(ence.)m 18 r 70 c -3(or)m 11(example,)m 13(if)m cmmi10.329 @sf 13 r 12 c cmr8.300 @sf 1719 2135 p 49 c cmr10.329 @sf 1751 2128 p (represen)s (ts)s 225 2185 p 99 c (hange)s 14(in)m 15 r 97 c 14(cost)m 14(measured)m 15(in)m 15(millions)m 13(of)m 15(dollars,)m 13(then)m 15(the)m 15 r 118 c -2(alue)m 14(10)m 14(migh)m 116 c 13 r 98 c 1 r 101 c 16(considered)m 225 2241 p (\\e\013ectiv)s (ely)s 13(zero")m 15(and)m 15(an)m 15(initial)m 13 r 118 c -2(alue)m 15(of)m cmmi10.329 @sf 15 r 12 c cmr8.300 @sf 1059 2226 p 48 c 1057 2253 p 49 c cmr10.329 @sf 1091 2241 p 61 c 13(10)m 15(is)m 14(preferable)m 16(to)m cmmi10.329 @sf 14 r 12 c cmr8.300 @sf 1540 2226 p 48 c 1538 2253 p 49 c cmr10.329 @sf 1573 2241 p 61 c 12 r 48 c cmmi10.329 @sf 58 c cmr10.329 @sf 225 2317 p (When)s 19(using)m 17(orthogonal)m 17(distance)m 18(regression)m 17(it)m 18(is)m 17(also)m 17(imp)m 1(ortan)m 116 c 16(to)m 18(ha)m 118 c -1 r 101 c 16(go)m 1 r 111 c 1 r 100 c 19(starting)m 225 2374 p 118 c -2(alues)m 18(for)m 18(the)m 18(estimated)m 18(errors)m 18(\001.)m 29(The)m 19(ODRP)m -3 r 65 c (CK)s 17(default)m 18(is)m 19(to)m 17(initialize)m 17 r 1 c 18(to)m 18(zero,)m 225 2430 p (whic)s 104 c 17(is)m 18(the)m 18(most)m 17(ob)m (vious)s 17(initial)m 16 r 118 c -2(alue.)m 28(\(Note)m 17(that)m 18(zero)m 18(starting)m 16 r 118 c -2(alues)m 18(for)m 17 r 1 c 18(do)m 18(not)m @eop %%Page: 14 28 14 @bop0 cmbx12.300 @sf [ 32 34 -2 0 35.226] 70 @dc [<0000E0000E00000000E0000E00000000F0001E00000001F0001F00000001F0001F00000003F800 3F80000003F8003F80000003FC007F80000007FC007FC0000007FC007FC000000FF600FFE00000 0FE600FE6000000FE600FE6000001FE301FC3000001FC301FC3000001FC383FC3000003F8183F8 1800003F8183F81800007F80C7F81C00007F00C7F00C00007F00C7F00C0000FF006FE0060000FE 006FE0060000FE007FE0060001FC003FC0030001FC003FC0030003FC003F80038003F8003F8001 8003F8007F80018007F0007F0000C007F0007F0000C00FF000FF0000E0FFFF0FFFF01FFEFFFF0F FFF01FFE> 56 34 -1 0 57.883] 87 @dc cmr10.329 @sf [ 24 31 -3 0 27.777] 90 @dc cmr6.300 @sf [ 16 16 -1 0 15.220] 50 @dc cmr9.300 @sf [ 16 26 -2 0 21.331] 83 @dc [ 16 24 -3 0 19.198] 49 @dc [<0FC01FE03C707038701C701CE01CE01CE01CE01CF01CF038F838FFF0EFE0E18060007000707838 783C781E780FF803F0> 16 24 -2 0 19.198] 54 @dc 14 @bop1 cmr10.329 @sf 0 114 p (14)s 1365(Getting)m 14(Started)m 0 134 p 1725 2 ru 0 259 p (cause)s 17(scaling)m 17(problems)m 17(similar)m 15(to)m 17(those)m 16(discussed)m 18(ab)m 1 r 111 c 118 c 101 c 15(for)m cmmi10.329 @sf 17 r 12 c cmr10.329 @sf 2(.\))m 25(Initializing)m 16 r 1 c 17(to)m 16(zero,)m 0 315 p (ho)s 119 c -1(ev)m -1(er,)m 15(is)m 17(equiv)m -2(alen)m 116 c 15(to)m 17(initiall)m -1 r 121 c 16(assigning)m 15(all)m 17(of)m 16(the)m 18(errors)m 16(to)m 17(the)m 17(dep)m 1(enden)m 116 c 18 r 118 c -2(ariable)m 0 372 p (as)s 18(is)m 19(done)m 19(for)m 18(ordinary)m 18(least)m 17(squares.)m 31(While)m 18(this)m 18(is)m 18(quite)m 18(adequate)m 19(in)m 19(man)m 121 c 17(cases,)m 19(in)m 0 428 p (others)s 16(it)m 17(is)m 16(not.)m 25 r 65 c 17(plot)m 16(of)m 16(the)m 17(observ)m (ed)s 16(data)m 17(and)m 17(of)m 16(the)m 17(curv)m 101 c 16(describ)m 1(ed)m 18 r 98 c 121 c 16(the)m 17(mo)m 1(del)m 0 484 p (function)s 15(for)m 14(the)m 15(initial)m 13(parameters)m 14(ma)m 121 c 13(indicate)m 15(whether)m 15(or)m 14(not)m 14(zero)m 15(starting)m 14 r 118 c -2(alues)m 14(for)m 0 541 p 1 c 14(are)m 15(reasonable)m 14(and)m 14(ma)m 121 c 13(mak)m 101 c 13(it)m 14 r 112 c 1(ossible)m 14(to)m 14(visually)m 14(determine)m 14 r 98 c 1(etter)m 15(starting)m 13 r 118 c -2(alues)m 0 597 p (for)s 14(some)m 14(of)m 14(the)m 14 r 1 c cmmi8.300 @sf 348 604 p (ij)s cmr10.329 @sf 378 597 p 46 c 20 r 70 c -3(or)m 13(example,)m 14(if)m 13(suc)m 104 c 14 r 97 c 14(plot)m 14(sho)m (ws)s 12(that)m 14(the)m 15 r 118 c (ertical)s 11(distance)m 15(from)m 13 r 97 c 0 654 p (data)s 13 r 112 c 1(oin)m 116 c 12 r 40 c cmmi10.329 @sf 120 c cmmi8.300 @sf 263 661 p 105 c cmmi10.329 @sf 276 654 p 59 c 8 r 121 c cmmi8.300 @sf 319 661 p 105 c cmr10.329 @sf 333 654 p 41 c 13(to)m 13(the)m 13(curv)m 101 c 12(is)m 13(far)m 13(larger)m 12(than)m 13(the)m 14(orthogonal)m 11(distance,)m 14(then)m cmmi10.329 @sf 13 r 14 c cmmi8.300 @sf 1568 661 p 105 c cmr10.329 @sf 1596 654 p (should)s 0 710 p (probably)s 13(not)m 13 r 98 c 1 r 101 c 14(initialized)m 12(to)m 13(zero)m 13(for)m 13(that)m 13 r 112 c 1(oin)m (t.)s 18(This)m 13(ma)m 121 c 11 r 111 c 1(ccur)m 14(near)m 14(an)m 13(asymptote)m 12(or)m 0 767 p (near)s 17 r 97 c 16(lo)m 1(cal)m 16(minim)m (um)s 15(or)m 17(maxim)m (um.)s 23(In)m 17(suc)m 104 c 17(cases,)m 16(it)m 17(is)m 16(often)m 17(appropriate)m 16(to)m 16(initialize)m cmmi10.329 @sf 0 823 p 14 c cmmi8.300 @sf 20 830 p 105 c cmr10.329 @sf 50 823 p (to)s 15(the)m 16(horizon)m (tal)s 13(distance)m 15(from)m 15(the)m 16(data)m 15 r 112 c 1(oin)m 116 c 14(to)m 16(the)m 15(curv)m (e.)s 21(\(See)m cmsy10.329 @sf 16 r 120 c cmr10.329 @sf (2.B.ii,)s 14(subroutine)m 0 880 p (argumen)s (ts)s cmtt10.329 @sf 13(JOB)m cmr10.329 @sf 15(and)m cmtt10.329 @sf 15(WORK)m cmr10.329 @sf (.\))s cmbx12.300 @sf 0 1024 p (1.F.)s 18 r 87 c -4(eigh)m -1(ts)m cmr10.329 @sf 0 1145 p 87 c -3(eigh)m -1(ts)m 19(can)m 20 r 98 c 1 r 101 c 21(used)m 21(to)m 20(eliminate)m 20(observ)m -2(ations)m 18(from)m 20(the)m 21(analysis,)m 20(to)m 20(comp)m 1(ensate)m 21(for)m 0 1201 p (unequal)s 13 r 118 c -2(ariances)m 12(or)m 12(correlations)m 11(in)m 12(the)m 13 r 118 c -2(ariables)m cmmi10.329 @sf 11 r 121 c cmr10.329 @sf 15(and)m cmmi10.329 @sf 13 r 120 c cmr10.329 @sf 44 c 13(or)m 12(simply)m 12(to)m 12(mo)m 1(dify)m 12(the)m 13(e\013ect)m 0 1258 p (of)s 15(the)m 15 r 118 c -2(arious)m 14(errors)m cmmi10.329 @sf 14 r 15 c cmr10.329 @sf 16(and)m cmmi10.329 @sf 15 r 14 c cmr10.329 @sf 17(on)m 15(the)m 16(\014t.)m 0 1334 p (The)s 18 r 119 c (eigh)s -1(ts)m cmmi10.329 @sf 15 r 119 c cmmi8.300 @sf 288 1341 p 15 c cmmi6.300 @sf 302 1346 p 105 c cmsy10.329 @sf 329 1334 p 50 c 13 r 60 c cmmi8.300 @sf 405 1319 p 113 c cmsy8.300 @sf 1 r 2 c cmmi8.300 @sf 113 c cmr10.329 @sf 486 1334 p (asso)s 1(ciated)m 17(with)m cmmi10.329 @sf 17 r 15 c cmmi8.300 @sf 829 1341 p 105 c cmr10.329 @sf 843 1334 p 44 c cmmi10.329 @sf 18 r 105 c cmr10.329 @sf 16 r 61 c 18 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 7 r 58 c 5 r 59 c 8(n;)m cmr10.329 @sf 17 r 109 c (ust)s 16 r 98 c 1 r 101 c 18 r 112 c 1(ositiv)m 101 c 16(semide\014nite)m 0 1390 p (matrices,)s 13(and)m 13(the)m 14 r 119 c (eigh)s -1(ts)m cmmi10.329 @sf 12 r 119 c cmmi8.300 @sf 546 1397 p 14 c cmmi6.300 @sf 562 1402 p 105 c cmsy10.329 @sf 588 1390 p 50 c 13 r 60 c cmmi8.300 @sf 664 1375 p 109 c cmsy8.300 @sf 2 c cmmi8.300 @sf 109 c cmr10.329 @sf 769 1390 p (asso)s 1(ciated)m 13(with)m cmmi10.329 @sf 13 r 14 c cmmi8.300 @sf 1106 1397 p 105 c cmr10.329 @sf 1120 1390 p 44 c cmmi10.329 @sf 14 r 105 c cmr10.329 @sf 12 r 61 c 13 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 7 r 58 c 6 r 59 c 8(n;)m cmr10.329 @sf 12 r 109 c (ust)s 13 r 98 c 1 r 101 c 14 r 112 c 1(ositiv)m 101 c 0 1447 p (de\014nite)s 15(matrices.)m cmr8.300 @sf 342 1432 p 50 c cmr10.329 @sf 380 1447 p (If)s cmmi10.329 @sf 14 r 119 c cmmi8.300 @sf 452 1454 p 15 c cmmi6.300 @sf 466 1459 p 105 c cmr10.329 @sf 495 1447 p (is)s 13(diagonal,)m 13(then)m 15(the)m 14(errors)m 13(in)m 14(the)m cmmi10.329 @sf 15 r 113 c cmr10.329 @sf 16(resp)m 1(onses)m 14(of)m cmmi10.329 @sf 14 r 121 c cmmi8.300 @sf 1480 1454 p 105 c cmr10.329 @sf 1509 1447 p (are)s 13(treated)m 0 1503 p (as)s 14(uncorrelated.)m 19(Similarly)m -4 r 44 c 12(if)m cmmi10.329 @sf 13 r 119 c cmmi8.300 @sf 604 1510 p 14 c cmmi6.300 @sf 620 1515 p 105 c cmr10.329 @sf 648 1503 p (is)s 13(diagonal,)m 12(then)m 15(the)m 14(errors)m 13(in)m 13(the)m cmmi10.329 @sf 14 r 109 c cmr10.329 @sf 14(elemen)m (ts)s 13(of)m cmmi10.329 @sf 13 r 120 c cmmi8.300 @sf 1636 1510 p 105 c cmr10.329 @sf 1664 1503 p (are)s 0 1560 p (treated)s 17(as)m 17(uncorrelated.)m 25(When)m 18(the)m 18 r 119 c (eigh)s -1(t)m -1 r 115 c 15(are)m 17(not)m 17(diagonal)m 16(matrices,)m 17(then)m 17(the)m 18(errors)m cmti10.329 @sf 0 1616 p (within)s cmr10.329 @sf 13(an)m 13(observ)m -2(ation)m 11(are)m 13(treated)m 12(as)m 13(correlated.)m 18(In)m 14(all)m 12(cases,)m 13(ho)m 119 c -1(ev)m -1(er,)m 11(the)m 13(errors)m cmti10.329 @sf 12 r 98 c -1(etwe)m -2(en)m cmr10.329 @sf 0 1672 p (observ)s -2(ations)m 13(are)m 15(treated)m 15(as)m cmti10.329 @sf 15(unc)m -1(orr)m -1(el)m -1(ate)m -2 r 100 c cmr10.329 @sf 46 c 0 1748 p (Observ)s -2(ations)m 20(can)m 21 r 98 c 1 r 101 c 22(eliminated)m 20(from)m 20(the)m 21(analysis)m 20 r 98 c 121 c 20(setting)m 20(the)m 21(appropriate)m 20 r 119 c (eigh)s -1 r 116 c 0 1805 p 118 c -2(alues)m cmmi10.329 @sf 20 r 119 c cmmi8.300 @sf 169 1812 p 15 c cmmi6.300 @sf 183 1817 p 105 c cmr10.329 @sf 198 1805 p (to)s 20(zero.)m 38(This)m 21(will)m 20(pro)m 1(duce)m 22(the)m 21(same)m 21(results)m 21(as)m 21(an)m 21(analysis)m 20(with)m 21(the)m 21(zero-)m 0 1861 p 119 c (eigh)s -1(ted)m 16 r 118 c -2(alues)m 16(remo)m 118 c -1(ed)m 16(from)m 17(the)m 17(data)m 17(prior)m 16(to)m 17(calling)m 16(ODRP)m -3 r 65 c (CK.)s 16(Zero)m 17 r 119 c (eigh)s -1(ts)m 15(can)m 0 1918 p 98 c 1 r 101 c 17(used)m 17(to)m 16(allo)m -1 r 119 c 15(for)m 15(cases)m 17(of)m 16 r 109 c (ultir)s -1(esp)m 1(onse)m 16(data)m 15(where)m 17(the)m 17 r 110 c (um)s 98 c 1(er)m 14(of)m 16(resp)m 1(onses)m 17(is)m 16(not)m 0 1974 p (constan)s 116 c 19(for)m 21(all)m 20(observ)m -2(ations.)m 36(They)m 22(also)m 20(allo)m 119 c 19(for)m 20(easy)m 21(examination)m 20(of)m 21(the)m 21(e\013ect)m 21(of)m 0 2031 p (outliers)s 14(and)m 15(in\015uen)m (tial)s 14(data)m 14 r 112 c 1(oin)m (ts.)s 0 2107 p (Outliers)s 10(can)m 11(often)m 10 r 98 c 1 r 101 c 11(iden)m (ti\014ed)s 10 r 98 c 121 c 9(large)m 10 r 118 c -2(alues)m 9(of)m cmmi10.329 @sf 10 r 15 c cmr10.329 @sf 11(and/or)m cmmi10.329 @sf 10 r 14 c cmr10.329 @sf 2 r 46 c 19(Careful)m 9 r 99 c (hec)s (king)s 9(of)m 10(the)m 11(data)m 0 2163 p (often)s 17(leads)m 17(to)m 17(con\014rmation)m 16(that)m 17(the)m 17(data)m 17(are)m 17(in)m 17(error,)m 17(and)m 17(sometimes)m 16(to)m 17 r 97 c 17(correction.)m 0 2220 p (When)s 15 r 97 c 14(cause)m 15(for)m 14(suspicious)m 14(data)m 14(cannot)m 15 r 98 c 1 r 101 c 15(found,)m 15(it)m 13(ma)m 121 c 13 r 98 c 1 r 101 c 16(advisable)m 14(to)m 13(compare)m 15(the)m 0 2276 p (analysis)s 12(with)m 13(and)m 14(without)m 13(the)m 14(questionable)m 13(data.)m 18(Caution)m 13(is)m 13(in)m 14(order)m 13(if)m 13(the)m 14(estimates)m 12(or)m 0 2333 p (conclusions)s 17(are)m 16(highly)m 17(sensitiv)m 101 c 15(to)m 16 r 97 c 17(small)m 15(amoun)m 116 c 16(of)m 16(suspicious)m 17(data.)m 24(Data)m 16(that)m 16(ha)m 118 c 101 c 0 2389 p 97 c 16 r 118 c (ery)s 16(high)m 16(in\015uence)m 18(on)m 17 r 97 c 16(\014tted)m 17(curv)m 101 c 15(ma)m 121 c 15(not)m 17(result)m 16(in)m 16(large)m 16(errors,)m 16(ho)m 119 c -1(ev)m -1(er,)m 14(ev)m (en)s 16(if)m 0 2424 p 690 2 ru cmr6.300 @sf 52 2452 p 50 c cmr9.300 @sf 69 2467 p (See)s 13(fo)m 1(otnote)m 14 r 49 c 13(on)m 13(page)m 14(6.)m @eop %%Page: 15 29 15 @bop0 cmmi8.300 @sf [<1FC07FF07078E018E000E000E000FFC0FFF0F07078383C381FF807F0> 16 14 -1 0 16.368] 101 @dc cmti10.329 @sf [ 24 32 -3 0 20.908] 107 @dc cmmi10.329 @sf [<0FE03FFC7C3E780FF003F000F000F000F000F8007800780078003C043C0F1E0F0F0F07C703FE00 FC> 16 20 -2 0 19.670] 99 @dc 15 @bop1 cmr10.329 @sf 225 114 p (Getting)s 14(Started)m 1365(15)m 225 134 p 1725 2 ru 225 259 p (they)s 16(are)m 15(in)m 16(error.)m 21(In)m 16(fact,)m 15(extremely)m 16(in\015uen)m (tial)s 13(observ)m -2(ations)m 15(ma)m 121 c 14(force)m 15(the)m 16(\014tted)m 16(curv)m 101 c 225 315 p (to)s 19 r 98 c 1 r 101 c 20 r 118 c (ery)s 18(close,)m 20(leading)m 19(to)m 18 r 118 c (ery)s 18(small)m 19(residuals.)m 31(It)m 20(is)m 19(therefore)m 19(desirable)m 19(to)m 19(iden)m (tify)s 225 372 p (in\015uen)s (tial)s 18(observ)m -2(ations)m 19(and)m 20(to)m 19(compare)m 20(the)m 21(results)m 19(obtained)m 20(with)m 19(and)m 21(without)m 19(these)m 225 428 p 112 c 1(oin)m (ts.)s 18(Sev)m (eral)s 12(metho)m 1(ds)m 14(for)m 13(detecting)m 13(in\015uen)m (tial)s 12(observ)m -2(ations)m 12(for)m 13(ordinary)m 13(least)m 13(squares)m 225 484 p (are)s 16(discussed)m 17(in)m 17([Belsley)m cmti10.329 @sf 15(et)m 18(al.)m cmr10.329 @sf 44 c 16(1980],)m 15([Bemen)m 116 c 15(and)m 17(Williams,)m 14(1969],)m 15([Co)m 1(ok,)m 16(1977],)m 15(and)m 225 541 p ([Hoaglin)s 14(and)m 15 r 87 c -3(elsc)m (h,)s 13(1978].)m 225 617 p (Using)s 18 r 119 c (eigh)s -1(ts)m 17(to)m 18(comp)m 1(ensate)m 19(for)m 18(unequal)m 19(error)m 18 r 118 c -2(ariances)m 18(is)m 18(not)m 18(as)m 19(straigh)m -1(tfo)m -1(rw)m -1(ar)m -1 r 100 c 17(as)m 225 673 p (using)s 14(zero)m 14 r 119 c (eigh)s -1(ts)m 12(to)m 13(eliminate)m 13(observ)m -2(ations)m 13(from)m 13(the)m 14(analysis.)m 19(When)m 14(the)m 14(errors)m cmmi10.329 @sf 14 r 101 c cmmi8.300 @sf 1838 680 p 105 c cmmi10.329 @sf 1852 673 p 59 c 21 r 105 c cmr10.329 @sf 13 r 61 c 225 730 p 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 7 r 58 c 6 r 59 c 8(n;)m cmr10.329 @sf 10(and)m cmmi10.329 @sf 12 r 14 c cmmi8.300 @sf 505 737 p 105 c cmmi10.329 @sf 520 730 p 59 c 19 r 105 c cmr10.329 @sf 12 r 61 c 13 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 7 r 58 c 6 r 59 c 8 r 110 c cmr10.329 @sf 44 c 11(ha)m 118 c 101 c 10(co)m 118 c -2(a)m -1(riances)m cmmi10.329 @sf 10 r 27 c cmr8.300 @sf 1168 715 p 50 c cmmi8.300 @sf 1166 741 p 101 c cmmi6.300 @sf 1182 746 p 105 c cmsy10.329 @sf 1210 730 p 50 c 13 r 60 c cmmi8.300 @sf 1286 715 p 113 c cmsy8.300 @sf 1 r 2 c cmmi8.300 @sf 113 c cmr10.329 @sf 1361 730 p (and)s cmmi10.329 @sf 12 r 27 c cmr8.300 @sf 1474 715 p 50 c cmmi8.300 @sf 1472 743 p 14 c cmmi6.300 @sf 1488 748 p 105 c cmsy10.329 @sf 1516 730 p 50 c 13 r 60 c cmmi8.300 @sf 1592 715 p 109 c cmsy8.300 @sf 2 c cmmi8.300 @sf 109 c cmr10.329 @sf 1683 730 p 44 c 12(resp)m 1(ectiv)m (ely)s -3 r 44 c 225 786 p (that)s 14(are)m cmti10.329 @sf 15(known)m cmr10.329 @sf 44 c 15(then)m 15(the)m 15 r 119 c (eigh)s (t)s -1 r 115 c 13(can)m 16 r 98 c 1 r 101 c 15(set)m 15(using)m cmmi10.329 @sf 714 882 p 119 c cmmi8.300 @sf 742 889 p 15 c cmmi6.300 @sf 756 894 p 105 c cmr10.329 @sf 783 882 p 61 c cmmi10.329 @sf 13 r 99 c cmr8.300 @sf 851 889 p 49 c cmmi10.329 @sf 871 882 p 27 c cmsy8.300 @sf 899 864 p 0 c cmr8.300 @sf 50 c cmmi8.300 @sf 897 893 p 101 c cmmi6.300 @sf 913 898 p 105 c cmr10.329 @sf 1036 882 p (and)s cmmi10.329 @sf 91 r 119 c cmmi8.300 @sf 1228 889 p 14 c cmmi6.300 @sf 1244 894 p 105 c cmr10.329 @sf 1271 882 p 61 c cmmi10.329 @sf 13 r 99 c cmr8.300 @sf 1339 889 p 50 c cmmi10.329 @sf 1358 882 p 27 c cmsy8.300 @sf 1386 864 p 0 c cmr8.300 @sf 50 c cmmi8.300 @sf 1384 896 p 14 c cmmi6.300 @sf 1400 901 p 105 c cmmi10.329 @sf 1448 882 p 59 c 225 978 p 105 c cmr10.329 @sf 23 r 61 c 24 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 7 r 58 c 5 r 59 c 8(n;)m cmr10.329 @sf 21(where)m cmmi10.329 @sf 22 r 99 c cmr8.300 @sf 666 985 p 49 c cmr10.329 @sf 706 978 p (and)s cmmi10.329 @sf 22 r 99 c cmr8.300 @sf 821 985 p 50 c cmr10.329 @sf 862 978 p (are)s 21(constan)m (ts)s 20(selected)m 22(so)m 21(that)m 21(the)m 22(magnitudes)m 21(of)m 21(the)m 225 1034 p 119 c (eigh)s -1(ted)m 13(errors)m cmmi10.329 @sf 15 r 15 c cmr6.300 @sf 562 1019 p 84 c cmmi8.300 @sf 562 1046 p 105 c cmmi10.329 @sf 586 1034 p 119 c cmmi8.300 @sf 614 1041 p 15 c cmmi6.300 @sf 628 1046 p 105 c cmmi10.329 @sf 642 1034 p 15 c cmmi8.300 @sf 660 1041 p 105 c cmr10.329 @sf 690 1034 p (and)s cmmi10.329 @sf 15 r 14 c cmr6.300 @sf 800 1019 p 84 c cmmi8.300 @sf 798 1046 p 105 c cmmi10.329 @sf 824 1034 p 119 c cmmi8.300 @sf 852 1041 p 14 c cmmi6.300 @sf 868 1046 p 105 c cmmi10.329 @sf 881 1034 p 14 c cmmi8.300 @sf 901 1041 p 105 c cmr10.329 @sf 931 1034 p (will)s 14 r 98 c 1 r 101 c 16(appro)m (xima)s -1(tely)m 13(the)m 15(same.)m 225 1110 p (In)s 17(practice,)m 15 r 119 c (eigh)s -1(ts)m 14(are)m 16(often)m 15(deriv)m (ed)s 15(from)m 16(theory)m 15(or)m 16(obtained)m 15(from)m 16(the)m 16(data)m 15 r 98 c 1(eing)m 16(\014t.)m 225 1166 p (Users)s 15 r 109 c (ust)s 14 r 98 c 1 r 101 c 17 r 97 c 119 c -1(a)m -1(re)m 14(that)m 15(incorrectly)m 14(sp)m 1(eci\014ed)m 17 r 119 c (eigh)s -1(ts)m 13(can)m 16(adv)m (ersely)s 14(a\013ect)m 14(the)m 16(results.)m 225 1223 p (\(See,)s 19(e.g.,)m 17([Boggs)m 17(and)m 18(Rogers,)m 18(1990a].\))m 26(Th)m (us,)s 18(when)m 18(the)m 18(need)m 19(for)m 18 r 119 c (eigh)s -1(t)m -1 r 115 c 16(is)m 18(susp)m 1(ected)m 225 1279 p (and)s 22(the)m 21(error)m 21(co)m 118 c -2(ar)m -1(iances)m 20(are)m 21(not)m 21(kno)m (wn,)s 21(it)m 21(is)m 21(extremely)m 21(imp)m 1(ortan)m 116 c 19(to)m 20(analyze)m 21(ho)m 119 c 225 1336 p (the)s 17 r 119 c (eigh)s -1(ts)m 14(are)m 17(a\013ecting)m 15(the)m 17(computed)m 17(results.)m 24(See)m 17([F)m -3(uller,)m 15(1987])m 15(for)m 16 r 97 c 17(more)m 16(complete)m 225 1392 p (discussion)s 21(of)m 21 r 119 c (eigh)s -1(ts)m 19(and)m 21(their)m 21(implications)m 20(for)m 20(the)m 22(estimation)m 20(of)m 20(the)m 22(parameters)m 20(of)m 225 1449 p (measuremen)s 116 c 15(error)m 15(mo)m 1(dels,)m 16(and)m 17(also)m 15([Bates)m 16(and)m 16 r 87 c -3(atts,)m 14(1988])m 15(for)m 15 r 97 c 16(pro)m 1(cedure)m 17(that)m 16(can)m 225 1505 p 98 c 1 r 101 c 20(used)m 19(to)m 19(estimate)m 18(the)m 19(co)m 118 c -2(ari)m -1(ance)m 18(matrix)m cmmi10.329 @sf 18 r 27 c cmr8.300 @sf 1130 1490 p 50 c cmmi8.300 @sf 1128 1516 p 101 c cmmi6.300 @sf 1144 1521 p 105 c cmr10.329 @sf 1178 1505 p (in)s 19(the)m 19(case)m 19(of)m 19 r 109 c (ultiresp)s 1(onse)m 17(nonlinear)m 225 1562 p (ordinary)s 14(least)m 15(squares.)m cmbx12.300 @sf 225 1707 p (1.G.)s 18(Default)m 18 r 86 c -4(alues)m 18(and)m 19(Structured)m 18(Argumen)m -1(ts)m cmr10.329 @sf 225 1828 p (ODRP)s -3 r 65 c (CK)s 12(uses)m 14(default)m 12 r 118 c -2(alues)m 13(and)m 14(structured)m 13(argumen)m (ts)s 11(to)m 13(simplify)m 12(the)m 14(user)m 13(in)m (terface.)s 225 1884 p (The)s 17 r 97 c 118 c -2(a)m -1(ila)m -1(bilit)m -2 r 121 c 14(of)m 17(default)m 16 r 118 c -2(alues)m 15(in)m 17(ODRP)m -3 r 65 c (CK)s 15(means)m 16(that)m 16(the)m 17(user)m 16(do)m 1(es)m 17(not)m 16(ha)m 118 c 101 c 15(to)m 225 1941 p 98 c 1 r 101 c 20(concerned)m 21(with)m 19(determining)m 19 r 118 c -2(alues)m 19(for)m 19(man)m 121 c 18(of)m 19(the)m 20(ODRP)m -3 r 65 c (CK)s 18(argumen)m (ts)s 18(unless)m 225 1997 p (the)s 16(problem)m 15 r 98 c 1(eing)m 16(solv)m (ed)s 14(requires)m 15(the)m 16(use)m 16(of)m 15(nondefault)m 16 r 118 c -2(alues.)m 20(Structured)m 16(argumen)m (ts,)s 225 2054 p (describ)s 1(ed)m 16 r 98 c 1(elo)m (w,)s 14(can)m 15(reduce)m 16(the)m 15(amoun)m 116 c 14(of)m 15(storage)m 14(space)m 15(required)m 16(for)m 14(some)m 15(argumen)m (ts,)s 225 2110 p (and)s 15(the)m 16 r 119 c (ork)s 13(required)m 15 r 98 c 121 c 14(the)m 16(user)m 15(to)m 14(initialize)m 14(those)m 15(argumen)m (ts.)s cmbx10.329 @sf 225 2249 p (1.G.i.)s 16(Default)m 17 r 86 c -3(alues)m cmr10.329 @sf 225 2354 p (Default)s 14 r 118 c -2(alues)m 15(ha)m 118 c -1 r 101 c 14 r 98 c 1(een)m 16(sp)m 1(eci\014ed)m 17(for)m 14(ODRP)m -3 r 65 c (CK)s 14(subroutine)m 15(argumen)m (ts)s 14(wherev)m (er)s 14(rea-)m 225 2411 p (sonable.)s 26(These)m 17(default)m 17 r 118 c -2(alues)m 16(are)m 17(in)m 118 c (o)s -1 r 107 c -1(ed)m 16(when)m 17(the)m 18(user)m 17(sets)m 17(the)m 17(corresp)m 1(onding)m 17(argu-)m 225 2467 p (men)s 116 c 14(to)m 15(an)m 121 c 14(negativ)m 101 c 14 r 118 c -2(alue.)m 19(Arra)m (ys)s 14(with)m 15(default)m 15 r 118 c -2(alues)m 14(are)m 15(in)m 118 c (o)s -1 r 107 c -1(ed)m 14 r 98 c 121 c 14(setting)m 15(the)m 15(\014rst)m @eop %%Page: 16 30 16 @bop0 cmti10.329 @sf [<07E000001FF800003C3C0000780F000070070000F0038000F001C000F000C000F000E000F00060 00F80060007800700078003000780030007C0030007C0038003C0018003C0018003E0018003E00 1C001E000C001E000C001F000C001F000E000F0006000F0006000F8006000F8007000780030007 C007C07FFC3FF87FFC3FF8> 32 32 -9 1 33.787] 85 @dc cmmi10.329 @sf [<070003800000070003800000078003C00000078003C0000007C003E0000007C003E0000007E003 F0000007E003F0000007B003D8000007B003DC0000079803CC0000079C03C60000078C03C60000 078603C300000F8603C300000F0303C180000F0307C180000F018780C0000F018780C0000F00C7 8060000F00C78070000F00678030000F00778018000F00378018000F001F800C000F001F800C00 0F000F8006000F000F8007000F00078003001F8007C007C0FFF07FF83FF8FFF07FF83FF8> 48 32 -2 1 42.928] 87 @dc cmr8.300 @sf [ 24 23 -2 0 29.403] 1 @dc [<038007000F000E001C00380038003800700070007000E000E000E000E000E000E000E000E000E0 00E000E000E0007000700070003800380038001C000E000F0007000380> 16 34 -2 9 13.722] 40 @dc [ 16 34 -2 9 13.722] 41 @dc 16 @bop1 cmr10.329 @sf 0 114 p (16)s 1365(Getting)m 14(Started)m 0 134 p 1725 2 ru 0 259 p (elemen)s 116 c 14(of)m 15(the)m 15(arra)m 121 c 14(to)m 14 r 97 c 15(negativ)m 101 c 14 r 118 c -2(alue,)m 14(in)m 15(whic)m 104 c 14(case)m 16(only)m 15(the)m 15(\014rst)m 15 r 118 c -2(alue)m 15(of)m 15(the)m 15(arra)m 121 c 0 315 p (will)s 13(ev)m (er)s 13 r 98 c 1 r 101 c 15(used.)m 20(This)m 14(allo)m -1(ws)m 12 r 97 c 14(scalar)m 13(to)m 14 r 98 c 1 r 101 c 15(used)m 15(to)m 13(in)m 118 c (o)s -1 r 107 c -1 r 101 c 12(the)m 15(default)m 13 r 118 c -2(alues)m 14(of)m 14(arra)m -1(ys,)m 0 372 p (th)s (us)s 14(sa)m (ving)s 13(space)m 16(and)m 15(eliminating)m 13(the)m 16(need)m 16(to)m 14(declare)m 15(suc)m 104 c 15(arra)m (ys.)s cmti10.329 @sf 0 448 p (Users)s 13(ar)m -1 r 101 c 12(enc)m -1(our)m -1(age)m -2 r 100 c 12(to)m 14(invoke)m 13(the)m 14(default)m 14(values)m 13(of)m 14(ar)m -1(guments)m 13(wher)m -1(ever)m 13 r 112 c -1(ossibl)m -1(e.)m cmr10.329 @sf 18(These)m 0 504 p 118 c -2(alues)m 13(ha)m 118 c -1 r 101 c 12 r 98 c 1(een)m 15(found)m 14(to)m 13 r 98 c 1 r 101 c 14(reasonable)m 13(for)m 13 r 97 c 13(wide)m 14(class)m 13(of)m 13(problems.)m 19(Fine)m 13(tuning)m 14(these)m 0 560 p (argumen)s (ts)s 13(can)m 16(then)m 15 r 98 c 1 r 101 c 16(done)m 16(later)m 14(if)m 14(necessary)m -3 r 46 c cmbx10.329 @sf 0 700 p (1.G.ii.)s 15(Structured)m 18(Argumen)m -1(ts)m cmr10.329 @sf 0 805 p (Certain)s 18(ODRP)m -3 r 65 c (CK)s 17(argumen)m (ts)s 16(sp)m 1(ecify)m 19(attributes)m 17(of)m 18(the)m 19(individual)m 18(comp)m 1(onen)m (ts)s 17(of)m cmmi10.329 @sf 18 r 88 c cmr10.329 @sf 4 r 44 c 0 862 p 1 c cmmi10.329 @sf 59 c cmr10.329 @sf 16(and)m cmmi10.329 @sf 16 r 89 c cmr10.329 @sf 10 r 46 c 23(These)m 17(attribute)m 15(arra)m (ys)s 14(are)m 16(frequen)m (tly)s 14(either)m 16(constan)m 116 c 15(for)m 15(all)m 15(comp)m 1(onen)m (ts)s 15(or)m 0 918 p (are)s 17(constan)m 116 c 16(within)m 17(eac)m 104 c 17(column)m 18(and)m 18 r 118 c -2(ary)m 16(only)m 18 r 98 c 1(et)m 119 c -1(een)m 17(the)m 17(columns.)m 28(The)m cmti10.329 @sf 18(structur)m -1 r 101 c -1 r 100 c 0 975 p (ar)s -1(gument)m cmr10.329 @sf 21(facilit)m -1 r 121 c 16(allo)m -1(ws)m 15 r 97 c 17(scalar)m 17(to)m 17(sp)m 1(ecify)m 18(an)m 17(attribute)m 17(of)m 17(an)m 17(en)m (tire)s 16(column)m 18(or)m 17(of)m 17(the)m 0 1031 p (whole)s 15(arra)m 121 c -4 r 46 c 0 1107 p 70 c -3(or)m 31(example,)m 36(ODRP)m -3 r 65 c (CK)s 31(argumen)m 116 c cmtt10.329 @sf 30(WD)m cmr10.329 @sf 32(sp)m 1(eci\014es)m 34(the)m 32(attribute)m 31(arra)m 121 c 30(of)m 32 r 119 c (eigh)s -1(ts)m cmmi10.329 @sf 0 1164 p 87 c cmr8.300 @sf 32 1171 p 1 c cmsy10.329 @sf 75 1164 p 50 c 13 r 60 c cmmi8.300 @sf 151 1149 p 110 c cmsy8.300 @sf 2 c cmr8.300 @sf 40 c cmmi8.300 @sf 109 c cmsy8.300 @sf 2 c cmmi8.300 @sf 109 c cmr8.300 @sf 41 c cmr10.329 @sf 339 1164 p (whose)s cmmi10.329 @sf 19 r 105 c cmr10.329 @sf (th)s 19(comp)m 1(onen)m 116 c 19(sp)m 1(eci\014es)m 21(the)m 19(elemen)m (ts)s 19(of)m cmmi10.329 @sf 19 r 119 c cmmi8.300 @sf 1330 1171 p 14 c cmmi6.300 @sf 1346 1176 p 105 c cmmi10.329 @sf 1359 1164 p 59 c 27 r 105 c cmr10.329 @sf 20 r 61 c 20 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 7 r 58 c 6 r 59 c 8 r 110 c cmr10.329 @sf 19(\(cf.)m 0 1220 p (\(1.8\))s 13(and)m 15(\(1.9\)\).)m 17(Supp)m 1(ose)m cmmi10.329 @sf 16 r 88 c cmr10.329 @sf 17(con)m (tains)s 13(temp)m 1(erature)m 14(measuremen)m (ts,)s 13(where)m 15(eac)m 104 c 14(ro)m 119 c 12(indi-)m 0 1277 p (cates)s 12 r 97 c 12(di\013eren)m 116 c 10(hour)m 13(at)m 11(whic)m 104 c 11(the)m 13(readings)m 11 r 119 c (ere)s 11(tak)m (en,)s 11(and)m 13(eac)m 104 c 11(column)m 12 r 97 c 12(di\013eren)m 116 c 10(da)m 121 c -3 r 46 c 0 1333 p (Then)s 16(the)m 15(user)m 16(migh)m 116 c 13 r 119 c (an)s -1 r 116 c 13(to)m 15 r 119 c (eigh)s -1 r 116 c 13(eac)m 104 c 15(comp)m 1(onen)m 116 c 14(of)m 15 r 1 c 15(equally)m -3 r 44 c 14(and)m 15(th)m (us)s cmmi10.329 @sf 15 r 87 c cmr8.300 @sf 1562 1340 p 1 c cmr10.329 @sf 1608 1333 p 119 c (ould)s 0 1390 p 98 c 1 r 101 c 13(constan)m 116 c 11(throughout.)m 18(If)m 12(one)m 13(column)m 12(of)m cmmi10.329 @sf 12 r 88 c cmr10.329 @sf 16(con)m (tained)s 11(hourly)m 12(temp)m 1(erature)m 12(readings)m 12(and)m 0 1446 p (the)s 14(other)m 13(hourly)m 13 r 104 c (umidit)s -1 r 121 c 11(readings,)m 13(ho)m 119 c (ev)s -2(er,)m 12(then)m 14(the)m 13(user)m 14 r 119 c (ould)s 12(probably)m 13(not)m 13 r 119 c (an)s -1 r 116 c 12(to)m 0 1502 p 119 c (eigh)s -1 r 116 c 14(the)m 16(errors)m 15(in)m 16(the)m 17(temp)m 1(erature)m 16(measuremen)m (ts)s 14(the)m 16(same)m 16(as)m 16(those)m 16(in)m 16(the)m 16 r 104 c (umidit)s -1 r 121 c 0 1559 p (measuremen)s (ts,)s 15(but)m 17(migh)m 116 c 14 r 119 c (an)s -1 r 116 c 15(to)m 15(sp)m 1(ecify)m 17(the)m 17(same)m 16 r 119 c (eigh)s -1 r 116 c cmmi10.329 @sf 14 r 119 c cmmi8.300 @sf 1214 1566 p 15 c cmr10.329 @sf 1246 1559 p (for)s 16(eac)m 104 c 15(observ)m -2(ation.)m 22(In)m 0 1615 p (this)s 18(case,)m 20(the)m 19(comp)m 1(onen)m (ts)s 18(of)m cmmi10.329 @sf 18 r 87 c cmr8.300 @sf 629 1622 p 1 c cmr10.329 @sf 679 1615 p 119 c (ould)s 17 r 98 c 1 r 101 c 19(constan)m 116 c 17(for)m 19(eac)m 104 c 18(ro)m 119 c cmmi10.329 @sf 17(i;)m 25 r 105 c cmr10.329 @sf 19 r 61 c 19 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 7 r 58 c 5 r 59 c 8 r 110 c cmr10.329 @sf 46 c 31(Of)m 0 1672 p (course,)s 16(in)m 15(other)m 16(cases,)m 16(the)m 16(user)m 16(migh)m 116 c 13 r 119 c (an)s 116 c 13(to)m 15 r 119 c (eigh)s 116 c 13(eac)m 104 c 15(comp)m 1(onen)m 116 c 15(of)m 16 r 1 c 15(di\013eren)m (tly)s -4 r 44 c 0 1728 p (and)s 15(th)m (us)s 14(eac)m 104 c 15(comp)m 1(onen)m 116 c 14(of)m cmmi10.329 @sf 15 r 87 c cmr8.300 @sf 607 1735 p 1 c cmr10.329 @sf 652 1728 p 119 c (ould)s 14 r 98 c 1 r 101 c 16(di\013eren)m (t.)s 0 1804 p (ODRP)s -3 r 65 c (CK)s 15(structured)m 17(argumen)m (ts)s 15(exploit)m 16(this)m 16(structure.)m 24(If)m 17(eac)m 104 c 16(of)m 16(the)m 17(elemen)m (ts)s 16(of)m 16(an)m 0 1861 p (attribute)s 11(arra)m 121 c 10(is)m 11(the)m 12(same,)m 12(then)m 12 r 97 c 12(scalar)m 11(can)m 12 r 98 c 1 r 101 c 13(used)m 12(to)m 12(sp)m 1(ecify)m 12(all)m 11(elemen)m (ts)s 11(of)m 11(the)m 12(arra)m 121 c -4 r 46 c 0 1917 p (If)s 16(the)m 15 r 118 c -2(alues)m 15(of)m 15(suc)m 104 c 15(an)m 16(arra)m -1 r 121 c 14(only)m 15 r 118 c -2(ary)m 14 r 98 c 1(et)m 119 c (een)s 14(the)m 16(columns,)m 15(then)m 16(eac)m 104 c 14(column)m 16(of)m 15(the)m 0 1974 p (arra)s 121 c 15(can)m 16 r 98 c 1 r 101 c 18(sp)m 1(eci\014ed)m 18 r 98 c 121 c 16 r 97 c 16(single)m 16 r 118 c -2(alue)m 16(using)m 17 r 97 c 16(ro)m 119 c 15 r 118 c (ector.)s 23(Th)m (us,)s 16(it)m 16(is)m 16(only)m 17(necessary)m 0 2030 p (for)s 17(the)m 19(user)m 18(to)m 17(supply)m 19(all)m 17(elemen)m (ts)s 17(of)m 17(an)m 18(attribute)m 17(arra)m 121 c 16(when)m 19(the)m 18(elemen)m (ts)s 17(of)m 17(one)m 18(or)m 0 2087 p (more)s 17(of)m 17(the)m 17(columns)m 17 r 109 c (ust)s 16 r 98 c 1 r 101 c 18(individually)m 16(sp)m 1(eci\014ed.)m 27(The)m 17(use)m 18(of)m 17(structured)m 17(argumen)m (ts)s 0 2143 p (in)s 15(describ)m 1(ed)m 16(in)m 15(detail)m 14(in)m cmsy10.329 @sf 15 r 120 c cmr10.329 @sf 1(2.B.ii.)m 18(\(See,)m 15(e.g.,)m 14(subroutine)m 15(argumen)m 116 c cmtt10.329 @sf 14(WD)m cmr10.329 @sf -1(.\))m @eop %%Page: 17 31 17 @bop0 cmcsc10.518 @sf [ 32 47 -5 0 39.650] 50 @dc [<000007F800000000003FFF0000000000FC07C000000001F000E000000003C000300000000F8000 180000001F80000C0000001F0000060000003F0000030000007E0000030000007E000001800000 FE000001800000FC000001800001FC000000C00001FC000000C00001FC000000C00001FC000000 C00001FC000000C00001FC000000C00001FC000000C00001FC000000C00001FC000000C00001FC 000000C00001FC000000C00001FC000000C00001FC000000C00001FC000000C00001FC000000C0 0001FC000000C00001FC000000C00001FC000000C00001FC000000C00001FC000000C00001FC00 0000C00001FC000000C00001FC000000C00001FC000000C00001FC000000C00001FC000000C000 01FC000000C00001FC000000C00001FC000000C00001FC000000C00001FC000000C00001FC0000 00C00001FC000001E00001FC000003F00003FE000007F800FFFFF8007FFF80FFFFF8007FFF80> 56 50 -4 1 58.379] 85 @dc [<00000FFC00000000007FFF8000000003F807F00000000FE001FC0000001F80007E0000007F0000 3F800000FE00001FC00001FC00000FE00003F8000007F00007F0000003F80007F0000003F8000F E0000001FC001FE0000001FE001FC0000000FE003FC0000000FF003F800000007F003F80000000 7F007F800000007F807F800000007F807F800000007F80FF000000003FC0FF000000003FC0FF00 0000003FC0FF000000003FC0FF000000003FC0FF000000003FC0FF000000003FC0FF000000003F C0FF000000003FC0FF000000003FC07F000000003F807F000000003F807F000000003F807F8000 00007F803F800000007F003F800000007F003F800000007F001FC0000000FE000FC0000000FC00 0FE0000001FC0007E0000001F80003F0000003F00003F8000007F00001F8000007E00000FC0000 0FC000003E00001F0000001F80007E0000000FE001FC00000003F807F0000000007FFF80000000 000FFC000000> 56 51 -5 1 60.571] 79 @dc [ 56 49 -4 0 59.475] 68 @dc [ 56 49 -4 0 60.471] 75 @dc cmbx12.300 @sf [ 24 32 -3 0 28.019] 50 @dc 17 @bop1 cmcsc10.518 @sf 225 519 p (2.)s 35(Using)m 27(ODRP)m -5 r 65 c -1(CK)m cmbx12.300 @sf 225 747 p (2.A.)s 18(Subroutine)m 18(Declaration)m 18(and)m 19(Call)m 19(Statemen)m -1(ts)m cmr10.329 @sf 225 868 p (The)s 19(declaration)m 17(and)m 18(call)m 18(statemen)m (ts)s 16(for)m 17(ODRP)m -3 r 65 c (CK's)s 17(user)m 18(callable)m 18(routines)m 17(are)m 18(giv)m (en)s 225 925 p 98 c 1(elo)m (w.)s cmtt10.329 @sf 24(DODR)m cmr10.329 @sf 16(and)m cmtt10.329 @sf 17(DODRC)m cmr10.329 @sf 17(in)m 118 c -1(ok)m -1 r 101 c 15(the)m 17(double)m 17(precision)m 17 r 118 c (ersion)s 15(of)m 16(the)m 18(co)m 1(de)m 17(and)m cmtt10.329 @sf 17(SODR)m cmr10.329 @sf 17(and)m cmtt10.329 @sf 225 981 p (SODRC)s cmr10.329 @sf 18(in)m 118 c (o)s -1 r 107 c -1 r 101 c 17(the)m 20(single)m 18(precision)m 19 r 118 c (ersion.)s cmtt10.329 @sf 29(DODR)m cmr10.329 @sf 19(and)m cmtt10.329 @sf 19(SODR)m cmr10.329 @sf 19(preset)m 19(man)m 121 c 17(argumen)m (ts)s 18(to)m 225 1038 p (their)s 16(default)m 16 r 118 c -2(alues)m 16(and)m 17(therefore)m 16(ha)m 118 c -1 r 101 c 15(shorter)m 16(call)m 16(statemen)m (ts)s 14(than)m cmtt10.329 @sf 16(DODRC)m cmr10.329 @sf 16(and)m cmtt10.329 @sf 17(SODRC)m cmr10.329 @sf -1 r 46 c 225 1094 p (In)s 16(con)m (trast)s -1 r 44 c cmtt10.329 @sf 13(DODRC)m cmr10.329 @sf 14(and)m cmtt10.329 @sf 15(SODRC)m cmr10.329 @sf 14(ha)m 118 c 101 c 13(expanded)m 16(call)m 14(statemen)m (ts)s 12(that)m 15(giv)m 101 c 13(the)m 15(user)m 15(greater)m 225 1150 p (con)s (trol)s 13(in)m 15(solving)m 14(the)m 15(orthogonal)m 14(distance)m 15(regression)m 14(problem.)m 225 1226 p (The)s 20(information)m 18(in)m 20(this)m 19(section,)m cmsy10.329 @sf 21 r 120 c cmr10.329 @sf (2.A,)s 20(is)m 19(pro)m (vided)s 19(primarily)m 18(for)m 20(reference.)m 34(Users)m 20(are)m 225 1283 p (directed)s 20(to)m cmsy10.329 @sf 19 r 120 c cmr10.329 @sf (2.B)s 19(for)m 19(de\014nitions)m 20(of)m 19(the)m 20(subroutine)m 20(argumen)m (ts,)s 18(and)m 20(to)m cmsy10.329 @sf 19 r 120 c cmr10.329 @sf (2.C)s 19(for)m 19(sample)m 225 1339 p (programs.)s 18(The)m 14(examples,)m 13(whic)m 104 c 12(use)m 14 r 70 c -3(ortra)m -1 r 110 c cmtt10.329 @sf 12(PARAMETER)m cmr10.329 @sf 12(statemen)m (ts)s 11(to)m 13(dimension)m 13(ODR-)m 225 1396 p 80 c -3 r 65 c (CK)s 16(arra)m (ys)s -1 r 44 c 16(pro)m (vide)s 17 r 97 c 17(recommended)m 18(format)m 17(for)m 17(creating)m 17(an)m 17(ODRP)m -3 r 65 c (CK)s 17(driv)m (er)s 16(that)m 225 1452 p (will)s 14(allo)m -1 r 119 c 13(future)m 15 r 99 c (hanges)s 15(to)m 14 r 98 c 1 r 101 c 16(made)m 15(easily)m -3 r 46 c 225 1528 p (Note)s 16(that)m 15(although)m 16(ODRP)m -3 r 65 c (CK)s 15(is)m 15(distributed)m 16(in)m 16 r 98 c 1(oth)m 16(single)m 16(precision)m 16(and)m 16(double)m 17(pre-)m 225 1585 p (cision)s 14 r 118 c (ersions,)s 13 r 98 c 1(oth)m 16 r 118 c (ersions)s 13(ma)m 121 c 13(not)m 15 r 98 c 1 r 101 c 16 r 97 c 118 c -2(ai)m -1(labl)m -1 r 101 c 14(to)m 14(all)m 14(users.)m 20(In)m 16(addition,)m 14(ev)m (en)s 14(when)m 225 1641 p 98 c 1(oth)m 16 r 118 c (ersions)s 13(are)m 15 r 97 c 118 c -2(ail)m -1(able,)m 13(the)m 16(single)m 14(precision)m 15 r 118 c (ersion)s 14(ma)m 121 c 14(not)m 15 r 98 c 1 r 101 c 16(appropriate)m 14(to)m 15(use.)m 225 1698 p (This)s 13(is)m 13 r 98 c 1(ecause)m 14(ODRP)m -3 r 65 c (CK)s 12(is)m 12(sensitiv)m 101 c 12(to)m 12(the)m 14(mac)m (hine's)s 11(precision,)m 13(and)m 13(requires)m 13(appro)m (x-)s 225 1754 p (imately)s 16(14)m 18(decimal)m 17(places.)m 27(Somewhat)m 17(few)m (er)s 17(places)m 17(should)m 18(still)m 16 r 119 c (ork,)s 16(but)m 18(six)m 17(or)m 18(sev)m (en)s 225 1811 p (decimal)s 17(places)m 16(are)m 17(de\014nitely)m 17(to)m 1 r 111 c 17(few)m 17(for)m 16(general)m 17(use,)m 17(since)m 17(only)m 17(the)m 17(simplest)m 16(problems)m 225 1867 p (could)s 14 r 98 c 1 r 101 c 16(solv)m (ed)s 12(correctly)m 14(at)m 14(suc)m 104 c 14(reduced)m 15(precisions.)m 19(When)m 15 r 98 c 1(oth)m 15 r 118 c (ersions)s 12(are)m 15 r 97 c 118 c -2(a)m -1(ila)m -1(ble,)m 225 1924 p (the)s 13(user)m 13 r 109 c (ust)s 11 r 99 c (ho)s 1(ose)m 12(whic)m 104 c 12 r 118 c (ersion)s 11(of)m 12(ODRP)m -3 r 65 c (CK)s 12(to)m 12(use)m 13(based)m 13(up)m 1(on)m 14(whic)m 104 c 11 r 118 c (ersion)s 11(sup-)m 225 1980 p (plies)s 13(adequate)m 13(precision)m 13(on)m 13(the)m 14(target)m 12(mac)m (hine.)s 18 r 84 c -3 r 111 c 12(our)m 13(kno)m (wledge,)s 12(at)m 13(presen)m 116 c 12(only)m 13(Cra)m 121 c 225 2036 p (and)s 13(CDC)m 13(mac)m (hines)s 11(o\013er)m 13(su\016cien)m 116 c 11(precision)m 13(to)m 13 r 112 c 1(ermit)m 12(general)m 13(use)m 13(of)m 13(the)m 13(single)m 12(precision)m 225 2093 p 118 c (ersion)s 11(of)m 12(ODRP)m -3 r 65 c (CK.)s 12 r 70 c -3(or)m 11(other)m 12(mac)m (hines,)s 12 r 119 c 101 c 11(recommend)m 14(the)m 13(double)m 13(precision)m 12 r 118 c (ersion.)s 225 2169 p (If)s 21 r 98 c 1(oth)m 21 r 118 c (ersions)s 19(of)m 20(ODRP)m -3 r 65 c (CK)s 20(ha)m 118 c -1 r 101 c 19(su\016cien)m 116 c 20(precision)m 20(on)m 21(the)m 20(user's)m 21(mac)m (hine,)s 21(then)m 225 2225 p (either)s 16(ma)m 121 c 14 r 98 c 1 r 101 c 17(used.)m 23(When)m 16 r 98 c 1(oth)m 16(the)m 16(single)m 16(and)m 16(double)m 16(precision)m 16 r 118 c (ersions)s 14(are)m 16 r 97 c 118 c -2(a)m -1(ila)m -1(ble,)m 225 2282 p (ho)s 119 c -1(ev)m -1(er,)m 20(there)m 22(are)m 21(generally)m 20(trade-o\013s)m 20 r 98 c 1(et)m 119 c (een)s 19(them.)m 38(The)m 22(double)m 21(precision)m 21 r 118 c (ersion)s 225 2338 p (will)s 15(o\013er)m 15(greater)m 15(accuracy)m 15(in)m 16(results,)m 15(while)m 15(the)m 16(single)m 16(precision)m 15 r 118 c (ersion)s 14(will)m 15(require)m 15(less)m 225 2395 p (storage)s 14(and)m 15 r 112 c 1(ossibly)m 15(less)m 15(mac)m (hine)s 14(time.)m 1065 2581 p (17)s @eop %%Page: 18 32 18 @bop0 1.000000 /cmtt10.300 @newfont cmtt10.300 @sf [ 24 25 0 0 21.793] 68 @dc [<1FFC003FFE007FFF00780F00F00780F00780E00380E00380E00380E00380E00380E00380E00380 E00380E00380E00380E00380E00380E00380E00380F00780780F007FFF003FFE001FFC00> 24 25 -2 0 21.793] 79 @dc [ 24 25 -1 0 21.793] 82 @dc cmr10.300 @sf [<70F8F8F870000000000000000070F8F8F870> 8 18 -3 0 11.531] 58 @dc [ 24 18 0 0 21.908] 120 @dc [<01C0700001C0700001C0700003E0F80003E0F80003E0F8000760CC000731CC000731CC000E318E 000E1B86000E1B86000E1B06001C1F03001C0F03003C0F0780FF3FCFE0FF3FCFE0> 32 18 -1 0 29.980] 119 @dc [<001FF0001FF000038000038000038000038000038000038007E3801FFB803E1F807C0F80780780 F80380F00380F00380F00380F00380F00380F003807803807807803C0F803F1F801FF98007F180> 24 26 -1 8 21.908] 113 @dc [ 24 28 -2 0 28.250] 80 @dc cmtt10.300 @sf [ 24 25 -1 0 21.793] 80 @dc [<03E7000FFF001FFF003F1F003C0F00780F00780F00700700F00700E07FC0E07FC0E07FC0E00000 E00000E00000E00000F00000700700780700780F003C0F003F1F001FFF000FFF0003F300> 24 25 -2 0 21.793] 71 @dc [ 24 25 -1 0 21.793] 65 @dc [ 24 25 -1 0 21.793] 77 @dc [ 16 25 -3 0 21.793] 73 @dc [ 24 25 -1 0 21.793] 78 @dc [ 8 32 -9 3 21.793] 124 @dc [ 24 25 -1 0 21.793] 69 @dc [ 24 25 -1 0 21.793] 88 @dc [<0FFE000FFE000FFE0000E00000E00000E00000E00000E00000E00000E00000E00000E00000E000 00E00000E00000E00000E00000E000E0E0E0E0E0E0E0E0E0E0E0E0FFFFE0FFFFE0FFFFE0> 24 25 -1 0 21.793] 84 @dc [ 24 25 -1 0 21.793] 76 @dc [<01C00001C00001C00001C00001C00001C00001C00001C000FFFF80FFFF80FFFF8001C00001C000 01C00001C00001C00001C00001C00001C000> 24 19 -2 -3 21.793] 43 @dc [ 24 25 -1 0 21.793] 70 @dc [<03F00007FC000FFE001F0F003C0780780380780380700380F00000E00000E00000E00000E00000 E00000E00000E00000F000007003807803807807803C07801F0F800FFF8007FF8003F180> 24 25 -2 0 21.793] 67 @dc [<60F8FC3C1E0E3E7E7E7C38> 8 11 -7 6 21.793] 44 @dc [<000700000700000F00000E00001E00001C001FFC003FFE007FFF00787F00F0F780E1E380E0E380 E00380E00380E00380E00380E00380E00380E00380E00380E00380E00380E00380E00380E00380 F00780780F007FFF003FFE001FFC00> 24 31 -2 6 21.793] 81 @dc [<07FC0007FC0007FC0000E00000E00000E00000E00000E00000E00000E00000E00001F00001F000 03B80003B800071C00071C00071C000E0E000E0E001C07001C0700FF1FE0FF1FE0FF1FE0> 24 25 -1 0 21.793] 89 @dc [<0E0E000F1E000F1E001B1B0019130019B30019B30019B30019B30019B30019B30039B38039F380 39F38038E3803803803803803803803001807001C07001C07001C0FE0FE0FE0FE0FE0FE0> 24 25 -1 0 21.793] 87 @dc [ 24 25 -2 0 21.793] 50 @dc [<1FC07FE0FFF0F0F8F078F038003800380038003800380038003800380038003800380038003800 380038003807FF07FF07FF> 16 25 -3 0 21.793] 74 @dc [ 24 25 -1 0 21.793] 66 @dc [<00F80003FE0007FF000F8F800F07801E03C01E03C01C01C01C01C01C01C01C01C01C01C01C01C0 1C01C01C01C01C01C01C01C01C01C01C01C01C01C01C01C01C01C0FF8FF8FF8FF8FF8FF8> 24 25 0 0 21.793] 85 @dc [ 24 25 0 0 21.793] 75 @dc [<00E001E007C007800F001E003C0038007800700070007000F000E000E000E000E000E000E000E0 00F000700070007000780038003C001E000F00078007C001E000E0> 16 33 -6 4 21.793] 40 @dc [ 16 33 -4 4 21.793] 41 @dc [ 24 25 -2 0 21.793] 83 @dc 18 @bop1 cmr10.329 @sf 0 114 p (18)s 1319(Using)m 15(ODRP)m -3 r 65 c (CK)s 0 134 p 1725 2 ru cmtt10.300 @sf 22 259 p (DODR)s cmr10.300 @sf -1 r 58 c 22(Compute)m 17(the)m 17(explicit)m 16(or)m 17(implicit)m 15 r 119 c (eigh)s (ted)s 15(orthogonal)m 15(distance)m 18(regression,)m 18(or)m 17(linear)m 16(or)m 143 308 p (nonlinear)s 19(ordinary)m 20(least)m 20(squares)m 21(solution)m 19(in)m 19(double)m 19(precision.)m 37(Deriv)m -1(ativ)m -2(es)m 19(are)m 20(either)m 143 358 p (supplied)s 13 r 98 c 121 c 12(the)m 13(user)m 15(or)m 12 r 110 c (umerically)s 11(appro)m (ximated)s 11 r 98 c 121 c 12(ODRP)m -2 r 65 c -1(CK.)m 11(Con)m (trol)s 11 r 118 c -1(ariables)m 11(are)m 143 408 p (preset)s 18(to)m 16(their)m 16(default)m 16 r 118 c -1(alues,)m 15(and)m 16 r 97 c 15(three)m 18(part)m 16(rep)m 1(ort)m 17(of)m 15(the)m 17(results)m 17(can)m 16 r 98 c 1 r 101 c 17(optionally)m 143 458 p (generated.)s cmtt10.300 @sf 367 545 p (PROGRAM)s 21(MAIN)m 367 595 p 124 c 367 645 p (EXTERNAL)s 346 695 p 43 c 65(FCN)m 367 744 p (INTEGER)s 346 794 p 43 c 65(N,M,NP,NQ,)m 346 844 p 43 c 65(LDY,LDX,)m 20(LDWE,LD2WE,LD)m -1(WD,L)m -1(D2WD,)m 346 894 p 43 c 65(JOB,)m 21(IPRINT,LUNER)m -1(R,LUN)m -1(RPT,)m 346 944 p 43 c 65(LWORK,LIWORK)m -1 r 44 c 20(INFO)m 367 994 p (INTEGER)s 346 1043 p 43 c 65(IWORK\(LIWORK)m -1 r 41 c 367 1093 p (DOUBLE)s 21(PRECISION)m 346 1143 p 43 c 65(BETA\(NP\),)m 20(Y\(LDY,NQ\),X\()m -1(LDX,)m -1(M\),)m 346 1193 p 43 c 65(WE\(LDWE,LD2W)m -1(E,NQ\))m -1(,WD\(L)m -1(DWD,)m -1(LD2WD)m -1(,M\),)m 346 1243 p 43 c 65(WORK\(LWORK\))m 367 1292 p 124 c 367 1342 p (CALL)s 21(DODR)m 346 1392 p 43 c 65(\(FCN,)m 346 1442 p 43 c 65(N,M,NP,NQ,)m 346 1492 p 43 c 65(BETA,)m 346 1541 p 43 c 65(Y,LDY,X,LDX,)m 346 1591 p 43 c 65(WE,LDWE,LD2W)m -1(E,WD,)m -1(LDWD,)m -1(LD2W)m -1(D,)m 346 1641 p 43 c 65(JOB,)m 346 1691 p 43 c 65(IPRINT,LUNER)m -1(R,LUN)m -1(RPT,)m 346 1741 p 43 c 65(WORK,LWORK,I)m -1(WORK,)m -1(LIWOR)m -1(K,)m 346 1791 p 43 c 65(INFO\))m 367 1840 p 124 c 367 1890 p (END)s @eop %%Page: 19 33 19 @bop0 19 @bop1 cmr10.329 @sf 225 114 p (Using)s 15(ODRP)m -3 r 65 c (CK)s 1318(19)m 225 134 p 1725 2 ru cmtt10.300 @sf 225 259 p (DODRC)s cmr10.300 @sf -1 r 58 c 22(Compute)m 17(the)m 17(explicit)m 16(or)m 17(implicit)m 15 r 119 c (eigh)s (ted)s 15(orthogonal)m 15(distance)m 18(regression,)m 18(or)m 17(linear)m 16(or)m 368 308 p (nonlinear)s 19(ordinary)m 20(least)m 20(squares)m 21(solution)m 19(in)m 19(double)m 19(precision.)m 37(Deriv)m -1(ativ)m -2(es)m 19(are)m 20(either)m 368 358 p (supplied)s 18 r 98 c 121 c 16(the)m 18(user)m 18(or)m 17 r 110 c (umerically)s 16(appro)m (xima)s -1(ted)m 16 r 98 c 121 c 16(ODRP)m -2 r 65 c (CK.)s 15(Con)m (trol)s 15 r 118 c -1(alues)m 16(are)m 368 408 p (supplied)s 13 r 98 c 121 c 12(the)m 14(user,)m 13(and)m 13 r 97 c 13(three)m 14(part)m 13(rep)m 1(ort)m 14(of)m 13(the)m 13(results)m 14(can)m 14 r 98 c 1 r 101 c 13(optionally)m 11(generated.)m cmtt10.300 @sf 592 495 p (PROGRAM)s 21(MAIN)m 592 545 p 124 c 592 595 p (EXTERNAL)s 571 645 p 43 c 65(FCN)m 592 695 p (INTEGER)s 571 744 p 43 c 65(N,M,NP,NQ,)m 571 794 p 43 c 65(LDY,LDX,)m 20(LDWE,LD2WE,L)m -1(DWD,L)m -1(D2WD,)m 19(LDIFX,)m 571 844 p 43 c 65(JOB,NDIGIT,)m 19(MAXIT,)m 21(IPRINT,LUNER)m -1(R,LUN)m -1(RPT,)m 571 894 p 43 c 65(LDSTPD,)m 20(LDSCLD,)m 21(LWORK,LIWO)m -1(RK,)m 20(INFO)m 592 944 p (INTEGER)s 571 994 p 43 c 65(IFIXB\(NP\),IF)m -1(IXX\(L)m -1(DIFX)m -1(,M\),)m 19(IWORK\(LIWORK\))m 592 1043 p (DOUBLE)s 21(PRECISION)m 571 1093 p 43 c 65(TAUFAC,)m 20(SSTOL,PARTOL)m 592 1143 p (DOUBLE)s 21(PRECISION)m 571 1193 p 43 c 65(BETA\(NP\),)m 20(Y\(LDY,NQ\),X)m -1(\(LDX,)m -1(M\),)m 571 1243 p 43 c 65(WE\(LDWE,LD2W)m -1(E,NQ\))m -1(,WD\()m -1(LDWD,)m -1(LD2WD)m -1(,M\),)m 571 1292 p 43 c 65(STPB\(NP\),STP)m -1(D\(LDS)m -1(TPD,)m -1(M\),)m 20(SCLB\(NP\),SC)m -1(LD\(LD)m -1(SCLD,)m -1(M\),)m 571 1342 p 43 c 65(WORK\(LWORK\))m 592 1392 p 124 c 592 1442 p (CALL)s 21(DODRC)m 571 1492 p 43 c 65(\(FCN,)m 571 1541 p 43 c 65(N,M,NP,NQ,)m 571 1591 p 43 c 65(BETA,)m 571 1641 p 43 c 65(Y,LDY,X,LDX,)m 571 1691 p 43 c 65(WE,LDWE,LD2W)m -1(E,WD,)m -1(LDWD)m -1(,LD2W)m -1(D,)m 571 1741 p 43 c 65(IFIXB,IFIXX,)m -1(LDIFX)m -1 r 44 c 571 1791 p 43 c 65(JOB,NDIGIT,T)m -1(AUFAC)m -1 r 44 c 571 1840 p 43 c 65(SSTOL,PARTOL)m -1(,MAXI)m -1(T,)m 571 1890 p 43 c 65(IPRINT,LUNER)m -1(R,LUN)m -1(RPT,)m 571 1940 p 43 c 65(STPB,STPD,LD)m -1(STPD,)m 571 1990 p 43 c 65(SCLB,SCLD,LD)m -1(SCLD,)m 571 2040 p 43 c 65(WORK,LWORK,I)m -1(WORK,)m -1(LIWO)m -1(RK,)m 571 2089 p 43 c 65(INFO\))m 592 2139 p 124 c 592 2189 p (END)s @eop %%Page: 20 34 20 @bop0 20 @bop1 cmr10.329 @sf 0 114 p (20)s 1319(Using)m 15(ODRP)m -3 r 65 c (CK)s 0 134 p 1725 2 ru cmtt10.300 @sf 22 259 p (SODR)s cmr10.300 @sf -1 r 58 c 22(Compute)m 17(the)m 17(explicit)m 16(or)m 17(implicit)m 15 r 119 c (eigh)s (ted)s 15(orthogonal)m 15(distance)m 18(regression,)m 18(or)m 17(linear)m 16(or)m 143 308 p (nonlinear)s 17(ordinary)m 17(least)m 17(squares)m 19(solution)m 16(in)m 17(single)m 17(precision.)m 29 r 40 c cmtt10.300 @sf (SODR)s cmr10.300 @sf 17(is)m 17(appropriate)m 17(for)m 143 358 p (general)s 11(use)m 11(only)m 10(on)m 10(mac)m (hines)s 10(with)m 10(appro)m (xim)s -1(ately)m 9(14)m 10(decimal)m 9(places)m 11(of)m 10(precision)m 11(for)m 10(single)m 143 408 p (precision.\))s 21(Deriv)m -1(ativ)m -1(es)m 14(are)m 15(either)m 15(supplied)m 15 r 98 c 121 c 14(the)m 15(user)m 16(or)m 15 r 110 c (umerically)s 12(appro)m (ximated)s 13 r 98 c 121 c 143 458 p (ODRP)s -2 r 65 c (CK.)s 10(Con)m (trol)s 10 r 118 c -1(ariables)m 11(are)m 13(preset)m 14(to)m 12(their)m 13(default)m 12 r 118 c -1(alues,)m 11(and)m 12 r 97 c 13(three)m 13(part)m 13(rep)m 1(ort)m 143 508 p (of)s 13(the)m 15(results)m 15(can)m 14 r 98 c 1 r 101 c 15(optionally)m 11(generated.)m cmtt10.300 @sf 367 595 p (PROGRAM)s 21(MAIN)m 367 645 p 124 c 367 695 p (EXTERNAL)s 346 744 p 43 c 65(FCN)m 367 794 p (INTEGER)s 346 844 p 43 c 65(N,M,NP,NQ,)m 346 894 p 43 c 65(LDY,LDX,)m 20(LDWE,LD2WE,LD)m -1(WD,L)m -1(D2WD,)m 346 944 p 43 c 65(JOB,)m 21(IPRINT,LUNER)m -1(R,LUN)m -1(RPT,)m 346 994 p 43 c 65(LWORK,LIWORK)m -1 r 44 c 20(INFO)m 367 1043 p (INTEGER)s 346 1093 p 43 c 65(IWORK\(LIWORK)m -1 r 41 c 367 1143 p (REAL)s 346 1193 p 43 c 65(BETA\(NP\),)m 20(Y\(LDY,NQ\),X\()m -1(LDX,)m -1(M\),)m 346 1243 p 43 c 65(WE\(LDWE,LD2W)m -1(E,NQ\))m -1(,WD\(L)m -1(DWD,)m -1(LD2WD)m -1(,M\),)m 346 1292 p 43 c 65(WORK\(LWORK\))m 367 1342 p 124 c 367 1392 p (CALL)s 21(SODR)m 346 1442 p 43 c 65(\(FCN,)m 346 1492 p 43 c 65(N,M,NP,NQ,)m 346 1541 p 43 c 65(BETA,)m 346 1591 p 43 c 65(Y,LDY,X,LDX,)m 346 1641 p 43 c 65(WE,LDWE,LD2W)m -1(E,WD,)m -1(LDWD,)m -1(LD2W)m -1(D,)m 346 1691 p 43 c 65(JOB,)m 346 1741 p 43 c 65(IPRINT,LUNER)m -1(R,LUN)m -1(RPT,)m 346 1791 p 43 c 65(WORK,LWORK,I)m -1(WORK,)m -1(LIWOR)m -1(K,)m 346 1840 p 43 c 65(INFO\))m 367 1890 p 124 c 367 1940 p (END)s @eop %%Page: 21 35 21 @bop0 21 @bop1 cmr10.329 @sf 225 114 p (Using)s 15(ODRP)m -3 r 65 c (CK)s 1318(21)m 225 134 p 1725 2 ru cmtt10.300 @sf 225 259 p (SODRC)s cmr10.300 @sf -1 r 58 c 22(Compute)m 17(the)m 17(explicit)m 16(or)m 17(implicit)m 15 r 119 c (eigh)s (ted)s 15(orthogonal)m 15(distance)m 18(regression,)m 18(or)m 17(linear)m 16(or)m 368 308 p (nonlinear)s 15(ordinary)m 15(least)m 16(squares)m 17(solution)m 15(in)m 15(single)m 16(precision.)m 23 r 40 c cmtt10.300 @sf (SODRC)s cmr10.300 @sf 15(is)m 16(appropriate)m 15(for)m 368 358 p (general)s 11(use)m 11(only)m 10(on)m 10(mac)m (hines)s 10(with)m 10(appro)m (xim)s -1(ately)m 9(14)m 10(decimal)m 9(places)m 11(of)m 10(precision)m 11(for)m 10(single)m 368 408 p (precision.\))s 21(Deriv)m -1(ativ)m -1(es)m 14(are)m 15(either)m 15(supplied)m 15 r 98 c 121 c 14(the)m 15(user)m 16(or)m 15 r 110 c (umerically)s 12(appro)m (ximated)s 13 r 98 c 121 c 368 458 p (ODRP)s -2 r 65 c (CK.)s 16(Con)m (trol)s 17 r 118 c -1(al)m -1(ues)m 18(are)m 19(supplied)m 18 r 98 c 121 c 18(the)m 19(user,)m 20(and)m 18 r 97 c 18(three)m 20(part)m 19(rep)m 1(ort)m 19(of)m 18(the)m 368 508 p (results)s 15(can)m 14 r 98 c 1 r 101 c 15(optionally)m 12(generated.)m cmtt10.300 @sf 592 595 p (PROGRAM)s 21(MAIN)m 592 645 p 124 c 592 695 p (EXTERNAL)s 571 744 p 43 c 65(FCN)m 592 794 p (INTEGER)s 571 844 p 43 c 65(N,M,NP,NQ,)m 571 894 p 43 c 65(LDY,LDX,)m 20(LDWE,LD2WE,L)m -1(DWD,L)m -1(D2WD,)m 19(LDIFX,)m 571 944 p 43 c 65(JOB,NDIGIT,)m 19(MAXIT,)m 21(IPRINT,LUNER)m -1(R,LUN)m -1(RPT,)m 571 994 p 43 c 65(LDSTPD,)m 20(LDSCLD,)m 21(LWORK,LIWO)m -1(RK,)m 20(INFO)m 592 1043 p (INTEGER)s 571 1093 p 43 c 65(IFIXB\(NP\),IF)m -1(IXX\(L)m -1(DIFX)m -1(,M\),)m 19(IWORK\(LIWORK\))m 592 1143 p (REAL)s 571 1193 p 43 c 65(TAUFAC,)m 20(SSTOL,PARTOL)m 592 1243 p (REAL)s 571 1292 p 43 c 65(BETA\(NP\),)m 20(Y\(LDY,NQ\),X)m -1(\(LDX,)m -1(M\),)m 571 1342 p 43 c 65(WE\(LDWE,LD2W)m -1(E,NQ\))m -1(,WD\()m -1(LDWD,)m -1(LD2WD)m -1(,M\),)m 571 1392 p 43 c 65(STPB\(NP\),STP)m -1(D\(LDS)m -1(TPD,)m -1(M\),)m 20(SCLB\(NP\),SC)m -1(LD\(LD)m -1(SCLD,)m -1(M\),)m 571 1442 p 43 c 65(WORK\(LWORK\))m 592 1492 p 124 c 592 1541 p (CALL)s 21(SODRC)m 571 1591 p 43 c 65(\(FCN,)m 571 1641 p 43 c 65(N,M,NP,NQ,)m 571 1691 p 43 c 65(BETA,)m 571 1741 p 43 c 65(Y,LDY,X,LDX,)m 571 1791 p 43 c 65(WE,LDWE,LD2W)m -1(E,WD,)m -1(LDWD)m -1(,LD2W)m -1(D,)m 571 1840 p 43 c 65(IFIXB,IFIXX,)m -1(LDIFX)m -1 r 44 c 571 1890 p 43 c 65(JOB,NDIGIT,T)m -1(AUFAC)m -1 r 44 c 571 1940 p 43 c 65(SSTOL,PARTOL)m -1(,MAXI)m -1(T,)m 571 1990 p 43 c 65(IPRINT,LUNER)m -1(R,LUN)m -1(RPT,)m 571 2040 p 43 c 65(STPB,STPD,LD)m -1(STPD,)m 571 2089 p 43 c 65(SCLB,SCLD,LD)m -1(SCLD,)m 571 2139 p 43 c 65(WORK,LWORK,I)m -1(WORK,)m -1(LIWO)m -1(RK,)m 571 2189 p 43 c 65(INFO\))m 592 2239 p 124 c 592 2289 p (END)s @eop %%Page: 22 36 22 @bop0 cmr10.300 @sf [<0FE03FF8787C703EF01EF00FF00FF00F000F000F000F000F301E381E3C3C3FF837E03000300030 003000300030003FE03FF83FFC301C> 16 27 -2 0 20.755] 53 @dc [ 16 18 -1 0 18.449] 122 @dc [<7F87F87F87F80E01C00E01C00E01C00E01C00E01C00E01C00E01C00E01C00E01C00E01C00E01C0 0E01C00E01C00E01C0FFFFC0FFFFC00E00000E00000E00000E00000E00000E03C00F03C00783C0 03C3C001FF80003F00> 24 29 0 0 23.061] 12 @dc [<0018001800001C003800003C003C00003C003C00003E007C00007E007E00007E007E00007E007E 0000FB00F70000F300F30000F300F30000F181E30001E181E18001E181E18001E1C3E18003C0C3 C0C003C0C3C0C003C0C3C0C007C06780E00780678060078067806007803F00600F003F00300F00 3F00300F001E00381F001E007CFFE0FFE1FFFFE0FFE1FF> 40 28 -1 0 42.663] 87 @dc [ 24 29 -1 0 21.908] 107 @dc 22 @bop1 cmr10.329 @sf 0 114 p (22)s 1319(Using)m 15(ODRP)m -3 r 65 c (CK)s 0 134 p 1725 2 ru cmbx12.300 @sf 0 259 p (2.B.)s 18(Subroutine)m 18(Argumen)m -1 r 116 c 18(Descriptions)m cmbx10.329 @sf 0 380 p (2.B.i.)s 16(Synopsis)m cmr10.329 @sf 0 485 p (The)s 21(argumen)m (ts)s 19(of)m 20(the)m 20(ODRP)m -3 r 65 c (CK)s 20(user)m 20(callable)m 20(subroutines)m 21(are)m 20(logically)m 18(group)m 1(ed)m 21(as)m 0 541 p (sho)s (wn)s 15 r 98 c 1(elo)m (w.)s 23(Argumen)m (ts)s 16(sho)m (wn)s 15(in)m 17(paren)m (thesis)s 15 r 40 c cmmi10.329 @sf 58 c 8 r 58 c 8 r 58 c cmr10.329 @sf -2 r 41 c 16(are)m 16(not)m 17(included)m 17(in)m 17(the)m cmtt10.329 @sf 17(DODR)m cmr10.329 @sf 16(and)m cmtt10.329 @sf 0 598 p (SODR)s cmr10.329 @sf 13(call)m 13(statemen)m (ts;)s cmtt10.329 @sf 12(DODR)m cmr10.329 @sf 13(and)m cmtt10.329 @sf 14(SODR)m cmr10.329 @sf 13(automaticall)m -1 r 121 c 12(preset)m 14(these)m 13 r 118 c -2(ariables)m 12(to)m 14(the)m 13(default)m 0 654 p 118 c -2(alues)m 12(giv)m (en)s 12(in)m cmsy10.329 @sf 13 r 120 c cmr10.329 @sf (2.B.ii.)s 18(All)m 13(other)m 13(argumen)m (ts)s 11(are)m 13(common)m 13(to)m 12(all)m 13(ODRP)m -3 r 65 c (CK)s 12(user)m 13(callable)m 0 711 p (subroutines.)s cmr10.300 @sf 54 819 p (Argumen)s 116 c 72 869 p (Num)s 98 c 1(er)m 67(Argumen)m (ts)s 461(Group)m 13(Description)m 29 886 p 1668 2 ru 134 921 p 49 c cmtt10.300 @sf 131(FCN,)m cmr10.300 @sf 572(Name)m 14(of)m 13(user)m 15(supplied)m 14(subroutine)m 946 970 p (for)s 13(function)m 14(and)m 14(deriv)m -1(ativ)m -1 r 101 c 12(computation)m 92 1070 p 50 c 13(to)m 14 r 53 c cmtt10.300 @sf 88(N,M,NP,NQ,)m cmr10.300 @sf 440(Problem)m 14(size)m 14(sp)m 1(eci\014cation)m 134 1170 p 54 c cmtt10.300 @sf 131(BETA,)m cmr10.300 @sf 550 r 70 c -2(unction)m 12(parameters)m 81 1269 p 55 c 14(to)m 14(10)m cmtt10.300 @sf 77(Y,LDY,X,LDX)m -1 r 44 c cmr10.300 @sf 397(Dep)m 1(enden)m 116 c 14(and)m 14(explanatory)m 13 r 118 c -1(ariables)m 71 1369 p (11)s 13(to)m 14(16)m cmtt10.300 @sf 67(WE,LDWE,LD2)m -1(WE,WD)m -1(,LDWD)m -1(,LD2W)m -1(D,)m cmr10.300 @sf 48 r 87 c -2(eigh)m -1(ts)m 71 1468 p (17)s 13(to)m 14(19)m cmtt10.300 @sf 67(\(IFIXB,IFIX)m -1(X,LDI)m -1(FX,\))m cmr10.300 @sf 222 r 80 c (arameter)s 13(and)m 14 r 118 c -1(ariable)m 12(\014xing)m 71 1568 p (20)s 13(to)m 14(22)m cmtt10.300 @sf 67(JOB,\(NDIGIT)m -1(,TAUF)m -1(AC,\))m cmr10.300 @sf 222(Computation)m 12(and)m 14(initializatio)m -1 r 110 c 12(con)m (trol)s 71 1668 p (23)s 13(to)m 14(25)m cmtt10.300 @sf 67(\(SSTOL,PART)m -1(OL,MA)m -1(XIT,\))m cmr10.300 @sf 200(Stopping)m 13(criteria)m 71 1767 p (26)s 13(to)m 14(28)m cmtt10.300 @sf 67(IPRINT,LUNE)m -1(RR,LU)m -1(NRPT,)m cmr10.300 @sf 200(Prin)m 116 c 13(con)m (trol)s 71 1867 p (29)s 13(to)m 14(31)m cmtt10.300 @sf 67(\(STPB,STPD,)m -1(LDSTP)m -1(D,\))m cmr10.300 @sf 244(Deriv)m -1(ativ)m -1 r 101 c 12(step)m 15(sizes)m 71 1967 p (32)s 13(to)m 14(34)m cmtt10.300 @sf 67(\(SCLB,SCLD,)m -1(LDSCL)m -1(D,\))m cmr10.300 @sf 244(Scaling)m 71 2066 p (35)s 13(to)m 14(38)m cmtt10.300 @sf 67(WORK,LWORK,)m -1(IWORK)m -1(,LIWO)m -1(RK,)m cmr10.300 @sf 135 r 87 c -2(ork)m 12 r 118 c (ectors)s 14(and)m 13(returned)m 16(results)m 124 2166 p (39)s cmtt10.300 @sf 120(INFO)m cmr10.300 @sf 572(Stopping)m 13(condition)m @eop %%Page: 23 37 23 @bop0 cmbx10.329 @sf [<3FF9FFC03FF9FFC007C03E0007C03E0007C03E0007C03E0007C03E0007C03E0007C03E0007C03E 0007C03E0007C03E0007C03E0007C03E0007C03E0007C03E0007C03E0007C03E00FFFFFE00FFFF FE0007C1FE0007C0000007C0000007C0000007C07C0007C07C0007C0FE0007E07C0003F07C0001 FC3C00007FF800000FF000> 32 32 0 0 29.040] 12 @dc cmtt10.329 @sf [<000380000F80001F80003F8000FE0001FC0003F8000FE0001FC0003F8000FE0000FC0000FC0000 FE00003F80001FC0000FE00003F80001FC0000FE00003F80001F80000F80000380> 24 24 -3 -2 23.863] 60 @dc [ 24 28 -2 0 23.863] 108 @dc [ 24 24 -3 -2 23.863] 62 @dc cmr10.329 @sf [ 24 2 0 -11 22.727] 123 @dc cmsy10.329 @sf [<0000060000000007000000000380000000038000000001C000000000E0000000007000FFFFFFF8 00FFFFFFFC000000001E00000000070000000003C000000000F8000000007C00000001F0000000 07C00000000F00FFFFFFFC00FFFFFFF8000000007000000000E000000001C00000000180000000 03800000000700000000060000> 40 26 -3 2 45.454] 41 @dc [<0001800000000380000000070000000007000000000E000000001C0000000038000000007FFFFF FC00FFFFFFFC01E000000003800000000F000000007C00000000F8000000003E000000000F8000 000003C000000000FFFFFFFC007FFFFFFC0038000000001C000000000E00000000060000000007 00000000038000000001800000> 40 26 -3 2 45.454] 40 @dc cmr10.329 @sf [<018001C001800180C183E187F99F7DBE1FF807E007E01FF87DBEF99FE187C1830180018001C001 80> 16 20 -3 -14 22.727] 42 @dc 23 @bop1 cmr10.329 @sf 225 114 p (Using)s 15(ODRP)m -3 r 65 c (CK)s 1318(23)m 225 134 p 1725 2 ru cmbx10.329 @sf 225 259 p (2.B.ii.)s 15(ODRP)m -3 r 65 c -1(CK)m 15(Subroutine)m 18(Argumen)m -1 r 116 c 16(De\014nitions)m cmr10.329 @sf 225 364 p (The)s 17(argumen)m (ts)s 14(of)m 17(ODRP)m -3 r 65 c (CK's)s 14(user)m 17(callable)m 16(subroutines)m 16(are)m 16(describ)m 1(ed)m 18 r 98 c 1(elo)m 119 c 15(in)m 16(order)m 225 420 p (of)s 15(their)m 14 r 111 c 1(ccurrence)m 17(in)m 15(the)m 15(call)m 14(statemen)m (ts.)s 18(Appropriate)m 14(declaration)m 14(statemen)m (ts)s 13(for)m 15(eac)m 104 c 225 477 p (argumen)s 116 c 12(are)m 14(sho)m (wn)s 12(in)m 14(brac)m 107 c -1(ets)m 12 r 91 c cmmi10.329 @sf 58 c 8 r 58 c 8 r 58 c cmr10.329 @sf -2 r 93 c 13(follo)m -1(wing)m 12(the)m 14(argumen)m 116 c 12(name;)m 14(the)m 14 r 99 c (haracter)s 12(string)m cmtt10.329 @sf 225 533 p ()s cmr10.329 @sf 14(denotes)m cmtt10.329 @sf 19(REAL)m cmr10.329 @sf 17(when)m 19(using)m 17(single)m 18(precision)m 17(subroutines)m cmtt10.329 @sf 18(SODR)m cmr10.329 @sf 18(and)m cmtt10.329 @sf 18(SODRC)m cmr10.329 @sf 17(\(whic)m 104 c 225 590 p (should)s 17 r 98 c 1 r 101 c 18(used)m 17(only)m 17(on)m 16(mac)m (hines)s 16(with)m 16(appro)m (ximately)s 15(14)m 16(decimal)m 16(digits)m 16(of)m 17(precision)m 16(in)m 225 646 p (single)s 15(precision\),)m 15(and)m 16(denotes)m cmtt10.329 @sf 16(DOUBLE)m 23(PRECISION)m cmr10.329 @sf 14(when)m 17(using)m 15(double)m 16(precision)m 16(subrou-)m 225 703 p (tines)s cmtt10.329 @sf 13(DODR)m cmr10.329 @sf 12(and)m cmtt10.329 @sf 14(DODRC)m cmr10.329 @sf -1 r 46 c 19(Eac)m 104 c 12(argumen)m 116 c 12(is)m 12 r 110 c (um)s 98 c 1(ered)m 12(as)m 13(sho)m (wn)s 12(in)m cmsy10.329 @sf 13 r 120 c cmr10.329 @sf (2.B.i,)s 12(and)m 14(will)m 11 r 98 c 1 r 101 c 14(cross)m 225 759 p (referenced)s 17 r 98 c 121 c 16 r 98 c 1(oth)m 16 r 110 c (um)s 98 c 1(er)m 15(and)m 17(name,)m 16(e.g.,)m 16(1{)m cmtt10.329 @sf (FCN)s cmr10.329 @sf -1 r 44 c 16(enabling)m 16(the)m 17(user)m 16(to)m 16(easily)m 16(\014nd)m 17(the)m 225 816 p (de\014nition)s 17(of)m 17 r 97 c 17(sp)m 1(eci\014c)m 18(argumen)m (t.)s 24(In)m 18(addition,)m 16 r 97 c 17(\015ag)m 17(indicating)m 16(whether)m 17(the)m 18(argumen)m 116 c 225 872 p (is)s 15(passed)m 16(to)m 16(or)m 15(from)m 15(ODRP)m -3 r 65 c (CK)s 14(is)m 16(placed)m 16(in)m 15(the)m 16(left)m 15(margin)m 15 r 98 c 121 c 15(the)m 16(argumen)m 116 c 14 r 110 c (um)s 98 c 1(er.)m 225 929 p (The)s 15(\015ags)m 15(are:)m 275 1007 p 61 c cmsy10.329 @sf -7 r 41 c cmr10.329 @sf 23(indicating)m 11(the)m 13(argumen)m 116 c 11(sp)m 1(eci\014es)m 13(information)m 10(that)m 12 r 109 c (ust)s 11 r 98 c 1 r 101 c cmti10.329 @sf 13(input)m cmr10.329 @sf 13(to)m 12(ODRP)m -3 r 65 c (CK,)s 371 1064 p (and)s 18(that)m 17(the)m 17(input)m 18(information)m 16(is)m 17(preserv)m (ed)s 17(up)m 1(on)m 18(return)m 18(from)m 17(the)m 17(ODRP)m -3 r 65 c (CK)s 371 1120 p (subroutine;)s cmsy10.329 @sf 275 1186 p 40 c cmr10.329 @sf -7 r 61 c 23(indicating)m 15(the)m 15(argumen)m 116 c 14(sp)m 1(eci\014es)m 17(information)m 14(that)m 15(is)m cmti10.329 @sf 15(output)m cmr10.329 @sf 17 r 98 c 121 c 15(the)m 15(ODRP)m -3 r 65 c (CK)s 371 1243 p (subroutine;)s 15(and)m cmsy10.329 @sf 265 1309 p 40 c -7 r 41 c cmr10.329 @sf 23(indicating)m 11(the)m 13(argumen)m 116 c 11(sp)m 1(eci\014es)m 13(information)m 10(that)m 12 r 109 c (ust)s 11 r 98 c 1 r 101 c cmti10.329 @sf 13(input)m cmr10.329 @sf 13(to)m 12(ODRP)m -3 r 65 c (CK,)s 371 1366 p (but)s 17(that)m 16(the)m 17(input)m 17 r 118 c -2(alues)m 16(will)m 15 r 98 c 1 r 101 c cmti10.329 @sf 17(overwritten)m cmr10.329 @sf 17 r 98 c 121 c 16(ODRP)m -3 r 65 c (CK)s 15(up)m 1(on)m 18(return)m 17(from)m 371 1422 p (the)s 15(subroutine.)m 1021 1548 p (NOTE)s 381 1661 p (Substitute)s cmtt10.329 @sf 15(DOUBLE)m 23(PRECISION)m cmr10.329 @sf 14(for)m cmtt10.329 @sf 14()m cmr10.329 @sf 15(when)m 15(using)m cmtt10.329 @sf 15(DODR)m cmr10.329 @sf 15(and)m cmtt10.329 @sf 15(DODRC)m cmr10.329 @sf 46 c 524 1774 p (Substitute)s cmtt10.329 @sf 15(REAL)m cmr10.329 @sf 15(for)m cmtt10.329 @sf 14()m cmr10.329 @sf 14(when)m 16(using)m cmtt10.329 @sf 15(SODR)m cmr10.329 @sf 15(and)m cmtt10.329 @sf 15(SODRC)m cmr10.329 @sf -1 r 46 c 1042 1899 p (****)s @eop %%Page: 24 38 24 @bop0 1.000000 /cmtt12.300 @newfont cmtt12.300 @sf [ 24 30 -1 0 25.632] 70 @dc [<00FE0003FF8007FFE00F83F01F00F03E00783C0078780038780038700038F00000F00000E00000 E00000E00000E00000E00000E00000F00000F000007000387800387800783C00783E00F81F01F8 0F83F807FFF803FFB800FE38> 24 30 -2 0 25.632] 67 @dc [ 24 30 -1 0 25.632] 78 @dc [ 16 39 -10 4 25.632] 91 @dc [ 24 30 -2 0 25.632] 69 @dc [ 24 30 -1 0 25.632] 88 @dc [<03FF8003FF8003FF80003800003800003800003800003800003800003800003800003800003800 003800003800003800003800003800003800003800003800003800003800E0380EE0380EE0380E E0380EFFFFFEFFFFFEFFFFFE> 24 30 -1 0 25.632] 84 @dc [ 24 30 -1 0 25.632] 82 @dc [ 24 30 -1 0 25.632] 65 @dc [ 24 30 -1 0 25.632] 76 @dc [ 16 39 -2 4 25.632] 93 @dc cmr6.300 @sf [ 16 17 0 0 11.023] 73 @dc [ 16 17 0 0 18.772] 76 @dc cmmi10.329 @sf [<0FE0001FF8003C3E00780F00700780F00380F003C0F001E0F001E0F000F0F800F07800F0780078 7800787C00783C007C1E007C1E007C0F00FC07C1FE03FF9E00FF1E00081E00001E00001E03801E 07C01C03C01C03803C03803801C07800E1F0007FE0003F80> 24 34 -2 1 24.131] 64 @dc cmr6.300 @sf [ 24 17 0 0 23.130] 75 @dc [<7F80FFC0F1E0F0E060E000E000E000E000E000E000E000E000E000E000E007F807F8> 16 17 0 0 15.543] 74 @dc cmti10.329 @sf [ 40 31 -3 0 33.787] 78 @dc 24 @bop1 cmr10.329 @sf 0 114 p (24)s 1319(Using)m 15(ODRP)m -3 r 65 c (CK)s 0 134 p 1725 2 ru 33 259 p 61 c cmsy10.329 @sf -7 r 41 c cmr10.329 @sf 49 c 23 r 123 c cmtt12.300 @sf 22(FCN)m 24([EXTERNAL)m 23(FCN])m cmr10.329 @sf 197 335 p (The)s 13(name)m 12(of)m 12(the)m 13(user)m 13(supplied)m 13(subroutine)m 12(that,)m 12(giv)m (en)s 11(the)m 13(curren)m 116 c 11 r 118 c -2(alues)m 12(of)m 12(the)m 197 391 p (explanatory)s 10 r 118 c -2(ariable,)m cmmi10.329 @sf 9 r 120 c cmr6.300 @sf 648 398 p 73 c cmr10.329 @sf 662 391 p 43 c cmmi10.329 @sf 1 r 14 c cmr6.300 @sf 718 398 p 73 c cmr10.329 @sf 732 391 p 44 c 11(and)m 11(the)m 10(curren)m 116 c 10 r 118 c -2(alues)m 10(of)m 10(the)m 11(function)m 10(parameters,)m cmmi10.329 @sf 197 448 p 12 c cmr10.329 @sf 2 r 44 c 15(computes)m 15(the)m 15(predicted)m 16 r 118 c -2(alues)m cmtt10.329 @sf 712 543 p (F\()s 73 c 44 c 76 c 41 c cmr10.329 @sf 12 r 61 c cmmi10.329 @sf 13 r 102 c cmr6.300 @sf 938 550 p 73 c 76 c cmr10.329 @sf 970 543 p 40 c cmmi10.329 @sf 120 c cmr6.300 @sf 1014 550 p 73 c cmr10.329 @sf 1037 543 p 43 c cmmi10.329 @sf 11 r 14 c cmr6.300 @sf 1103 550 p 73 c cmr10.329 @sf 1116 543 p 59 c cmmi10.329 @sf 8 r 12 c cmr10.329 @sf 2 r 41 c cmmi10.329 @sf 14 r 59 c cmtt10.329 @sf 197 639 p 73 c cmr10.329 @sf 15 r 61 c 15 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 8 r 58 c 5 r 59 c 8(n;)m cmr10.329 @sf 16(and)m cmtt10.329 @sf 17 r 76 c cmr10.329 @sf 15 r 61 c 15 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 7 r 58 c 6 r 59 c 8 r 113 c 2 r 59 c cmr10.329 @sf 15(and)m 17(optionally)m 15(computes)m 17(the)m 16(matrices)m 16(of)m 16(\014rst)m 197 696 p (partial)s 14(deriv)m -2(ativ)m -1(es,)m 13(i.e.,)m 13(the)m 16(Jacobian)m 15(matrices)m cmtt10.329 @sf 622 813 p (FJACB\()s 73 c -1 r 44 c 75 c 44 c 76 c 41 c cmr10.329 @sf 12 r 61 c cmmi10.329 @sf 974 782 p 64 c 3 r 102 c cmr6.300 @sf 1023 789 p 73 c 76 c cmr10.329 @sf 1055 782 p 40 c cmmi10.329 @sf 120 c cmr6.300 @sf 1099 789 p 73 c cmr10.329 @sf 1122 782 p 43 c cmmi10.329 @sf 10 r 14 c cmr6.300 @sf 1187 789 p 73 c cmr10.329 @sf 1201 782 p 59 c cmmi10.329 @sf 8 r 12 c cmr10.329 @sf 2 r 41 c 974 802 p 293 2 ru cmmi10.329 @sf 1082 844 p 64 c 3 r 12 c cmr6.300 @sf 1135 851 p 75 c cmmi10.329 @sf 1287 813 p 59 c cmr10.329 @sf 197 928 p (for)s cmtt10.329 @sf 15 r 73 c cmr10.329 @sf 12 r 61 c 13 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 7 r 58 c 6 r 59 c 8 r 110 c cmr10.329 @sf 44 c cmtt10.329 @sf 14 r 75 c cmr10.329 @sf 12 r 61 c 13 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 8 r 58 c 5 r 59 c 8 r 112 c cmr10.329 @sf 44 c 14(and)m cmtt10.329 @sf 15 r 76 c cmr10.329 @sf 13 r 61 c 12 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 8 r 58 c 5 r 59 c 8 r 113 c cmr10.329 @sf 2 r 44 c 14(and)m cmtt10.329 @sf 622 1053 p (FJACD\()s 73 c -1 r 44 c 74 c 44 c 76 c 41 c cmr10.329 @sf 12 r 61 c cmmi10.329 @sf 974 1023 p 64 c 3 r 102 c cmr6.300 @sf 1023 1030 p 73 c 76 c cmr10.329 @sf 1055 1023 p 40 c cmmi10.329 @sf 120 c cmr6.300 @sf 1099 1030 p 73 c cmr10.329 @sf 1122 1023 p 43 c cmmi10.329 @sf 10 r 14 c cmr6.300 @sf 1187 1030 p 73 c cmr10.329 @sf 1201 1023 p 59 c cmmi10.329 @sf 8 r 12 c cmr10.329 @sf 2 r 41 c 974 1043 p 293 2 ru cmmi10.329 @sf 1074 1085 p 64 c cmr10.329 @sf 3 r 1 c cmr6.300 @sf 1139 1092 p 73 c 74 c cmmi10.329 @sf 1287 1053 p 59 c cmr10.329 @sf 197 1151 p (for)s cmtt10.329 @sf 17 r 73 c cmr10.329 @sf 17 r 61 c 18 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 7 r 58 c 5 r 59 c 8 r 110 c cmr10.329 @sf 44 c cmtt10.329 @sf 18 r 74 c cmr10.329 @sf 17 r 61 c 17 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 8 r 58 c 5 r 59 c 8 r 109 c cmr10.329 @sf 44 c 17(and)m cmtt10.329 @sf 18 r 76 c cmr10.329 @sf 17 r 61 c 18 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 7 r 58 c 5 r 59 c 8 r 113 c cmr10.329 @sf 2 r 46 c 27(The)m 18(co)m 1(de)m 19(for)m 17(ev)m -2(aluating)m cmtt10.329 @sf 16 r 70 c cmr10.329 @sf 197 1207 p 109 c (ust)s 9(alw)m 97 c -1(ys)m 8 r 98 c 1 r 101 c 12(pro)m (vided.)s 17(The)m 11(co)m 1(de)m 12(for)m 10(ev)m -2(aluating)m cmtt10.329 @sf 9(FJACB)m cmr10.329 @sf 10(and)m cmtt10.329 @sf 11(FJACD)m cmr10.329 @sf 10(is)m 11(required)m 197 1264 p (only)s 18(when)m 20(the)m 18(second)m 20(digit)m 17(of)m 19(argumen)m 116 c 17(20{)m cmtt10.329 @sf (JOB)s cmr10.329 @sf 17(is)m 18(greater)m 18(than)m 19(or)m 18(equal)m 19(to)m 197 1320 p 116 c 119 c -1(o.)m 29(\(When)m 19(the)m 19(second)m 19(digit)m 18(of)m cmtt10.329 @sf 18(JOB)m cmr10.329 @sf 19(is)m 18(zero)m 19(or)m 18(one,)m 20(the)m 19(necessary)m 19(Jacobian)m 197 1377 p (matrices)s 20(will)m 19 r 98 c 1 r 101 c 21(appro)m (ximated)s 19 r 98 c 121 c 19(ODRP)m -3 r 65 c (CK)s 20(using)m 20(\014nite)m 21(di\013erences.)m 36(See)m 197 1433 p (argumen)s 116 c 16(20{)m cmtt10.329 @sf (JOB)s cmr10.329 @sf -1 r 44 c 18(and)m 19(also)m cmsy10.329 @sf 17 r 120 c cmr10.329 @sf (4.A.\))s 27(The)m 19(co)m 1(de)m 18(for)m cmtt10.329 @sf 18(FJACD)m cmr10.329 @sf 17(do)m 1(es)m 18(not)m 18(need)m 19(to)m 17 r 98 c 1 r 101 c 197 1490 p (supplied)s 16(when)m 15(the)m 15(\014t)m 16(is)m 14 r 98 c 121 c 14(OLS.)m 197 1552 p 65 c 116 c 11 r 97 c 11(giv)m (en)s 11(call)m 11(to)m 12(subroutine)m cmtt10.329 @sf 12(FCN)m cmr10.329 @sf 44 c 12(ODRP)m -3 r 65 c (CK)s 11(will)m 11(nev)m (er)s 11(request)m 12(that)m 12 r 98 c 1(oth)m 12(the)m 197 1608 p (function)s 12 r 118 c -2(alues)m 12 r 40 c cmtt10.329 @sf 70 c cmr10.329 @sf -1 r 41 c 12(and)m 13(the)m 12(deriv)m -2(ativ)m -1 r 101 c 10 r 118 c -2(alues)m 12 r 40 c cmtt10.329 @sf (FJACB)s cmr10.329 @sf 11(and)m cmtt10.329 @sf 13(FJACD)m cmr10.329 @sf -1 r 41 c 12 r 98 c 1 r 101 c 13(computed.)m 197 1665 p (While)s 13(it)m 13(is)m 14(generally)m 13(most)m 13(cost)m 13(e\013ectiv)m 101 c 12(if)m 14(the)m 14(user)m 14(only)m 13 r 112 c 1(erforms)m 14(the)m 14(required)m 197 1721 p (computations,)s 12(it)m 13(is)m 13(not)m 13(an)m 14(error)m 12(for)m 13 r 98 c 1(oth)m 14(function)m 13 r 118 c -2(alues)m 13(and)m 14(deriv)m -2(ativ)m -1(es)m 11(to)m 13 r 98 c 1 r 101 c 197 1778 p (computed)s 19(eac)m 104 c 17(time)m cmtt10.329 @sf 18(FCN)m cmr10.329 @sf 18(is)m 17(in)m 118 c (o)s -1 r 107 c -1(ed.)m cmti10.329 @sf 28(Note,)m 20(however,)m 20(that)m 20(arr)m -1(ay)m cmtt10.329 @sf 18(FJACD)m cmti10.329 @sf 19(must)m 197 1834 p (never)s 20 r 98 c -1 r 101 c 18(alter)m -1 r 101 c -1 r 100 c 18(when)m 20(the)m 20(\014t)m 20(is)m 20(by)m 20(or)m -1(dinary)m 20(le)m -1(ast)m 18(squar)m -1(es,)m 19(sinc)m -1 r 101 c 18(no)m 20(sp)m -1(ac)m -2 r 101 c 18(is)m 197 1891 p (assigne)s -2 r 100 c 15(to)m 16(that)m 17(arr)m -1(ay)m 16(in)m 16(that)m 17 r 99 c -1(ase.)m cmr10.329 @sf 197 1953 p (The)s 13(user)m 13 r 109 c (ust)s 11(supply)m 14 r 97 c 12 r 118 c -2(alue)m 12(for)m 12(ev)m (ery)s 12(elemen)m 116 c 12(of)m 12(the)m 13(selected)m 13(arra)m (ys.)s 17(If)m 13(some)m 197 2010 p (resp)s 1(onses)m 14(of)m 13(some)m 14(observ)m -2(ations)m 12(are)m 13(actually)m 12(missing,)m 13(then)m 14(the)m 14(user)m 14(can)m 13(set)m 14(the)m 197 2066 p (corresp)s 1(onding)m 13 r 119 c (eigh)s -1(t)m -1 r 115 c 11(in)m 12(argumen)m 116 c 11(11{)m cmtt10.329 @sf (WE)s cmr10.329 @sf 11(to)m 12(zero)m 13(in)m 12(order)m 13(to)m 12(remo)m 118 c -1 r 101 c 10(the)m 13(e\013ect)m 197 2122 p (of)s 15(the)m 15(missing)m 14(observ)m -2(ation)m 14(from)m 14(the)m 15(analysis.)m 19(\(See)m cmsy10.329 @sf 16 r 120 c cmr10.329 @sf (1.F.\))s 197 2185 p (ODRP)s -3 r 65 c (CK's)s 11(parameter)m 12(\014xing)m 12(argumen)m (ts)s cmtt10.329 @sf 11(IFIXB)m cmr10.329 @sf -1 r 44 c cmtt10.329 @sf 13(IFIXX)m cmr10.329 @sf 12(and)m cmtt10.329 @sf 12(LDIFX)m cmr10.329 @sf 12(are)m 13(passed)m 197 2241 p (to)s 12(subroutine)m cmtt10.329 @sf 13(FCN)m cmr10.329 @sf 13(for)m 12(the)m 13(user's)m 13(con)m 118 c -1(enience.)m 18(When)m 14 r 97 c 12(parameter)m 12(is)m 13(\014xed,)m 14(then)m 197 2298 p (the)s 15(deriv)m -2(ativ)m -1 r 101 c 13(with)m 13(resp)m 1(ect)m 16(to)m 14(that)m 13(parameter)m 14(can)m 15 r 98 c 1 r 101 c 15(set)m 15(to)m 14(zero.)m 19(ODRP)m -3 r 65 c (CK)s 197 2354 p (will)s 19(automatical)m -1(ly)m 18(zero)m 20(these)m 20(deriv)m -2(ativ)m -1 r 101 c 18 r 118 c -2(alues,)m 20(ho)m 119 c -1(ev)m -1(er,)m 19(and)m 20(th)m (us)s 19(it)m 19(is)m 19(not)m 197 2411 p (necessary)s 15(for)m 14(the)m 14(user)m 15(to)m 14 r 98 c 1 r 101 c 15(concerned)m 16(with)m 14(this)m 14(unless)m 15(the)m 15(deriv)m -2(ativ)m -1 r 101 c 12(compu-)m 197 2467 p (tations)s 14(are)m 15(esp)m 1(ecially)m 14(exp)m 1(ensiv)m (e.)s 20(\(See)m 15(Chapter)m 15(3.\))m @eop %%Page: 25 39 25 @bop0 cmtt10.300 @sf [<00E00001F00001F00001B00003B80003B80003B800031800071C00071C00071C00071C00060C00 0E0E000E0E000E0E000E0E001C07001C07001C07001C0700380380FF1FE0FF1FE0FF1FE0> 24 25 -1 0 21.793] 86 @dc [ 24 25 -1 0 21.793] 72 @dc [<000380000F80001F80007E0000FC0003F00007E0001F80003F0000FC0000F80000FC00003F0000 1F800007E00003F00000FC00007E00001F80000F80000380> 24 21 -2 -2 21.793] 60 @dc [ 24 18 -1 0 21.793] 114 @dc [<03F00FFC3FFE7E1F780FF007F000E000FFFFFFFFFFFFF007F00F781F7C3E3FFC1FF807E0> 16 18 -3 0 21.793] 101 @dc [<1FC3E03FFFE07FFFE0F83E00F01E00E00E00E00E00F80E007FCE003FFE000FFE00007E00000E00 301E00783C007FFC007FF8001FE000> 24 18 -2 0 21.793] 97 @dc [ 24 25 -2 0 21.793] 108 @dc [ 24 21 -2 -2 21.793] 62 @dc [ 16 18 -3 0 21.793] 115 @dc [<00F80003FE0003FF00078F80070780070380070380070100070000070000070000070000070000 070000070000FFFF00FFFF00FFFF00070000070000070000070000070000> 24 23 -1 0 21.793] 116 @dc [<70F8F8F870> 8 5 -8 0 21.793] 46 @dc [<03E0000FF8001FFC001E3C003C1E00780F00700700700700F00780E00380E00380E00380E00380 E00380E00380E00380E00380700700700700780F00380E001E3C001FFC000FF80003E000> 24 25 -2 0 21.793] 48 @dc [<7FFC7FFC7FFC03800380038003800380038003800380038003800380038003800380F380FF80FF 801F800F80078003800380> 16 25 -4 0 21.793] 49 @dc [<03F00FFC1FFE3E1F7C077007F000E000E000E000E000F0007000780C3E1E1FFE0FFE03FC> 16 18 -3 0 21.793] 99 @dc [<03E0000FF8001FFC003C1E00780F00700700F00780E00380E00380E00380E00380E00380700700 780F003C1E001FFC000FF80003E000> 24 18 -2 0 21.793] 111 @dc [ 24 18 0 0 21.793] 109 @dc [ 24 27 0 9 21.793] 112 @dc [<03F3F807FFF80FFFF80F0F800E07800E03800E03800E03800E03800E03800E03800E03800E0380 0E03800E0380FE3F80FE3F80FE3F80> 24 18 0 0 21.793] 117 @dc [<7FFF00FFFF80FFFF80000000000000000000000000000000FFFF80FFFF807FFF00> 24 11 -2 -7 21.793] 61 @dc [<1F0F007FFFC07FFFC0F1F9C0F0F1C0E1F9C0E1F800F3FC00F7FC007F9C007F1E003F1E001F8E00 0F8F001FCF001FE7E01DF7E01CF7E01C70001C70001C70001EF0001FF0000FE00003C000> 24 25 -1 0 21.793] 38 @dc [ 24 32 -2 3 21.793] 47 @dc 25 @bop1 cmr10.329 @sf 225 114 p (Using)s 15(ODRP)m -3 r 65 c (CK)s 1318(25)m 225 134 p 1725 2 ru 422 259 p (The)s 16(argumen)m 116 c 14(list)m 15(and)m 16(dimension)m 16(statemen)m (t)s -1 r 115 c 14(for)m 16(subroutine)m cmtt10.329 @sf 15(FCN)m cmr10.329 @sf 16 r 109 c (ust)s 14 r 98 c 1 r 101 c 17(ex-)m 422 315 p (actly)s 14(as)m 15(sho)m (wn)s 14 r 98 c 1(elo)m (w.)s cmtt10.300 @sf 553 434 p (SUBROUTINE)s 19(FCN\(N,M,NP,NQ,)m 531 483 p 43 c 327(LDN,LDM,LDN)m -1(P,)m 531 533 p 43 c 327(BETA,XPLUSD)m -1 r 44 c 531 583 p 43 c 327(IFIXB,IFIXX)m -1(,LDI)m -1(FX,)m 531 633 p 43 c 327(IDEVAL,F,FJ)m -1(ACB,)m -1(FJACD)m -1 r 44 c 531 683 p 43 c 327(ISTOP\))m 422 782 p 67 c 43(INPUT)m 21(ARGUMENTS)m 422 832 p 67 c 43(\(WHICH)m 21(MUST)m 21(NOT)m 21(BE)m 21(CHANGED)m 21(BY)m 21(THIS)m 21(ROUTINE\))m 553 882 p (INTEGER)s 20(IDEVAL,LDFIX,)m -1(LDM,L)m -1(DN,L)m -1(DNP,M)m -1(,N,NP)m -1(,NQ)m 553 932 p (INTEGER)s 20(IFIXB\(NP\),IFI)m -1(XX\(LD)m -1(IFX,)m -1(M\),)m 553 981 p ()s 42(BETA\(NP\),XPLU)m -1(SD\(LD)m -1(N,M\))m 422 1081 p 67 c 43(OUTPUT)m 21(ARGUMENTS)m 553 1131 p (INTEGER)s 20(ISTOP)m 553 1181 p ()s 42(F\(LDN,NQ\),FJA)m -1(CB\(LD)m -1(N,LD)m -1(NP,NQ)m -1(\),FJA)m -1(CD\(LD)m -1(N,LDM)m -1(,NQ\))m 553 1280 p 60 c 21(set)m 21(ISTOP)m 21 r 62 c 553 1380 p (IF)s 21(\(ISTOP.NE.0\))m 19(RETURN)m 422 1480 p 67 c 43(COMPUTE)m 21(FUNCTION)m 553 1529 p (IF)s 21(\(MOD\(IDEVAL,1)m -1(0\).GE)m -1(.1\))m 20(THEN)m 618 1579 p 60 c 22(compute)m 20(F\(I,L\),)m 20(I=1,...,N,)m 20 r 38 c 22(L=1,...,NQ)m 19 r 62 c 553 1629 p (END)s 21(IF)m 422 1729 p 67 c 43(COMPUTE)m 21(DERIVATIVES)m 19(WITH)m 21(RESPECT)m 20(TO)m 22(BETA)m 553 1778 p (IF)s 21(\(MOD\(IDEVAL/1)m -1(0,10\))m -1(.GE.1)m -1 r 41 c 20(THEN)m 618 1828 p 60 c 22(compute)m 20(FJACB\(I,K,L\),)m 19(I=1,...,N,)m 20(K=1,...,NP,)m 19 r 38 c 22(L=1,...,NQ)m 20 r 62 c 553 1878 p (END)s 21(IF)m 422 1978 p 67 c 43(COMPUTE)m 21(DERIVATIVES)m 19(WITH)m 21(RESPECT)m 20(TO)m 22(DELTA)m 553 2028 p (IF)s 21(\(MOD\(IDEVAL/1)m -1(00,10)m -1(\).GE.)m -1(1\))m 20(THEN)m 618 2077 p 60 c 22(compute)m 20(FJACD\(I,J,L\),)m 19(I=1,...,N,)m 20(J=1,...,M,)m 41 r 38 c 22(L=1,...,NQ)m 20 r 62 c 553 2127 p (END)s 21(IF)m 553 2227 p (RETURN)s 553 2277 p (END)s cmr10.329 @sf 422 2418 p (where)s @eop %%Page: 26 40 26 @bop0 cmtt10.329 @sf [<00700000F80000F80000D80001DC0001DC0001DC00018C00038E00038E00038E00038E00070700 0707000707000707000F07800E03800E03800E03800E03801C01C01C01C01C01C01C01C0FF07F8 FF07F8FF07F8> 24 28 -1 0 23.863] 86 @dc cmsy10.329 @sf [ 32 31 1 0 24.750] 73 @dc 1.000000 /cmsy10.300 @newfont cmsy10.300 @sf [ 32 28 1 0 22.603] 73 @dc cmr10.300 @sf [ 32 12 -2 -4 32.286] 61 @dc [<7F87FC007F87FC000E01C0000E01C0000E01C0000E01C0000E01C0000E01C0000E01C0000E01C0 000E01C0000E01C0000E01C0000E01C0000E01C0000E01C000FFFFFC00FFFFFC000E01C0000E01 C0000E01C0000E01C0000E01C0000E01C0000F03E3C00783E3C003C3F3C001FFFFC0003F1F80> 32 29 0 0 24.214] 11 @dc 1.000000 /cmmi10.300 @newfont cmmi10.300 @sf [ 24 28 -2 0 25.454] 83 @dc [ 32 37 1 8 23.479] 12 @dc [<60E070303818181878F8F8F870> 8 13 -3 8 11.531] 59 @dc [<0200001FC0007FE000787000F03000F03800F01800F01C00F00C00F00C00F80C00780E00780E00 3C0E003C0E001E1E000FBC0003FC0001F80003F00003E00007C000078000070000030000038000 03C00001E38000FF00003E00> 24 30 -1 1 18.449] 14 @dc cmsy10.329 @sf [ 24 24 -6 1 35.353] 2 @dc 26 @bop1 cmr10.329 @sf 0 114 p (26)s 1319(Using)m 15(ODRP)m -3 r 65 c (CK)s 0 134 p 1725 2 ru cmtt10.329 @sf 333 259 p 78 c cmr10.329 @sf 23(is)m 14(the)m 16 r 110 c (um)s 98 c 1(er)m 13(of)m 15(observ)m -2(ations,)m cmmi10.329 @sf 13 r 110 c cmr10.329 @sf 46 c cmtt10.329 @sf 333 325 p 77 c cmr10.329 @sf 23(is)m 12(the)m 12 r 110 c (um)s 98 c 1(er)m 11(of)m 12(elemen)m (ts,)s cmmi10.329 @sf 12 r 109 c cmr10.329 @sf 44 c 12(in)m 13(eac)m 104 c 11(explanatory)m 12 r 118 c -2(ariable,)m cmmi10.329 @sf 11 r 120 c cmmi8.300 @sf 1577 332 p 105 c cmsy10.329 @sf 1603 325 p 50 c 13 r 60 c cmmi8.300 @sf 1679 310 p 109 c cmmi10.329 @sf 1712 325 p 59 c cmr10.329 @sf 380 381 p (i.e.,)s 14(the)m 15 r 110 c (um)s 98 c 1(er)m 13(of)m 15(columns)m 15(of)m 15(data)m 14(in)m cmmi10.329 @sf 15 r 88 c cmr10.329 @sf 14 r 43 c 10(\001.)m cmtt10.329 @sf 309 448 p (NP)s cmr10.329 @sf 23(is)m 14(the)m 16 r 110 c (um)s 98 c 1(er)m 13(of)m 15(function)m 15(parameters,)m cmmi10.329 @sf 14 r 112 c cmr10.329 @sf 46 c cmtt10.329 @sf 309 514 p (NQ)s cmr10.329 @sf 23(is)m 14(the)m 16 r 110 c (um)s 98 c 1(er)m 13(of)m 15(resp)m 1(onses,)m cmmi10.329 @sf 15 r 113 c cmr10.329 @sf 2 r 44 c 15 r 112 c 1(er)m 16(observ)m -2(ation.)m cmtt10.329 @sf 285 580 p (LDN)s cmr10.329 @sf 23(is)m 14(an)m 16(arra)m -1 r 121 c 13(leading)m 15(dimension)m 15(declarator)m 14(that)m 14(equals)m 15(or)m 15(exceeds)m cmmi10.329 @sf 16 r 110 c cmr10.329 @sf 46 c cmtt10.329 @sf 285 646 p (LDM)s cmr10.329 @sf 23(is)m 14(an)m 16(arra)m -1 r 121 c 13(leading)m 15(dimension)m 15(declarator)m 14(that)m 14(equals)m 15(or)m 15(exceeds)m cmmi10.329 @sf 16 r 109 c cmr10.329 @sf 46 c cmtt10.329 @sf 262 712 p (LDNP)s cmr10.329 @sf 22(is)m 14(an)m 16(arra)m -1 r 121 c 13(leading)m 15(dimension)m 15(declarator)m 14(that)m 14(equals)m 15(or)m 15(exceeds)m cmmi10.329 @sf 16 r 112 c cmr10.329 @sf 46 c cmtt10.329 @sf 262 779 p (BETA)s cmr10.329 @sf 22(is)m 14(the)m 14(singly)m 13(subscripted)m 15(arra)m 121 c 12(that)m 14(con)m (tains)s 12(the)m 15(curren)m 116 c 13 r 118 c -2(alues)m 13(of)m cmmi10.329 @sf 14 r 12 c cmr10.329 @sf 2 r 46 c cmtt10.329 @sf 214 845 p (XPLUSD)s cmr10.329 @sf 22(is)m 19(the)m 20(doubly)m 19(subscripted)m 20(arra)m 121 c 18(that)m 19(con)m (tai)s -1(ns)m 18(the)m 20(curren)m 116 c 18 r 118 c -2(alue)m 19(of)m 380 901 p (the)s 15(explanatory)m 14 r 118 c -2(ariables,)m 13(i.e.,)m cmmi10.329 @sf 14 r 88 c cmr10.329 @sf 13 r 43 c 11(\001.)m cmtt10.329 @sf 238 968 p (IFIXB)s cmr10.329 @sf 22(is)m 10(the)m 10(singly)m 10(subscripted)m 11(arra)m 121 c 8(designating)m 10(whether)m 10 r 97 c 11(giv)m (en)s 9(parameter)m cmmi10.329 @sf 380 1024 p 12 c cmr6.300 @sf 406 1031 p 75 c cmr10.329 @sf 446 1024 p (is)s 14(to)m 15 r 98 c 1 r 101 c 16(treated)m 15(as)m 14(\014xed.)m 21(\(See)m 15(argumen)m 116 c 14(17{)m cmtt10.329 @sf (IFIXB)s cmr10.329 @sf 13 r 98 c 1(elo)m (w.\))s cmtt10.329 @sf 238 1090 p (IFIXX)s cmr10.329 @sf 22(is)m 14(the)m 14(doubly)m 15(subscripted)m 15(arra)m -1 r 121 c 13(designating)m 13(whether,)m 15(when)m 15(the)m 14(solu-)m 380 1147 p (tion)s 14(is)m 14(found)m 15 r 98 c 121 c 14(orthogonal)m 13(distance)m 15(regression,)m 13 r 97 c 15(giv)m (en)s 13(explanatory)m 380 1203 p 118 c -2(ariable)m cmmi10.329 @sf 17 r 88 c cmr6.300 @sf 592 1210 p 73 c 74 c cmr10.329 @sf 639 1203 p (is)s 19(to)m 18 r 98 c 1 r 101 c 20(treated)m 18(as)m 19(without)m 18(error.)m 30(\(See)m 20(argumen)m 116 c 17(18{)m cmtt10.329 @sf 380 1260 p (IFIXX)s cmr10.329 @sf 14 r 98 c 1(elo)m (w.\))s cmtt10.329 @sf 238 1326 p (LDIFX)s cmr10.329 @sf 22(is)m 18(the)m 19(leading)m 17(dimension)m 19(of)m 18(arra)m 121 c cmtt10.329 @sf 16(IFIXX)m cmr10.329 @sf 46 c 30(\(See)m 19(argumen)m 116 c 16(19{)m cmtt10.329 @sf (LDIFX)s cmr10.329 @sf 380 1382 p 98 c 1(elo)m (w.\))s cmtt10.329 @sf 214 1449 p (IDEVAL)s cmr10.329 @sf 22(is)m 22 r 97 c 23(three)m 24(digit)m cmtt10.329 @sf 22(INTEGER)m cmr10.329 @sf 22 r 118 c -2(ariable)m 21(with)m 23(decimal)m 22(expansion)m cmsy10.329 @sf 24 r 73 c cmr8.300 @sf 1617 1456 p 51 c cmsy10.329 @sf 1636 1449 p 73 c cmr8.300 @sf 1661 1456 p 50 c cmsy10.329 @sf 1680 1449 p 73 c cmr8.300 @sf 1705 1456 p 49 c cmr10.329 @sf 380 1505 p (passed)s 19(to)m 18(subroutine)m cmtt10.329 @sf 19(FCN)m cmr10.329 @sf 19 r 98 c 121 c 18(ODRP)m -3 r 65 c (CK)s 17(to)m 19(designate)m 18(what)m 19 r 118 c -2(alues)m 380 1562 p (are)s 15(to)m 14 r 98 c 1 r 101 c 16(computed.)m 392 1588 p 1334 2 ru 392 1650 p 2 62 ru cmr10.300 @sf 417 1624 p (Computation)s 680 1651 p 2 62 ru 9 r 2 62 ru 689 1650 p 2 62 ru 727 1624 p (Digit)s 1724 1650 p 2 62 ru 392 1651 p 1334 2 ru 392 1701 p 2 50 ru cmtt10.300 @sf 526 1687 p 70 c 680 1701 p 2 50 ru 9 r 2 50 ru cmsy10.300 @sf 714 1686 p 73 c cmr7.300 @sf 737 1692 p 49 c cmr10.300 @sf 767 1686 p 61 c 12 r 48 c 50(arra)m 121 c cmtt10.300 @sf 12 r 70 c cmr10.300 @sf 14(need)m 15(not)m 14 r 98 c 1 r 101 c 14(computed)m 1724 1701 p 2 50 ru 392 1751 p 2 50 ru 288 r 2 50 ru 9 r 2 50 ru 767 1736 p 61 c 12 r 49 c 50(function)m 13 r 118 c -1(alues)m cmtt10.300 @sf 13 r 70 c cmr10.300 @sf 13 r 109 c (ust)s 13 r 98 c 1 r 101 c 15(computed)m 1724 1751 p 2 50 ru 392 1801 p 2 50 ru 288 r 2 50 ru 9 r 2 50 ru 882 1786 p (\(for)s 13(constructing)m 15(\014nite)m 14(di\013erence)m 16(deriv)m -1(ativ)m -1(es\))m 1724 1801 p 2 50 ru 392 1851 p 2 50 ru 288 r 2 50 ru 9 r 2 50 ru 767 1836 p 61 c 12 r 50 c 50(function)m 13 r 118 c -1(alues)m cmtt10.300 @sf 13 r 70 c cmr10.300 @sf 13 r 109 c (ust)s 13 r 98 c 1 r 101 c 15(computed)m 1724 1851 p 2 50 ru 392 1900 p 2 50 ru 288 r 2 50 ru 9 r 2 50 ru 882 1885 p (\(for)s 13(ev)m -1(aluating)m cmmi10.300 @sf 12 r 83 c cmr10.300 @sf 2 r 40 c cmmi10.300 @sf 12 c 2 r 59 c 7 r 14 c cmr10.300 @sf 2 r 41 c 15(at)m 14(new)m 14 r 112 c 1(oin)m (t\))s 1724 1900 p 2 50 ru 392 1950 p 2 50 ru 288 r 2 50 ru 9 r 2 50 ru 767 1935 p 61 c 12 r 51 c 50(function)m 13 r 118 c -1(alues)m cmtt10.300 @sf 13 r 70 c cmr10.300 @sf 13 r 109 c (ust)s 13 r 98 c 1 r 101 c 15(computed)m 1724 1950 p 2 50 ru 392 2000 p 2 50 ru 288 r 2 50 ru 9 r 2 50 ru 882 1985 p (\(for)s 13(miscellaneous)m 14(calculations\))m 1724 2000 p 2 50 ru 392 2002 p 1334 2 ru 392 2052 p 2 50 ru cmtt10.300 @sf 482 2038 p (FJACB)s 680 2052 p 2 50 ru 9 r 2 50 ru cmsy10.300 @sf 714 2037 p 73 c cmr7.300 @sf 737 2043 p 50 c cmr10.300 @sf 767 2037 p 61 c 12 r 48 c 50(arra)m 121 c cmtt10.300 @sf 12(FJACB)m cmr10.300 @sf 13(need)m 15(not)m 14 r 98 c 1 r 101 c 14(computed)m 1724 2052 p 2 50 ru 392 2101 p 2 50 ru 288 r 2 50 ru 9 r 2 50 ru 767 2086 p 61 c 12 r 49 c 50(deriv)m -1(ativ)m -1 r 101 c 12 r 118 c -1(alues)m cmtt10.300 @sf 13(FJACB)m cmr10.300 @sf 12 r 109 c (ust)s 13 r 98 c 1 r 101 c 15(computed)m 1724 2101 p 2 50 ru 392 2103 p 1334 2 ru 392 2153 p 2 50 ru cmtt10.300 @sf 482 2139 p (FJACD)s 680 2153 p 2 50 ru 9 r 2 50 ru cmsy10.300 @sf 714 2138 p 73 c cmr7.300 @sf 737 2144 p 51 c cmr10.300 @sf 767 2138 p 61 c 12 r 48 c 50(arra)m 121 c cmtt10.300 @sf 12(FJACD)m cmr10.300 @sf 13 r 109 c (ust)s 13(not)m 14 r 98 c 1 r 101 c 14(altered)m 1724 2153 p 2 50 ru 392 2203 p 2 50 ru 288 r 2 50 ru 9 r 2 50 ru 767 2188 p 61 c 12 r 49 c 50(deriv)m -1(ativ)m -1 r 101 c 12 r 118 c -1(alues)m cmtt10.300 @sf 13(FJACD)m cmr10.300 @sf 12 r 109 c (ust)s 13 r 98 c 1 r 101 c 15(computed)m 1724 2203 p 2 50 ru 392 2252 p 2 50 ru 288 r 2 50 ru 9 r 2 50 ru 882 2237 p (\(required)s 15(for)m 13(ODR)m 13(\014ts)m 15(only\))m 1724 2252 p 2 50 ru 392 2254 p 1334 2 ru cmtt10.329 @sf 333 2324 p 70 c cmr10.329 @sf 23(is)m 13(the)m 13(doubly)m 14(subscripted)m 14(arra)m 121 c 11(in)m 13(whic)m 104 c 13(the)m cmmi10.329 @sf 13 r 110 c cmsy10.329 @sf 7 r 2 c cmmi10.329 @sf 7 r 113 c cmr10.329 @sf 16(arra)m 121 c 11(of)m 13(predicted)m 380 2381 p 118 c -2(alues)m 14(for)m 15(eac)m 104 c 14(resp)m 1(onse)m 16(of)m 14(eac)m 104 c 15(observ)m -2(ation)m 13 r 109 c (ust)s 14 r 98 c 1 r 101 c 16(stored.)m @eop %%Page: 27 41 27 @bop0 cmmi10.300 @sf [<000001800000078000001F0000007C000001F0000007C000001F0000007C000001F0000007C000 001F0000007C000000F0000000F00000007C0000001F00000007C0000001F00000007C0000001F 00000007C0000001F00000007C0000001F800000078000000180> 32 26 -3 3 32.286] 60 @dc cmr10.300 @sf [ 32 28 -2 0 34.592] 1 @dc cmmi10.300 @sf [ 32 26 -3 3 32.286] 62 @dc cmtt12.300 @sf [ 24 30 -4 0 25.632] 73 @dc [<01F8E007FEE00FFFE01F0FE01E07E03C03E07C01E07801E07001E0F000E0F000E0E00FF8E00FF8 E00FF8E00000E00000E00000E00000E00000F00000F000E07000E07800E07C01E03C03E01E03E0 1F0FE00FFFE007FEE001F8E0> 24 30 -2 0 25.632] 71 @dc [ 32 30 0 0 25.632] 77 @dc [ 24 30 -2 0 25.632] 80 @dc [<0001C00001C00003C0000380000780000700000F000FFE003FFF807FFFC07C3FC07079C0F079E0 E0F0E0E070E0E000E0E000E0E000E0E000E0E000E0E000E0E000E0E000E0E000E0E000E0E000E0 E000E0E000E0E000E0E000E0E000E0F001E07001C07C07C07FFFC03FFF800FFE00> 24 37 -3 7 25.632] 81 @dc [ 24 30 -2 0 25.632] 66 @dc [<0000E00003E00007E0001FE0003F80007F0001FC0003F80007F0001FC0003F8000FF0000FC0000 FC0000FF00003F80001FC00007F00003F80001FC00007F00003F80001FE00007E00003E00000E0> 24 26 -3 -2 25.632] 60 @dc [ 24 21 -2 0 25.632] 114 @dc [<01FF0007FFC00FFFE03F01F03E00F0780070780000F00000F00000FFFFF0FFFFF0FFFFF0E00070 F000F0F000F07801E07C03E03F07C01FFF8007FF0001FC00> 24 21 -3 0 25.632] 101 @dc [<07F0FC1FFFFC7FFFFC7C1F80F00780F00380E00380F00380F003807C03807F83801FFF8007FF80 00FF80000380000780780780781F007FFF007FFC001FF000> 24 21 -3 0 25.632] 97 @dc [ 24 30 -3 0 25.632] 108 @dc [ 24 26 -3 -2 25.632] 62 @dc [<0038007801F803F007C00F800F001E001E003C003C00780078007000F000F000E000E000E000E0 00E000E000E000E000F000F0007000780078003C003C001E001E000F000F8007C003F001F80078 0038> 16 40 -8 5 25.632] 40 @dc [ 16 40 -4 5 25.632] 41 @dc 27 @bop1 cmr10.329 @sf 225 114 p (Using)s 15(ODRP)m -3 r 65 c (CK)s 1318(27)m 225 134 p 1725 2 ru cmtt10.329 @sf 463 259 p (FJACB)s cmr10.329 @sf 22(is)m 13(the)m 14(triply)m 13(subscripted)m 14(arra)m 121 c 12(in)m 13(whic)m 104 c 13(the)m cmmi10.329 @sf 14 r 110 c cmsy10.329 @sf 7 r 2 c cmmi10.329 @sf 7 r 112 c cmsy10.329 @sf 7 r 2 c cmmi10.329 @sf 8 r 113 c cmr10.329 @sf 17(arra)m 121 c 12(of)m 14(partial)m 605 315 p (deriv)s -2(ativ)m -1(es)m 16(with)m 17(resp)m 1(ect)m 18(to)m cmmi10.329 @sf 17 r 12 c cmr10.329 @sf 20(for)m 17(eac)m 104 c 16(resp)m 1(onse)m 19(of)m 17(eac)m 104 c 17(observ)m -2(ation)m 605 372 p 109 c (ust)s 13 r 98 c 1 r 101 c 16(stored.)m cmtt10.329 @sf 463 438 p (FJACD)s cmr10.329 @sf 22(is)m 12(the)m 13(triply)m 12(subscripted)m 13(arra)m 121 c 11(in)m 13(whic)m 104 c 12(the)m cmmi10.329 @sf 13 r 110 c cmsy10.329 @sf 6 r 2 c cmmi10.329 @sf 6 r 109 c cmsy10.329 @sf 6 r 2 c cmmi10.329 @sf 6 r 113 c cmr10.329 @sf 14(arra)m 121 c 11(of)m 13(partial)m 605 494 p (deriv)s -2(ativ)m -1(es)m 15(with)m 16(resp)m 1(ect)m 17(to)m 16 r 1 c 16(for)m 17(eac)m 104 c 15(resp)m 1(onse)m 18(of)m 16(eac)m 104 c 16(observ)m -2(ation)m 605 551 p 109 c (ust)s 13 r 98 c 1 r 101 c 16(stored.)m cmtt10.329 @sf 463 617 p (ISTOP)s cmr10.329 @sf 22(is)m 16 r 97 c 17 r 118 c -2(ariable)m 16(that)m 16(enables)m 17(the)m 18(user)m 17(to)m 16(instruct)m 17(ODRP)m -3 r 65 c (CK)s 16(to)m 16(reject)m 605 673 p (the)s 15(curren)m 116 c 14 r 118 c -2(alues)m 14(in)m cmtt10.329 @sf 15(BETA)m cmr10.329 @sf 15(and)m cmtt10.329 @sf 15(XPLUSD)m cmr10.329 @sf 15(as)m 15(unacceptable.)m 622 700 p 1311 2 ru 622 762 p 2 62 ru cmtt10.300 @sf 647 736 p (ISTOP)s 780 762 p 2 62 ru 9 r 2 62 ru cmr10.300 @sf 814 735 p (Meaning)s 1932 762 p 2 62 ru 622 763 p 1311 2 ru 622 813 p 2 50 ru cmmi10.300 @sf 669 799 p 60 c cmr10.300 @sf 12 r 48 c 780 814 p 2 50 ru 9 r 2 50 ru 814 798 p (regression)s 15(pro)m 1(cedure)m 16(should)m 14 r 98 c 1 r 101 c 14(stopp)m 1(ed)m 1932 813 p 2 50 ru 622 863 p 2 50 ru 669 849 p 61 c 12 r 48 c 780 864 p 2 50 ru 9 r 2 50 ru 814 848 p (curren)s 116 c cmmi10.300 @sf 14 r 12 c cmr10.300 @sf 17(and)m 14 r 1 c 13(are)m 14(acceptable)m 15(for)m 14(use)m 15 r 98 c 121 c cmtt10.300 @sf 12(FCN)m cmr10.300 @sf 58 c 1932 863 p 2 50 ru 622 913 p 2 50 ru 158 r 2 50 ru 9 r 2 50 ru 869 898 p (requested)s 16 r 118 c -1(alues)m 13 r 119 c (ere)s 14(prop)m 1(erly)m 14(computed)m 14(within)m cmtt10.300 @sf 14(FCN)m cmr10.300 @sf 13(and)m 1932 913 p 2 50 ru 622 962 p 2 50 ru 158 r 2 50 ru 9 r 2 50 ru 869 947 p (regression)s 15(pro)m 1(cedure)m 16(should)m 14(con)m (tin)s (ue)s 1932 962 p 2 50 ru 622 1012 p 2 50 ru cmmi10.300 @sf 669 998 p 62 c cmr10.300 @sf 12 r 48 c 780 1013 p 2 50 ru 9 r 2 50 ru 814 997 p (curren)s 116 c cmmi10.300 @sf 14 r 12 c cmr10.300 @sf 17(and)m 14 r 1 c 13(are)m 14(unacceptable)m 15(for)m 14(use)m 15 r 98 c 121 c cmtt10.300 @sf 12(FCN)m cmr10.300 @sf 58 c 1932 1012 p 2 50 ru 622 1062 p 2 50 ru 158 r 2 50 ru 9 r 2 50 ru 869 1047 p (if)s 13(call)m 14(to)m cmtt10.300 @sf 13(FCN)m cmr10.300 @sf 13 r 119 c (as)s 13(for)m 14(constructing)m 15(deriv)m -1(ativ)m -1(es)m 1932 1062 p 2 50 ru 622 1112 p 2 50 ru 158 r 2 50 ru 9 r 2 50 ru 925 1097 p (regression)s 15(pro)m 1(cedure)m 16(will)m 12 r 98 c 1 r 101 c 15(stopp)m 1(ed)m 1932 1112 p 2 50 ru 622 1162 p 2 50 ru 158 r 2 50 ru 9 r 2 50 ru 869 1147 p (if)s 13(call)m 14(to)m cmtt10.300 @sf 13(FCN)m cmr10.300 @sf 13 r 119 c (as)s 13(for)m 14(ev)m -1(aluating)m cmmi10.300 @sf 11 r 83 c cmr10.300 @sf 2 r 40 c cmmi10.300 @sf 12 c 2 r 59 c 7 r 14 c cmr10.300 @sf 2 r 41 c 1932 1162 p 2 50 ru 622 1211 p 2 50 ru 158 r 2 50 ru 9 r 2 50 ru 925 1196 p 97 c 13(new)m 15 r 112 c 1(oin)m 116 c 12(will)m 12 r 98 c 1 r 101 c 15(selected)m 16(closer)m 14(to)m 14(the)m 15(most)m 1932 1211 p 2 50 ru 622 1261 p 2 50 ru 158 r 2 50 ru 9 r 2 50 ru 925 1246 p (recen)s (tly)s 14(tried)m 14(acceptable)m 15 r 118 c -1(alues)m 12(of)m cmmi10.300 @sf 14 r 12 c cmr10.300 @sf 16(and)m 14 r 1 c 1932 1261 p 2 50 ru 622 1311 p 2 50 ru 158 r 2 50 ru 9 r 2 50 ru 869 1296 p (if)s 13(call)m 14(to)m cmtt10.300 @sf 13(FCN)m cmr10.300 @sf 13 r 119 c (as)s 13(for)m 14(miscellaneous)m 14(calculations)m 1932 1311 p 2 50 ru 622 1361 p 2 50 ru 158 r 2 50 ru 9 r 2 50 ru 925 1346 p (regression)s 15(pro)m 1(cedure)m 16(will)m 12 r 98 c 1 r 101 c 15(stopp)m 1(ed)m 1932 1361 p 2 50 ru 622 1363 p 1311 2 ru cmr10.329 @sf 605 1410 p (Note)s 13(that)m 12(ev)m (en)s 13(when)m cmtt10.329 @sf 14(ISTOP)m cmr10.329 @sf 12(is)m 13(used)m 14(to)m 13(stop)m 13(the)m 13(regression)m 12(pro)m 1(cedure,)m 605 1466 p (the)s 16(\014nal)m 15(summary)m 15(of)m 16(the)m 16(computation)m 14(rep)m 1(ort)m 16(will)m 14(still)m 14 r 98 c 1 r 101 c 17(generated)m 605 1523 p (if)s 14(it)m 15(has)m 15 r 98 c 1(een)m 16(requested.)m 21(\(See)m 15(argumen)m 116 c 13(26{)m cmtt10.329 @sf (IPRINT)s cmr10.329 @sf -1(.\))m 258 1621 p 61 c cmsy10.329 @sf -7 r 41 c cmr10.329 @sf 50 c 23 r 123 c cmtt12.300 @sf 22 r 78 c 25([INTEGER)m 23(N])m cmr10.329 @sf 422 1697 p (The)s 15 r 110 c (um)s 98 c 1(er)m 14(of)m 15(observ)m -2(ations,)m cmmi10.329 @sf 13 r 110 c cmr10.329 @sf 46 c 258 1794 p 61 c cmsy10.329 @sf -7 r 41 c cmr10.329 @sf 51 c 23 r 123 c cmtt12.300 @sf 22 r 77 c 25([INTEGER)m 23(M])m cmr10.329 @sf 422 1870 p (The)s 19 r 110 c (um)s -1 r 98 c 1(er)m 17(of)m 18(elemen)m (ts,)s cmmi10.329 @sf 17 r 109 c cmr10.329 @sf 44 c 19(in)m 18(eac)m 104 c 18(explanatory)m 17 r 118 c -2(ariable)m cmmi10.329 @sf 16 r 120 c cmmi8.300 @sf 1630 1877 p 105 c cmsy10.329 @sf 1657 1870 p 50 c 13 r 60 c cmmi8.300 @sf 1733 1855 p 109 c cmmi10.329 @sf 1766 1870 p 59 c cmr10.329 @sf 18(i.e.,)m 18(the)m 422 1927 p 110 c (um)s 98 c 1(er)m 13(of)m 15(columns)m 15(of)m 15(data)m 15(in)m cmmi10.329 @sf 15 r 88 c cmr10.329 @sf 4 r 46 c 258 2025 p 61 c cmsy10.329 @sf -7 r 41 c cmr10.329 @sf 52 c 23 r 123 c cmtt12.300 @sf 22(NP)m 25([INTEGE)m -1 r 82 c 24(NP])m cmr10.329 @sf 422 2101 p (The)s 15 r 110 c (um)s 98 c 1(er)m 14(of)m 15(function)m 15(parameters,)m cmmi10.329 @sf 14 r 112 c cmr10.329 @sf 46 c 258 2198 p 61 c cmsy10.329 @sf -7 r 41 c cmr10.329 @sf 53 c 23 r 123 c cmtt12.300 @sf 22(NQ)m 25([INTEGE)m -1 r 82 c 24(NQ])m cmr10.329 @sf 422 2275 p (The)s 15 r 110 c (um)s 98 c 1(er)m 14(of)m 15(resp)m 1(onses,)m cmmi10.329 @sf 15 r 113 c cmr10.329 @sf 2 r 44 c 15 r 112 c 1(er)m 15(observ)m -2(ation.)m cmsy10.329 @sf 248 2372 p 40 c -7 r 41 c cmr10.329 @sf 54 c 23 r 123 c cmtt12.300 @sf 22(BETA)m 24 r 91 c ()s 23(BETA\(NP\))m -1 r 93 c cmr10.329 @sf 422 2448 p (The)s 15(singly)m 15(subscripted)m 15(arra)m 121 c 13(that)m 15(con)m (tains)s 13(the)m 15(\(curren)m (t\))s 14 r 118 c -2(alues)m 14(of)m cmmi10.329 @sf 15 r 12 c cmr10.329 @sf 2 r 46 c @eop %%Page: 28 42 28 @bop0 cmtt12.300 @sf [<01FF0001FF0001FF00003800003800003800003800003800003800003800003800003800003800 007C00007C0000EE0000EE0001C70001C70003C7800383800783C00701C00701C00E00E00E00E0 1C0070FF01FEFF01FEFF01FE> 24 30 -1 0 25.632] 89 @dc [ 24 30 -1 0 25.632] 68 @dc [ 8 13 -9 7 25.632] 44 @dc cmtt10.329 @sf [<03FE0003FE0003FE0000700000700000700000700000700000700000700000700000700000F800 00F80001FC0001DC0001DC00038E00038E000707000707000F07800E03801E03C01C01C0FF07F8 FF07F8FF07F8> 24 28 -1 0 23.863] 89 @dc cmtt12.300 @sf [<0701C00F83E00F83E00D83600D83600D83600DC7600DC7600DC7601CC6701CC6701CEE701CEE70 1CEE701CEE701CEE701C7C70387C3838003838003838003838003838003838003838003878003C 70001CFF01FEFF01FEFF01FE> 24 30 -1 0 25.632] 87 @dc [ 24 30 -3 0 25.632] 50 @dc 28 @bop1 cmr10.329 @sf 0 114 p (28)s 1319(Using)m 15(ODRP)m -3 r 65 c (CK)s 0 134 p 1725 2 ru 215 259 p (On)s 16(input:)m cmtt10.329 @sf 22(BETA)m cmr10.329 @sf 13 r 109 c (ust)s 13(con)m (tain)s 12(initial)m 12(appro)m (xima)s -1(tio)m -1(ns)m 12(for)m 14(the)m 14(function)m 13(param-)m 432 315 p (eters)s cmmi10.329 @sf 17 r 12 c cmr10.329 @sf 2 r 46 c 25(Initial)m 16(appro)m (ximat)s -1(ions)m 15(should)m 17 r 98 c 1 r 101 c 17 r 99 c (hosen)s 17(with)m 16(care)m 17(since)m 432 372 p 112 c 1 r 111 c 1(or)m 15(initial)m 13(appro)m (ximat)s -1(ions)m 13(can)m 15(signi\014can)m (tl)s -1 r 121 c 13(increase)m 15(the)m 15 r 110 c (um)s -1 r 98 c 1(er)m 432 428 p (of)s 16(iterations)m 15(required)m 17(to)m 16(\014nd)m 17 r 97 c 17(solution)m 15(and)m 17 r 112 c 1(ossibly)m 16(prev)m (en)s 116 c 15(the)m 432 484 p (solution)s 14(from)m 14 r 98 c 1(eing)m 16(found)m 15(at)m 15(all.)m 19(\(See)m cmsy10.329 @sf 15 r 120 c cmr10.329 @sf 1(1.E.\))m 197 541 p (On)s 16(return:)m cmtt10.329 @sf 22(BETA)m cmr10.329 @sf 19(con)m (tains)s 18(the)m 20(\\b)m 1(est")m 19(estimate)m 19(of)m 19(the)m 20(parameters,)m 1547 530 p 94 c cmmi10.329 @sf 1540 542 p 12 c cmr10.329 @sf 1568 541 p 44 c 21(at)m 19(the)m 432 597 p (time)s 15(the)m 15(computations)m 14(stopp)m 1(ed.)m 33 695 p 61 c cmsy10.329 @sf -7 r 41 c cmr10.329 @sf 55 c 23 r 123 c cmtt12.300 @sf 22 r 89 c 25 r 91 c ()s 23(Y\(LDY,NQ)m -1(\)])m cmr10.329 @sf 197 771 p (The)s 13(double)m 12(subscripted)m 13(arra)m 121 c 10(that)m 12(con)m (tains)s 10(the)m 13 r 118 c -2(alues)m 11(of)m 12(the)m 13(resp)m 1(onse)m 13 r 118 c -2(ariable)m cmmi10.329 @sf 197 828 p 89 c cmr6.300 @sf 223 835 p 73 c 76 c cmmi10.329 @sf 255 828 p 59 c cmtt10.329 @sf 8 r 73 c cmr10.329 @sf 20 r 61 c 20 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 8 r 58 c 5 r 59 c 8(n;)m cmtt10.329 @sf 26 r 76 c cmr10.329 @sf 21 r 61 c 20 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 8 r 58 c 5 r 59 c 8 r 113 c cmr10.329 @sf 2 r 46 c 33(When)m 20(the)m 20(mo)m 1(del)m 20(is)m cmti10.329 @sf 19(explicit)m cmr10.329 @sf 44 c 21(the)m 19(user)m 20 r 109 c (ust)s 197 884 p (supply)s 16 r 97 c 15 r 118 c -2(alue)m 15(for)m 15(eac)m 104 c 15(of)m 15(the)m cmmi10.329 @sf 16 r 110 c cmsy10.329 @sf 11 r 2 c cmmi10.329 @sf 11 r 113 c cmr10.329 @sf 17(elemen)m (ts)s 15(of)m cmtt10.329 @sf 15 r 89 c cmr10.329 @sf 59 c 15(if)m 15(some)m 16(resp)m 1(onses)m 16(of)m 15(some)m 197 940 p (observ)s -2(ations)m 19(are)m 20(actually)m 20(missing,)m 21(then)m 21(the)m 21(user)m 21(can)m 21(set)m 20(the)m 21(corresp)m 1(onding)m 197 997 p 119 c (eigh)s -1 r 116 c 12(in)m 14(argumen)m 116 c 12(11{)m cmtt10.329 @sf (WE)s cmr10.329 @sf 14(to)m 13(zero)m 14(in)m 14(order)m 14(to)m 14(remo)m 118 c -1 r 101 c 13(the)m 14(e\013ect)m 14(of)m 14(the)m 14(missing)m 197 1053 p (observ)s -2(ation)m 10(from)m 11(the)m 12(analysis.)m 18(When)m 12(the)m 12(mo)m 1(del)m 12(is)m cmti10.329 @sf 12(implicit)m cmr10.329 @sf 44 c cmtt10.329 @sf 12 r 89 c cmr10.329 @sf 11(is)m 12(not)m 11(referenced.)m 197 1110 p (\(See)s 15(argumen)m 116 c 14(20-)m cmtt10.329 @sf (JOB)s cmr10.329 @sf -1 r 44 c 15(and)m cmsy10.329 @sf 15 r 120 c cmr10.329 @sf (1.F.\))s 33 1208 p 61 c cmsy10.329 @sf -7 r 41 c cmr10.329 @sf 56 c 23 r 123 c cmtt12.300 @sf 22(LDY)m 24([INTEGER)m 23(LDY])m cmr10.329 @sf 197 1284 p (The)s 13(leading)m 12(dimension)m 13(of)m 12(arra)m 121 c cmtt10.329 @sf 11 r 89 c cmr10.329 @sf 46 c 19(When)m 13(the)m 13(mo)m 1(del)m 13(is)m cmti10.329 @sf 12(explicit)m cmr10.329 @sf 44 c cmtt10.329 @sf 13(LDY)m cmr10.329 @sf 12 r 109 c (ust)s 11(equal)m 197 1340 p (or)s 15(exceed)m cmmi10.329 @sf 16 r 110 c cmr10.329 @sf 46 c 20(When)m 16(the)m 15(mo)m 1(del)m 15(is)m cmti10.329 @sf 15(implicit)m cmr10.329 @sf 44 c cmtt10.329 @sf 14(LDY)m cmr10.329 @sf 15 r 109 c (ust)s 14(equal)m 15(or)m 14(exceed)m 16(1.)m 33 1438 p 61 c cmsy10.329 @sf -7 r 41 c cmr10.329 @sf 57 c 23 r 123 c cmtt12.300 @sf 22 r 88 c 25 r 91 c ()s 23(X\(LDX,M\))m -1 r 93 c cmr10.329 @sf 197 1514 p (The)s 21(doubly)m 20(subscripted)m 21(arra)m 121 c 18(that)m 20(con)m (tains)s 18(the)m 21(observ)m (ed)s 19 r 118 c -2(alues)m 20(of)m 20(the)m 21(ex-)m 197 1570 p (planatory)s 14 r 118 c -2(ariable)m cmmi10.329 @sf 13 r 88 c cmr10.329 @sf 4 r 46 c 10 1668 p 61 c cmsy10.329 @sf -7 r 41 c cmr10.329 @sf (10)s 23 r 123 c cmtt12.300 @sf 22(LDX)m 24([INTEGER)m 23(LDX])m cmr10.329 @sf 197 1744 p (The)s 15(leading)m 15(dimension)m 15(of)m 15(arra)m -1 r 121 c cmtt10.329 @sf 14 r 88 c cmr10.329 @sf -1 r 46 c cmtt10.329 @sf 20(LDX)m cmr10.329 @sf 15 r 109 c (ust)s 14(equal)m 15(or)m 14(exceed)m cmmi10.329 @sf 16 r 110 c cmr10.329 @sf 46 c 10 1842 p 61 c cmsy10.329 @sf -7 r 41 c cmr10.329 @sf (11)s 23 r 123 c cmtt12.300 @sf 22(WE)m 25 r 91 c ()s 23(WE\(LDWE)m -1(,LD)m -1(2WE)m -1(,N)m -1(Q\)])m cmr10.329 @sf 197 1918 p (The)s 20(triply)m 18(subscripted)m 20(arra)m 121 c 18(that,)m 19(when)m 20(the)m 20(mo)m 1(del)m 20(is)m cmti10.329 @sf 19(explicit)m cmr10.329 @sf 19(sp)m 1(eci\014es)m 20(ho)m 119 c 197 1974 p (eac)s 104 c cmmi10.329 @sf 16 r 15 c cmr6.300 @sf 319 1981 p 73 c cmr10.329 @sf 349 1974 p (is)s 16(to)m 16 r 98 c 1 r 101 c 17 r 119 c (eigh)s -1(ted)m 15(in)m 16(the)m 17 r 119 c (eigh)s -1(ted)m 15(orthogonal)m 15(distance,)m 16(and)m 17(when)m 17(the)m 197 2031 p (mo)s 1(del)m 15(is)m cmti10.329 @sf 15(implicit)m cmr10.329 @sf 15(sp)m 1(eci\014es)m 15(the)m 16(starting)m 13 r 112 c 1(enalt)m 121 c 14(parameter)m 14 r 118 c -2(alue,)m cmmi10.329 @sf 14 r 114 c cmr8.300 @sf 1497 2038 p 48 c cmr10.329 @sf 1532 2031 p (\(see)s cmsy10.329 @sf 15 r 120 c cmr10.329 @sf (1.A,)s cmsy10.329 @sf 197 2087 p 120 c cmr10.329 @sf (1.B,)s cmsy10.329 @sf 14 r 120 c cmr10.329 @sf 1(1.F,)m 13(and)m 16(argumen)m 116 c 13(20{)m cmtt10.329 @sf (JOB)s cmr10.329 @sf -1(\).)m 197 2171 p 70 c -3(or)m cmti10.329 @sf 16(explicit)m cmr10.329 @sf 17(mo)m 1(dels,)m cmtt10.329 @sf 18(WE)m cmr10.329 @sf 17(is)m 18 r 97 c 17(structured)m 18(argumen)m (t:)s 23(only)m 17(the)m 18(sp)m 1(eci\014c)m 18(elemen)m (ts)s 197 2227 p (of)s cmtt10.329 @sf 15(WE)m cmr10.329 @sf 15(iden)m (ti\014ed)s 14(in)m 15(the)m 15(table)m 15 r 98 c 1(elo)m 119 c 14(are)m 14(referenced)m 17 r 98 c 121 c 14(ODRP)m -3 r 65 c (CK.)s 13(\(See)m cmsy10.329 @sf 16 r 120 c cmr10.329 @sf (1.G.\))s @eop %%Page: 29 43 29 @bop0 cmmi10.300 @sf [<70F8F8F870> 8 5 -3 0 11.531] 58 @dc [<3801E03C03F03C07B81C071C1C078C1E038E1E038E0E03C00E01C00F01C00F01E00700E0C780E0 E7C0E067E0E07771E03F3FE03E1F80> 24 18 -1 0 24.916] 110 @dc [<03F0F80007FFFE000F1FCF000E0F83000E0783800E0781800E0381C00E0380C00E0380C00F0380 C00703C0E00701C060C781C0E0E381C0E06381E1E07380E1E03F80E1E01F00E1E0> 32 18 -1 0 29.718] 119 @dc 1.000000 /cmmi7.300 @newfont cmmi7.300 @sf [<3E007F00E300C000C000C000FF00FF00E000600078003F800F80> 16 13 -3 0 13.835] 15 @dc cmr10.300 @sf [ 48 2 0 -10 41.510] 124 @dc cmsy10.300 @sf [ 32 2 -3 -9 32.286] 0 @dc cmmi10.300 @sf [ 24 28 -1 0 18.247] 73 @dc cmmi7.300 @sf [<3F803F8006000700030003003F007F80E780C380C180E1C061C060C070C030E039E01FE00FA0> 16 19 -2 6 15.214] 113 @dc cmmi10.300 @sf [<0FFC0FFC01E000E000E000F0007000701F707FF879F8F0F8F078F03CF01CF01CF01CF81E780E78 0E7C0E3C0F1E1F0F3F07FF01F1> 16 26 -1 8 18.531] 113 @dc cmsy10.300 @sf [ 24 20 -6 0 32.286] 2 @dc [ 32 34 -3 8 32.286] 21 @dc [<001F007F00F801E001C001C001C001C001C001C001C001C001C001C001C001C001C003C00F80FF 00FC00FF000F8003C001C001C001C001C001C001C001C001C001C001C001C001C001C001E000F8 007F001F> 16 41 -2 10 20.755] 102 @dc [ 16 41 -2 10 20.755] 103 @dc cmr10.300 @sf [<0FE03F003FF9FF807C3FE1C0780FC0E0F80F0060F01F8000F03FC000F03CE000F078600070F070 0078F030003DE038001FC018000FC01C0007C00E0003C01F0003E07FE007F07FE0077000000738 0000071C0000071C0000070C0000070C0000070C0000070C0000039C000001F8000000F00000> 32 29 -2 0 32.286] 38 @dc cmmi10.300 @sf [<38003C003C001C001C001E001E000E000E000F000F00070FC78FE78F67C777E33F7F3E3E> 16 18 -1 0 18.728] 114 @dc cmr7.300 @sf [<0FC01FE0387070386018E01CE01CE01CE01CE01CE01CE01CE01CE01C6018703838701FE00FC0> 16 19 -1 0 16.546] 48 @dc cmsy10.300 @sf [ 32 34 -3 8 32.286] 20 @dc cmmi7.300 @sf [<08007E007F00E300C180C180E18060C060C070C030C03DC01FC007800E000C000C000C000E6007 E003E0> 16 21 -2 1 15.088] 14 @dc [<30180780381C0FC0381C0EE0180C0E60180C06601C0E06001C0E07000E070300CE070300CF0783 006FC7E3007DFEFF003C7C3E00> 32 13 0 0 29.456] 109 @dc cmmi10.300 @sf [<3803801E003C03C03F003C03C07B801C01C071C01C01C078C01E01E038E01E01E038E00E00E03C 000E00E01C000F00F01C000F00F01E000780700E00C780780E00E7C07C0E0067E07E0E007778F7 1E003F3FE3FE003E0FC1F800> 40 18 -1 0 36.446] 109 @dc 29 @bop1 cmr10.329 @sf 225 114 p (Using)s 15(ODRP)m -3 r 65 c (CK)s 1318(29)m 225 134 p 1725 2 ru 465 219 p 1456 2 ru 465 269 p 2 50 ru 541 r 2 50 ru 9 r 2 50 ru cmr10.300 @sf 1040 254 p 70 c -2(or)m cmtt10.300 @sf 12 r 73 c cmr10.300 @sf 12 r 61 c 11 r 49 c cmmi10.300 @sf 59 c 7 r 58 c 7 r 58 c 7 r 58 c 5 r 59 c 7(n;)m 1920 269 p 2 50 ru 465 330 p 2 62 ru cmtt10.300 @sf 490 304 p (WE\(1,1,1\))s 736 303 p (LDWE)s 49(LD2WE)m 1006 330 p 2 62 ru 9 r 2 62 ru cmmi10.300 @sf 1095 303 p 119 c cmmi7.300 @sf 1120 309 p 15 c cmr6.300 @sf 1134 316 p 73 c 1920 330 p 2 62 ru 465 332 p 1456 2 ru 465 382 p 2 50 ru cmmi10.300 @sf 556 368 p 60 c cmr10.300 @sf 11 r 48 c 759 367 p 124 c 106 r 124 c 1006 382 p 2 50 ru 9 r 2 50 ru 1040 367 p 61 c cmsy10.300 @sf 12 r 0 c cmtt10.300 @sf (WE\(1,1,1\))s cmmi10.300 @sf -2 r 73 c cmmi7.300 @sf 1330 373 p 113 c cmr10.300 @sf 1349 367 p 44 c cmmi10.300 @sf 13 r 73 c cmmi7.300 @sf 1392 373 p 113 c cmr10.300 @sf 1424 367 p 97 c cmmi10.300 @sf 14 r 113 c cmsy10.300 @sf 10 r 2 c cmmi10.300 @sf 10 r 113 c cmr10.300 @sf 15(iden)m (tit)s -1 r 121 c 12(matrix)m 1920 382 p 2 50 ru 465 432 p 2 50 ru cmsy10.300 @sf 556 418 p 21 c cmr10.300 @sf 11 r 48 c 747 417 p 61 c 12 r 49 c 83 r 61 c 12 r 49 c 1006 432 p 2 50 ru 9 r 2 50 ru 1040 417 p 61 c 12(diag)m cmsy10.300 @sf 102 c cmtt10.300 @sf (WE\(1,)s -1(1,)m 76 c -2 r 50 c 41 c cmmi10.300 @sf -1 r 59 c cmtt10.300 @sf 21 r 76 c cmr10.300 @sf 50 c 11 r 61 c 12 r 49 c cmmi10.300 @sf 59 c 7 r 58 c 7 r 58 c 7 r 58 c 4 r 59 c 7 r 113 c cmsy10.300 @sf 1 r 103 c 1920 432 p 2 50 ru 465 481 p 2 50 ru 745 466 p 21 c cmmi10.300 @sf 12 r 110 c cmr10.300 @sf 81 r 61 c 12 r 49 c 1006 481 p 2 50 ru 9 r 2 50 ru 1040 466 p 61 c 12(diag)m cmsy10.300 @sf 102 c cmtt10.300 @sf (WE\()s 73 c -2(,1,)m 76 c -1 r 50 c 41 c cmmi10.300 @sf -1 r 59 c cmtt10.300 @sf 21 r 76 c cmr10.300 @sf 50 c 11 r 61 c 12 r 49 c cmmi10.300 @sf 59 c 7 r 58 c 7 r 58 c 7 r 58 c 4 r 59 c 7 r 113 c cmsy10.300 @sf 1 r 103 c 1920 481 p 2 50 ru 465 531 p 2 50 ru cmr10.300 @sf 747 516 p 61 c 12 r 49 c cmsy10.300 @sf 83 r 21 c cmmi10.300 @sf 12 r 113 c 1006 531 p 2 50 ru 9 r 2 50 ru cmr10.300 @sf 1040 516 p 61 c cmtt10.300 @sf 12(WE\(1,)m 76 c -2 r 49 c 44 c 76 c 50 c 41 c cmr10.300 @sf -1 r 44 c cmtt10.300 @sf 28 r 76 c cmr10.300 @sf -1 r 49 c 12 r 61 c 11 r 49 c cmmi10.300 @sf 59 c 7 r 58 c 7 r 58 c 7 r 58 c 5 r 59 c 7 r 113 c 1 r 59 c cmr10.300 @sf 13 r 38 c cmtt10.300 @sf 14 r 76 c cmr10.300 @sf 50 c 11 r 61 c 12 r 49 c cmmi10.300 @sf 59 c 7 r 58 c 7 r 58 c 7 r 58 c 4 r 59 c 7 r 113 c 1920 531 p 2 50 ru 465 581 p 2 50 ru cmsy10.300 @sf 745 566 p 21 c cmmi10.300 @sf 12 r 110 c cmsy10.300 @sf 81 r 21 c cmmi10.300 @sf 12 r 113 c 1006 581 p 2 50 ru 9 r 2 50 ru cmr10.300 @sf 1040 566 p 61 c cmtt10.300 @sf 12(WE\()m 73 c -1 r 44 c 76 c -1 r 49 c 44 c 76 c 50 c 41 c cmr10.300 @sf -1 r 44 c cmtt10.300 @sf 28 r 76 c cmr10.300 @sf -1 r 49 c 12 r 61 c 11 r 49 c cmmi10.300 @sf 59 c 7 r 58 c 7 r 58 c 7 r 58 c 5 r 59 c 7 r 113 c 1 r 59 c cmr10.300 @sf 13 r 38 c cmtt10.300 @sf 14 r 76 c cmr10.300 @sf 50 c 11 r 61 c 12 r 49 c cmmi10.300 @sf 59 c 7 r 58 c 7 r 58 c 7 r 58 c 4 r 59 c 7 r 113 c 1920 581 p 2 50 ru 465 583 p 1456 2 ru cmr10.329 @sf 422 661 p 70 c -3(or)m cmti10.329 @sf 15(implicit)m cmr10.329 @sf 16(mo)m 1(dels,)m 16(only)m 16(the)m 16(\014rst)m 16(elemen)m 116 c 15(of)m cmtt10.329 @sf 16(WE)m cmr10.329 @sf 16(is)m 16(ev)m (er)s 15(referenced,)m 17(and)m cmmi10.329 @sf 17 r 114 c cmr8.300 @sf 1884 668 p 48 c cmr10.329 @sf 1919 661 p (is)s 422 717 p (set)s 15(as)m 15(follo)m -1(ws.)m 914 723 p 545 2 ru 914 785 p 2 62 ru cmtt10.300 @sf 939 759 p (WE\(1,1,1\))s 1159 785 p 2 62 ru 9 r 2 62 ru cmmi10.300 @sf 1235 758 p 114 c cmr7.300 @sf 1254 764 p 48 c 1457 785 p 2 62 ru 914 786 p 545 2 ru 914 836 p 2 50 ru cmsy10.300 @sf 1005 822 p 20 c cmr10.300 @sf 11 r 48 c 1159 837 p 2 50 ru 9 r 2 50 ru 1193 821 p 61 c 12(10)m 1457 836 p 2 50 ru 914 886 p 2 50 ru cmmi10.300 @sf 1005 872 p 62 c cmr10.300 @sf 11 r 48 c 1159 887 p 2 50 ru 9 r 2 50 ru 1193 871 p 61 c cmtt10.300 @sf 12(WE\(1,1,1\))m 1457 886 p 2 50 ru 914 888 p 545 2 ru cmr10.329 @sf 235 968 p 61 c cmsy10.329 @sf -7 r 41 c cmr10.329 @sf (12)s 23 r 123 c cmtt12.300 @sf 22(LDWE)m 24([INTEGER)m 23(LDWE])m cmr10.329 @sf 422 1044 p (The)s 19(leading)m 18(dimension)m 18(of)m 18(arra)m 121 c cmtt10.329 @sf 16(WE)m cmr10.329 @sf 46 c cmtt10.329 @sf 29(LDWE)m cmr10.329 @sf 18 r 109 c (ust)s 17(either)m 18(exactly)m 18(equal)m 18(one,)m 19(or)m 422 1100 p 109 c (ust)s 14(equal)m 15(or)m 14(exceed)m cmmi10.329 @sf 16 r 110 c cmr10.329 @sf 46 c 21(See)m 15(argumen)m 116 c 14(11{)m cmtt10.329 @sf (WE)s cmr10.329 @sf 14(for)m 14(further)m 15(details.)m 235 1198 p 61 c cmsy10.329 @sf -7 r 41 c cmr10.329 @sf (13)s 23 r 123 c cmtt12.300 @sf 22(LD2WE)m 24([INTEGE)m -1 r 82 c 23(LD2WE])m cmr10.329 @sf 422 1274 p (The)s 18(second)m 18(dimension)m 17(of)m 17(arra)m 121 c cmtt10.329 @sf 15(WE)m cmr10.329 @sf 46 c cmtt10.329 @sf 27(LD2WE)m cmr10.329 @sf 16 r 109 c (ust)s 16(either)m 18(exactly)m 16(equal)m 18(one,)m 17(or)m 422 1330 p 109 c (ust)s 14(equal)m 15(or)m 14(exceed)m cmmi10.329 @sf 16 r 113 c cmr10.329 @sf 2 r 46 c 20(See)m 16(argumen)m 116 c 13(11{)m cmtt10.329 @sf (WE)s cmr10.329 @sf 14(for)m 15(further)m 15(details.)m 235 1428 p 61 c cmsy10.329 @sf -7 r 41 c cmr10.329 @sf (14)s 23 r 123 c cmtt12.300 @sf 22(WD)m 25 r 91 c ()s 23(WD\(LDWD)m -1(,LD)m -1(2WD)m -1(,M)m -1(\)])m cmr10.329 @sf 422 1504 p (The)s 18(triply)m 18(subscripted)m 18(arra)m 121 c 16(that)m 18(sp)m 1(eci\014es)m 19(ho)m 119 c 17(eac)m 104 c cmmi10.329 @sf 17 r 14 c cmr6.300 @sf 1516 1511 p 73 c cmr10.329 @sf 1547 1504 p (is)s 18(to)m 18 r 98 c 1 r 101 c 19 r 119 c (eigh)s -1(t)m -1(ed)m 17(in)m 422 1561 p (the)s 19 r 119 c (eigh)s -1(ted)m 18(orthogonal)m 17(distance.)m 31(\(See)m cmsy10.329 @sf 20 r 120 c cmr10.329 @sf (1.A)s 19(and)m cmsy10.329 @sf 19 r 120 c cmr10.329 @sf (1.F.\))s cmtt10.329 @sf 31(WD)m cmr10.329 @sf 18(is)m 19 r 97 c 19(structured)m 422 1617 p (argumen)s (t:)s 24(only)m 17(the)m 19(sp)m 1(eci\014c)m 19(elemen)m (ts)s 16(of)m cmtt10.329 @sf 18(WD)m cmr10.329 @sf 18(iden)m (ti\014ed)s 17(in)m 18(the)m 18(table)m 18 r 98 c 1(elo)m 119 c 16(are)m 422 1674 p (ev)s (er)s 14(referenced)m 16 r 98 c 121 c 14(ODRP)m -3 r 65 c (CK.)s 14(\(See)m cmsy10.329 @sf 15 r 120 c cmr10.329 @sf (1.G.\))s 453 1703 p 1481 2 ru 453 1752 p 2 50 ru 541 r 2 50 ru 9 r 2 50 ru cmr10.300 @sf 1028 1737 p 70 c -2(or)m cmtt10.300 @sf 12 r 73 c cmr10.300 @sf 11 r 61 c 12 r 49 c cmmi10.300 @sf 59 c 7 r 58 c 7 r 58 c 7 r 58 c 5 r 59 c 7(n;)m 1932 1752 p 2 50 ru 453 1814 p 2 62 ru cmtt10.300 @sf 478 1788 p (WD\(1,1,1\))s 723 1787 p (LDWD)s 49(LD2WD)m 994 1814 p 2 62 ru 9 r 2 62 ru cmmi10.300 @sf 1083 1787 p 119 c cmmi7.300 @sf 1108 1793 p 14 c cmr6.300 @sf 1123 1800 p 73 c 1932 1814 p 2 62 ru 453 1816 p 1481 2 ru 453 1866 p 2 50 ru cmmi10.300 @sf 543 1852 p 60 c cmr10.300 @sf 12 r 48 c 746 1851 p 124 c 106 r 124 c 994 1866 p 2 50 ru 9 r 2 50 ru 1028 1851 p 61 c cmsy10.300 @sf 11 r 0 c cmtt10.300 @sf (WD\(1,1,1\))s cmmi10.300 @sf -1 r 73 c cmmi7.300 @sf 1318 1857 p 109 c cmr10.300 @sf 1350 1851 p 44 c cmmi10.300 @sf 13 r 73 c cmmi7.300 @sf 1393 1857 p 109 c cmr10.300 @sf 1439 1851 p (an)s cmmi10.300 @sf 13 r 109 c cmsy10.300 @sf 10 r 2 c cmmi10.300 @sf 9 r 109 c cmr10.300 @sf 15(iden)m (tit)s -1 r 121 c 12(matrix)m 1932 1866 p 2 50 ru 453 1915 p 2 50 ru 543 1901 p 61 c 12 r 48 c 746 1900 p 124 c 106 r 124 c 994 1915 p 2 50 ru 9 r 2 50 ru 1028 1900 p 61 c cmmi10.300 @sf 11 r 73 c cmmi7.300 @sf 1089 1906 p 109 c cmr10.300 @sf 1121 1900 p 44 c cmmi10.300 @sf 14 r 73 c cmmi7.300 @sf 1165 1906 p 109 c cmr10.300 @sf 1210 1900 p (an)s cmmi10.300 @sf 14 r 109 c cmsy10.300 @sf 9 r 2 c cmmi10.300 @sf 10 r 109 c cmr10.300 @sf 14(iden)m (tit)s 121 c 12(matrix)m 1932 1915 p 2 50 ru 453 1965 p 2 50 ru cmmi10.300 @sf 543 1951 p 62 c cmr10.300 @sf 12 r 48 c 735 1950 p 61 c 12 r 49 c 83 r 61 c 11 r 49 c 994 1965 p 2 50 ru 9 r 2 50 ru 1028 1950 p 61 c 11(diag)m cmsy10.300 @sf 102 c cmtt10.300 @sf (WD\(1,1,)s 74 c -2 r 50 c -1 r 41 c cmmi10.300 @sf 59 c cmtt10.300 @sf 20 r 74 c cmr10.300 @sf 50 c 12 r 61 c 11 r 49 c cmmi10.300 @sf 59 c 7 r 58 c 7 r 58 c 7 r 58 c 5 r 59 c 7 r 109 c cmsy10.300 @sf 103 c 1932 1965 p 2 50 ru 453 2015 p 2 50 ru 733 2000 p 21 c cmmi10.300 @sf 12 r 110 c cmr10.300 @sf 81 r 61 c 11 r 49 c 994 2015 p 2 50 ru 9 r 2 50 ru 1028 2000 p 61 c 11(diag)m cmsy10.300 @sf 102 c cmtt10.300 @sf (WD\()s 73 c -2(,1,)m 74 c 50 c -1 r 41 c cmmi10.300 @sf 59 c cmtt10.300 @sf 20 r 74 c cmr10.300 @sf 50 c 12 r 61 c 11 r 49 c cmmi10.300 @sf 59 c 7 r 58 c 7 r 58 c 7 r 58 c 5 r 59 c 7 r 109 c cmsy10.300 @sf 103 c 1932 2015 p 2 50 ru 453 2065 p 2 50 ru cmr10.300 @sf 735 2050 p 61 c 12 r 49 c cmsy10.300 @sf 75 r 21 c cmmi10.300 @sf 12 r 109 c 994 2065 p 2 50 ru 9 r 2 50 ru cmr10.300 @sf 1028 2050 p 61 c cmtt10.300 @sf 11(WD\(1,)m 74 c -1 r 49 c 44 c 74 c -1 r 50 c 41 c cmr10.300 @sf 44 c cmtt10.300 @sf 27 r 74 c cmr10.300 @sf 49 c 11 r 61 c 12 r 49 c cmmi10.300 @sf 59 c 7 r 58 c 7 r 58 c 7 r 58 c 5 r 59 c 7(m;)m cmr10.300 @sf 7 r 38 c cmtt10.300 @sf 74 c cmr10.300 @sf -1 r 50 c 11 r 61 c 12 r 49 c cmmi10.300 @sf 59 c 7 r 58 c 7 r 58 c 7 r 58 c 5 r 59 c 7 r 109 c 1932 2065 p 2 50 ru 453 2115 p 2 50 ru cmsy10.300 @sf 733 2100 p 21 c cmmi10.300 @sf 12 r 110 c cmsy10.300 @sf 73 r 21 c cmmi10.300 @sf 12 r 109 c 994 2115 p 2 50 ru 9 r 2 50 ru cmr10.300 @sf 1028 2100 p 61 c cmtt10.300 @sf 11(WD\()m 73 c 44 c 74 c -1 r 49 c 44 c 74 c -1 r 50 c 41 c cmr10.300 @sf 44 c cmtt10.300 @sf 27 r 74 c cmr10.300 @sf 49 c 11 r 61 c 12 r 49 c cmmi10.300 @sf 59 c 7 r 58 c 7 r 58 c 7 r 58 c 5 r 59 c 7(m;)m cmr10.300 @sf 7 r 38 c cmtt10.300 @sf 74 c cmr10.300 @sf -1 r 50 c 11 r 61 c 12 r 49 c cmmi10.300 @sf 59 c 7 r 58 c 7 r 58 c 7 r 58 c 5 r 59 c 7 r 109 c 1932 2115 p 2 50 ru 453 2117 p 1481 2 ru cmr10.329 @sf 235 2196 p 61 c cmsy10.329 @sf -7 r 41 c cmr10.329 @sf (15)s 23 r 123 c cmtt12.300 @sf 22(LDWD)m 24([INTEGER)m 23(LDWD])m cmr10.329 @sf 422 2272 p (The)s 19(leading)m 18(dimension)m 18(of)m 18(arra)m 121 c cmtt10.329 @sf 16(WD)m cmr10.329 @sf 46 c cmtt10.329 @sf 29(LDWD)m cmr10.329 @sf 18 r 109 c (ust)s 17(either)m 18(exactly)m 18(equal)m 18(one,)m 19(or)m 422 2329 p 109 c (ust)s 14(equal)m 15(or)m 14(exceed)m cmmi10.329 @sf 16 r 110 c cmr10.329 @sf 46 c 21(See)m 15(argumen)m 116 c 14(14{)m cmtt10.329 @sf (WD)s cmr10.329 @sf 14(for)m 14(further)m 15(details.)m @eop %%Page: 30 44 30 @bop0 cmsy10.329 @sf [<3E000000007F80000000FFE0000000FC7000000038780000001038000000003C000000001C0000 00001E000000001E000000000E000000000F000000000700000000078000000003FFE0000003FF F8000003FFF8000001C000000001E000000001E000000000E000000000F000000000F000000300 F0000001C070000001E078000000E07800000070780080001C3800C0000FFFFFF00003FFFFF000 007FFFF0> 40 32 -1 1 32.670] 70 @dc [ 24 44 -6 11 0.000] 54 @dc cmmi10.300 @sf [ 24 26 1 8 20.885] 112 @dc cmsy10.300 @sf [<7E000000FF800000F8C0000030E0000000700000007000000038000000380000003C0000001C00 00001C0000000E0000000E0000000FFF800007FFC0000700000007800000038000000380000003 C0000601C0000701C0000381E0000181E00000C1E00C0070E00F001FFFFF0003FFFF> 32 28 -1 0 29.835] 70 @dc cmmi7.300 @sf [ 24 26 0 6 18.822] 12 @dc 30 @bop1 cmr10.329 @sf 0 114 p (30)s 1319(Using)m 15(ODRP)m -3 r 65 c (CK)s 0 134 p 1725 2 ru 10 259 p 61 c cmsy10.329 @sf -7 r 41 c cmr10.329 @sf (16)s 23 r 123 c cmtt12.300 @sf 22(LD2WD)m 24([INTEGE)m -1 r 82 c 23(LD2WD])m cmr10.329 @sf 197 335 p (The)s 18(second)m 18(dimension)m 17(of)m 17(arra)m 121 c cmtt10.329 @sf 15(WD)m cmr10.329 @sf 46 c cmtt10.329 @sf 27(LD2WD)m cmr10.329 @sf 16 r 109 c (ust)s 16(either)m 18(exactly)m 16(equal)m 18(one,)m 17(or)m 197 391 p 109 c (ust)s 14(equal)m 15(or)m 14(exceed)m cmmi10.329 @sf 16 r 109 c cmr10.329 @sf 46 c 20(See)m 16(argumen)m 116 c 13(14{)m cmtt10.329 @sf (WD)s cmr10.329 @sf 14(for)m 15(further)m 15(details.)m 10 489 p 61 c cmsy10.329 @sf -7 r 41 c cmr10.329 @sf (17)s 23 r 123 c cmtt12.300 @sf 22(IFIXB)m 24([INTEGE)m -1 r 82 c 23(IFIXB\(NP\))m -1 r 93 c cmr10.329 @sf 197 565 p (The)s 21(singly)m 20(subscripted)m 21(arra)m 121 c 19(that)m 20(sp)m 1(eci\014es)m 21(the)m 21(indicator)m 20 r 118 c -2(ariable)m cmsy10.329 @sf 19 r 70 c cmmi8.300 @sf 1579 572 p 12 c cmr6.300 @sf 1599 578 p 75 c cmr10.329 @sf 1646 565 p (des-)s 197 621 p (ignating)s 19(whether)m cmmi10.329 @sf 21 r 12 c cmr6.300 @sf 585 628 p 75 c cmr10.329 @sf 630 621 p (is)s 20(to)m 20 r 98 c 1 r 101 c 21(treated)m 20(as)m 21(\\\014xed,")m 21(i.e.,)m 21(is)m 20(to)m 20 r 98 c 1 r 101 c 21(treated)m 20(as)m 20 r 97 c 197 678 p (constan)s (t,)s 13(or)m 15(is)m 14(to)m 15 r 98 c 1 r 101 c 16(\\un\014xed")m 16(and)m 15(th)m (us)s 14(is)m 15(to)m 14 r 98 c 1 r 101 c 16(estimated.)m cmsy10.329 @sf 298 744 p 15 c cmr10.329 @sf 22(If)m cmsy10.329 @sf 16 r 70 c cmmi8.300 @sf 422 751 p 12 c cmr6.300 @sf 442 757 p 75 c cmr10.329 @sf 481 744 p 61 c 13 r 48 c 15(then)m cmmi10.329 @sf 15 r 12 c cmr6.300 @sf 696 751 p 75 c cmr10.329 @sf 736 744 p (is)s 15(\014xed)m 16(and)m cmtt10.329 @sf 15(BETA)m cmr10.329 @sf 40 c cmtt10.329 @sf 75 c cmr10.329 @sf -1 r 41 c 15(is)m 15(not)m 15 r 99 c (hanged.)s cmsy10.329 @sf 298 815 p 15 c cmr10.329 @sf 22(If)m cmsy10.329 @sf 16 r 70 c cmmi8.300 @sf 422 822 p 12 c cmr6.300 @sf 442 828 p 75 c cmsy10.329 @sf 481 815 p 54 c cmr10.329 @sf 61 c 13 r 48 c 15(then)m cmmi10.329 @sf 15 r 12 c cmr6.300 @sf 696 822 p 75 c cmr10.329 @sf 736 815 p (is)s 15(un\014xed)m 16(and)m cmtt10.329 @sf 16(BETA)m cmr10.329 @sf -1 r 40 c cmtt10.329 @sf 75 c cmr10.329 @sf 41 c 15(is)m 14 r 111 c 118 c -1(erwrit)m -1(ten)m 14 r 98 c 121 c 1557 804 p 94 c cmmi10.329 @sf 1551 816 p 12 c cmr6.300 @sf 1577 823 p 75 c cmr10.329 @sf 1602 815 p 46 c 197 878 p (The)s 15(default)m 15 r 118 c -2(alues)m 15(are)m cmsy10.329 @sf 14 r 70 c cmmi8.300 @sf 687 885 p 12 c cmr6.300 @sf 707 891 p 75 c cmr10.329 @sf 747 878 p 61 c 13(1,)m cmtt10.329 @sf 14 r 75 c cmr10.329 @sf 13 r 61 c 13 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 7 r 58 c 5 r 59 c 8(p:)m 671 909 p 580 2 ru 671 959 p 2 50 ru 224 r 2 50 ru 9 r 2 50 ru cmr10.300 @sf 929 944 p 70 c -2(or)m cmtt10.300 @sf 12 r 75 c cmr10.300 @sf 11 r 61 c 12 r 49 c cmmi10.300 @sf 59 c 7 r 58 c 7 r 58 c 7 r 58 c 5 r 59 c 7(p;)m 1250 959 p 2 50 ru 671 1021 p 2 62 ru cmtt10.300 @sf 696 995 p (IFIXB\(1\))s 895 1021 p 2 62 ru 9 r 2 62 ru cmsy10.300 @sf 970 994 p 70 c cmmi7.300 @sf 1000 1000 p 12 c cmr6.300 @sf 1019 1007 p 75 c 1250 1021 p 2 62 ru 671 1022 p 580 2 ru 671 1072 p 2 50 ru cmmi10.300 @sf 751 1058 p 60 c cmr10.300 @sf 12 r 48 c 895 1073 p 2 50 ru 9 r 2 50 ru 929 1057 p 61 c 11 r 49 c 1250 1072 p 2 50 ru 671 1122 p 2 50 ru cmsy10.300 @sf 751 1108 p 21 c cmr10.300 @sf 12 r 48 c 895 1123 p 2 50 ru 9 r 2 50 ru 929 1107 p 61 c cmtt10.300 @sf 11(IFIXB\()m 75 c -1 r 41 c 1250 1122 p 2 50 ru 671 1124 p 580 2 ru cmr10.329 @sf 10 1204 p 61 c cmsy10.329 @sf -7 r 41 c cmr10.329 @sf (18)s 23 r 123 c cmtt12.300 @sf 22(IFIXX)m 24([INTEGE)m -1 r 82 c 23(IFIXX\(LDI)m -1(FX)m -1(,M\))m -1 r 93 c cmr10.329 @sf 197 1280 p (The)s 15(doubly)m 14(subscripted)m 15(arra)m 121 c 12(that)m 14(sp)m 1(eci\014es)m 16(the)m 14(indicator)m 13 r 118 c -2(ariable)m cmsy10.329 @sf 13 r 70 c cmtt10.329 @sf 1542 1292 p 88 c cmr6.300 @sf 1566 1298 p 73 c 1577 1297 p 74 c cmr10.329 @sf 1611 1280 p (desig-)s 197 1336 p (nating)s 13(whether,)m 13(when)m 14(the)m 13(solution)m 13(is)m 12(found)m 14 r 98 c 121 c 12(orthogonal)m 12(distance)m 13(regression,)m 197 1393 p (the)s 16 r 40 c cmtt10.329 @sf 73 c cmmi10.329 @sf -1 r 59 c cmtt10.329 @sf 8 r 74 c cmr10.329 @sf (\)th)s 15(elemen)m 116 c 15(of)m 15(the)m 16(explanatory)m 15 r 118 c -2(ariable)m cmmi10.329 @sf 14 r 88 c cmr6.300 @sf 1198 1400 p 73 c 74 c cmr10.329 @sf 1242 1393 p (is)s 16(to)m 15 r 98 c 1 r 101 c 17(treated)m 15(as)m 15(with-)m 197 1449 p (out)s 14(error)m 13(and)m 14(th)m (us)s 13 r 1 c cmr6.300 @sf 611 1456 p 73 c 74 c cmr10.329 @sf 653 1449 p (is)s 14(to)m 13 r 98 c 1 r 101 c 15(\\\014xed")m 14(at)m 13(zero,)m 14(or)m 14(whether)m 14(that)m 13(observ)m -2(ation)m 12(is)m 197 1505 p (\\un\014xed")s 16(and)m 15(therefore)m 15(the)m 15(error)m 14 r 1 c cmr6.300 @sf 909 1512 p 73 c 74 c cmr10.329 @sf 952 1505 p (is)s 15(to)m 14 r 98 c 1 r 101 c 16(estimated.)m 19(\(When)m 15(the)m 15(solution)m 197 1562 p (is)s 18(found)m 18 r 98 c 121 c 17(ordinary)m 17(least)m 17(squares,)m 19(the)m cmmi10.329 @sf 18 r 88 c cmr6.300 @sf 1034 1569 p 73 c 74 c cmr10.329 @sf 1080 1562 p (are)s 18(alw)m 97 c -2(ys)m 16(treated)m 18(as)m 18(\014xed,)m 19(and)m 197 1618 p (th)s (us)s 14 r 1 c cmr6.300 @sf 335 1625 p 73 c 74 c cmr10.329 @sf 376 1618 p 61 c 13 r 48 c 15(for)m 15(all)m cmtt10.329 @sf 14 r 73 c cmr10.329 @sf 12 r 61 c 13 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 7 r 58 c 6 r 59 c 8(n;)m cmr10.329 @sf 14(and)m cmtt10.329 @sf 15 r 74 c cmr10.329 @sf 13 r 61 c 13 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 7 r 58 c 5 r 59 c 8 r 109 c cmr10.329 @sf (.\))s cmsy10.329 @sf 298 1685 p 15 c cmr10.329 @sf 22(If)m cmsy10.329 @sf 16 r 70 c cmtt10.329 @sf 422 1697 p 88 c cmr6.300 @sf 445 1703 p 73 c 456 1702 p 74 c cmr10.329 @sf 488 1685 p 61 c 13 r 48 c 15(then)m cmmi10.329 @sf 16 r 88 c cmr6.300 @sf 716 1692 p 73 c -1 r 74 c cmr10.329 @sf 759 1685 p (is)s 15(\014xed)m 16(and)m 15 r 1 c cmr6.300 @sf 1041 1692 p 73 c 74 c cmr10.329 @sf 1085 1685 p (is)s 15(set)m 14(to)m 15(zero.)m cmsy10.329 @sf 298 1751 p 15 c cmr10.329 @sf 22(If)m cmsy10.329 @sf 16 r 70 c cmtt10.329 @sf 422 1763 p 88 c cmr6.300 @sf 445 1769 p 73 c 74 c cmsy10.329 @sf 488 1751 p 54 c cmr10.329 @sf 61 c 13 r 48 c 15(then)m cmmi10.329 @sf 16 r 88 c cmr6.300 @sf 716 1758 p 73 c -1 r 74 c cmr10.329 @sf 759 1751 p (is)s 15(un\014xed)m 16(and)m 16 r 1 c cmr6.300 @sf 1092 1758 p 73 c 74 c cmr10.329 @sf 1135 1751 p (is)s 15(estimated.)m 197 1813 p (The)s 15(default)m 15 r 118 c -2(alues)m 15(are)m cmsy10.329 @sf 14 r 70 c cmtt10.329 @sf 687 1825 p 88 c cmr6.300 @sf 711 1831 p 73 c 74 c cmr10.329 @sf 754 1813 p 61 c 13(1,)m cmtt10.329 @sf 15 r 73 c cmr10.329 @sf 12 r 61 c 13 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 8 r 58 c 5 r 59 c 8 r 110 c cmr10.329 @sf 44 c 14(and)m cmtt10.329 @sf 15 r 74 c cmr10.329 @sf 13 r 61 c 13 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 7 r 58 c 5 r 59 c 8(m:)m cmtt10.329 @sf 197 1875 p (IFIXX)s cmr10.329 @sf 12(is)m 13 r 97 c 13(structured)m 13(argumen)m (t:)s 17(only)m 12(the)m 13(sp)m 1(eci\014c)m 14(elemen)m (ts)s 12(of)m cmtt10.329 @sf 13(IFIXX)m cmr10.329 @sf 12(iden)m (ti\014ed)s 197 1932 p (in)s 15(the)m 15(table)m 15 r 98 c 1(elo)m 119 c 14(are)m 15(referenced)m 16 r 98 c 121 c 14(ODRP)m -3 r 65 c (CK.)s 13(\(See)m cmsy10.329 @sf 16 r 120 c cmr10.329 @sf (1.G.\))s 568 1961 p 786 2 ru 568 2011 p 2 50 ru 426 r 2 50 ru 9 r 2 50 ru cmr10.300 @sf 1028 1996 p 70 c -2(or)m cmtt10.300 @sf 12 r 73 c cmr10.300 @sf 12 r 61 c 11 r 49 c cmmi10.300 @sf 59 c 7 r 58 c 7 r 58 c 7 r 58 c 5 r 59 c 7(n;)m 1353 2011 p 2 50 ru 568 2061 p 2 50 ru 426 r 2 50 ru 9 r 2 50 ru cmr10.300 @sf 1028 2046 p 38 c cmtt10.300 @sf 14 r 74 c cmr10.300 @sf 11 r 61 c 12 r 49 c cmmi10.300 @sf 59 c 7 r 58 c 7 r 58 c 7 r 58 c 5 r 59 c 7(m;)m 1353 2061 p 2 50 ru 568 2122 p 2 62 ru cmtt10.300 @sf 593 2096 p (IFIXX\(1,1\))s 861 2095 p (LDIFX)s 994 2122 p 2 62 ru 9 r 2 62 ru cmsy10.300 @sf 1069 2095 p 70 c cmtt10.300 @sf 1099 2106 p 88 c cmr6.300 @sf 1121 2113 p 73 c 74 c 1353 2122 p 2 62 ru 568 2124 p 786 2 ru 568 2174 p 2 50 ru cmmi10.300 @sf 670 2160 p 60 c cmr10.300 @sf 12 r 48 c 894 2159 p 124 c 994 2174 p 2 50 ru 9 r 2 50 ru 1028 2159 p 61 c 12 r 49 c 1353 2174 p 2 50 ru 568 2223 p 2 50 ru cmsy10.300 @sf 670 2209 p 21 c cmr10.300 @sf 12 r 48 c 883 2208 p 61 c 12 r 49 c 994 2223 p 2 50 ru 9 r 2 50 ru 1028 2208 p 61 c cmtt10.300 @sf 12(IFIXX\(1,)m 74 c -2 r 41 c 1353 2223 p 2 50 ru 568 2273 p 2 50 ru cmsy10.300 @sf 881 2258 p 21 c cmmi10.300 @sf 12 r 110 c 994 2273 p 2 50 ru 9 r 2 50 ru cmr10.300 @sf 1028 2258 p 61 c cmtt10.300 @sf 12(IFIXX\()m 73 c -2 r 44 c 74 c 41 c 1353 2273 p 2 50 ru 568 2275 p 786 2 ru cmr10.329 @sf 10 2355 p 61 c cmsy10.329 @sf -7 r 41 c cmr10.329 @sf (19)s 23 r 123 c cmtt12.300 @sf 22(LDIFX)m 24([INTEGE)m -1 r 82 c 23(LDIFX])m cmr10.329 @sf 197 2431 p (The)s 16(leading)m 15(dimension)m 15(of)m 16(arra)m 121 c cmtt10.329 @sf 13(IFIXX)m cmr10.329 @sf 46 c cmtt10.329 @sf 21(LDIFX)m cmr10.329 @sf 15 r 109 c (ust)s 14(either)m 16(exactly)m 15(equal)m 15(one,)m @eop %%Page: 31 45 31 @bop0 cmtt12.300 @sf [<0FE0003FF800FFFC00F83E00F01E00F00E00F00E00000E00000E00000E00000E00000E00000E00 000E00000E00000E00000E00000E00000E00000E00000E00000E00000E00000E00000E00000E00 000E0003FFC003FFC003FFC0> 24 30 -4 0 25.632] 74 @dc [<0FFE003FFF807FFFC07C07C07001C0F001E0F001E0E000E0E000E0E000E0E000E0E000E0E000E0 E000E0E000E0E000E0E000E0E000E0E000E0E000E0E000E0E000E0E000E0E000E0F001E07001C0 7C07C07FFFC03FFF800FFE00> 24 30 -3 0 25.632] 79 @dc cmsy10.329 @sf [ 32 36 -4 7 35.353] 20 @dc cmsy10.300 @sf [<1F007F8073C0E1E0E0E0E0E0E0E000E000E001C003C007800F803FC079C071E0F0E0E0E0E0E0E0 E0E1E0F1C073C07F803E003C0078007000E000E000E0E0E0E0E0E0F0E079C03FC01F00> 16 37 -3 8 18.449] 120 @dc cmmi10.300 @sf [<0180000001C0000001E0000001E0000003F0000003F0000003D8000003CC000003CC000003C600 0003C6000003C3000003C1800007C180000780C0000780E0000780600007803000078030000780 180007801C0007800C000F8006000F0006000F0003800F8007C0FFF01FF87FF01FF8> 32 28 -2 0 24.214] 86 @dc [<1F80003FE00078F800F03C00E01C00E00E00E00F00E00700E00700F00700700780700380380700 3C07001F0F000FFFFC07FFFC01FFFC> 24 18 -1 0 23.719] 27 @dc cmr10.300 @sf [ 24 28 -2 0 28.250] 69 @dc [ 24 2 0 -10 20.755] 123 @dc cmmi10.329 @sf [<00300000003000000030000000380000001800000018000000180000001C0000000C0000007FC0 0001FFF00003EE780007861C0007060E00070607000707038007030180070301C0078300C00383 80E00381806003C18060E1C1806061C1C07061E0C0F070E0C1F039E0C1F01FC0E1E00F8060E000 006000000060000000700000003000000030000000300000003800000018000000180000001800 00001C0000000C00> 32 41 -1 9 29.608] 32 @dc 31 @bop1 cmr10.329 @sf 225 114 p (Using)s 15(ODRP)m -3 r 65 c (CK)s 1318(31)m 225 134 p 1725 2 ru 422 259 p (or)s 15 r 109 c (ust)s 13(equal)m 15(or)m 15(exceed)m cmmi10.329 @sf 16 r 110 c cmr10.329 @sf 46 c 20(See)m 16(argumen)m 116 c 13(18{)m cmtt10.329 @sf (IFIXX)s cmr10.329 @sf 14(for)m 15(further)m 15(details.)m 235 356 p 61 c cmsy10.329 @sf -7 r 41 c cmr10.329 @sf (20)s 23 r 123 c cmtt12.300 @sf 22(JOB)m 24([INTEGER)m 23(JOB])m cmr10.329 @sf 422 432 p (The)s 13 r 118 c -2(ariable)m 10(that)m 12(sp)m 1(eci\014es)m 13(problem)m 12(initializati)m -1(on)m 11(and)m 12(computational)m 11(metho)m 1(ds.)m 422 489 p (\(See)s cmsy10.329 @sf 15 r 120 c cmr10.329 @sf 1(1.C.\))m 18(The)m 16(default)m 15(options,)m 14(selected)m 15(when)m cmtt10.329 @sf 16(JOB)m cmsy10.329 @sf 12 r 20 c cmr10.329 @sf 13(0,)m 14(are)m 15(that)m cmsy10.329 @sf 422 555 p 15 c cmr10.329 @sf 22(the)m 16(solution)m 14(will)m 14 r 98 c 1 r 101 c 15(found)m 16 r 98 c 121 c 14(explicit)m 14(orthogonal)m 14(distance)m 15(regression;)m cmsy10.329 @sf 422 621 p 15 c cmr10.329 @sf 22(the)m 16(deriv)m -2(ativ)m -1(es)m 13(will)m 14 r 98 c 1 r 101 c 16(computed)m 15 r 98 c 121 c 15(forw)m (a)s -1(rd)m 13(\014nite)m 16(di\013erences;)m cmsy10.329 @sf 422 688 p 15 c cmr10.329 @sf 22(the)m 19(co)m 118 c -2(aria)m -1(nce)m 18(matrix)m 18(will)m 17 r 98 c 1 r 101 c 20(computed)m 19(using)m 19(Jacobian)m 19(matrices)m 18(recalcu-)m 467 744 p (lated)s 15(at)m 15(the)m 15(solution;)m cmsy10.329 @sf 422 810 p 15 c cmr10.329 @sf 22 r 1 c 15(will)m 14 r 98 c 1 r 101 c 16(initialized)m 14(to)m 14(zero;)m 15(and)m cmsy10.329 @sf 422 876 p 15 c cmr10.329 @sf 22(the)m 16(\014t)m 15(will)m 14(not)m 14 r 98 c 1 r 101 c 16 r 97 c 15(restart.)m 422 939 p (When)s cmtt10.329 @sf 15(JOB)m cmsy10.329 @sf 12 r 21 c cmr10.329 @sf 13(0,)m 14(it)m 14(is)m 14(assumed)m 15(to)m 13 r 98 c 1 r 101 c 16 r 97 c 14 r 53 c 14(digit)m cmtt10.329 @sf 14(INTEGER)m cmr10.329 @sf 13(with)m 14(decimal)m 14(expansion)m cmsy10.329 @sf 422 995 p 73 c cmr8.300 @sf 447 1002 p 53 c cmsy10.329 @sf 466 995 p 73 c cmr8.300 @sf 491 1002 p 52 c cmsy10.329 @sf 511 995 p 73 c cmr8.300 @sf 536 1002 p 51 c cmsy10.329 @sf 555 995 p 73 c cmr8.300 @sf 580 1002 p 50 c cmsy10.329 @sf 600 995 p 73 c cmr8.300 @sf 625 1002 p 49 c cmr10.329 @sf 644 995 p 44 c 15(where)m 16(eac)m 104 c 14(digit)m 14(con)m (trols)s 13 r 97 c 15(di\013eren)m 116 c 13(option.)m 475 1022 p 1422 2 ru 475 1084 p 2 62 ru cmr10.300 @sf 500 1058 p (Option)s 971 1085 p 2 62 ru 9 r 2 62 ru 979 1084 p 2 62 ru 1018 1058 p (Digit)s 1172 1057 p (Selection)s 1896 1084 p 2 62 ru 475 1085 p 1422 2 ru 475 1135 p 2 50 ru 500 1121 p (Computational)s 12(metho)m 1 r 100 c 971 1136 p 2 50 ru 9 r 2 50 ru cmsy10.300 @sf 1005 1120 p 73 c cmr7.300 @sf 1028 1126 p 49 c cmr10.300 @sf 1058 1120 p 61 c 11 r 48 c 50(explicit)m 13(orthogonal)m 13(distance)m 15(regression)m 1896 1135 p 2 50 ru 475 1185 p 2 50 ru 500 1171 p (\(see)s cmsy10.300 @sf 15 r 120 c cmr10.300 @sf 1(1.A\))m 971 1186 p 2 50 ru 9 r 2 50 ru 1058 1170 p 61 c 11 r 49 c 50(implicit)m 12(orthogonal)m 13(distance)m 14(regression)m 1896 1185 p 2 50 ru 475 1234 p 2 50 ru 496 r 2 50 ru 9 r 2 50 ru cmsy10.300 @sf 1058 1219 p 21 c cmr10.300 @sf 11 r 50 c 50(ordinary)m 13(least)m 14(squares)m 1896 1234 p 2 50 ru 475 1236 p 1422 2 ru 475 1286 p 2 50 ru 500 1272 p (Deriv)s -1(ativ)m -1 r 101 c 12(calculation)m 971 1287 p 2 50 ru 9 r 2 50 ru cmsy10.300 @sf 1005 1271 p 73 c cmr7.300 @sf 1028 1277 p 50 c cmr10.300 @sf 1058 1271 p 61 c 11 r 48 c 50(forw)m (ard)s 12(\014nite)m 14(di\013erences)m 1896 1286 p 2 50 ru 475 1336 p 2 50 ru 500 1322 p (\(see)s cmsy10.300 @sf 15 r 120 c cmr10.300 @sf 1(4.A\))m 971 1337 p 2 50 ru 9 r 2 50 ru 1058 1321 p 61 c 11 r 49 c 50(cen)m (tral)s 13(\014nite)m 14(di\013erences)m 1896 1336 p 2 50 ru 475 1386 p 2 50 ru 496 r 2 50 ru 9 r 2 50 ru 1058 1371 p 61 c 11 r 50 c 50(user)m 15(supplied)m 14(deriv)m -1(ativ)m -1 r 101 c 12(co)m 1(de,)m 1896 1386 p 2 50 ru 475 1435 p 2 50 ru 496 r 2 50 ru 9 r 2 50 ru 1172 1420 p 99 c (hec)s 107 c (ed)s 12 r 98 c 121 c 13(ODRP)m -2 r 65 c -1(CK)m 1896 1435 p 2 50 ru 475 1485 p 2 50 ru 496 r 2 50 ru 9 r 2 50 ru cmsy10.300 @sf 1058 1470 p 21 c cmr10.300 @sf 11 r 51 c 50(user)m 15(supplied)m 14(deriv)m -1(ativ)m -1 r 101 c 12(co)m 1(de,)m 1896 1485 p 2 50 ru 475 1535 p 2 50 ru 496 r 2 50 ru 9 r 2 50 ru 1172 1520 p (not)s 14 r 99 c (hec)s 107 c (ed)s 12 r 98 c 121 c 13(ODRP)m -2 r 65 c -1(CK)m 1896 1535 p 2 50 ru 475 1537 p 1422 2 ru 475 1587 p 2 50 ru 500 1573 p (Co)s 118 c -2(ariance)m 12(matrix)m cmmi10.300 @sf 13 r 86 c cmmi7.300 @sf 871 1579 p 12 c cmr10.300 @sf 894 1573 p 44 c 971 1588 p 2 50 ru 9 r 2 50 ru cmsy10.300 @sf 1005 1572 p 73 c cmr7.300 @sf 1028 1578 p 51 c cmr10.300 @sf 1058 1572 p 61 c 11 r 48 c cmmi10.300 @sf 50 r 86 c cmmi7.300 @sf 1196 1578 p 12 c cmr10.300 @sf 1232 1572 p (and)s cmmi10.300 @sf 14 r 27 c cmmi7.300 @sf 1337 1578 p 12 c cmr10.300 @sf 1373 1572 p (calculated)s 14(using)m 1896 1587 p 2 50 ru 475 1636 p 2 50 ru 500 1622 p 38 c 14(standard)m 15(deviation)m cmmi10.300 @sf 13 r 27 c cmmi7.300 @sf 925 1628 p 12 c 971 1637 p 2 50 ru 8 r 2 50 ru cmr10.300 @sf 1172 1621 p (deriv)s -1(ativ)m -1(es)m 13(recomputed)m 15(at)m 14(solution)m 1896 1636 p 2 50 ru 475 1686 p 2 50 ru 500 1672 p (\(see)s cmsy10.300 @sf 15 r 120 c cmr10.300 @sf 1(4.B\))m 971 1687 p 2 50 ru 9 r 2 50 ru 1058 1671 p 61 c 11 r 49 c cmmi10.300 @sf 50 r 86 c cmmi7.300 @sf 1196 1677 p 12 c cmr10.300 @sf 1232 1671 p (and)s cmmi10.300 @sf 14 r 27 c cmmi7.300 @sf 1337 1677 p 12 c cmr10.300 @sf 1373 1671 p (calculated)s 14(using)m 1896 1686 p 2 50 ru 475 1736 p 2 50 ru 496 r 2 50 ru 9 r 2 50 ru 1172 1721 p (deriv)s -1(ativ)m -1(es)m 13(from)m 13(last)m 13(iteration)m 1896 1736 p 2 50 ru 475 1786 p 2 50 ru 496 r 2 50 ru 9 r 2 50 ru cmsy10.300 @sf 1058 1771 p 21 c cmr10.300 @sf 11 r 50 c cmmi10.300 @sf 50 r 86 c cmmi7.300 @sf 1196 1777 p 12 c cmr10.300 @sf 1232 1771 p (and)s cmmi10.300 @sf 14 r 27 c cmmi7.300 @sf 1337 1777 p 12 c cmr10.300 @sf 1373 1771 p (not)s 14(calculated)m 1896 1786 p 2 50 ru 475 1788 p 1422 2 ru 475 1837 p 2 50 ru 500 1823 p 1 c 14(Initializatio)m -1 r 110 c 971 1838 p 2 50 ru 9 r 2 50 ru cmsy10.300 @sf 1005 1822 p 73 c cmr7.300 @sf 1028 1828 p 52 c cmr10.300 @sf 1058 1822 p 61 c 11 r 48 c 50 r 1 c 13(initialized)m 13(to)m 14(zero)m 14 r 98 c 121 c 13(ODRP)m -2 r 65 c -1(CK)m 1896 1837 p 2 50 ru 475 1887 p 2 50 ru 500 1873 p (\(see)s cmsy10.300 @sf 15 r 120 c cmr10.300 @sf 1(1.E\))m 971 1888 p 2 50 ru 9 r 2 50 ru cmsy10.300 @sf 1058 1872 p 21 c cmr10.300 @sf 11 r 49 c 50 r 1 c 13(initialized)m 13 r 98 c 121 c 12(user)m 1896 1887 p 2 50 ru 475 1937 p 2 50 ru 496 r 2 50 ru 9 r 2 50 ru 1172 1922 p (\(see)s 15(argumen)m 116 c 13(36{)m cmtt10.300 @sf (WORK)s cmr10.300 @sf -2 r 41 c 1896 1937 p 2 50 ru 475 1939 p 1422 2 ru 475 1988 p 2 50 ru 500 1974 p (Restart)s 15(facilit)m -1 r 121 c 971 1989 p 2 50 ru 9 r 2 50 ru cmsy10.300 @sf 1005 1973 p 73 c cmr7.300 @sf 1028 1979 p 53 c cmr10.300 @sf 1058 1973 p 61 c 11 r 48 c 50(\014t)m 14(is)m 14(not)m 14 r 97 c 13(restart)m 1896 1988 p 2 50 ru 475 2038 p 2 50 ru 500 2024 p (\(see)s 15(Chapter)m 15(3\))m 971 2039 p 2 50 ru 9 r 2 50 ru cmsy10.300 @sf 1058 2023 p 21 c cmr10.300 @sf 11 r 49 c 50(\014t)m 14(is)m 14 r 97 c 13(restart)m 1896 2038 p 2 50 ru 475 2040 p 1422 2 ru cmr10.329 @sf 235 2120 p 61 c cmsy10.329 @sf -7 r 41 c cmr10.329 @sf (21)s 23 r 123 c cmtt12.300 @sf 22(NDIGIT)m 23([INTEGER)m 23(NDIGIT])m cmr10.329 @sf 422 2196 p (The)s 22 r 118 c -2(ariable)m 21(that)m 21(sp)m 1(eci\014es)m 23(the)m 22 r 110 c (um)s 98 c 1(er)m 20(of)m 22(reliable)m 21(decimal)m 21(digits)m cmmi10.329 @sf 21 r 32 c cmr10.329 @sf 23(in)m 22(the)m 422 2252 p 118 c -2(alues)m 12(computed)m 13(using)m 12(subroutine)m cmtt10.329 @sf 13(FCN)m cmr10.329 @sf 46 c 19(The)m 13 r 118 c -2(alue)m cmmi10.329 @sf 12 r 32 c cmr10.329 @sf 14(is)m 12(needed)m 14(to)m 12(calculate)m 12(the)m 422 2309 p (default)s 18 r 118 c -2(alues)m 18(for)m 18(the)m 19(relativ)m 101 c 16(step)m 19(sizes)m 19(used)m 19(in)m 19(calculating)m 17(\014nite)m 19(di\013erence)m 422 2365 p (deriv)s -2(ativ)m -1(es.)m 18(\(See)m 16(argumen)m (ts)s 14(29{)m cmtt10.329 @sf (STPB)s cmr10.329 @sf 14(and)m 15(30{)m cmtt10.329 @sf (STPD)s cmr10.329 @sf -1 r 44 c 15(and)m cmsy10.329 @sf 15 r 120 c cmr10.329 @sf (4.A.\))s 20(It)m 15(is)m 15(also)m 14(used)m 422 2422 p (to)s 11(determine)m 12(when)m 12(the)m 12(Jacobian)m 12(with)m 11(resp)m 1(ect)m 12(to)m 11(one)m 12(or)m 11(more)m 12(of)m 11(the)m 12(parameters)m @eop %%Page: 32 46 32 @bop0 cmr10.329 @sf [<03FFFC0003FFFC00000F0000000F0000000F0000000F0000000F0000003FC00000FFF00003FFFC 0007CF3E00078F1E000F0F0F000F0F0F001F0F0F801E0F07801E0F07801E0F07801E0F07801E0F 07801E0F07803E0F07C07E0F07E0FC0F03F0F80F01F0000F0000000F0000000F0000000F000003 FFFC0003FFFC00> 32 31 -3 0 35.353] 9 @dc cmmi10.300 @sf [<00C00000E00000600000600000600000700000300000300000FF0003FFC007D9E00F18F00E1838 0E1C1C0E0C0C0E0C0E0E0C060F0E06070607070603C78607E3870763830F73830F3F830F1F038F 0001800001800001800001C00000C00000C00000C00000E0000060000060000060> 24 37 -1 8 27.039] 32 @dc cmr10.300 @sf [<01FFF80001FFF800000F0000000F0000000F0000000F0000003FC00001FFF00003FFF80007CF7C 000F8F3E000F0F1E000F0F1F001E0F0F001E0F0F001E0F0F001E0F0F001E0F0F001E0F0F003E0F 0F807E0F0FC0FC0F07E0F80F03E0000F0000000F0000000F000001FFF80001FFF800> 32 28 -2 0 32.286] 9 @dc cmtt12.300 @sf [<007C0001FF0007FFC007C7C00F01E00F01E01E00F01E00F01C00701C00701C00701C00701C0070 1C00701C00701C00701C00701C00701C00701C00701C00701C00701C00701C00701C00701C0070 1C0070FF83FEFF83FEFF83FE> 24 30 -1 0 25.632] 85 @dc cmmi10.329 @sf [<03800003800001C00001C00001C00001C00000E00000E00000E00000E000006000007000007000 E030006030007038003C38001FFFFC0FFFFC07FFFC> 24 20 0 0 19.870] 28 @dc [<00000040000001C0000007C000001F0000007C000001F0000007C000001F0000007C000001F000 0007C000001F0000007C000000F0000000F00000007C0000001F00000007C0000001F00000007C 0000001F00000007C0000001F00000007C0000001F00000007C0000001C000000040> 32 28 -4 3 35.353] 60 @dc cmmi10.300 @sf [<07000007000003800003800003800003800001C00001C00001C00001C00000C00000E000E0E000 6060007860003FFFF01FFFF00FFFF0> 24 18 -1 0 18.146] 28 @dc cmtt12.300 @sf [ 24 30 -3 0 25.632] 83 @dc cmsy10.329 @sf [<1FFE0000000FFF80000003FFC0000000E000000000700000000078000000003C000000003C0000 00001E000000001E000000001F000000000F000000000F000000000F8000000007800000000780 00000007C000000007C000000003C000000003C000000003E00000C003E00000F001E000007801 E000007801F000003C00F000001C00F000000E0078000003FFFFF00001FFFFFE00003FFFFF0000 000001800000000040> 40 33 -2 0 24.756] 84 @dc cmmi8.300 @sf [ 24 23 -2 0 21.459] 83 @dc cmmi10.329 @sf [<01F80003FC00038E00000E00000E00003E0001FE0007FC001FE0003F80007C0000780000F00000 F00000F000007000007000007800003800003C00001E00000F000007FE0003FF0007FE000F8000 0F00000F00000F00000F00000F800007800007C00003C00003E00000FFC0007FE0001FE0001800 001800001800001800> 24 42 -1 9 19.886] 24 @dc cmmi8.300 @sf [ 16 33 -2 8 17.642] 61 @dc cmsy10.300 @sf [<1FFE000007FF000001C0000000E00000007000000078000000380000003C0000003C0000001C00 00001E0000001E0000000E0000000F0000000F000000070000000780000007800000078000C003 8000F003C0007003C0007801C0003801E0001C01E0000E00E00003FFFFF000FFFFFC0000000E> 32 29 -1 0 22.608] 84 @dc cmmi7.300 @sf [ 24 20 -2 0 20.383] 83 @dc cmmi10.300 @sf [<01F80003FC00031C00000E00003E0001FC0007FC001FF0003F80007E0000F80000F00000F00000 F000007000007000007800003800001C00001E00000FFC0007FC000FFC000F00000F00000F0000 0F00000F00000F800007800007C00003FF8000FF80003F80001800001800001800000800> 24 38 0 8 18.161] 24 @dc cmmi7.300 @sf [ 16 29 -2 7 17.008] 61 @dc cmmi8.300 @sf [ 24 23 -1 0 22.370] 80 @dc 32 @bop1 cmr10.329 @sf 0 114 p (32)s 1319(Using)m 15(ODRP)m -3 r 65 c (CK)s 0 134 p 1725 2 ru cmmi10.329 @sf 197 259 p 12 c cmr10.329 @sf 23(app)m 1(ears)m 22(to)m 20 r 98 c 1 r 101 c 22(rank)m 21(de\014cien)m (t.)s 37(It)m 21(can)m 22(not)m 21(exceed)m 22(the)m 21 r 110 c (um)s 98 c 1(er)m 20(of)m 20(decimal)m 197 315 p (digits)s 12 r 9 c 14(carried)m 13 r 98 c 121 c 13(the)m 14(user's)m 13(computer)m 14(for)m 12 r 97 c cmtt10.329 @sf 14()m cmr10.329 @sf 14 r 118 c -2(alue.)m 19(The)m 14(default)m 13 r 118 c -2(alue)m 197 372 p (is)s 16(exp)m 1(erimen)m (tally)s 14(determined)m 17 r 98 c 121 c 15(ODRP)m -3 r 65 c (CK)s 15(for)m 15(the)m 17(user's)m 15(particular)m 15(mo)m 1(del.)m 197 428 p (This)s 20(determination)m 18(of)m cmmi10.329 @sf 20 r 32 c cmr10.329 @sf 21(requires)m 20 r 52 c 19(ev)m -2(aluations)m 18(of)m 20(the)m 20(mo)m 1(del)m 20(function)m 20(from)m 197 484 p (user)s 15(supplied)m 16(subroutine)m cmtt10.329 @sf 15(FCN)m cmr10.329 @sf 46 c 681 511 p 575 2 ru 681 573 p 2 62 ru cmtt10.300 @sf 705 547 p (NDIGIT)s 860 573 p 2 62 ru 9 r 2 62 ru cmmi10.300 @sf 936 546 p 32 c 1254 573 p 2 62 ru 681 574 p 575 2 ru 681 624 p 2 50 ru cmsy10.300 @sf 739 610 p 20 c cmr10.300 @sf 11 r 49 c 860 625 p 2 50 ru 9 r 2 50 ru 894 609 p 61 c 14(default)m 14 r 118 c -1(alue)m 1254 624 p 2 50 ru 681 674 p 2 50 ru cmsy10.300 @sf 739 660 p 21 c cmr10.300 @sf 11 r 50 c 860 675 p 2 50 ru 9 r 2 50 ru 894 659 p 61 c 12(min)m cmsy10.300 @sf -1 r 102 c cmtt10.300 @sf (NDIGIT)s cmmi10.300 @sf -1 r 59 c cmr10.300 @sf 7 r 9 c cmsy10.300 @sf 103 c 1254 674 p 2 50 ru 681 676 p 575 2 ru cmr10.329 @sf 10 755 p 61 c cmsy10.329 @sf -7 r 41 c cmr10.329 @sf (22)s 23 r 123 c cmtt12.300 @sf 22(TAUFAC)m 23 r 91 c ()s 23(TAUFAC])m cmr10.329 @sf 197 832 p (The)s 23 r 118 c -2(ariable)m 20(that)m 22(sp)m 1(eci\014es)m 23(the)m 23(factor)m cmmi10.329 @sf 21 r 28 c cmr10.329 @sf 27(used)m 23(to)m 22(initialize)m 21(the)m 22(trust)m 22(region)m 197 888 p (radius.)s 32(The)m 20(trust)m 19(region)m 18(is)m 19(the)m 20(region)m 18(in)m 20(whic)m 104 c 18(the)m 20(lo)m 1(cal)m 18(appro)m (ximati)s -1(on)m 18(to)m cmmi10.329 @sf 197 944 p 83 c cmr10.329 @sf 3 r 40 c cmmi10.329 @sf 12 c 2 r 59 c 8 r 14 c cmr10.329 @sf 2 r 41 c 11(is)m 12(considered)m 13(reliable.)m 18(The)m 13(diameter)m 12(of)m 13(this)m 12(region)m 12(is)m 12(adaptiv)m (ely)s 11 r 99 c (hosen)s 197 1001 p (at)s 11(eac)m 104 c 10(iteration)m 10(based)m 12(on)m 12(informatio)m -1 r 110 c 10(from)m 11(the)m 12(previous)m 11(iteration.)m 17 r 65 c 116 c 10(the)m 11(\014rst)m 197 1057 p (iteration,)s 16(the)m 18(initial)m 16(diameter)m 17(is)m 17(set)m 18(to)m cmmi10.329 @sf 17 r 28 c cmr10.329 @sf 23(times)m 17(the)m 18(length)m 17(of)m 17(the)m 18(full)m 17(Gauss-)m 197 1114 p (Newton)s 15(step)m 15(calculated)m 15(at)m 14(the)m 16(initial)m 13 r 118 c -2(alues)m 14(of)m cmmi10.329 @sf 15 r 12 c cmr10.329 @sf 18(and)m 15(\001.)m 20(The)m 15(default)m 15 r 118 c -2(alue)m 14(is)m cmmi10.329 @sf 197 1170 p 28 c cmr10.329 @sf 18 r 61 c 13(1.)m 19(When)m cmmi10.329 @sf 15 r 28 c 18 r 60 c cmr10.329 @sf 12 r 49 c 15(the)m 14(size)m 15(of)m 14(the)m 15(initial)m 12(step)m 15(attempted)m 14(at)m 14(the)m 14(\014rst)m 15(iteration)m 197 1227 p (is)s 18(smaller)m 16(than)m 18(the)m 18(full)m 18(Gauss-Newton)m 17(step.)m 29(This)m 18(ma)m 121 c 16 r 98 c 1 r 101 c 19(appropriate)m 17(if,)m 18(at)m 197 1283 p (the)s 15(\014rst)m 14(iteration,)m 13(the)m 14(computed)m 15(results)m 14(for)m 14(the)m 15(full)m 14(Gauss-Newton)m 14(step)m 15(cause)m 197 1340 p (an)s 15 r 111 c 118 c -1(er\015o)m -1(w,)m 13(or)m 14(cause)m cmmi10.329 @sf 16 r 12 c cmr10.329 @sf 17(and/or)m 15 r 1 c 15(lea)m 118 c -1 r 101 c 13(the)m 15(region)m 15(of)m 15(in)m (terest.)s 686 1369 p 564 2 ru 686 1430 p 2 62 ru cmtt10.300 @sf 711 1404 p (TAUFAC)s 866 1430 p 2 62 ru 9 r 2 62 ru cmmi10.300 @sf 942 1403 p 28 c 1249 1430 p 2 62 ru 686 1432 p 564 2 ru 686 1482 p 2 50 ru cmsy10.300 @sf 744 1468 p 20 c cmr10.300 @sf 12 r 48 c 866 1483 p 2 50 ru 9 r 2 50 ru 900 1467 p 61 c 12 r 49 c 1249 1482 p 2 50 ru 686 1532 p 2 50 ru cmmi10.300 @sf 744 1518 p 62 c cmr10.300 @sf 12 r 48 c 866 1533 p 2 50 ru 9 r 2 50 ru 900 1517 p 61 c 12(min)m cmsy10.300 @sf -1 r 102 c cmtt10.300 @sf (TAUFAC)s cmmi10.300 @sf -1 r 59 c cmr10.300 @sf 7 r 49 c cmsy10.300 @sf 103 c 1249 1532 p 2 50 ru 686 1534 p 564 2 ru cmr10.329 @sf 10 1613 p 61 c cmsy10.329 @sf -7 r 41 c cmr10.329 @sf (23)s 23 r 123 c cmtt12.300 @sf 22(SSTOL)m 24 r 91 c ()s 23(SSTOL])m cmr10.329 @sf 197 1689 p (The)s 15 r 118 c -2(ariable)m 13(that)m 13(sp)m 1(eci\014es)m cmsy10.329 @sf 16 r 84 c cmmi8.300 @sf 758 1696 p 83 c cmr10.329 @sf 783 1689 p 44 c 14(the)m 15(stopping)m 14(tolerance)m 14(for)m 14(sum)m 14(of)m 14(squares)m 15(con-)m 197 1746 p 118 c (ergence,)s 19(i.e.,)m 20(for)m 18(con)m 118 c (ergence)s 18(based)m 20(on)m 19(the)m 20(relativ)m -1 r 101 c 18 r 99 c (hange)s 18(in)m cmmi10.329 @sf 20 r 83 c cmr10.329 @sf 3 r 40 c cmmi10.329 @sf 12 c 2 r 59 c 8 r 14 c cmr10.329 @sf 2 r 41 c cmmi10.329 @sf 58 c cmr10.329 @sf 17(The)m 197 1802 p (default)s 16 r 118 c -2(alue)m 15(is)m cmsy10.329 @sf 15 r 84 c cmmi8.300 @sf 540 1809 p 83 c cmr10.329 @sf 579 1802 p 61 c cmmi10.329 @sf 15 r 24 c cmr8.300 @sf 651 1787 p 49 c cmmi8.300 @sf 61 c cmr8.300 @sf 50 c cmr10.329 @sf 706 1802 p 44 c 16(where)m cmmi10.329 @sf 16 r 24 c cmr10.329 @sf 18(is)m 15(de\014ned)m 18(as)m 15(the)m 16(smallest)m 15 r 118 c -2(alue)m 15(suc)m 104 c 16(that)m 197 1859 p 49 c 10 r 43 c cmmi10.329 @sf 10 r 24 c 15 r 62 c cmr10.329 @sf 13 r 49 c 15(for)m 14 r 97 c cmtt10.329 @sf 15()m cmr10.329 @sf 14(computation)m 15(on)m 15(the)m 15(mac)m (hine)s 14 r 98 c 1(eing)m 16(used.)m 708 1885 p 520 2 ru 708 1947 p 2 62 ru cmtt10.300 @sf 733 1921 p (SSTOL)s 866 1947 p 2 62 ru 9 r 2 62 ru cmsy10.300 @sf 942 1920 p 84 c cmmi7.300 @sf 965 1926 p 83 c 1227 1947 p 2 62 ru 708 1948 p 520 2 ru 708 2000 p 2 52 ru cmmi10.300 @sf 755 1986 p 60 c cmr10.300 @sf 12 r 48 c 866 2001 p 2 52 ru 9 r 2 52 ru 900 1985 p 61 c cmmi10.300 @sf 12 r 24 c cmr7.300 @sf 964 1971 p 49 c cmmi7.300 @sf 61 c cmr7.300 @sf 50 c 1227 2000 p 2 52 ru 708 2050 p 2 50 ru cmsy10.300 @sf 755 2036 p 21 c cmr10.300 @sf 12 r 48 c 866 2051 p 2 50 ru 9 r 2 50 ru 900 2035 p 61 c 12(min)m cmsy10.300 @sf -1 r 102 c cmtt10.300 @sf (SSTOL)s cmmi10.300 @sf -1 r 59 c cmr10.300 @sf 7 r 49 c cmsy10.300 @sf 103 c 1227 2050 p 2 50 ru 708 2052 p 520 2 ru cmr10.329 @sf 10 2132 p 61 c cmsy10.329 @sf -7 r 41 c cmr10.329 @sf (24)s 23 r 123 c cmtt12.300 @sf 22(PARTOL)m 23 r 91 c ()s 23(PARTOL])m cmr10.329 @sf 197 2208 p (The)s 17 r 118 c -2(ariable)m 16(that)m 16(sp)m 1(eci\014es)m cmsy10.329 @sf 18 r 84 c cmmi8.300 @sf 768 2215 p 80 c cmr10.329 @sf 798 2208 p 44 c 17(the)m 17(stopping)m 17(tolerance)m 16(for)m 17(parameter)m 16(con)m 118 c (er-)s 197 2264 p (gence,)s 16(i.e.,)m 14(for)m 15(con)m 118 c -1(ergence)m 14(based)m 16(on)m 15(relativ)m 101 c 13 r 99 c (hange)s 15(in)m 15(the)m 16(estimated)m 14(param-)m 197 2321 p (eters)s cmmi10.329 @sf 14 r 12 c cmr10.329 @sf 15(and)m 15(\001.)m 19(When)m 14(the)m 14(mo)m 1(del)m 14(is)m cmti10.329 @sf 13(explicit)m cmr10.329 @sf 14(the)m 13(default)m 14 r 118 c -2(alue)m 13(is)m cmsy10.329 @sf 13 r 84 c cmmi8.300 @sf 1458 2328 p 80 c cmr10.329 @sf 1500 2321 p 61 c cmmi10.329 @sf 13 r 24 c cmr8.300 @sf 1570 2306 p 50 c cmmi8.300 @sf 61 c cmr8.300 @sf 51 c cmr10.329 @sf 1625 2321 p 44 c 14(and)m 197 2377 p (when)s 17(the)m 16(mo)m 1(del)m 16(is)m cmti10.329 @sf 16(implicit)m cmr10.329 @sf 16(the)m 16(default)m 15 r 118 c -2(alue)m 16(is)m cmsy10.329 @sf 16 r 84 c cmmi8.300 @sf 1168 2384 p 80 c cmr10.329 @sf 1211 2377 p 61 c cmmi10.329 @sf 14 r 24 c cmr8.300 @sf 1282 2362 p 49 c cmmi8.300 @sf 61 c cmr8.300 @sf 51 c cmr10.329 @sf 1337 2377 p 44 c 16(where)m cmmi10.329 @sf 17 r 24 c cmr10.329 @sf 18(is)m 16(de\014ned)m 197 2433 p (as)s 18(the)m 18(smallest)m 16 r 118 c -2(alue)m 18(suc)m 104 c 17(that)m 17 r 49 c 12 r 43 c cmmi10.329 @sf 12 r 24 c 20 r 62 c cmr10.329 @sf 18 r 49 c 17(for)m 18 r 97 c cmtt10.329 @sf 18()m cmr10.329 @sf 14(computation)m 17(on)m 18(the)m @eop %%Page: 33 47 33 @bop0 cmmi7.300 @sf [ 24 20 -1 0 21.134] 80 @dc cmmi8.300 @sf [ 16 23 -2 0 15.298] 73 @dc 1.000000 /cmsy6.300 @newfont cmsy6.300 @sf [ 24 2 -3 -5 23.983] 0 @dc cmmi7.300 @sf [ 16 20 -1 0 14.712] 73 @dc 1.000000 /cmsy5.300 @newfont cmsy5.300 @sf [ 16 2 -3 -4 22.485] 0 @dc cmr10.300 @sf [<000600000006000000060000000600000006000000060000000600000006000000060000000600 00000600000006000000060000FFFFFFE0FFFFFFE0000600000006000000060000000600000006 00000006000000060000000600000006000000060000000600000006000000060000> 32 28 -2 4 32.286] 43 @dc cmsy10.329 @sf [ 32 33 -1 1 31.350] 76 @dc cmmi8.300 @sf [<07F0001FFC003E0F00780780F00180F001C0F000E0E00060E00060F00000F00000F00000F00000 F800007800187C00183C00181E00380F003C07C07C03F0FC00FFEC003F86> 24 23 -2 0 25.147] 67 @dc [ 32 23 -1 0 26.574] 82 @dc 33 @bop1 cmr10.329 @sf 225 114 p (Using)s 15(ODRP)m -3 r 65 c (CK)s 1318(33)m 225 134 p 1725 2 ru 422 259 p (mac)s (hine)s 14 r 98 c 1(eing)m 15(used.)m 911 285 p 564 2 ru 911 347 p 2 62 ru cmtt10.300 @sf 936 321 p (PARTOL)s 1091 347 p 2 62 ru 9 r 2 62 ru cmsy10.300 @sf 1167 320 p 84 c cmmi7.300 @sf 1190 326 p 80 c 1474 347 p 2 62 ru 911 348 p 564 2 ru 911 398 p 2 50 ru cmmi10.300 @sf 969 384 p 60 c cmr10.300 @sf 12 r 48 c 1091 399 p 2 50 ru 9 r 2 50 ru 1125 383 p 61 c 14(default)m 14 r 118 c -1(alue)m 1474 398 p 2 50 ru 911 448 p 2 50 ru cmsy10.300 @sf 969 434 p 21 c cmr10.300 @sf 12 r 48 c 1091 449 p 2 50 ru 9 r 2 50 ru 1125 433 p 61 c 12(min)m cmsy10.300 @sf -1 r 102 c cmtt10.300 @sf (PARTOL)s cmmi10.300 @sf -1 r 59 c cmr10.300 @sf 7 r 49 c cmsy10.300 @sf 103 c 1474 448 p 2 50 ru 911 450 p 564 2 ru cmr10.329 @sf 235 530 p 61 c cmsy10.329 @sf -7 r 41 c cmr10.329 @sf (25)s 23 r 123 c cmtt12.300 @sf 22(MAXIT)m 24([INTEGE)m -1 r 82 c 23(MAXIT])m cmr10.329 @sf 422 606 p (The)s 10 r 118 c -2(ariable)m 9(that)m 9(sp)m 1(eci\014es)m cmsy10.329 @sf 11 r 84 c cmmi8.300 @sf 965 613 p 73 c cmr10.329 @sf 985 606 p 44 c 11(the)m 10(maxim)m (um)s 8 r 110 c (um)s 98 c 1(er)m 9(of)m 10(iterations)m 8(allo)m -1 r 119 c -1(ed.)m 17(The)m 422 662 p (default)s 17 r 118 c -2(alue)m 17(dep)m 1(ends)m 19(on)m 18(whether)m 18(the)m 17(\014t)m 18(is)m 17 r 97 c 17(restart)m 17(or)m 17(not.)m 27(\(See)m 18(argumen)m 116 c 422 719 p (20{)s cmtt10.329 @sf (JOB)s cmr10.329 @sf -1(.\))m 19(If)m 16(the)m 15(\014t)m 15(is)m 15(not)m 15 r 97 c 14(restart,)m 14(then)m cmsy10.329 @sf 1097 821 p 84 c cmmi8.300 @sf 1122 828 p 73 c cmr10.329 @sf 1154 821 p 61 c 13(50)m cmmi10.329 @sf 15 r 58 c cmr10.329 @sf 422 923 p (If)s 15(the)m 16(\014t)m 15(is)m 14 r 97 c 15(restart,)m 14(then)m cmsy10.329 @sf 1034 979 p 84 c cmmi8.300 @sf 1059 986 p 73 c cmr10.329 @sf 1091 979 p 61 c cmsy10.329 @sf 13 r 84 c cmmi8.300 @sf 1164 989 p 73 c cmsy6.300 @sf 1182 981 p 0 c cmr10.329 @sf 1220 979 p 43 c 10(10)m cmmi10.329 @sf 15 r 59 c cmr10.329 @sf 422 1063 p (where)s cmsy10.329 @sf 20 r 84 c cmmi8.300 @sf 583 1073 p 73 c cmsy6.300 @sf 601 1065 p 0 c cmr10.329 @sf 649 1063 p (is)s 19(the)m 20 r 110 c (um)s 98 c 1(er)m 18(of)m 19(iterations)m 18(completed)m 20(in)m 20(the)m 20(previous)m 19(run,)m 21(th)m (us)s 422 1119 p (indicating)s 14(that)m 15(the)m 15(pro)m 1(cedure)m 16(will)m 14(con)m (tin)s -1(ue)m 14(for)m 14(an)m 15(additional)m 14(10)m 15(iterations.)m 843 1146 p 685 2 ru 843 1208 p 2 62 ru cmtt10.300 @sf 868 1182 p (MAXIT)s cmr10.300 @sf 1027 1181 p (Restart)s 1186 1208 p 2 62 ru 9 r 2 62 ru cmsy10.300 @sf 1261 1181 p 84 c cmmi7.300 @sf 1284 1187 p 73 c 1528 1207 p 2 62 ru 843 1209 p 685 2 ru 843 1259 p 2 50 ru cmmi10.300 @sf 891 1245 p 60 c cmr10.300 @sf 11 r 48 c 1073 1244 p (no)s 1186 1259 p 2 50 ru 9 r 2 50 ru 1220 1244 p 61 c 12(50)m 1528 1259 p 2 50 ru 843 1309 p 2 50 ru 1067 1294 p 121 c (es)s 1186 1309 p 2 50 ru 9 r 2 50 ru 1220 1294 p 61 c cmsy10.300 @sf 12 r 84 c cmmi7.300 @sf 1287 1302 p 73 c cmsy5.300 @sf 1304 1295 p 0 c cmr10.300 @sf 1339 1294 p 43 c 10(10)m 1528 1309 p 2 50 ru 843 1358 p 2 50 ru cmsy10.300 @sf 891 1344 p 21 c cmr10.300 @sf 11 r 48 c 1073 1343 p (no)s 1186 1358 p 2 50 ru 9 r 2 50 ru 1220 1343 p 61 c cmtt10.300 @sf 12(MAXIT)m 1528 1358 p 2 50 ru 843 1408 p 2 50 ru cmr10.300 @sf 1067 1393 p 121 c (es)s 1186 1408 p 2 50 ru 9 r 2 50 ru 1220 1393 p 61 c cmsy10.300 @sf 12 r 84 c cmmi7.300 @sf 1287 1401 p 73 c cmsy5.300 @sf 1304 1394 p 0 c cmr10.300 @sf 1339 1393 p 43 c cmtt10.300 @sf 10(MAXIT)m 1528 1408 p 2 50 ru 843 1410 p 685 2 ru cmr10.329 @sf 422 1451 p (If)s cmtt10.329 @sf 13(MAXIT)m cmr10.329 @sf 25 r 61 c 13 r 48 c 13(then)m 13(no)m 13(iterations)m 12(will)m 11 r 98 c 1 r 101 c 14(tak)m (en,)s 12(but)m 13(whatev)m (er)s 11(computations)m 12(are)m 422 1508 p (required)s 13(to)m 12(complete)m 13(the)m 13(\014nal)m 13(computation)m 11(rep)m 1(ort)m 13(will)m 11 r 98 c 1 r 101 c 14(made.)m 19 r 70 c -3(or)m 11(example,)m 422 1564 p 98 c 121 c 13(setting)m cmtt10.329 @sf 13(MAXIT)m cmr10.329 @sf 12 r 61 c 13 r 48 c 13(and)m 14(the)m 14(third)m 13(digit)m 13(of)m cmtt10.329 @sf 14(JOB)m cmr10.329 @sf 13(to)m 13(zero,)m 14(the)m 14(user)m 14(can)m 14(compute)m 422 1621 p (the)s 11(co)m 118 c -2(aria)m -1(nce)m 10(matrix)m cmmi10.329 @sf 10 r 86 c cmmi8.300 @sf 883 1628 p 12 c cmr10.329 @sf 917 1621 p (for)s 11(the)m 11(input)m 11 r 118 c -2(alues)m cmmi10.329 @sf 10 r 12 c cmr10.329 @sf 14(and)m 11(\001.)m 18(\(See)m 12(argumen)m (ts)s 9(20{)m cmtt10.329 @sf (JOB)s cmr10.329 @sf 422 1677 p (and)s 15(26{)m cmtt10.329 @sf (IPRINT)s cmr10.329 @sf -1 r 44 c 14(and)m 16(also)m cmsy10.329 @sf 14 r 120 c cmr10.329 @sf (1.D.\))s 235 1775 p 61 c cmsy10.329 @sf -7 r 41 c cmr10.329 @sf (26)s 23 r 123 c cmtt12.300 @sf 22(IPRINT)m 23([INTEGER)m 23(IPRINT])m cmr10.329 @sf 422 1851 p (The)s 14 r 118 c -2(ariable)m 11(that)m 13(con)m (trols)s 11(generation)m 13(of)m 13(the)m 13(computation)m 13(rep)m 1(orts)m 13(describ)m 1(ed)m 14(in)m cmsy10.329 @sf 422 1907 p 120 c cmr10.329 @sf (1.D.)s 19(The)m 15(default)m 15(computation)m 14(rep)m 1(orts)m 15(include)m cmsy10.329 @sf 422 1974 p 15 c cmr10.329 @sf 22 r 97 c 15(long)m 15(initial)m 13(summary)m -3 r 44 c cmsy10.329 @sf 422 2040 p 15 c cmr10.329 @sf 22(no)m 16(iteration)m 13(summary)m -3 r 44 c 13(and)m cmsy10.329 @sf 422 2106 p 15 c cmr10.329 @sf 22 r 97 c 15(short)m 15(\014nal)m 15(summary)m -3 r 46 c 422 2169 p (When)s cmtt10.329 @sf 13(IPRINT)m cmmi10.329 @sf 25 r 60 c cmr10.329 @sf 13(0,)m 12(the)m 13(default)m 13(rep)m 1(orts)m 12(are)m 13(generated)m 13(only)m 12(on)m cmsy10.329 @sf 13 r 76 c cmmi8.300 @sf 1665 2176 p 67 c 2 r 82 c cmr10.329 @sf 1722 2169 p 44 c 13(the)m 13(logical)m 422 2225 p (unit)s 20(sp)m 1(eci\014ed)m 21 r 98 c 121 c 19(argumen)m 116 c 19(28{)m cmtt10.329 @sf (LUNRPT)s cmr10.329 @sf -2 r 46 c 35(When)m cmtt10.329 @sf 20(IPRINT)m cmsy10.329 @sf 41 r 21 c cmr10.329 @sf 21(0,)m 21(it)m 19(is)m 20(assumed)m 422 2281 p (to)s 17 r 98 c 1 r 101 c 19 r 97 c 18 r 52 c 18(digit)m cmtt10.329 @sf 16(INTEGER)m cmr10.329 @sf 18(with)m 17(decimal)m 17(expansion)m cmsy10.329 @sf 18 r 73 c cmr8.300 @sf 1435 2288 p 52 c cmsy10.329 @sf 1455 2281 p 73 c cmr8.300 @sf 1480 2288 p 51 c cmsy10.329 @sf 1499 2281 p 73 c cmr8.300 @sf 1524 2288 p 50 c cmsy10.329 @sf 1544 2281 p 73 c cmr8.300 @sf 1569 2288 p 49 c cmr10.329 @sf 1588 2281 p 44 c 19(where)m 18(eac)m 104 c 17(digit)m 422 2338 p (con)s (trols)s 15 r 97 c 17(di\013eren)m 116 c 16(part)m 17(of)m 16(the)m 18(computation)m 16(rep)m 1(ort)m 17(and)m 18(whether)m 18(that)m 16(rep)m 1(ort)m 422 2394 p (is)s 15(to)m 14 r 98 c 1 r 101 c 16(generated)m 15(only)m 15(on)m cmsy10.329 @sf 15 r 76 c cmmi8.300 @sf 986 2401 p 67 c 2 r 82 c cmr10.329 @sf 1058 2394 p (or)s 15(to)m 14 r 98 c 1(oth)m cmsy10.329 @sf 16 r 76 c cmmi8.300 @sf 1308 2401 p 67 c 2 r 82 c cmr10.329 @sf 1379 2394 p (and)s 16(unit)m 15(6.)m 19(\(See)m cmsy10.329 @sf 16 r 120 c cmr10.329 @sf (1.D\).)s @eop %%Page: 34 48 34 @bop0 cmsy10.300 @sf [ 32 28 -1 0 28.630] 76 @dc cmmi7.300 @sf [<07F0001FFC003E1E00780700700380F00180E001C0E000C0E00000F00000700000700000780060 3800703C00701E00700F00F007E1F801FFB8007F18> 24 20 -2 0 23.809] 67 @dc [ 24 20 -1 0 25.007] 82 @dc cmmi8.300 @sf [ 32 23 -1 0 25.858] 69 @dc cmmi7.300 @sf [ 24 20 -1 0 24.370] 69 @dc 34 @bop1 cmr10.329 @sf 0 114 p (34)s 1319(Using)m 15(ODRP)m -3 r 65 c (CK)s 0 134 p 1725 2 ru 305 219 p 1312 2 ru 305 269 p 2 50 ru cmr10.300 @sf 359 255 p (Initial)s 13(summary)m 703 270 p 2 50 ru 703 269 p 2 50 ru 791 255 p (Iteration)s 14(summary)m 1217 270 p 2 50 ru 1217 269 p 2 50 ru 1280 255 p (Final)s 12(summary)m 1616 270 p 2 50 ru 305 318 p 2 50 ru cmsy10.300 @sf 353 304 p 73 c cmr7.300 @sf 376 310 p 52 c cmr10.300 @sf 497 303 p 45 c 14(unit)m 14 r 45 c 703 318 p 2 50 ru cmsy10.300 @sf 752 303 p 73 c cmr7.300 @sf 775 309 p 51 c cmsy10.300 @sf 867 303 p 73 c cmr7.300 @sf 890 309 p 50 c cmr10.300 @sf 1011 303 p 45 c 13(unit)m 14 r 45 c 1217 318 p 2 50 ru cmsy10.300 @sf 1266 303 p 73 c cmr7.300 @sf 1289 309 p 49 c cmr10.300 @sf 1410 303 p 45 c 14(unit)m 13 r 45 c 1616 318 p 2 50 ru 305 380 p 2 62 ru cmsy10.300 @sf 450 353 p 76 c cmmi7.300 @sf 479 359 p 67 c 2 r 82 c cmr10.300 @sf 623 353 p 54 c 703 380 p 2 62 ru cmsy10.300 @sf 963 353 p 76 c cmmi7.300 @sf 992 359 p 67 c 2 r 82 c cmr10.300 @sf 1136 353 p 54 c 1217 380 p 2 62 ru cmsy10.300 @sf 1362 353 p 76 c cmmi7.300 @sf 1391 359 p 67 c 2 r 82 c cmr10.300 @sf 1535 353 p 54 c 1616 380 p 2 62 ru 305 382 p 1312 2 ru 305 432 p 2 50 ru 398 r 2 50 ru cmsy10.300 @sf 729 417 p 21 c cmr10.300 @sf 12 r 48 c 49 r 61 c 12 r 48 c 53(none)m 58(none)m 1217 432 p 2 50 ru 399 r 2 50 ru 305 481 p 2 50 ru 330 467 p 61 c 12 r 48 c 448 466 p (none)s 57(none)m 703 481 p 2 50 ru 729 466 p 61 c 12 r 48 c cmsy10.300 @sf 49 r 21 c cmr10.300 @sf 12 r 49 c 53(none)m 58(none)m 1217 481 p 2 50 ru 1243 466 p 61 c 11 r 48 c 54(none)m 57(none)m 1616 481 p 2 50 ru 305 531 p 2 50 ru 330 517 p 61 c 12 r 49 c 444 516 p (short)s 54(none)m 703 531 p 2 50 ru 729 516 p 61 c 12 r 49 c cmsy10.300 @sf 49 r 21 c cmr10.300 @sf 12 r 49 c 50(short)m 54(none)m 1217 531 p 2 50 ru 1243 516 p 61 c 11 r 49 c 50(short)m 54(none)m 1616 531 p 2 50 ru 305 581 p 2 50 ru 330 567 p 61 c 12 r 50 c 453 566 p (long)s 60(none)m 703 581 p 2 50 ru 729 566 p 61 c 12 r 50 c cmsy10.300 @sf 49 r 21 c cmr10.300 @sf 12 r 49 c 58(long)m 61(none)m 1217 581 p 2 50 ru 1243 566 p 61 c 11 r 50 c 58(long)m 61(none)m 1616 581 p 2 50 ru 305 631 p 2 50 ru 330 617 p 61 c 12 r 51 c 444 616 p (short)s 51(short)m 703 631 p 2 50 ru 729 616 p 61 c 12 r 51 c cmsy10.300 @sf 49 r 21 c cmr10.300 @sf 12 r 49 c 50(short)m 50(short)m 1217 631 p 2 50 ru 1243 616 p 61 c 11 r 51 c 50(short)m 50(short)m 1616 631 p 2 50 ru 305 681 p 2 50 ru 330 667 p 61 c 12 r 52 c 453 666 p (long)s 57(short)m 703 681 p 2 50 ru 729 666 p 61 c 12 r 52 c cmsy10.300 @sf 49 r 21 c cmr10.300 @sf 12 r 49 c 58(long)m 57(short)m 1217 681 p 2 50 ru 1243 666 p 61 c 11 r 52 c 58(long)m 57(short)m 1616 681 p 2 50 ru 305 730 p 2 50 ru 330 716 p 61 c 12 r 53 c 444 715 p (short)s 59(long)m 703 730 p 2 50 ru 729 715 p 61 c 12 r 53 c cmsy10.300 @sf 49 r 21 c cmr10.300 @sf 12 r 49 c 50(short)m 58(long)m 1217 730 p 2 50 ru 1243 715 p 61 c 11 r 53 c 50(short)m 59(long)m 1616 730 p 2 50 ru 305 780 p 2 50 ru 330 766 p 61 c 12 r 54 c 453 765 p (long)s 65(long)m 703 780 p 2 50 ru 729 765 p 61 c 12 r 54 c cmsy10.300 @sf 49 r 21 c cmr10.300 @sf 12 r 49 c 58(long)m 65(long)m 1217 780 p 2 50 ru 1243 765 p 61 c 11 r 54 c 58(long)m 66(long)m 1616 780 p 2 50 ru 305 782 p 1312 2 ru cmr10.329 @sf 250 852 p (If)s cmsy10.329 @sf 15 r 73 c cmr8.300 @sf 320 859 p 50 c cmr10.329 @sf 355 852 p 61 c 16 r 48 c 22(no)m 17(iteration)m 16(summary)m 16(will)m 16 r 98 c 1 r 101 c 18(generated,)m 18(ev)m (en)s 16(if)m 17(the)m 17 r 118 c -2(alue)m 17(of)m cmsy10.329 @sf 16 r 73 c cmr8.300 @sf 1705 859 p 51 c cmr10.329 @sf 451 909 p (is)s 15(nonzero.)m 250 975 p (If)s cmsy10.329 @sf 15 r 73 c cmr8.300 @sf 320 982 p 50 c cmsy10.329 @sf 355 975 p 21 c cmr10.329 @sf 16 r 49 c 22(an)m 16(iteration)m 14(summary)m 15(will)m 14 r 98 c 1 r 101 c 16(generated)m 16(ev)m (ery)s cmsy10.329 @sf 14 r 73 c cmr8.300 @sf 1400 982 p 50 c cmmi10.329 @sf 1420 975 p (th)s cmr10.329 @sf 16(iteration)m 14 r 98 c 1(e-)m 451 1031 p (ginning)s 15(with)m 14(iteration)m 14(one.)m 10 1129 p 61 c cmsy10.329 @sf -7 r 41 c cmr10.329 @sf (27)s 23 r 123 c cmtt12.300 @sf 22(LUNERR)m 23([INTEGER)m 23(LUNERR])m cmr10.329 @sf 197 1205 p (The)s 16 r 118 c -2(ariable)m 14(that)m 15(sp)m 1(eci\014es)m cmsy10.329 @sf 16 r 76 c cmmi8.300 @sf 768 1212 p 69 c 2 r 82 c cmr10.329 @sf 825 1205 p 44 c 15(the)m 16(logical)m 14(unit)m 15 r 110 c (um)s 98 c 1(er)m 14(to)m 15 r 98 c 1 r 101 c 16(used)m 17(for)m 15(error)m 197 1262 p (messages.)s 19(\(See)m cmsy10.329 @sf 16 r 120 c cmr10.329 @sf (1.D.\))s 19(By)m 15(default,)m cmsy10.329 @sf 14 r 76 c cmmi8.300 @sf 914 1269 p 69 c 2 r 82 c cmr10.329 @sf 984 1262 p 61 c 13(6.)m 612 1291 p 711 2 ru 612 1352 p 2 62 ru cmtt10.300 @sf 637 1326 p (LUNERR)s 792 1352 p 2 62 ru 9 r 2 62 ru cmsy10.300 @sf 826 1325 p 76 c cmmi7.300 @sf 855 1331 p 69 c 2 r 82 c 1323 1352 p 2 62 ru 612 1354 p 711 2 ru 612 1404 p 2 50 ru cmmi10.300 @sf 670 1390 p 60 c cmr10.300 @sf 12 r 48 c 792 1405 p 2 50 ru 9 r 2 50 ru 826 1389 p 61 c 12 r 54 c 1323 1404 p 2 50 ru 612 1454 p 2 50 ru 670 1440 p 61 c 12 r 48 c 792 1455 p 2 50 ru 9 r 2 50 ru 826 1439 p (error)s 15(messages)m 15(suppressed)m 1323 1454 p 2 50 ru 612 1503 p 2 50 ru cmsy10.300 @sf 670 1489 p 21 c cmr10.300 @sf 12 r 48 c 792 1504 p 2 50 ru 9 r 2 50 ru 826 1488 p 61 c cmtt10.300 @sf 12(LUNERR)m 1323 1503 p 2 50 ru 612 1505 p 711 2 ru cmr10.329 @sf 10 1585 p 61 c cmsy10.329 @sf -7 r 41 c cmr10.329 @sf (28)s 23 r 123 c cmtt12.300 @sf 22(LUNRPT)m 23([INTEGER)m 23(LUNRPT])m cmr10.329 @sf 197 1661 p (The)s 16 r 118 c -2(ariable)m 14(that)m 15(sp)m 1(eci\014es)m cmsy10.329 @sf 16 r 76 c cmmi8.300 @sf 768 1668 p 67 c 2 r 82 c cmr10.329 @sf 825 1661 p 44 c 15(the)m 16(logical)m 14(unit)m 15 r 110 c (um)s 98 c 1(er)m 14(to)m 15 r 98 c 1 r 101 c 17(used)m 16(for)m 15(com-)m 197 1717 p (putation)s 21(rep)m 1(orts.)m 39(\(See)m 22(also)m 21(argumen)m 116 c 20(26{)m cmtt10.329 @sf (IPRINT)s cmr10.329 @sf -2 r 44 c 23(and)m cmsy10.329 @sf 22 r 120 c cmr10.329 @sf (1.D.\))s 39(By)m 22(default,)m cmsy10.329 @sf 197 1774 p 76 c cmmi8.300 @sf 228 1781 p 67 c 2 r 82 c cmr10.329 @sf 297 1774 p 61 c 13(6.)m 459 1799 p 1017 2 ru 459 1860 p 2 62 ru cmtt10.300 @sf 484 1834 p (LUNRPT)s 639 1860 p 2 62 ru 9 r 2 62 ru cmsy10.300 @sf 673 1833 p 76 c cmmi7.300 @sf 702 1839 p 67 c 2 r 82 c 1475 1860 p 2 62 ru 459 1862 p 1017 2 ru 459 1912 p 2 50 ru cmmi10.300 @sf 517 1898 p 60 c cmr10.300 @sf 12 r 48 c 639 1913 p 2 50 ru 9 r 2 50 ru 673 1897 p 61 c 12 r 54 c 1475 1912 p 2 50 ru 459 1962 p 2 50 ru 517 1948 p 61 c 12 r 48 c 639 1963 p 2 50 ru 9 r 2 50 ru 673 1947 p (computation)s 13(rep)m 1(orts)m 16(suppressed,)m 1475 1962 p 2 50 ru 459 2011 p 2 50 ru 180 r 2 50 ru 9 r 2 50 ru 673 1996 p (ev)s (en)s 14(when)m 14(argumen)m 116 c 13(26{)m cmtt10.300 @sf (IPRINT)s cmr10.300 @sf 12(is)m 14(nonzero)m 1475 2011 p 2 50 ru 459 2061 p 2 50 ru cmsy10.300 @sf 517 2047 p 21 c cmr10.300 @sf 12 r 48 c 639 2062 p 2 50 ru 9 r 2 50 ru 673 2046 p 61 c cmtt10.300 @sf 12(LUNRPT)m 1475 2061 p 2 50 ru 459 2063 p 1017 2 ru cmr10.329 @sf 10 2143 p 61 c cmsy10.329 @sf -7 r 41 c cmr10.329 @sf (29)s 23 r 123 c cmtt12.300 @sf 22(STPB)m 24 r 91 c ()s 23(STPB\(NP\))m -1 r 93 c cmr10.329 @sf 197 2219 p (The)s 19(singly)m 17(subscripted)m 19(arra)m -1 r 121 c 17(that)m 17(sp)m 1(eci\014es)m 19(the)m cmti10.329 @sf 19 r 114 c -1(elative)m cmr10.329 @sf 16(step)m 19(sizes,)m cmmi10.329 @sf 18 r 104 c cmmi8.300 @sf 1562 2226 p 12 c cmr6.300 @sf 1582 2232 p 75 c cmmi10.329 @sf 1609 2219 p 59 c cmtt10.329 @sf 26 r 75 c cmr10.329 @sf 18 r 61 c 197 2275 p 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 7 r 58 c 5 r 59 c 8 r 112 c cmr10.329 @sf 44 c 13(used)m 14(to)m 13(compute)m 14(the)m 14(\014nite)m 14(di\013erence)m 14(deriv)m -2(ativ)m -1(es)m 12(with)m 13(resp)m 1(ect)m 14(to)m 13(eac)m 104 c 197 2332 p (of)s 12(the)m 13(parameters)m cmmi10.329 @sf 12 r 12 c cmr10.329 @sf 15(as)m 13(discussed)m 13(in)m cmsy10.329 @sf 13 r 120 c cmr10.329 @sf (4.A.)s 18(The)m 13(default)m 13 r 118 c -2(alue)m 12(is)m 12(set)m 13(as)m 12(describ)m 1(ed)m 197 2388 p (in)s cmsy10.329 @sf 11 r 120 c cmr10.329 @sf (4.A.iii)s 9(dep)m 1(ending)m 13(on)m 11(whether)m 11(forw)m (ard)s 9(or)m 11(cen)m (tral)s 9(\014nite)m 11(di\013erence)m 12(deriv)m -2(ativ)m -1(es)m 197 2445 p (are)s 15 r 98 c 1(eing)m 15(computed.)m 21(\(See)m 15(argumen)m 116 c 13(20{)m cmtt10.329 @sf (JOB)s cmr10.329 @sf -1(.\))m @eop %%Page: 35 49 35 @bop0 cmmi10.300 @sf [ 24 29 -2 0 23.916] 104 @dc cmr7.300 @sf [ 24 20 -2 0 27.270] 1 @dc 1.000000 /cmcsc10.329 @newfont cmcsc10.329 @sf [<87E0D810E008C0048006800680060006000E001C01FC1FF83FE07F007000E000C004C004C00440 0C601C306C0F84> 16 23 -2 0 20.808] 115 @dc [<007E000381800700600C00101C0010380008780008700008F00000F00000F00000F00000F00000 F00000F000007000087800083800181C00180C0038070078038198007E08> 24 23 -2 0 26.868] 99 @dc [ 24 23 -1 0 27.878] 97 @dc [ 16 23 -3 0 23.333] 108 @dc [ 24 23 -3 0 25.353] 101 @dc cmsy10.329 @sf [<001F007F00F801E001E001C001C001C001C001C001C001C001C001C001C001C001C001C003C003 800F80FE00F800FE000F80038003C001C001C001C001C001C001C001C001C001C001C001C001C0 01C001E001E000F8007F001F> 16 45 -3 11 22.727] 102 @dc [ 16 45 -3 11 22.727] 103 @dc 1.000000 /cmcsc10.300 @newfont cmcsc10.300 @sf [ 16 21 -2 0 19.002] 115 @dc [<01FC0007FF001F83803E01C03C00E07800E0780060F00060F00000F00000F00000F00000F00000 F000607800607800E03C00E03E01E01F87E007FFE001FC60> 24 21 -2 0 24.537] 99 @dc [ 24 21 -1 0 25.459] 97 @dc [ 24 21 -1 0 21.308] 108 @dc [ 24 21 -1 0 23.153] 101 @dc 35 @bop1 cmr10.329 @sf 225 114 p (Using)s 15(ODRP)m -3 r 65 c (CK)s 1318(35)m 225 134 p 1725 2 ru 914 219 p 558 2 ru 914 269 p 2 50 ru 202 r 2 50 ru 9 r 2 50 ru cmr10.300 @sf 1150 254 p 70 c -2(or)m cmtt10.300 @sf 12 r 75 c cmr10.300 @sf 11 r 61 c 12 r 49 c cmmi10.300 @sf 59 c 7 r 58 c 7 r 58 c 7 r 58 c 5 r 59 c 7(p;)m 1471 269 p 2 50 ru 914 330 p 2 62 ru cmtt10.300 @sf 939 304 p (STPB\(1\))s 1116 330 p 2 62 ru 9 r 2 62 ru cmmi10.300 @sf 1191 303 p 104 c cmmi7.300 @sf 1215 309 p 12 c cmr6.300 @sf 1234 316 p 75 c 1471 330 p 2 62 ru 914 332 p 558 2 ru 914 382 p 2 50 ru cmsy10.300 @sf 983 368 p 20 c cmr10.300 @sf 12 r 48 c 1116 383 p 2 50 ru 9 r 2 50 ru 1150 367 p 61 c 14(default)m 13 r 118 c -1(alue)m 1471 382 p 2 50 ru 914 432 p 2 50 ru cmmi10.300 @sf 983 418 p 62 c cmr10.300 @sf 12 r 48 c 1116 433 p 2 50 ru 9 r 2 50 ru 1150 417 p 61 c cmtt10.300 @sf 12(STPB\()m 75 c -2 r 41 c 1471 432 p 2 50 ru 914 434 p 558 2 ru cmr10.329 @sf 235 513 p 61 c cmsy10.329 @sf -7 r 41 c cmr10.329 @sf (30)s 23 r 123 c cmtt12.300 @sf 22(STPD)m 24 r 91 c ()s 23(STPD\(LDS)m -1(TPD)m -1(,M)m -1(\)])m cmr10.329 @sf 422 589 p (The)s 17(doubly)m 16(subscripted)m 17(arra)m -1 r 121 c 15(that)m 15(sp)m 1(eci\014es)m 17(the)m cmti10.329 @sf 17 r 114 c -1(elative)m cmr10.329 @sf 15(step)m 16(sizes,)m cmmi10.329 @sf 16 r 104 c cmr8.300 @sf 1787 596 p 1 c cmr6.300 @sf 1816 602 p 73 c 1 r 74 c cmmi10.329 @sf 1847 589 p 59 c cmtt10.329 @sf 16 r 73 c cmr10.329 @sf 15 r 61 c 422 646 p 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 7 r 58 c 5 r 59 c 8(n;)m cmr10.329 @sf 17(and)m cmtt10.329 @sf 18 r 74 c cmr10.329 @sf 17 r 61 c 17 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 8 r 58 c 5 r 59 c 8 r 109 c cmr10.329 @sf 44 c 17(used)m 18(to)m 17(compute)m 18(the)m 18(\014nite)m 18(di\013erence)m 18(deriv)m -2(ativ)m -1(es)m 422 702 p (with)s 16(resp)m 1(ect)m 16(to)m 16(the)m 17(errors)m 15(in)m 16(eac)m 104 c 16(of)m 16(the)m 16(elemen)m (ts)s 15(of)m cmmi10.329 @sf 16 r 88 c cmr10.329 @sf 20(as)m 16(discussed)m 16(in)m cmsy10.329 @sf 17 r 120 c cmr10.329 @sf (4.A.)s 422 759 p (The)s 13(default)m 13 r 118 c -2(alue)m 12(is)m 13(set)m 13(as)m 12(describ)m 1(ed)m 14(in)m cmsy10.329 @sf 13 r 120 c cmr10.329 @sf 1(4.A.iii)m 11(dep)m 1(ending)m 14(on)m 13(whether)m 13(forw)m (ard)s 422 815 p (or)s 20(cen)m (tral)s 20(\014nite)m 21(di\013erence)m 21(deriv)m -2(ativ)m -1(es)m 19(are)m 21 r 98 c 1(eing)m 21(computed.)m 37(\(See)m 22(argumen)m 116 c 422 871 p (20{)s cmtt10.329 @sf (JOB)s cmr10.329 @sf -1(.\))m cmtt10.329 @sf 26(STPD)m cmr10.329 @sf 17(is)m 17 r 97 c 18(structured)m 17(argumen)m (t:)s 23(only)m 17(the)m 18(sp)m 1(eci\014c)m 18(elemen)m (ts)s 16(of)m cmtt10.329 @sf 18(STPD)m cmr10.329 @sf 422 928 p (iden)s (ti\014ed)s 14(in)m 15(the)m 15(table)m 15 r 98 c 1(elo)m 119 c 14(are)m 15(referenced)m 16 r 98 c 121 c 14(ODRP)m -3 r 65 c (CK.)s 14(\(See)m cmsy10.329 @sf 15 r 120 c cmr10.329 @sf (1.G.\))s 800 957 p 786 2 ru 800 1007 p 2 50 ru 245 r 2 50 ru 181 r 2 50 ru 9 r 2 50 ru cmr10.300 @sf 1260 992 p 70 c -2(or)m cmtt10.300 @sf 12 r 73 c cmr10.300 @sf 12 r 61 c 11 r 49 c cmmi10.300 @sf 59 c 7 r 58 c 7 r 58 c 7 r 58 c 5 r 59 c 7(n;)m 1585 1007 p 2 50 ru 800 1057 p 2 50 ru 245 r 2 50 ru 181 r 2 50 ru 9 r 2 50 ru cmr10.300 @sf 1260 1042 p 38 c cmtt10.300 @sf 14 r 74 c cmr10.300 @sf 11 r 61 c 12 r 49 c cmmi10.300 @sf 59 c 7 r 58 c 7 r 58 c 7 r 58 c 5 r 59 c 7(m;)m 1585 1057 p 2 50 ru 800 1118 p 2 62 ru cmtt10.300 @sf 825 1092 p (STPD\(1,1\))s 1045 1118 p 2 62 ru 1071 1091 p (LDSTPD)s 1226 1118 p 2 62 ru 9 r 2 62 ru cmmi10.300 @sf 1301 1091 p 104 c cmr7.300 @sf 1325 1097 p 1 c cmr6.300 @sf 1352 1104 p 73 c 74 c 1585 1118 p 2 62 ru 800 1120 p 786 2 ru 800 1170 p 2 50 ru cmsy10.300 @sf 891 1156 p 20 c cmr10.300 @sf 12 r 48 c 1045 1171 p 2 50 ru 1115 1155 p 124 c 1226 1170 p 2 50 ru 9 r 2 50 ru 1260 1155 p 61 c 14(default)m 13 r 118 c -1(alue)m 1585 1170 p 2 50 ru 800 1219 p 2 50 ru cmmi10.300 @sf 891 1205 p 62 c cmr10.300 @sf 12 r 48 c 1045 1220 p 2 50 ru 1104 1204 p 61 c 12 r 49 c 1226 1219 p 2 50 ru 9 r 2 50 ru 1260 1204 p 61 c cmtt10.300 @sf 12(STPD\(1,)m 74 c -2 r 41 c 1585 1219 p 2 50 ru 800 1269 p 2 50 ru 245 r 2 50 ru cmsy10.300 @sf 1102 1254 p 21 c cmmi10.300 @sf 12 r 110 c 1226 1269 p 2 50 ru 9 r 2 50 ru cmr10.300 @sf 1260 1254 p 61 c cmtt10.300 @sf 12(STPD\()m 73 c -2 r 44 c 74 c 41 c 1585 1269 p 2 50 ru 800 1271 p 786 2 ru cmr10.329 @sf 235 1351 p 61 c cmsy10.329 @sf -7 r 41 c cmr10.329 @sf (31)s 23 r 123 c cmtt12.300 @sf 22(LDSTPD)m 23([INTEGER)m 23(LDSTPD])m cmr10.329 @sf 422 1427 p (The)s 16(leading)m 15(dimension)m 15(of)m 16(arra)m 121 c cmtt10.329 @sf 13(STPD)m cmr10.329 @sf 46 c cmtt10.329 @sf 21(LDSTPD)m cmr10.329 @sf 15 r 109 c (ust)s 14(either)m 16(exactly)m 15(equal)m 15(one,)m 422 1483 p (or)s 15 r 109 c (ust)s 13(equal)m 15(or)m 15(exceed)m cmmi10.329 @sf 16 r 110 c cmr10.329 @sf 46 c 20(See)m 16(argumen)m 116 c 13(30{)m cmtt10.329 @sf (STPD)s cmr10.329 @sf 14(for)m 15(further)m 15(details.)m 235 1581 p 61 c cmsy10.329 @sf -7 r 41 c cmr10.329 @sf (32)s 23 r 123 c cmtt12.300 @sf 22(SCLB)m 24 r 91 c ()s 23(SCLB\(NP\))m -1 r 93 c cmr10.329 @sf 422 1657 p (The)s 26(singly)m 26(subscripted)m 26(arra)m 121 c 24(that)m 26(sp)m 1(eci\014es)m 27(the)m 26(scale)m 26 r 118 c -2(alues,)m cmcsc10.329 @sf 28(scale)m cmsy10.329 @sf 102 c cmmi10.329 @sf 12 c cmr6.300 @sf 1890 1664 p 75 c cmsy10.329 @sf 1915 1657 p 103 c cmr10.329 @sf 44 c cmtt10.329 @sf 422 1714 p 75 c cmr10.329 @sf 15 r 61 c 15 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 7 r 58 c 5 r 59 c 8 r 112 c cmr10.329 @sf 44 c 16(of)m 16(the)m 16(function)m 17(parameters,)m 15(i.e.,)m 16(the)m 16(recipro)m 1(cals)m 16(of)m 16(the)m 17(exp)m 1(ected)m 422 1770 p (magnitudes)s 21(or)m 21 r 116 c (ypical)s 19(sizes)m 22(of)m cmmi10.329 @sf 21 r 12 c cmr6.300 @sf 1083 1777 p 75 c cmmi10.329 @sf 1108 1770 p 59 c cmtt10.329 @sf 8 r 75 c cmr10.329 @sf 22 r 61 c 23 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 8 r 58 c 5 r 59 c 8(p:)m cmr10.329 @sf 20(Scaling)m 21(is)m 21(used)m 22(within)m 21(the)m 422 1827 p (regression)s 18(pro)m 1(cedure)m 20(in)m 19(order)m 19(that)m 18(the)m 19(units)m 19(of)m 19(the)m 19 r 118 c -2(ariable)m 17(space)m 20(will)m 17(ha)m 118 c 101 c 422 1883 p (appro)s (ximat)s -1(ely)m 16(the)m 18(same)m 18(magnitude.)m 28(This)m 18(increases)m 17(the)m 18(stabilit)m -1 r 121 c 16(of)m 18(the)m 18(pro-)m 422 1939 p (cedure,)s 18(but)m 17(do)m 1(es)m 17(not)m 16(a\013ect)m 16(the)m 17(problem)m 17(sp)m 1(eci\014cation.)m 25(Scaling)m 16(should)m 17(not)m 16 r 98 c 1 r 101 c 422 1996 p (confused)s 16(with)m 15(the)m 16 r 119 c (eigh)s -1(ting)m 13(matrices)m cmmi10.329 @sf 15 r 119 c cmmi8.300 @sf 1207 2003 p 15 c cmr6.300 @sf 1221 2009 p 73 c cmr10.329 @sf 1251 1996 p (and)s cmmi10.329 @sf 15 r 119 c cmmi8.300 @sf 1367 2003 p 14 c cmr6.300 @sf 1383 2009 p 73 c cmr10.329 @sf 1413 1996 p (sp)s 1(eci\014ed)m 16 r 98 c 121 c 15(argumen)m (ts)s 14(11{)m cmtt10.329 @sf 422 2052 p (WE)s cmr10.329 @sf 15(and)m 16(14{)m cmtt10.329 @sf (WD)s cmr10.329 @sf -1 r 46 c 20(\(See)m cmsy10.329 @sf 16 r 120 c cmr10.329 @sf (1.A,)s 14(and)m cmsy10.329 @sf 16 r 120 c cmr10.329 @sf (1.F.\))s 19(Except)m 16(as)m 15(noted)m 16 r 98 c 1(elo)m (w,)s 13(the)m 16(scale)m 15 r 118 c -2(alues)m 422 2109 p (sp)s 1(eci\014ed)m 19(for)m 18(eac)m 104 c 17 r 118 c -2(alue)m 18(of)m cmmi10.329 @sf 17 r 12 c cmr10.329 @sf 21 r 109 c (ust)s 16 r 98 c 1 r 101 c 19(greater)m 18(than)m 18(zero.)m 28(The)m 19(default)m 18 r 118 c -2(alues)m 422 2165 p (are)s 15(set)m 15(as)m 15(describ)m 1(ed)m 16(in)m cmsy10.329 @sf 15 r 120 c cmr10.329 @sf (4.D.i.)s 914 2192 p 558 2 ru 914 2242 p 2 50 ru 202 r 2 50 ru 9 r 2 50 ru cmr10.300 @sf 1150 2227 p 70 c -2(or)m cmtt10.300 @sf 12 r 75 c cmr10.300 @sf 11 r 61 c 12 r 49 c cmmi10.300 @sf 59 c 7 r 58 c 7 r 58 c 7 r 58 c 5 r 59 c 7(p;)m 1471 2242 p 2 50 ru 914 2303 p 2 62 ru cmtt10.300 @sf 939 2277 p (SCLB\(1\))s 1116 2303 p 2 62 ru 9 r 2 62 ru cmcsc10.300 @sf 1191 2276 p (scale)s cmsy10.300 @sf 1 r 102 c cmmi10.300 @sf 12 c cmr6.300 @sf 1349 2282 p 75 c cmsy10.300 @sf 1374 2276 p 103 c 1471 2303 p 2 62 ru 914 2305 p 558 2 ru 914 2355 p 2 50 ru 983 2341 p 20 c cmr10.300 @sf 12 r 48 c 1116 2356 p 2 50 ru 9 r 2 50 ru 1150 2340 p 61 c 14(default)m 13 r 118 c -1(alue)m 1471 2355 p 2 50 ru 914 2405 p 2 50 ru cmmi10.300 @sf 983 2391 p 62 c cmr10.300 @sf 12 r 48 c 1116 2406 p 2 50 ru 9 r 2 50 ru 1150 2390 p 61 c cmtt10.300 @sf 12(SCLB\()m 75 c -2 r 41 c 1471 2405 p 2 50 ru 914 2407 p 558 2 ru @eop %%Page: 36 50 36 @bop0 cmtt12.300 @sf [ 24 30 -1 0 25.632] 75 @dc 36 @bop1 cmr10.329 @sf 0 114 p (36)s 1319(Using)m 15(ODRP)m -3 r 65 c (CK)s 0 134 p 1725 2 ru 10 259 p 61 c cmsy10.329 @sf -7 r 41 c cmr10.329 @sf (33)s 23 r 123 c cmtt12.300 @sf 22(SCLD)m 24 r 91 c ()s 23(SCLD\(LDS)m -1(CLD)m -1(,M)m -1(\)])m cmr10.329 @sf 197 335 p (The)s 12(doubly)m 12(subscripted)m 13(arra)m 121 c 10(that)m 11(sp)m 1(eci\014es)m 13(the)m 12(scale)m 12 r 118 c -2(alues)m 11(for)m 12(the)m 12(errors)m 11 r 1 c 12(in)m 197 391 p (the)s 12(explanatory)m 11 r 118 c -2(ariable)m cmmi10.329 @sf 11 r 88 c cmr10.329 @sf 4 r 44 c 11(i.e.,)m 11(the)m 13(recipro)m 1(cals)m 11(of)m 12(the)m 12(exp)m 1(ected)m 13(magnitudes)m 11(or)m 197 448 p 116 c (ypical)s 12(sizes)m 14(of)m 14 r 1 c cmr6.300 @sf 537 455 p 73 c 74 c cmmi10.329 @sf 566 448 p 59 c cmtt10.329 @sf 14 r 73 c cmr10.329 @sf 12 r 61 c 13 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 7 r 58 c 6 r 59 c 8(n;)m cmr10.329 @sf 13(and)m cmtt10.329 @sf 15 r 74 c cmr10.329 @sf 12 r 61 c 13 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 7 r 58 c 6 r 59 c 8(m:)m cmr10.329 @sf 13(Scaling)m 13(is)m 14(used)m 15(within)m 14(the)m 197 504 p (regression)s 11(pro)m 1(cedure)m 12(in)m 12(order)m 11(to)m 11(ensure)m 12(that)m 11(the)m 12(units)m 11(of)m 12(the)m 11 r 118 c -2(ariable)m 10(space)m 12(will)m 197 560 p (ha)s 118 c -1 r 101 c 16(appro)m (ximat)s -1(ely)m 15(the)m 18(same)m 17(magnitude.)m 25(This)m 17(increases)m 17(the)m 18(stabilit)m -1 r 121 c 15(of)m 17(the)m 197 617 p (pro)s 1(cedure,)m 17(but)m 17(do)m 1(es)m 17(not)m 16(a\013ect)m 16(the)m 17(problem)m 16(sp)m 1(eci\014cation.)m 24(Scaling)m 16(should)m 16(not)m 197 673 p 98 c 1 r 101 c 18(confused)m 19(with)m 17(the)m 17 r 119 c (eigh)s -1(ting)m 15(matrices)m cmmi10.329 @sf 17 r 119 c cmmi8.300 @sf 1056 680 p 15 c cmr6.300 @sf 1070 686 p 73 c cmr10.329 @sf 1102 673 p (and)s cmmi10.329 @sf 17 r 119 c cmmi8.300 @sf 1220 680 p 14 c cmr6.300 @sf 1236 686 p 73 c cmr10.329 @sf 1267 673 p (sp)s 1(eci\014ed)m 19 r 98 c 121 c 17(argumen)m (ts)s 197 730 p (11{)s cmtt10.329 @sf (WE)s cmr10.329 @sf 18(and)m 20(14{)m cmtt10.329 @sf (WD)s cmr10.329 @sf -1 r 46 c 33(\(See)m cmsy10.329 @sf 19 r 120 c cmr10.329 @sf 1(1.A,)m 19(and)m cmsy10.329 @sf 20 r 120 c cmr10.329 @sf (1.F.\))s 32(Except)m 19(as)m 19(noted)m 20 r 98 c 1(elo)m (w,)s 19(the)m 19(scale)m 197 786 p 118 c -2(alues)m 17(sp)m 1(eci\014ed)m 18(for)m 17(eac)m 104 c 17 r 118 c -2(alue)m 17(of)m 17 r 1 c 17 r 109 c (ust)s 16 r 98 c 1 r 101 c 19(greater)m 16(than)m 18(zero.)m 27(The)m 17(default)m 197 843 p 118 c -2(alues)m 18(are)m 19(set)m 18(as)m 19(describ)m 1(ed)m 19(in)m cmsy10.329 @sf 19 r 120 c cmr10.329 @sf (4.D.ii.)s cmtt10.329 @sf 29(SCLD)m cmr10.329 @sf 18(is)m 19 r 97 c 18(structured)m 19(argumen)m (t:)s 25(only)m 197 899 p (the)s 18(sp)m 1(eci\014c)m 19(elemen)m (ts)s 16(of)m cmtt10.329 @sf 17(SCLD)m cmr10.329 @sf 18(iden)m (ti\014ed)s 16(in)m 18(the)m 18(table)m 17 r 98 c 1(elo)m 119 c 17(are)m 17(referenced)m 19 r 98 c 121 c 197 956 p (ODRP)s -3 r 65 c (CK.)s 13(\(See)m cmsy10.329 @sf 16 r 120 c cmr10.329 @sf (1.G.\))s 575 985 p 786 2 ru 575 1034 p 2 50 ru 245 r 2 50 ru 181 r 2 50 ru 9 r 2 50 ru cmr10.300 @sf 1035 1019 p 70 c -2(or)m cmtt10.300 @sf 12 r 73 c cmr10.300 @sf 12 r 61 c 11 r 49 c cmmi10.300 @sf 59 c 7 r 58 c 7 r 58 c 7 r 58 c 5 r 59 c 7(n;)m 1360 1034 p 2 50 ru 575 1084 p 2 50 ru 245 r 2 50 ru 181 r 2 50 ru 9 r 2 50 ru cmr10.300 @sf 1035 1069 p 38 c cmtt10.300 @sf 14 r 74 c cmr10.300 @sf 11 r 61 c 12 r 49 c cmmi10.300 @sf 59 c 7 r 58 c 7 r 58 c 7 r 58 c 5 r 59 c 7(m;)m 1360 1084 p 2 50 ru 575 1146 p 2 62 ru cmtt10.300 @sf 600 1120 p (SCLD\(1,1\))s 820 1146 p 2 62 ru 846 1119 p (LDSCLD)s 1001 1146 p 2 62 ru 9 r 2 62 ru cmcsc10.300 @sf 1076 1119 p (scale)s cmsy10.300 @sf 1 r 102 c cmr10.300 @sf 1 c cmr6.300 @sf 1246 1125 p 73 c -1 r 74 c cmsy10.300 @sf 1274 1119 p 103 c 1360 1146 p 2 62 ru 575 1148 p 786 2 ru 575 1197 p 2 50 ru 666 1183 p 20 c cmr10.300 @sf 12 r 48 c 820 1198 p 2 50 ru 891 1182 p 124 c 1001 1197 p 2 50 ru 9 r 2 50 ru 1035 1182 p 61 c 14(default)m 13 r 118 c -1(alue)m 1360 1197 p 2 50 ru 575 1247 p 2 50 ru cmmi10.300 @sf 666 1233 p 62 c cmr10.300 @sf 12 r 48 c 820 1248 p 2 50 ru 879 1232 p 61 c 12 r 49 c 1001 1247 p 2 50 ru 9 r 2 50 ru 1035 1232 p 61 c cmtt10.300 @sf 12(SCLD\(1,)m 74 c -2 r 41 c 1360 1247 p 2 50 ru 575 1297 p 2 50 ru 245 r 2 50 ru cmsy10.300 @sf 877 1282 p 21 c cmmi10.300 @sf 12 r 110 c 1001 1297 p 2 50 ru 9 r 2 50 ru cmr10.300 @sf 1035 1282 p 61 c cmtt10.300 @sf 12(SCLD\()m 73 c -2 r 44 c 74 c 41 c 1360 1297 p 2 50 ru 575 1299 p 786 2 ru cmr10.329 @sf 10 1379 p 61 c cmsy10.329 @sf -7 r 41 c cmr10.329 @sf (34)s 23 r 123 c cmtt12.300 @sf 22(LDSCLD)m 23([INTEGER)m 23(LDSCLD])m cmr10.329 @sf 197 1455 p (The)s 16(leading)m 15(dimension)m 15(of)m 16(arra)m 121 c cmtt10.329 @sf 13(SCLD)m cmr10.329 @sf 46 c cmtt10.329 @sf 21(LDSCLD)m cmr10.329 @sf 15 r 109 c (ust)s 14(either)m 16(exactly)m 15(equal)m 15(one,)m 197 1511 p (or)s 15 r 109 c (ust)s 13(equal)m 15(or)m 15(exceed)m cmmi10.329 @sf 16 r 110 c cmr10.329 @sf 46 c 20(See)m 16(argumen)m 116 c 13(33{)m cmtt10.329 @sf (SCLD)s cmr10.329 @sf 14(for)m 15(further)m 15(details.)m cmsy10.329 @sf 0 1609 p 40 c -7 r 41 c cmr10.329 @sf (35)s 23 r 123 c cmtt12.300 @sf 22(WORK)m 24 r 91 c ()s 23(WORK\(LWO)m -1(RK\))m -1 r 93 c cmr10.329 @sf 197 1685 p (The)s 21(singly)m 19(subscripted)m 21(arra)m 121 c 18(used)m 21(for)m cmtt10.329 @sf 20()m cmr10.329 @sf 15 r 119 c (ork)s 18(space,)m 22(and)m 20(an)m 21(arra)m 121 c 18(in)m 197 1741 p (whic)s 104 c 13 r 118 c -2(arious)m 13(computed)m 15 r 118 c -2(alues)m 13(are)m 14(returned.)m 20(The)m 14(smallest)m 13(acceptable)m 15(dimen-)m 197 1798 p (sion)s 13(of)m cmtt10.329 @sf 13(WORK)m cmr10.329 @sf 13(is)m 13(giv)m (en)s 12 r 98 c 1(elo)m 119 c 13(in)m 13(the)m 14(de\014nition)m 13(of)m 13(argumen)m 116 c 12(36{)m cmtt10.329 @sf (LWORK)s cmr10.329 @sf -1 r 46 c 19(The)m 14 r 119 c (ork)s 197 1854 p (area)s 15(do)m 1(es)m 16(not)m 15(need)m 16(to)m 15 r 98 c 1 r 101 c 16(initiali)m -1(zed)m 14 r 98 c 121 c 15(the)m 15(user)m 16(unless)m 15(the)m 16(user)m 15(wishes)m 16(to)m 14(ini-)m 197 1911 p (tialize)s 12(\001,)m 14(whic)m 104 c 13(is)m 13(stored)m 13(in)m 14(the)m 14(\014rst)m cmmi10.329 @sf 13 r 110 c cmsy10.329 @sf 7 r 2 c cmmi10.329 @sf 7 r 109 c cmr10.329 @sf 15(lo)m 1(cations)m 13(of)m cmtt10.329 @sf 13(WORK)m cmr10.329 @sf 46 c 19(An)m 14(easy)m 14 r 119 c 97 c -1 r 121 c 12(to)m 197 1967 p (access)s 18(these)m 18 r 118 c -2(alues,)m 17(either)m 18(for)m 17(initializati)m -1(on,)m 16(as)m 18(is)m 17(necessary)m 18(when)m 18(the)m 18(fourth)m 197 2024 p (digit)s 14(of)m 16(argumen)m 116 c 14(20{)m cmtt10.329 @sf (JOB)s cmr10.329 @sf 14(is)m 15(nonzero)m 16(and)m 16(the)m 15(\014t)m 16(is)m 15 r 98 c 121 c 15(orthogonal)m 13(distance)m 16(re-)m 197 2080 p (gression,)s 19(or)m 19(for)m 19(analysis)m 18(up)m 1(on)m 20(return)m 20(from)m 18(ODRP)m -3 r 65 c (CK,)s 18(is)m 19(to)m 19(include)m 20(in)m 19(the)m 197 2137 p (user's)s 15(program)m 14(the)m 15(declaration)m 14(statemen)m (ts)s cmtt10.329 @sf 197 2199 p ()s 23(DELTA\(,\))m 197 2255 p (EQUIVALENCE)s 22(\(WORK\(1\),)m 23(DELTA\(1,1\)\))m cmr10.329 @sf 197 2318 p (where)s cmtt10.329 @sf 17 r 60 c 78 c -1 r 62 c cmr10.329 @sf 17(indicates)m 16(that)m 16(the)m 16(\014rst)m 16(dimension)m 17(of)m 16(the)m 16(arra)m 121 c cmtt10.329 @sf 15(DELTA)m cmr10.329 @sf 15 r 109 c (ust)s 15 r 98 c 1 r 101 c 18(ex-)m 197 2374 p (actly)s 17(the)m 17 r 110 c (um)s 98 c 1(er)m 16(of)m 17(observ)m -2(ations,)m cmtt10.329 @sf 16 r 78 c cmr10.329 @sf 17 r 61 c cmmi10.329 @sf 17 r 110 c cmr10.329 @sf 59 c 18(and)m cmtt10.329 @sf 18 r 60 c 77 c 62 c cmr10.329 @sf 17(indicates)m 17(that)m 17(the)m 17(second)m 197 2431 p (dimension)s 13(of)m 13(the)m 13(arra)m 121 c cmtt10.329 @sf 11(DELTA)m cmr10.329 @sf 12 r 109 c (ust)s 12 r 98 c 1 r 101 c 14(exactly)m 12(the)m 14 r 110 c (um)s -1 r 98 c 1(er)m 12(of)m 13(columns,)m cmtt10.329 @sf 13 r 77 c cmr10.329 @sf 12 r 61 c cmmi10.329 @sf 13 r 109 c cmr10.329 @sf 44 c @eop %%Page: 37 51 37 @bop0 cmtt10.329 @sf [<00F00000F00000F00000F00000F00000F00000F00000F000FFFFE0FFFFE0FFFFE0FFFFE000F000 00F00000F00000F00000F00000F00000F00000F000> 24 20 -2 -4 23.863] 43 @dc [ 24 4 -3 -12 23.863] 45 @dc [<01C00001C00001C00001C000C1C180F1C780F9CF807FFF001FFC0007F00007F0001FFC007FFF00 F9CF80F1C780C1C18001C00001C00001C00001C000> 24 20 -3 -4 23.863] 42 @dc cmtt10.300 @sf [<01C00001C00001C00001C00071C700F9CF807FFF001FFC0007F00007F0001FFC007FFF00F9CF80 71C70001C00001C00001C00001C000> 24 18 -2 -4 21.793] 42 @dc 37 @bop1 cmr10.329 @sf 225 114 p (Using)s 15(ODRP)m -3 r 65 c (CK)s 1318(37)m 225 134 p 1725 2 ru 422 259 p (of)s 14(the)m 14(explanatory)m 14 r 118 c -2(ariable)m cmmi10.329 @sf 12 r 88 c cmr10.329 @sf 4 r 46 c 19(This)m 14(allo)m -1(ws)m 12(the)m 15(error)m 13(asso)m 1(ciated)m 14(with)m 14(observ)m -2(a-)m 422 315 p (tion)s cmtt10.329 @sf 14(X\()m 73 c 44 c 74 c 41 c cmr10.329 @sf 15(to)m 14 r 98 c 1 r 101 c 16(accessed)m 16(as)m cmtt10.329 @sf 15(DELTA\()m 73 c -1 r 44 c 74 c 41 c cmr10.329 @sf 15(rather)m 14(than)m 16(as)m cmtt10.329 @sf 14(WORK\()m 73 c (+\()s 74 c -1(-1\)*N\))m cmr10.329 @sf 46 c 422 372 p (The)s 17 r 118 c -2(alues)m 16(in)m cmtt10.329 @sf 16(DELTA)m cmr10.329 @sf 16(will)m 15 r 98 c 1 r 101 c 18 r 111 c 118 c -1(er)m 15(written)m 15 r 98 c 121 c 16(the)m 17(\014nal)m 16(estimates)m 16(of)m 16(the)m 17(errors)m 422 428 p (in)s 18(the)m 19(explanatory)m 17 r 118 c -2(ariable)m 17(when)m 19(this)m 18(equiv)m -2(alencing)m 18(metho)m 1 r 100 c 18(is)m 18(used.)m 31(Other)m 422 484 p 118 c -2(alues)m 15(returned)m 16(in)m 15(arra)m 121 c cmtt10.329 @sf 13(WORK)m cmr10.329 @sf 15(ma)m 121 c 14(also)m 15 r 98 c 1 r 101 c 16(of)m 15(in)m (terest)s 14(and)m 15(can)m 16 r 98 c 1 r 101 c 16(accessed)m 16(as)m 422 541 p (describ)s 1(ed)m 16(in)m cmsy10.329 @sf 15 r 120 c cmr10.329 @sf (5.A.)s 422 603 p (N.B.,)s 22(if)m 20(the)m 21(\014t)m 21(is)m 21 r 97 c 21(\\restart,")m 20(i.e.,)m 21(if)m 21(the)m 21(\014fth)m 21(digit)m 20(of)m 20(argumen)m 116 c 20(20{)m cmtt10.329 @sf (JOB)s cmr10.329 @sf 19(is)m 422 660 p (nonzero,)s 13(then)m 14(all)m 11(elemen)m (ts)s 12(of)m 13 r 118 c (ector)s cmtt10.329 @sf 11(WORK)m cmr10.329 @sf -1 r 44 c 14(including)m 12(the)m 13 r 118 c -2(alues)m 13(of)m cmtt10.329 @sf 12(DELTA)m cmr10.329 @sf -1 r 44 c 13 r 109 c (ust)s 422 716 p 98 c 1 r 101 c 16(exactly)m 14(as)m 15(returned)m 16(from)m 14 r 97 c 15(previous)m 15(call)m 14(to)m 15(ODRP)m -3 r 65 c (CK.)s 235 814 p 61 c cmsy10.329 @sf -7 r 41 c cmr10.329 @sf (36)s 23 r 123 c cmtt12.300 @sf 22(LWORK)m 24([INTEGE)m -1 r 82 c 23(LWORK])m cmr10.329 @sf 422 890 p (The)s 15(length)m 15(of)m 15(arra)m 121 c cmtt10.329 @sf 13(WORK)m cmr10.329 @sf -1 r 46 c 422 952 p 70 c -3(or)m 14(orthogonal)m 13(distance)m 15(regression)m cmtt10.329 @sf 14(LWORK)m cmr10.329 @sf 15 r 109 c (ust)s 13(equal)m 15(or)m 15(exceed)m cmr10.300 @sf 463 1015 p (18)s 1 r 43 c 1(11)m cmmi10.300 @sf 112 c cmr10.300 @sf 1 r 43 c cmmi10.300 @sf 1 r 112 c cmr7.300 @sf 657 1001 p 50 c cmr10.300 @sf 674 1015 p 43 c cmmi10.300 @sf 1 r 109 c cmr10.300 @sf 1 r 43 c cmmi10.300 @sf 1 r 109 c cmr7.300 @sf 813 1001 p 50 c cmr10.300 @sf 832 1015 p 43 c 1 r 52 c cmmi10.300 @sf (nq)s cmr10.300 @sf 2 r 43 c 1 r 54 c cmmi10.300 @sf (nm)s cmr10.300 @sf 1 r 43 c 1 r 50 c cmmi10.300 @sf (nq)s 1 r 112 c cmr10.300 @sf 43 c 1 r 50 c cmmi10.300 @sf (nq)s 109 c cmr10.300 @sf 1 r 43 c cmmi10.300 @sf 1 r 113 c cmr7.300 @sf 1356 1001 p 50 c cmr10.300 @sf 1374 1015 p 43 c 1 r 53 c cmmi10.300 @sf 113 c cmr10.300 @sf 2 r 43 c cmmi10.300 @sf 1 r 113 c cmr10.300 @sf 1 r 40 c cmmi10.300 @sf 112 c cmr10.300 @sf 1 r 43 c cmmi10.300 @sf 1 r 109 c cmr10.300 @sf 41 c 1 r 43 c cmtt10.300 @sf 1(\(L)m -1(DWE*L)m -1(D2WE\))m cmmi10.300 @sf -3 r 113 c cmr10.300 @sf 1 r 46 c cmr10.329 @sf 422 1077 p 70 c -3(or)m 14(ordinary)m 14(least)m 14(squares)m cmtt10.329 @sf 15(LWORK)m cmr10.329 @sf 15 r 109 c (ust)s 13(equal)m 15(or)m 15(exceed)m cmr10.300 @sf 463 1139 p (18)s 9 r 43 c 10(11)m cmmi10.300 @sf 112 c cmr10.300 @sf 8 r 43 c cmmi10.300 @sf 10 r 112 c cmr7.300 @sf 690 1125 p 50 c cmr10.300 @sf 718 1139 p 43 c cmmi10.300 @sf 9 r 109 c cmr10.300 @sf 10 r 43 c cmmi10.300 @sf 9 r 109 c cmr7.300 @sf 882 1125 p 50 c cmr10.300 @sf 911 1139 p 43 c 9 r 52 c cmmi10.300 @sf (nq)s cmr10.300 @sf 10 r 43 c 9 r 50 c cmmi10.300 @sf (nm)s cmr10.300 @sf 10 r 43 c 9 r 50 c cmmi10.300 @sf (nq)s 1 r 112 c cmr10.300 @sf 9 r 43 c 10 r 53 c cmmi10.300 @sf 113 c cmr10.300 @sf 10 r 43 c cmmi10.300 @sf 9 r 113 c cmr10.300 @sf 1 r 40 c cmmi10.300 @sf 112 c cmr10.300 @sf 9 r 43 c cmmi10.300 @sf 10 r 109 c cmr10.300 @sf 41 c 10 r 43 c cmtt10.300 @sf 9(\(LDWE*LD2WE\))m cmmi10.300 @sf -2 r 113 c cmr10.300 @sf 1 r 46 c cmsy10.329 @sf 235 1237 p 40 c cmr10.329 @sf -7(=37)m 23 r 123 c cmtt12.300 @sf 22(IWORK)m 24([INTEGE)m -1 r 82 c 23(IWORK\(LIW)m -1(OR)m -1(K\)])m cmr10.329 @sf 422 1313 p (The)s 18(singly)m 18(subscripted)m 18(arra)m 121 c 16(used)m 18(for)m cmtt10.329 @sf 18(INTEGER)m cmr10.329 @sf 17 r 119 c (ork)s 16(space,)m 19(and)m 18(an)m 18(arra)m 121 c 16(in)m 422 1369 p (whic)s 104 c 13 r 118 c -2(arious)m 13(computed)m 15 r 118 c -2(alues)m 13(are)m 14(returned.)m 20(The)m 14(smallest)m 13(acceptable)m 15(dimen-)m 422 1426 p (sion)s 15(of)m cmtt10.329 @sf 14(IWORK)m cmr10.329 @sf 15(is)m 15(giv)m (en)s 13 r 98 c 1(elo)m 119 c 14(in)m 15(the)m 15(de\014nition)m 15(of)m 15(argumen)m 116 c 14(38{)m cmtt10.329 @sf (LIWORK)s cmr10.329 @sf -2 r 46 c 422 1488 p (Certain)s 20 r 118 c -2(alues)m 20(returned)m 22(in)m 21(arra)m 121 c cmtt10.329 @sf 19(IWORK)m cmr10.329 @sf 20(are)m 21(of)m 21(general)m 20(in)m (terest)s 20(and)m 21(can)m 21 r 98 c 1 r 101 c 422 1545 p (accessed)s 12(as)m 12(describ)m 1(ed)m 13 r 98 c 1(elo)m 119 c 10(in)m cmsy10.329 @sf 12 r 120 c cmr10.329 @sf (5.B.)s 19(In)m 12(particular,)m 11(the)m 12(results)m 11(of)m 12(the)m 12(deriv)m -2(ativ)m -1 r 101 c 422 1601 p 99 c (hec)s (king)s 17(pro)m 1(cedure)m 21(are)m 19(enco)m 1(ded)m 21(in)m cmtt10.329 @sf 19(IWORK)m cmr10.329 @sf -1 r 46 c 33(These)m 20(results)m 18(ma)m 121 c 18 r 98 c 1 r 101 c 20(esp)m 1(ecially)m 422 1658 p (useful)s 21(if)m 21(ODRP)m -3 r 65 c (CK's)s 19(error)m 21(rep)m 1(orts)m 21(ha)m 118 c -1 r 101 c 20 r 98 c 1(een)m 22(suppressed.)m 39(\(See)m 22(argumen)m 116 c 422 1714 p (27{)s cmtt10.329 @sf (LUNERR)s cmr10.329 @sf -2(.\))m 422 1776 p (N.B.,)s 22(if)m 20(the)m 21(\014t)m 21(is)m 21 r 97 c 21(\\restart,")m 20(i.e.,)m 21(if)m 21(the)m 21(\014fth)m 21(digit)m 20(of)m 20(argumen)m 116 c 20(20{)m cmtt10.329 @sf (JOB)s cmr10.329 @sf 19(is)m 422 1833 p (nonzero,)s 16(then)m 16(all)m 14(elemen)m (ts)s 15(of)m 15 r 118 c (ector)s cmtt10.329 @sf 14(IWORK)m cmr10.329 @sf 15 r 109 c (ust)s 15 r 98 c 1 r 101 c 16(exactly)m 15(as)m 15(returned)m 17(from)m 422 1889 p 97 c 15(previous)m 15(call)m 14(to)m 15(ODRP)m -3 r 65 c (CK.)s 235 1987 p 61 c cmsy10.329 @sf -7 r 41 c cmr10.329 @sf (38)s 23 r 123 c cmtt12.300 @sf 22(LIWORK)m 23([INTEGER)m 23(LIWORK])m cmr10.329 @sf 422 2063 p (The)s 15(length)m 15(of)m 15(arra)m 121 c cmtt10.329 @sf 13(IWORK)m cmr10.329 @sf -1 r 46 c 422 2125 p 70 c -3(or)m 18 r 98 c 1(oth)m 20(orthogonal)m 18(distance)m 20(regression)m 19(and)m 20(ordinary)m 19(least)m 19(squares)m cmtt10.329 @sf 20(LIWORK)m cmr10.329 @sf 422 2182 p 109 c (ust)s 14(equal)m 15(or)m 14(exceed)m cmr10.300 @sf 463 2244 p (20)s 9 r 43 c cmmi10.300 @sf 10 r 112 c cmr10.300 @sf 9 r 43 c cmmi10.300 @sf 9 r 113 c cmr10.300 @sf 1 r 40 c cmmi10.300 @sf 112 c cmr10.300 @sf 10 r 43 c cmmi10.300 @sf 9 r 109 c cmr10.300 @sf (\).)s cmsy10.329 @sf 235 2342 p 40 c cmr10.329 @sf -7(=39)m 23 r 123 c cmtt12.300 @sf 22(INFO)m 24([INTEGER)m 23(INFO])m cmr10.329 @sf 422 2418 p (The)s 15 r 118 c -2(ariable)m 14(used)m 16(to)m 14(indicate)m 15(wh)m 121 c 14(the)m 15(computations)m 14(stopp)m 1(ed.)m @eop %%Page: 38 52 38 @bop0 cmr10.329 @sf [<0000078000001FC000001FE000003FE000003FF000007C700000783000007010001FF01000FFF0 1001F8F80007F0FE000FB0FF000F38CF001E1F87803E0F07C03C0003C07C0003E07C0003E07800 01E0F80001F0F80001F0F80001F0F80001F0F80001F0F80001F0F80001F0F80001F0F80001F078 0001E07C0003E07C0003E03C0003C03E0007C01E0007800F000F000F801F0007C03E0001E07800 00FFF000001F8000> 32 41 -3 9 35.353] 81 @dc 38 @bop1 cmr10.329 @sf 0 114 p (38)s 1319(Using)m 15(ODRP)m -3 r 65 c (CK)s 0 134 p 1725 2 ru 438 219 p 1062 2 ru 438 281 p 2 62 ru cmtt10.300 @sf 462 255 p (INFO)s 574 281 p 2 62 ru cmr10.300 @sf 599 254 p (Stopping)s 14(Condition)m 1499 281 p 2 62 ru 438 282 p 1062 2 ru 438 332 p 2 50 ru 485 318 p 61 c 12 r 49 c 574 333 p 2 50 ru 599 317 p (sum)s 14(of)m 14(squares)m 15(con)m 118 c -1(ergence)m 1499 332 p 2 50 ru 438 382 p 2 50 ru 485 368 p 61 c 12 r 50 c 574 383 p 2 50 ru 599 367 p (parameter)s 15(con)m 118 c (ergence)s 1499 382 p 2 50 ru 438 432 p 2 50 ru 485 418 p 61 c 12 r 51 c 574 433 p 2 50 ru 599 417 p 98 c 1(oth)m 14(sum)m 14(of)m 14(squares)m 15(and)m 13(parameter)m 15(con)m 118 c (ergence)s 1499 432 p 2 50 ru 438 481 p 2 50 ru 485 467 p 61 c 12 r 52 c 574 482 p 2 50 ru 599 466 p (iteration)s 14(limit)m 12(reac)m (hed)s 1499 481 p 2 50 ru 438 531 p 2 50 ru cmsy10.300 @sf 485 517 p 21 c cmr10.300 @sf 12 r 53 c 574 532 p 2 50 ru 599 516 p (questionable)s 14(results)m 15(or)m 14(fatal)m 13(errors)m 15(detected)m 1499 531 p 2 50 ru 438 533 p 1062 2 ru cmr10.329 @sf 197 574 p (When)s cmtt10.329 @sf 19(INFO)m cmsy10.329 @sf 36 r 21 c cmr10.329 @sf 19 r 53 c 18(the)m 19(questionable)m 18(results)m 18(or)m 18(fatal)m 17(errors)m 18(detected)m 19 r 98 c 121 c 17(ODR-)m 197 631 p 80 c -3 r 65 c (CK)s 10(are)m 13(rep)m 1(orted)m 12(in)m 12(the)m 13(messages)m 12(generated)m 12(on)m 12(the)m 13(logical)m 10(units)m 12(sp)m 1(eci\014ed)m 14 r 98 c 121 c 197 687 p (argumen)s (ts)s 12(27{)m cmtt10.329 @sf (LUNERR)s cmr10.329 @sf 13(and)m 14(28{)m cmtt10.329 @sf (LUNRPT)s cmr10.329 @sf -2 r 46 c 20(In)m 15(this)m 13(case,)m cmtt10.329 @sf 14(INFO)m cmr10.329 @sf 14(is)m 13 r 97 c 14 r 53 c 14(digit)m cmtt10.329 @sf 13(INTEGER)m cmr10.329 @sf 197 744 p (with)s 13(decimal)m 13(expansion)m cmsy10.329 @sf 14 r 73 c cmr8.300 @sf 699 751 p 53 c cmsy10.329 @sf 718 744 p 73 c cmr8.300 @sf 743 751 p 52 c cmsy10.329 @sf 762 744 p 73 c cmr8.300 @sf 787 751 p 51 c cmsy10.329 @sf 807 744 p 73 c cmr8.300 @sf 832 751 p 50 c cmsy10.329 @sf 851 744 p 73 c cmr8.300 @sf 876 751 p 49 c cmr10.329 @sf 896 744 p 44 c 13(where)m cmsy10.329 @sf 14 r 73 c cmr8.300 @sf 1077 751 p 53 c cmr10.329 @sf 1109 744 p 61 c 13 r 48 c 14(indicates)m 13(that)m 13(questionable)m 197 800 p (conditions)s 16 r 119 c (ere)s 16(found,)m 18(and)m cmsy10.329 @sf 17 r 73 c cmr8.300 @sf 781 807 p 53 c cmsy10.329 @sf 817 800 p 21 c cmr10.329 @sf 16 r 49 c 17(indicates)m 17(that)m 16(fatal)m 16(errors)m 17 r 119 c (ere)s 16(detected.)m 197 857 p (The)s 17(nonzero)m 16 r 118 c -2(alues)m 16(of)m cmsy10.329 @sf 15 r 73 c cmr8.300 @sf 676 864 p 53 c cmr10.329 @sf 696 857 p 44 c cmsy10.329 @sf 16 r 73 c cmr8.300 @sf 750 864 p 52 c cmr10.329 @sf 770 857 p 44 c cmsy10.329 @sf 16 r 73 c cmr8.300 @sf 824 864 p 51 c cmr10.329 @sf 843 857 p 44 c cmsy10.329 @sf 17 r 73 c cmr8.300 @sf 898 864 p 50 c cmr10.329 @sf 933 857 p (and)s cmsy10.329 @sf 17 r 73 c cmr8.300 @sf 1048 864 p 49 c cmr10.329 @sf 1084 857 p (are)s 16(used)m 17(to)m 15(iden)m (tify)s 15(what)m 16(condi-)m 197 913 p (tions)s 14 r 119 c (ere)s 14(detected)m 16(at)m 15(the)m 15(time)m 14(the)m 16(program)m 14(stopp)m 1(ed.)m 254 940 p 1414 2 ru 254 1008 p 2 69 ru 279 980 p (Questionable)s 15(Results:)m 1667 1008 p 2 69 ru 254 1064 p 2 57 ru cmsy10.329 @sf 374 1047 p 73 c cmr8.300 @sf 399 1054 p 53 c cmr10.329 @sf 431 1047 p 61 c 13 r 48 c 12(with)m cmsy10.329 @sf 11 r 73 c cmr8.300 @sf 639 1054 p 52 c cmsy10.329 @sf 671 1047 p 54 c cmr10.329 @sf 61 c 13 r 48 c 50(deriv)m -2(ativ)m -1(es)m 13 r 112 c 1(ossibly)m 15(not)m 15(correct)m 15(\(see)m cmsy10.329 @sf 15 r 120 c cmr10.329 @sf (4.A\))s 1667 1064 p 2 57 ru 254 1121 p 2 57 ru cmsy10.329 @sf 614 1104 p 73 c cmr8.300 @sf 639 1111 p 51 c cmsy10.329 @sf 671 1104 p 54 c cmr10.329 @sf 61 c 13 r 48 c 50(ISTOP)m cmsy10.329 @sf 16 r 54 c cmr10.329 @sf 61 c 15 r 48 c 15(at)m 15(last)m 14(call)m 14(to)m cmtt10.329 @sf 15(FCN)m 1667 1121 p 2 57 ru 254 1177 p 2 57 ru cmr10.329 @sf 792 1160 p (\(see)s 15(argumen)m 116 c 13(1-)m cmtt10.329 @sf (FCN)s cmr10.329 @sf 41 c 1667 1177 p 2 57 ru 254 1234 p 2 57 ru cmsy10.329 @sf 614 1217 p 73 c cmr8.300 @sf 639 1224 p 50 c cmsy10.329 @sf 671 1217 p 54 c cmr10.329 @sf 61 c 13 r 48 c 50(problem)m 15(is)m 14(not)m 15(full)m 15(rank)m 15(at)m 14(solution)m 1667 1234 p 2 57 ru 254 1290 p 2 57 ru cmsy10.329 @sf 614 1273 p 73 c cmr8.300 @sf 639 1280 p 49 c cmr10.329 @sf 671 1273 p 61 c 13 r 49 c 50(sum)m 15(of)m 15(squares)m 15(con)m 118 c -1(ergence)m 1667 1290 p 2 57 ru 254 1347 p 2 57 ru 671 1330 p 61 c 13 r 50 c 50(parameter)m 14(con)m 118 c (ergence)s 1667 1347 p 2 57 ru 254 1403 p 2 57 ru 671 1386 p 61 c 13 r 51 c 50(sum)m 15(of)m 15(squares)m 15(and)m 15(parameter)m 15(con)m 118 c -1(ergence)m 1667 1403 p 2 57 ru 254 1459 p 2 57 ru 671 1442 p 61 c 13 r 52 c 50(iteration)m 13(limit)m 14(reac)m (hed)s 1667 1459 p 2 57 ru 254 1461 p 1414 2 ru 254 1530 p 2 69 ru 279 1502 p 70 c -3(alal)m 13(Errors:)m 1667 1530 p 2 69 ru 254 1586 p 2 57 ru cmsy10.329 @sf 374 1569 p 73 c cmr8.300 @sf 399 1576 p 53 c cmr10.329 @sf 431 1569 p 61 c 13 r 49 c 12(with)m cmsy10.329 @sf 11 r 73 c cmr8.300 @sf 639 1576 p 52 c cmsy10.329 @sf 671 1569 p 54 c cmr10.329 @sf 61 c 13 r 48 c cmtt10.329 @sf 50 r 78 c cmmi10.329 @sf 15 r 60 c cmr10.329 @sf 15 r 49 c 1667 1586 p 2 57 ru 254 1642 p 2 57 ru cmsy10.329 @sf 614 1625 p 73 c cmr8.300 @sf 639 1632 p 51 c cmsy10.329 @sf 671 1625 p 54 c cmr10.329 @sf 61 c 13 r 48 c cmtt10.329 @sf 50 r 77 c cmmi10.329 @sf 15 r 60 c cmr10.329 @sf 15 r 49 c 1667 1642 p 2 57 ru 254 1699 p 2 57 ru cmsy10.329 @sf 614 1682 p 73 c cmr8.300 @sf 639 1689 p 50 c cmsy10.329 @sf 671 1682 p 54 c cmr10.329 @sf 61 c 13 r 48 c cmtt10.329 @sf 50(NP)m cmmi10.329 @sf 15 r 60 c cmr10.329 @sf 15 r 49 c 15(or)m cmtt10.329 @sf 15(NP)m cmmi10.329 @sf 15 r 62 c cmtt10.329 @sf 15 r 78 c 1667 1699 p 2 57 ru 254 1755 p 2 57 ru cmsy10.329 @sf 614 1738 p 73 c cmr8.300 @sf 639 1745 p 49 c cmsy10.329 @sf 671 1738 p 54 c cmr10.329 @sf 61 c 13 r 48 c cmtt10.329 @sf 50(NQ)m cmmi10.329 @sf 15 r 60 c cmr10.329 @sf 15 r 49 c 1667 1755 p 2 57 ru 254 1812 p 2 57 ru cmsy10.329 @sf 374 1795 p 73 c cmr8.300 @sf 399 1802 p 53 c cmr10.329 @sf 431 1795 p 61 c 13 r 50 c 12(with)m cmsy10.329 @sf 11 r 73 c cmr8.300 @sf 639 1802 p 52 c cmsy10.329 @sf 671 1795 p 54 c cmr10.329 @sf 61 c 13 r 48 c cmtt10.329 @sf 50(LDY)m cmr10.329 @sf 15(and/or)m cmtt10.329 @sf 14(LDX)m cmr10.329 @sf 15(incorrect)m 1667 1812 p 2 57 ru 254 1868 p 2 57 ru cmsy10.329 @sf 614 1851 p 73 c cmr8.300 @sf 639 1858 p 51 c cmsy10.329 @sf 671 1851 p 54 c cmr10.329 @sf 61 c 13 r 48 c cmtt10.329 @sf 50(LDWE)m cmr10.329 @sf -1 r 44 c cmtt10.329 @sf 15(LD2WE)m cmr10.329 @sf -1 r 44 c cmtt10.329 @sf 15(LDWD)m cmr10.329 @sf 15(and/or)m cmtt10.329 @sf 14(LD2WD)m cmr10.329 @sf 15(incorrect)m 1667 1868 p 2 57 ru 254 1925 p 2 57 ru cmsy10.329 @sf 614 1908 p 73 c cmr8.300 @sf 639 1915 p 50 c cmsy10.329 @sf 671 1908 p 54 c cmr10.329 @sf 61 c 13 r 48 c cmtt10.329 @sf 50(LDIFX)m cmr10.329 @sf -1 r 44 c cmtt10.329 @sf 15(LDSTPD)m cmr10.329 @sf 14(and/or)m cmtt10.329 @sf 15(LDSCLD)m cmr10.329 @sf 14(incorrect)m 1667 1925 p 2 57 ru 254 1981 p 2 57 ru cmsy10.329 @sf 614 1964 p 73 c cmr8.300 @sf 639 1971 p 49 c cmsy10.329 @sf 671 1964 p 54 c cmr10.329 @sf 61 c 13 r 48 c cmtt10.329 @sf 50(LWORK)m cmr10.329 @sf 14(and/or)m cmtt10.329 @sf 15(LIWORK)m cmr10.329 @sf 14(to)m 1 r 111 c 15(small)m 1667 1981 p 2 57 ru 254 2037 p 2 57 ru cmsy10.329 @sf 374 2020 p 73 c cmr8.300 @sf 399 2027 p 53 c cmr10.329 @sf 431 2020 p 61 c 13 r 51 c 12(with)m cmsy10.329 @sf 11 r 73 c cmr8.300 @sf 639 2027 p 52 c cmsy10.329 @sf 671 2020 p 54 c cmr10.329 @sf 61 c 13 r 48 c cmtt10.329 @sf 50(STPB)m cmr10.329 @sf 14(and/or)m cmtt10.329 @sf 15(STPD)m cmr10.329 @sf 15(incorrect)m 1667 2037 p 2 57 ru 254 2094 p 2 57 ru cmsy10.329 @sf 614 2077 p 73 c cmr8.300 @sf 639 2084 p 51 c cmsy10.329 @sf 671 2077 p 54 c cmr10.329 @sf 61 c 13 r 48 c cmtt10.329 @sf 50(SCLB)m cmr10.329 @sf 14(and/or)m cmtt10.329 @sf 15(SCLD)m cmr10.329 @sf 15(incorrect)m 1667 2094 p 2 57 ru 254 2150 p 2 57 ru cmsy10.329 @sf 614 2133 p 73 c cmr8.300 @sf 639 2140 p 50 c cmsy10.329 @sf 671 2133 p 54 c cmr10.329 @sf 61 c 13 r 48 c cmtt10.329 @sf 50(WE)m cmr10.329 @sf 15(incorrect)m 1667 2150 p 2 57 ru 254 2207 p 2 57 ru cmsy10.329 @sf 614 2190 p 73 c cmr8.300 @sf 639 2197 p 49 c cmsy10.329 @sf 671 2190 p 54 c cmr10.329 @sf 61 c 13 r 48 c cmtt10.329 @sf 50(WD)m cmr10.329 @sf 15(incorrect)m 1667 2207 p 2 57 ru 254 2263 p 2 57 ru cmsy10.329 @sf 374 2246 p 73 c cmr8.300 @sf 399 2253 p 53 c cmr10.329 @sf 431 2246 p 61 c 13 r 52 c 290(error)m 14(in)m 15(deriv)m -2(ativ)m -1(es)m 1667 2263 p 2 57 ru 254 2320 p 2 57 ru cmsy10.329 @sf 374 2303 p 73 c cmr8.300 @sf 399 2310 p 53 c cmr10.329 @sf 431 2303 p 61 c 13 r 53 c cmtt10.329 @sf 290(ISTOP)m cmsy10.329 @sf 27 r 54 c cmr10.329 @sf 61 c 13 r 48 c 15(at)m 14(last)m 14(call)m 15(to)m cmtt10.329 @sf 14(FCN)m 1667 2320 p 2 57 ru 254 2376 p 2 57 ru cmr10.329 @sf 792 2359 p (\(see)s 15(argumen)m 116 c 13(1-)m cmtt10.329 @sf (FCN)s cmr10.329 @sf 41 c 1667 2376 p 2 57 ru 254 2433 p 2 57 ru cmsy10.329 @sf 374 2416 p 73 c cmr8.300 @sf 399 2423 p 53 c cmr10.329 @sf 431 2416 p 61 c 13 r 54 c 290 r 110 c (umerical)s 13(error)m 15(detected)m 1667 2433 p 2 57 ru 254 2435 p 1414 2 ru @eop %%Page: 39 53 39 @bop0 cmbx12.300 @sf [ 32 22 -1 0 29.576] 120 @dc 39 @bop1 cmr10.329 @sf 225 114 p (Using)s 15(ODRP)m -3 r 65 c (CK)s 1318(39)m 225 134 p 1725 2 ru 422 259 p (Note)s 21(that)m cmtt10.329 @sf 21(INFO)m cmr10.329 @sf 21 r 61 c 22(60000)m 20(indicates)m 21(an)m 21(error)m 21 r 112 c 1(ossibly)m 21(caused)m 22 r 98 c 121 c 21(incorrectly)m 422 315 p (sp)s 1(eci\014ed)m 17(user)m 17(input)m 16(to)m 16(ODRP)m -3 r 65 c (CK,)s 14(and)m 17(more)m 15(commonly)m 16 r 98 c 121 c 15 r 97 c 16 r 112 c 1 r 111 c 1(or)m 16 r 99 c (hoice)s 15(of)m 422 372 p (scale)s 15(or)m 14 r 119 c (eigh)s (t)s -1(s,)m 13(or)m 15 r 97 c 15(discon)m (tin)s -1(ui)m -1 r 116 c -1 r 121 c 13(in)m 15(the)m 15(deriv)m -2(ativ)m -1(es.)m cmbx12.300 @sf 225 517 p (2.C.)s 18(Examples)m cmr10.329 @sf 225 638 p (The)s 13(follo)m -1(wi)m -1(ng)m 11(sample)m 12(programs)m 11(in)m 118 c -1(ok)m -1 r 101 c cmtt10.329 @sf 10(DODR)m cmr10.329 @sf 12(and)m cmtt10.329 @sf 13(DODRC)m cmr10.329 @sf 11(to)m 12(solv)m 101 c 11(the)m 12(examples)m 12(of)m 12(explicit,)m 225 694 p (implicit)s 14(and)m 15 r 109 c (ultiresp)s 1(onse)m 14(problems)m 14(sho)m (wn)s 14(in)m cmsy10.329 @sf 15 r 120 c cmr10.329 @sf (1.A.)s 225 770 p (The)s 20(\014rst)m 20(program)m 18(in)m 118 c (o)s -1 r 107 c -1(es)m cmtt10.329 @sf 18(DODRC)m cmr10.329 @sf 19(with)m 20(user)m 20(supplied)m 20(deriv)m -2(ativ)m -1(es,)m 19(the)m 20(second)m 20(program)m 225 827 p (in)s 118 c -1(ok)m -1(es)m cmtt10.329 @sf 19(DODR)m cmr10.329 @sf 21(with)m 21(the)m 22(deriv)m -2(ativ)m -1(es)m 20(appro)m (xim)s -1(ated)m 20 r 98 c 121 c 20(ODRP)m -3 r 65 c (CK)s 20(using)m 22(forw)m (a)s -1(rd)m 20(\014nite)m 225 883 p (di\013erences,)s 17(and)m 17(the)m 17(third)m 17(in)m 118 c -1(ok)m -2(es)m cmtt10.329 @sf 15(DODRC)m cmr10.329 @sf 16(with)m 17(cen)m (tral)s 15(\014nite)m 17(di\013erence)m 17(deriv)m -2(ativ)m -1(es.)m 23(The)m 225 940 p (use)s 14(of)m 14(forw)m (ar)s -1 r 100 c 13(or)m 13(cen)m (tral)s 12(di\013erence)m 14(deriv)m -2(ativ)m (es)s 12(generally)m 13(causes)m 14 r 118 c (ery)s 13(little)m 12 r 99 c (hange)s 13(in)m 14(the)m 225 996 p (results)s 15(from)m 14(those)m 15(obtained)m 15(using)m 15(analytic)m 14(deriv)m -2(ativ)m -1(es.)m 18(\(See)m cmsy10.329 @sf 15 r 120 c cmr10.329 @sf (4.A.\))s 225 1072 p (Users)s 17(are)m 17(encouraged)m 17(to)m 17(use)m 17(these)m 18(examples,)m 17(mo)m 1(di\014ed)m 17(as)m 17(necessary)m -3 r 44 c 17(to)m 16(form)m 17(their)m 16 r 111 c (wn)s 225 1129 p (ODRP)s -3 r 65 c (CK)s 9(driv)m (ers.)s 16(Single)m 10(precision)m 10(sample)m 10(programs)m 9(can)m 11 r 98 c 1 r 101 c 11(easily)m 9(generated)m 10(from)m 10(these)m 225 1185 p 116 c 119 c -1 r 111 c 16(programs)m 17 r 98 c 121 c 17 r 99 c (hanging)s 17(all)m cmtt10.329 @sf 18(DOUBLE)m 23(PRECISION)m cmr10.329 @sf 17 r 118 c -2(ariables)m 16(to)m cmtt10.329 @sf 18(REAL)m cmr10.329 @sf 44 c 18(and)m 18(substituting)m cmtt10.329 @sf 225 1241 p (SODR)s cmr10.329 @sf 10(for)m cmtt10.329 @sf 11(DODR)m cmr10.329 @sf 10(and)m cmtt10.329 @sf 11(SODRC)m cmr10.329 @sf 11(for)m cmtt10.329 @sf 10(DODRC)m cmr10.329 @sf 46 c 18(Note)m 11(esp)m 1(ecially)m 10(that)m 11 r 98 c 121 c 10(using)m cmtt10.329 @sf 10(MAXN)m cmr10.329 @sf 44 c cmtt10.329 @sf 10(MAXM)m cmr10.329 @sf 44 c cmtt10.329 @sf 10(MAXNP)m cmr10.329 @sf 11(and)m cmtt10.329 @sf 225 1298 p (MAXNQ)s cmr10.329 @sf 15(to)m 16(sp)m 1(ecify)m 16(the)m 16(largest)m 15(problem)m 16(the)m 16(program)m 15(can)m 16(solv)m 101 c 15(without)m 15(mo)m 1(di\014cation,)m 15(and)m 225 1354 p 98 c 121 c 13(sp)m 1(ecifying)m cmtt10.329 @sf 14(LWORK)m cmr10.329 @sf 14(and)m cmtt10.329 @sf 14(LIWORK)m cmr10.329 @sf 14(exactly)m 14(as)m 13(sho)m (wn,)s 13(the)m 15(user)m 14(greatly)m 13(reduces)m 15(the)m 15 r 110 c (um)s -1 r 98 c 1(er)m 225 1411 p (of)s 15 r 99 c (hanges)s 14(that)m 14 r 109 c (ust)s 14 r 98 c 1 r 101 c 16(made)m 15(to)m 15(the)m 15(program)m 14(in)m 15(order)m 15(to)m 15(solv)m 101 c 13 r 97 c 15(larger)m 14(problem.)m cmbx10.329 @sf 225 1550 p (2.C.i.)s 15(Example)m 17(Problem)m 16(for)m 17(an)m 18(Explicit)m 17(Mo)m 1(del)m cmr10.329 @sf 225 1655 p (The)s 17(follo)m (w)s -1(ing)m 15(sample)m 16(program)m 16(in)m 118 c (o)s -1 r 107 c -1(es)m cmtt10.329 @sf 15(DODRC)m cmr10.329 @sf 16(to)m 17(solv)m 101 c 15(example)m 16(3.2.2)m 16(on)m 17(pages)m 16(230-238)m 225 1711 p (of)s 15([F)m -3(uller,)m 13(1987].)m 19(The)m 15(data)m 15 r 40 c cmmi10.329 @sf 120 c cmmi8.300 @sf 810 1718 p 105 c cmmi10.329 @sf 824 1711 p 59 c 8 r 121 c cmmi8.300 @sf 867 1718 p 105 c cmr10.329 @sf 880 1711 p 41 c 15(are)m 15(the)m 16 r 112 c 1(ercen)m 116 c 15(saturation)m 13(of)m 15(nitrogen)m 15(gas)m 15(in)m 15 r 97 c 15(brine)m 225 1768 p (solution)s 9(forced)m 11(in)m (to)s 8(the)m 11 r 112 c 1(ores)m 10(of)m 10(sandstone,)m 11(and)m 11(the)m 10(observ)m (ed)s 10(compressional)m 9 r 119 c 97 c -1 r 118 c -1 r 101 c 8 r 118 c (elo)s 1(cit)m -1 r 121 c 225 1824 p (of)s 13(ultrasonic)m 12(signals)m 13(propagated)m 13(through)m 13(the)m 14(sandstone,)m 13(resp)m 1(ectiv)m (ely)s -3 r 46 c 17(These)m 14(data)m 13(\(listed)m 225 1881 p (in)s cmsy10.329 @sf 15 r 120 c cmr10.329 @sf (2.C.i.b\))s 13(are)m 15(mo)m 1(deled)m 16 r 98 c 121 c 14(the)m 15(explicit)m 15(function)m cmmi10.329 @sf 599 1977 p 121 c cmmi8.300 @sf 621 1984 p 105 c cmsy10.329 @sf 648 1977 p 25 c cmmi10.329 @sf 13 r 102 c cmr10.329 @sf 5 r 40 c cmmi10.329 @sf 120 c cmmi8.300 @sf 767 1984 p 105 c cmr10.329 @sf 781 1977 p 59 c cmmi10.329 @sf 8 r 12 c cmr10.329 @sf 2 r 41 c cmsy10.329 @sf 11 r 17 c cmmi10.329 @sf 13 r 12 c cmr8.300 @sf 933 1984 p 49 c cmr10.329 @sf 963 1977 p 43 c cmmi10.329 @sf 10 r 12 c cmr8.300 @sf 1034 1984 p 50 c cmr10.329 @sf 1054 1977 p 91 c cmmi10.329 @sf 101 c cmmi8.300 @sf 1088 1959 p 12 c cmr6.300 @sf 1108 1964 p 51 c cmmi8.300 @sf 1125 1959 p 120 c cmmi6.300 @sf 1145 1964 p 105 c cmsy10.329 @sf 1170 1977 p 0 c cmr10.329 @sf 10(1])m cmr8.300 @sf 1251 1959 p 50 c cmmi10.329 @sf 1270 1977 p 59 c 53 r 105 c cmr10.329 @sf 12 r 61 c 13 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 8 r 58 c 5 r 59 c 8(n:)m cmr10.329 @sf 225 2073 p (The)s 15(starting)m 14 r 118 c -2(alues)m 14(for)m 15(the)m 15(mo)m 1(del)m 15(parameters)m 15(are)m cmmi10.329 @sf 789 2169 p 12 c cmr10.329 @sf 44 r 61 c 41(\(1500)m cmmi10.329 @sf 58 c cmr10.329 @sf 48 c cmmi10.329 @sf 59 c cmsy10.329 @sf 8 r 0 c cmr10.329 @sf (50)s cmmi10.329 @sf -1 r 58 c cmr10.329 @sf 48 c cmmi10.329 @sf 59 c cmsy10.329 @sf 7 r 0 c cmr10.329 @sf 48 c cmmi10.329 @sf 58 c cmr10.329 @sf (1)s -1 r 41 c cmr6.300 @sf 1349 2151 p 84 c cmr10.329 @sf 225 2335 p (and)s 15 r 1 c 15(is)m 15(initialized)m 14(to)m 14(zero.)m 225 2411 p 70 c -3(uller)m 18(notes)m 19(that)m 19(it)m 19(is)m 19(reasonable)m 19(to)m 19 r 98 c 1(eliev)m 101 c 19(that)m 18(the)m 20(saturation)m 18(measuremen)m (ts)s 18(of)m 19(0%)m 225 2467 p (and)s 21(100%)m 19(are)m 21(more)m 20(precise)m 20(than)m 21(the)m 21(other)m 20(saturation)m 19(measuremen)m (ts.)s 34 r 87 c -3 r 101 c 20(ha)m 118 c -1 r 101 c 19(th)m (us)s @eop %%Page: 40 54 40 @bop0 cmtt9.300 @sf [ 24 23 0 0 19.613] 80 @dc [ 24 23 -1 0 19.613] 82 @dc [<1FF07FFC7FFC783CF01EE00EE00EE00EE00EE00EE00EE00EE00EE00EE00EE00EE00EE00EF01E70 1C7FFC7FFC1FF0> 16 23 -2 0 19.613] 79 @dc [<07EE000FFE001FFE003E3E003C1E00781E00700E00F00E00E07F80E07F80E07F80E00000E00000 E00000E00000F00E00700E00780E003C1E003E3E001FFE000FFE0007E600> 24 23 -1 0 19.613] 71 @dc [ 24 23 -1 0 19.613] 65 @dc [ 24 23 0 0 19.613] 77 @dc [ 16 16 -2 0 19.613] 115 @dc [<1F8F807FFF807FFF80F87C00E03C00E01C00F01C007F9C007FFC001FFC0000FC00301C00787C00 7FF8007FF0003FC000> 24 16 -2 0 19.613] 97 @dc [ 24 16 0 0 19.613] 109 @dc [ 24 24 0 8 19.613] 112 @dc [ 16 23 -2 0 19.613] 108 @dc [<07E01FF83FFC7E1E780EF00EE000FFFEFFFEFFFEF00E781E7C3C3FFC1FF807E0> 16 16 -2 0 19.613] 101 @dc [<07F01FF83FFC7E1E780EF00EE000E000E000E000F00078187C3C3FFC1FFC07F8> 16 16 -2 0 19.613] 99 @dc [ 24 23 -1 0 19.613] 68 @dc [<07E00FF81FF83E3C3C1E780E700EF00EE000E000E000E000E000E000E000F00E700E780E3C1E3E 3E1FFE0FFE07E6> 16 23 -2 0 19.613] 67 @dc [ 16 23 -1 0 19.613] 75 @dc [ 24 16 0 0 19.613] 114 @dc [<07F0001FFC007FFF007C1F00F00780E00380E00380E00780F00F807FFF003FFE003FF800780000 77C0007FF0003FF8007C7C00783C00701C00701C00783C007C7F003FFF801FFF8007CF00> 24 25 -1 9 19.613] 103 @dc [<07F7E00FFFE01FFFE01C1F001C07001C07001C07001C07001C07001C07001C07001C07001C0700 FC3F00FC3F00FC3F00> 24 16 0 0 19.613] 117 @dc [ 24 16 0 0 19.613] 110 @dc [<01F003F807FC079E070E070E070E070007000700070007000700FFFCFFFCFFFC07000700070007 000700> 16 21 -1 0 19.613] 116 @dc [<7FFC7FFC7FFC0380038003800380038003800380038003800380FFFEFFFEFFFE03800380038C03 DE01FE00FE007C> 16 23 -1 0 19.613] 102 @dc [ 16 24 -3 0 19.613] 105 @dc [<07C01FF03FF87C7C701CF01EE00EE00EE00EE00EF01E701C783C3FF81FF007C0> 16 16 -2 0 19.613] 111 @dc [ 24 9 -1 -7 19.613] 61 @dc [<4000F000F8007E003F000F8007E003F000FC007E001E007E00FC03F007E00F803F007E00F800F0 004000> 16 21 -2 -1 19.613] 62 @dc [ 24 23 0 0 19.613] 104 @dc [<0FCFC01FFFC03FFFC07C7E00703E00F01E00E00E00E00E00E00E00E00E00F00E00781E007C3E00 3FFE001FFE000FCE00000E00000E00000E00000E00007E00007E00007E00> 24 23 -1 0 19.613] 100 @dc [<1CFC001FFE001FFF001F8F801E07801E03C01C01C01C01C01C01C01C01C01C03C01E03801F8F80 1FFF001FFE001CFC001C00001C00001C00001C0000FC0000FC0000FC0000> 24 23 0 0 19.613] 98 @dc [<03E00003E00003E0000770000770000770000630000E38000E38000E38001C1C001C1C001C1C00 FF7F80FF7F80FF7F80> 24 16 -1 0 19.613] 118 @dc [ 24 16 -1 0 19.613] 120 @dc [<3C00007E00007F00007F80007B800001C00001C00001C00001E00001E00001E000037000037000 0730000730000738000E38000E38000E1C001C1C001C1C00FF3F80FF3F80FF3F80> 24 24 -1 8 19.613] 121 @dc [<007FC0007FC0007FC0000E00000E00000E00000E00000E000FCE001FFE003FFE007C3E00781E00 F01E00E00E00E00E00E00E00E00E00F01E00781E007C3E003FFE001FFE0007EE00> 24 24 -1 8 19.613] 113 @dc [<0004001E003E00FC01F803E00FC01F807E00FC00F000FC007E001F800FC003E001F800FC003E00 1E0004> 16 21 -2 -1 19.613] 60 @dc [<1E3C001E3C001F7C001B6C001B6C001B6C003B6E003BEE003BEE003BEE00380E00380E00380E00 FF7F80FF7F80FF7F80> 24 16 -1 0 19.613] 119 @dc [<7070707070707070F078F078F078F078F078F0786030> 16 11 -3 -13 19.613] 34 @dc [<01C003C007800F001E003C003800780070007000F000E000E000E000E000E000E000E000F00070 007000780038003C001E000F00078003C001C0> 16 29 -6 3 19.613] 40 @dc [ 16 29 -3 3 19.613] 41 @dc [<7F00FFC0FFE0F1E060F00070007000700070007000700070007000700070007000700070007000 7000701FF01FF01FF00000000000000000006000F000F00060> 16 32 -2 8 19.613] 106 @dc [ 24 23 -1 0 19.613] 107 @dc [ 16 16 -1 0 19.613] 122 @dc [<00F80003FE0007FF000F8F800E03801E03C01C01C01C01C01C01C01C01C01C01C01C01C01C01C0 1C01C01C01C01C01C01C01C01C01C01C01C01C01C0FF8FF8FF8FF8FF8FF8> 24 23 1 0 19.613] 85 @dc [ 24 23 0 0 19.613] 66 @dc [ 24 23 -1 0 19.613] 76 @dc [ 24 23 0 0 19.613] 69 @dc [ 16 23 -2 0 19.613] 73 @dc [ 16 23 -2 0 19.613] 83 @dc [ 24 23 -1 0 19.613] 78 @dc [<0FF8000FF8000FF80001C00001C00001C00001C00001C00001C00001C00001C00001C00001C000 01C00001C00001C000E1C380E1C380E1C380E1C380FFFF80FFFF80FFFF80> 24 23 -1 0 19.613] 84 @dc 40 @bop1 cmr10.329 @sf 0 114 p (40)s 1319(Using)m 15(ODRP)m -3 r 65 c (CK)s 0 134 p 1725 2 ru 0 259 p (\\\014xed")s cmmi10.329 @sf 18 r 120 c cmr8.300 @sf 184 266 p 49 c cmr10.329 @sf 204 259 p 44 c cmmi10.329 @sf 18 r 120 c cmr8.300 @sf 261 266 p 50 c cmr10.329 @sf 299 259 p (and)s cmmi10.329 @sf 18 r 120 c cmr8.300 @sf 416 266 p (12)s cmr10.329 @sf 471 259 p (at)s 17(their)m 18(original)m 16 r 118 c -2(alues.)m 27(As)m 18 r 97 c 17(consequence,)m cmmi10.329 @sf 20 r 14 c cmsy8.300 @sf 1374 244 p 3 c cmr8.300 @sf 1372 270 p 49 c cmr10.329 @sf 1411 259 p 61 c cmmi10.329 @sf 18 r 14 c cmsy8.300 @sf 1486 244 p 3 c cmr8.300 @sf 1484 270 p 50 c cmr10.329 @sf 1522 259 p 61 c cmmi10.329 @sf 18 r 14 c cmsy8.300 @sf 1597 244 p 3 c cmr8.300 @sf 1595 270 p (12)s cmr10.329 @sf 1650 259 p 61 c 17 r 48 c 0 315 p (at)s 14(the)m 16(solution.)m 18 r 87 c -3 r 101 c 14(assume)m 15(the)m 15(remaining)m 15(observ)m (ed)s 14(data)m 14(are)m 15(all)m 14(of)m 15(equal)m 14(precision,)m 15(and)m 0 372 p (th)s (us)s 15(set)m cmmi10.329 @sf 17 r 119 c cmmi8.300 @sf 202 379 p 15 c cmr10.329 @sf 232 372 p 61 c cmmi10.329 @sf 15 r 119 c cmmi8.300 @sf 310 379 p 14 c cmr10.329 @sf 343 372 p 61 c 15 r 49 c 16(using)m 17(ODRP)m -3 r 65 c (CK's)s 15(structured)m 16(argumen)m 116 c 15(feature.)m 24(The)m 17(remaining)m 0 428 p (argumen)s (ts)s 13(are)m 15(set)m 15(to)m 15(their)m 14(default)m 15 r 118 c -2(alues.)m 19(\(See)m cmsy10.329 @sf 16 r 120 c cmr10.329 @sf (1.G.\))s cmbx10.329 @sf 0 568 p (2.C.i.a.)s 15(User)m 17(Supplied)m 17(Co)m 1(de)m cmtt9.300 @sf 196 662 p (PROGRAM)s 17(sample)m 78 753 p 99 c 39(ODRPACK)m 17(Argumen)m -1 r 116 c 18(Defini)m -1(tio)m -1(ns)m 78 799 p 99 c 118(==>)m 18(fcn)m 117(name)m 18(of)m 19(the)m 18(user)m 18(supplie)m -1 r 100 c 18(functi)m -1(on)m 17(subrout)m -1(ine)m 78 845 p 99 c 118(==>)m 18 r 110 c 157(number)m 17(of)m 19(observa)m -1(ti)m -1(ons)m 78 890 p 99 c 118(==>)m 18 r 109 c 157(column)m -1 r 115 c 18(of)m 18(data)m 19(in)m 18(the)m 19(explana)m -1(to)m -1(ry)m 17(variabl)m -1 r 101 c 78 936 p 99 c 118(==>)m 18(np)m 137(number)m 17(of)m 19(paramet)m -1(er)m -1 r 115 c 78 982 p 99 c 118(==>)m 18(nq)m 137(number)m 17(of)m 19(respons)m -1(es)m 17(per)m 18(observat)m -1(ion)m 78 1027 p 99 c 98(<==>)m 18(beta)m 97(functi)m -1(on)m 17(paramete)m -1(rs)m 78 1073 p 99 c 118(==>)m 18 r 121 c 157(respon)m -1(se)m 17(variable)m 78 1119 p 99 c 118(==>)m 18(ldy)m 117(leadin)m -1 r 103 c 18(dimens)m -1(ion)m 17(of)m 19(array)m 17 r 121 c 78 1164 p 99 c 118(==>)m 18 r 120 c 157(explan)m -1(ato)m -1(ry)m 17(variabl)m -1 r 101 c 78 1210 p 99 c 118(==>)m 18(ldx)m 117(leadin)m -1 r 103 c 18(dimens)m -1(ion)m 17(of)m 19(array)m 17 r 120 c 78 1256 p 99 c 118(==>)m 18(we)m 137("epsil)m -1(on")m 17(weights)m 78 1301 p 99 c 118(==>)m 18(ldwe)m 97(leadin)m -1 r 103 c 18(dimens)m -1(ion)m 17(of)m 19(array)m 17(we)m 78 1347 p 99 c 118(==>)m 18(ld2we)m 77(second)m 17(dimensi)m -1(on)m 17(of)m 19(array)m 18(we)m 78 1393 p 99 c 118(==>)m 18(wd)m 137("delta)m -1 r 34 c 18(weight)m -1 r 115 c 78 1438 p 99 c 118(==>)m 18(ldwd)m 97(leadin)m -1 r 103 c 18(dimens)m -1(ion)m 17(of)m 19(array)m 17(wd)m 78 1484 p 99 c 118(==>)m 18(ld2wd)m 77(second)m 17(dimensi)m -1(on)m 17(of)m 19(array)m 18(wd)m 78 1530 p 99 c 118(==>)m 18(ifixb)m 77(indica)m -1(tor)m -1 r 115 c 17(for)m 19("fixing)m -1 r 34 c 17(paramete)m -1(rs)m 17(\(beta\))m 78 1575 p 99 c 118(==>)m 18(ifixx)m 77(indica)m -1(tor)m -1 r 115 c 17(for)m 19("fixing)m -1 r 34 c 17(explanat)m -1(ory)m 17(variab)m -1(le)m 17(\(x\))m 78 1621 p 99 c 118(==>)m 18(ldifx)m 77(leadin)m -1 r 103 c 18(dimens)m -1(ion)m 17(of)m 19(array)m 17(ifixx)m 78 1667 p 99 c 118(==>)m 18(job)m 117(task)m 18(to)m 19(be)m 18(performe)m -1 r 100 c 78 1712 p 99 c 118(==>)m 18(ndigit)m 57(good)m 18(digits)m 17(in)m 19(subrout)m -1(in)m -1 r 101 c 18(functi)m -1(on)m 17(results)m 78 1758 p 99 c 118(==>)m 18(taufac)m 57(trust)m 17(region)m 18(initia)m -1(liz)m -1(at)m -1(ion)m 17(factor)m 78 1804 p 99 c 118(==>)m 18(sstol)m 77(sum)m 18(of)m 19(squares)m 17(converg)m -1(en)m -1(ce)m 17(criterio)m -1 r 110 c 78 1849 p 99 c 118(==>)m 18(partol)m 57(parame)m -1(ter)m 17(converg)m -1(en)m -1(ce)m 17(criterio)m -1 r 110 c 78 1895 p 99 c 118(==>)m 18(maxit)m 77(maximu)m -1 r 109 c 18(number)m 17(of)m 19(iterat)m -1(ion)m -1 r 115 c 78 1941 p 99 c 118(==>)m 18(iprint)m 57(print)m 17(control)m 78 1986 p 99 c 118(==>)m 18(lunerr)m 57(logica)m -1 r 108 c 18(unit)m 18(for)m 18(error)m 18(reports)m 78 2032 p 99 c 118(==>)m 18(lunrpt)m 57(logica)m -1 r 108 c 18(unit)m 18(for)m 18(computa)m -1(tio)m -1 r 110 c 18(report)m -1 r 115 c 78 2078 p 99 c 118(==>)m 18(stpb)m 97(step)m 18(sizes)m 17(for)m 19(finite)m 17(differen)m -1(ce)m 17(derivat)m -1(iv)m -1(es)m 17(wrt)m 19(beta)m 78 2123 p 99 c 118(==>)m 18(stpd)m 97(step)m 18(sizes)m 17(for)m 19(finite)m 17(differen)m -1(ce)m 17(derivat)m -1(iv)m -1(es)m 17(wrt)m 19(delta)m 78 2169 p 99 c 118(==>)m 18(ldstpd)m 57(leadin)m -1 r 103 c 18(dimens)m -1(ion)m 17(of)m 19(array)m 17(stpd)m 78 2215 p 99 c 118(==>)m 18(sclb)m 97(scale)m 17(values)m 18(for)m 18(paramet)m -1(ers)m 17(beta)m 78 2260 p 99 c 118(==>)m 18(scld)m 97(scale)m 17(values)m 18(for)m 18(errors)m 17(delta)m 18(in)m 19(explana)m -1(to)m -1(ry)m 17(variable)m 78 2306 p 99 c 118(==>)m 18(ldscld)m 57(leadin)m -1 r 103 c 18(dimens)m -1(ion)m 17(of)m 19(array)m 17(scld)m 78 2352 p 99 c 98(<==>)m 18(work)m 97(DOUBLE)m 17(PRECISI)m -1(ON)m 17(work)m 18(vector)m 78 2397 p 99 c 118(==>)m 18(lwork)m 77(dimens)m -1(ion)m 17(of)m 19(vector)m 17(work)m 78 2443 p 99 c 98(<==)m 38(iwork)m 77(INTEGE)m -1 r 82 c 18(work)m 18(vector)m @eop %%Page: 41 55 41 @bop0 cmtt9.300 @sf [<70F8FC1E1E3E7E7E7C38> 8 10 -6 5 19.613] 44 @dc [<01C00001C00001C00001C00001C00001C00001C000FFFF80FFFF80FFFF8001C00001C00001C000 01C00001C00001C00001C000> 24 17 -1 -3 19.613] 43 @dc [<1FC03FF07FF8F07CF01EF01E600E000E000E701E7C3C7FF87FF077E07000700070007000700070 007FFC7FFC7FFC> 16 23 -2 0 19.613] 53 @dc [<07C01FF03FF8783CF01EE00EE00EE00EE00E701C783C1FF00FE03FF8783CF01EE00EE00EF01E78 3C7FFC1FF00FE0> 16 23 -2 0 19.613] 56 @dc [<038003800380638CF39EFFFE3FF80FE00FE03FF8FFFEF39E638C038003800380> 16 16 -2 -3 19.613] 42 @dc [<03FF8003FF8003FF80003800003800003800003800FFFF80FFFF80FFFF80F03800783800383800 3C38001C38000E38000F380007380007380003B80001B80001F80000F800> 24 23 -1 0 19.613] 52 @dc [<07E01FF03FF83C7C781E700EF00EF00EF00EF01EF83EFFFCFFF8EFF0F080F000700078183C3C1F 3C0FFC07F801F0> 16 23 -2 0 19.613] 54 @dc [<07C00FE01FF03C783838701C701CF01EE00EE00EE00EE00EE00EE00EE00EE00E701C701C38383C 781FF00FE007C0> 16 23 -2 0 19.613] 48 @dc [<01C00003E00003E0000360000360000770000770000770000630000E38000E38000E38000E3800 1C1C001C1C001C1C001C1C001C1C00380E00380E00FE3F80FE3F80FE3F80> 24 23 -1 0 19.613] 86 @dc [ 24 23 -1 0 19.613] 88 @dc [ 16 3 -2 -10 19.613] 45 @dc [<70F8F8F870> 8 5 -7 0 19.613] 46 @dc 41 @bop1 cmr10.329 @sf 225 114 p (Using)s 15(ODRP)m -3 r 65 c (CK)s 1318(41)m 225 134 p 1725 2 ru cmtt9.300 @sf 303 259 p 99 c 118(==>)m 18(liwork)m 57(dimens)m -1(ion)m 17(of)m 19(vector)m 17(iwork)m 303 304 p 99 c 98(<==)m 38(info)m 97(stoppi)m -1(ng)m 17(conditio)m -1 r 110 c 303 396 p 99 c 39(Paramete)m -1(rs)m 17(specify)m -1(ing)m 17(maximu)m -1 r 109 c 18(proble)m -1 r 109 c 18(sizes)m 17(handled)m 17(by)m 19(this)m 18(driver)m 303 441 p 99 c 98(maxn)m 195(maximu)m -1 r 109 c 18(number)m 17(of)m 19(observ)m -1(ati)m -1(on)m -1 r 115 c 303 487 p 99 c 98(maxm)m 195(maximu)m -1 r 109 c 18(number)m 17(of)m 19(column)m -1 r 115 c 18(in)m 18(explanat)m -1(ory)m 17(variabl)m -1 r 101 c 303 533 p 99 c 98(maxnp)m 175(maximu)m -1 r 109 c 18(number)m 17(of)m 19(functi)m -1(on)m 17(paramete)m -1(rs)m 303 578 p 99 c 98(maxnq)m 175(maximu)m -1 r 109 c 18(number)m 17(of)m 19(respon)m -1(ses)m 17(per)m 18(observat)m -1(io)m -1 r 110 c 303 670 p 99 c 39(Paramete)m -1 r 114 c 17(Declarat)m -1(ion)m -1 r 115 c 17(and)m 19(Specifi)m -1(ca)m -1(tio)m -1(ns)m 421 715 p (INTEGER)s 76(ldifx,l)m -1(ds)m -1(cld)m -1(,l)m -1(dst)m -1(pd,)m -1(ld)m -1(wd,)m -1(ld)m -1(we,)m -1(ld)m -1(x,l)m -1(dy,)m -1(ld)m -1(2wd)m -1(,l)m -1(d2w)m -1(e,)m 402 761 p 43 c 215(liwork,)m -1(lw)m -1(ork)m -1(,m)m -1(axm)m -1(,ma)m -1(xn)m -1(,ma)m -1(xn)m -1(p,m)m -1(ax)m -1(nq)m 421 807 p (PARAMET)s -1(ER)m 17(\(maxm=5,)m -1(ma)m -1(xn=)m -1(25)m -1(,ma)m -1(xnp)m -1(=5)m -1(,ma)m -1(xn)m -1(q=1)m -1 r 44 c 402 852 p 43 c 215(ldy=max)m -1(n,)m -1(ldx)m -1(=m)m -1(axn)m -1 r 44 c 402 898 p 43 c 215(ldwe=1,)m -1(ld)m -1(2we)m -1(=1)m -1(,ld)m -1(wd=)m -1(1,)m -1(ld2)m -1(wd)m -1(=1,)m 402 944 p 43 c 215(ldifx=m)m -1(ax)m -1(n,l)m -1(ds)m -1(tpd)m -1(=1,)m -1(ld)m -1(scl)m -1(d=)m -1(1,)m 402 989 p 43 c 215(lwork=1)m -1 r 56 c 17 r 43 c 20(11*max)m -1(np)m 17 r 43 c 19(maxnp**2)m 17 r 43 c 19(maxm)m 18 r 43 c 19(maxm**2)m 17 r 43 c 402 1035 p 43 c 333(4*maxn)m -1(*m)m -1(axn)m -1 r 113 c 18 r 43 c 19(6*maxn)m -1(*ma)m -1(xm)m 17 r 43 c 19(2*maxn*m)m -1(ax)m -1(nq*)m -1(max)m -1(np)m 17 r 43 c 402 1080 p 43 c 333(2*maxn)m -1(*m)m -1(axn)m -1(q*m)m -1(ax)m -1 r 109 c 18 r 43 c 19(maxnq*)m -1(*2)m 17 r 43 c 402 1126 p 43 c 333(5*maxn)m -1 r 113 c 17 r 43 c 20(maxnq*)m -1(\(ma)m -1(xn)m -1(p+m)m -1(ax)m -1(m\))m 17 r 43 c 20(ldwe*l)m -1(d2)m -1(we*)m -1(max)m -1(nq)m -1 r 44 c 402 1172 p 43 c 215(liwork=)m -1(20)m -1(+ma)m -1(xn)m -1(p+m)m -1(axn)m -1(q*)m -1(\(ma)m -1(xn)m -1(p+m)m -1(ax)m -1(m\)\))m 303 1263 p 99 c 39(Variable)m 17(Declar)m -1(ati)m -1(ons)m 421 1309 p (INTEGER)s 194(i,info)m -1(,i)m -1(pri)m -1(nt,)m -1(j,)m -1(job)m -1(,l)m -1(,lu)m -1(ne)m -1(rr,)m -1(lun)m -1(rp)m -1(t,m)m -1(,m)m -1(axi)m -1(t,n)m -1 r 44 c 402 1354 p 43 c 333(ndigit)m -1(,n)m -1(p,n)m -1 r 113 c 421 1400 p (INTEGER)s 194(ifixb\()m -1(ma)m -1(xnp)m -1(\),i)m -1(fi)m -1(xx\()m -1(ld)m -1(ifx)m -1(,m)m -1(axm)m -1(\),i)m -1(wo)m -1(rk\()m -1(li)m -1(wor)m -1(k\))m 421 1446 p (DOUBLE)s 17(PRECISIO)m -1 r 78 c 18(partol)m -1(,s)m -1(sto)m -1(l,t)m -1(au)m -1(fac)m 421 1491 p (DOUBLE)s 17(PRECISIO)m -1 r 78 c 18(beta\(m)m -1(ax)m -1(np\))m -1(,sc)m -1(lb)m -1(\(ma)m -1(xn)m -1(p\),)m -1(sc)m -1(ld\()m -1(lds)m -1(cl)m -1(d,m)m -1(ax)m -1(m\),)m 402 1537 p 43 c 333(stpb\(m)m -1(ax)m -1(np\))m -1(,st)m -1(pd)m -1(\(ld)m -1(st)m -1(pd,)m -1(ma)m -1(xm\))m -1 r 44 c 402 1583 p 43 c 333(wd\(ldw)m -1(d,)m -1(ld2)m -1(wd,)m -1(ma)m -1(xm\))m -1(,w)m -1(e\(l)m -1(dw)m -1(e,l)m -1(d2w)m -1(e,)m -1(max)m -1(nq)m -1(\),)m 402 1628 p 43 c 333(work\(l)m -1(wo)m -1(rk\))m -1(,x\()m -1(ld)m -1(x,m)m -1(ax)m -1(m\),)m -1(y\()m -1(ldy)m -1(,ma)m -1(xn)m -1(q\))m 421 1674 p (EXTERNA)s -1 r 76 c 175(fcn)m 303 1811 p 99 c 39(Specify)m 17(default)m 17(values)m 17(for)m 19(dodrc)m 18(argume)m -1(nt)m -1 r 115 c 421 1857 p (we\(1,1,)s -1(1\))m 37 r 61 c 19(-1.0d0)m 421 1902 p (wd\(1,1,)s -1(1\))m 37 r 61 c 19(-1.0d0)m 421 1948 p (ifixb\(1)s -1 r 41 c 57 r 61 c 19(-1)m 421 1994 p (ifixx\(1)s -1(,1\))m 17 r 61 c 19(-1)m 421 2039 p (job)s 156 r 61 c 19(-1)m 421 2085 p (ndigit)s 96 r 61 c 19(-1)m 421 2131 p (taufac)s 96 r 61 c 19(-1.0d0)m 421 2176 p (sstol)s 116 r 61 c 19(-1.0d0)m 421 2222 p (partol)s 96 r 61 c 19(-1.0d0)m 421 2268 p (maxit)s 116 r 61 c 19(-1)m 421 2313 p (iprint)s 96 r 61 c 19(-1)m 421 2359 p (lunerr)s 96 r 61 c 19(-1)m 421 2405 p (lunrpt)s 96 r 61 c 19(-1)m 421 2450 p (stpb\(1\))s 76 r 61 c 19(-1.0d0)m @eop %%Page: 42 56 42 @bop0 cmtt9.300 @sf [<1F803FE07FF078F87878303C001C001E020E1FEE3FFE7FFEF83EF01EE00EE01EE01EF01CF03C7C 783FF81FF00FC0> 16 23 -2 0 19.613] 57 @dc [ 8 12 -7 -11 19.613] 39 @dc [ 24 23 -1 0 19.613] 70 @dc [<70F8F8F87000000000000070F8F8F870> 8 16 -7 0 19.613] 58 @dc 42 @bop1 cmr10.329 @sf 0 114 p (42)s 1319(Using)m 15(ODRP)m -3 r 65 c (CK)s 0 134 p 1725 2 ru cmtt9.300 @sf 196 259 p (stpd\(1,)s -1(1\))m 37 r 61 c 19(-1.0d0)m 196 304 p (sclb\(1\))s 76 r 61 c 19(-1.0d0)m 196 350 p (scld\(1,)s -1(1\))m 37 r 61 c 19(-1.0d0)m 78 441 p 99 c 39(Set)m 19(up)m 19(ODRPAC)m -1 r 75 c 17(report)m 18(files)m 196 487 p (lunerr)s 37 r 61 c 58 r 57 c 196 533 p (lunrpt)s 37 r 61 c 58 r 57 c 196 578 p (OPEN)s 18(\(unit=9)m -1(,fi)m -1(le=)m -1('r)m -1(epo)m -1(rt)m -1(1'\))m 78 670 p 99 c 39(Read)m 18(problem)m 17(data,)m 18(and)m 18(set)m 19(nondefa)m -1(ul)m -1 r 116 c 18(value)m 17(for)m 19(argume)m -1(nt)m 17(ifixx)m 196 715 p (OPEN)s 18(\(unit=5)m -1(,fi)m -1(le=)m -1('d)m -1(ata)m -1(1')m -1 r 41 c 196 761 p (READ)s 18(\(5,FMT=)m -1(*\))m 17(n,m,np,n)m -1 r 113 c 196 807 p (READ)s 18(\(5,FMT=)m -1(*\))m 17(\(beta\(i\))m -1(,i)m -1(=1,)m -1(np\))m 196 852 p (DO)s 19(10)m 19(i=1,n)m 255 898 p (READ)s 18(\(5,FMT=)m -1(*\))m 17(\(x\(i,j\))m -1(,j=)m -1(1,m)m -1(\),)m -1(\(y\()m -1(i,)m -1(l\),)m -1(l=1)m -1(,n)m -1(q\))m 255 944 p (if)s 19(\(x\(i,1)m -1(\).e)m -1(q.0)m -1(.0)m -1(d0)m 17(.or.)m 18(x\(i,1\).e)m -1(q.)m -1(100)m -1(.0d)m -1(0\))m 17(then)m 314 989 p (ifixx\()s -1(i,1)m -1 r 41 c 18 r 61 c 19 r 48 c 255 1035 p (else)s 314 1080 p (ifixx\()s -1(i,1)m -1 r 41 c 18 r 61 c 19 r 49 c 255 1126 p (end)s 18(if)m 137 1172 p (10)s 19(CONTINU)m -1 r 69 c 78 1263 p 99 c 39(Specify)m 17(task:)m 18(explici)m -1 r 116 c 17(orthogon)m -1(al)m 17(distanc)m -1 r 101 c 18(regres)m -1(sio)m -1 r 110 c 78 1309 p 99 c 314(with)m 18(user)m 18(supplie)m -1 r 100 c 18(deriva)m -1(ti)m -1(ves)m 17(\(checke)m -1(d\))m 78 1354 p 99 c 314(covaria)m -1(nc)m -1 r 101 c 18(matrix)m 17(constru)m -1(ct)m -1(ed)m 17(with)m 18(recomput)m -1(ed)m 17(derivat)m -1(ive)m -1 r 115 c 78 1400 p 99 c 314(delta)m 18(initia)m -1(li)m -1(zed)m 17(to)m 19(zero)m 78 1446 p 99 c 314(not)m 18 r 97 c 20(restar)m -1 r 116 c 78 1491 p 99 c 39(and)m 19(indica)m -1(te)m 17(short)m 18(initial)m 17(report)m 78 1537 p 99 c 294(short)m 18(iterati)m -1(on)m 17(reports)m 17(every)m 18(iterat)m -1(ion)m -1 r 44 c 17(and)m 78 1583 p 99 c 294(long)m 18(final)m 18(report)m 196 1628 p (job)s 97 r 61 c 19(00020)m 196 1674 p (iprint)s 37 r 61 c 19(1112)m 78 1765 p 99 c 39(Compute)m 17(solutio)m -1 r 110 c 196 1811 p (CALL)s 18(dodrc\(f)m -1(cn,)m 177 1857 p 43 c 215(n,m,np,)m -1(nq)m -1 r 44 c 177 1902 p 43 c 215(beta,)m 177 1948 p 43 c 215(y,ldy,x)m -1(,l)m -1(dx,)m 177 1994 p 43 c 215(we,ldwe)m -1(,l)m -1(d2w)m -1(e,)m -1(wd,)m -1(ldw)m -1(d,)m -1(ld2)m -1(wd)m -1 r 44 c 177 2039 p 43 c 215(ifixb,i)m -1(fi)m -1(xx,)m -1(ld)m -1(ifx)m -1 r 44 c 177 2085 p 43 c 215(job,ndi)m -1(gi)m -1(t,t)m -1(au)m -1(fac)m -1 r 44 c 177 2131 p 43 c 215(sstol,p)m -1(ar)m -1(tol)m -1(,m)m -1(axi)m -1(t,)m 177 2176 p 43 c 215(iprint,)m -1(lu)m -1(ner)m -1(r,)m -1(lun)m -1(rpt)m -1 r 44 c 177 2222 p 43 c 215(stpb,st)m -1(pd)m -1(,ld)m -1(st)m -1(pd,)m 177 2268 p 43 c 215(sclb,sc)m -1(ld)m -1(,ld)m -1(sc)m -1(ld,)m 177 2313 p 43 c 215(work,lw)m -1(or)m -1(k,i)m -1(wo)m -1(rk,)m -1(liw)m -1(or)m -1(k,)m 177 2359 p 43 c 215(info\))m 196 2405 p (END)s @eop %%Page: 43 57 43 @bop0 cmtt9.300 @sf [<3FC07FE0FFF0F078F0386038003800380038003800380038003800380038003800380038003800 3807FF07FF07FF> 16 23 -2 0 19.613] 74 @dc [<60F0F83C1C3C7C7C7C38000000000000387C7C7C38> 8 21 -6 5 19.613] 59 @dc [ 24 23 -1 0 19.613] 72 @dc 43 @bop1 cmr10.329 @sf 225 114 p (Using)s 15(ODRP)m -3 r 65 c (CK)s 1318(43)m 225 134 p 1725 2 ru cmtt9.300 @sf 421 304 p (SUBROUT)s -1(INE)m 17(fcn\(n,m)m -1(,n)m -1(p,n)m -1(q,)m 402 350 p 43 c 293(ldn,ldm,)m -1(ld)m -1(np,)m 402 396 p 43 c 293(beta,xpl)m -1(us)m -1(d,)m 402 441 p 43 c 293(ifixb,if)m -1(ix)m -1(x,l)m -1(dif)m -1(x,)m 402 487 p 43 c 293(ideval,f)m -1(,f)m -1(jac)m -1(b,f)m -1(ja)m -1(cd,)m 402 533 p 43 c 293(istop\))m 303 624 p 99 c 39(Subrouti)m -1(ne)m 17(Argumen)m -1(ts)m 303 670 p 99 c 118(==>)m 18 r 110 c 157(number)m 17(of)m 19(observa)m -1(ti)m -1(ons)m 303 715 p 99 c 118(==>)m 18 r 109 c 157(number)m 17(of)m 19(columns)m 17(in)m 19(explan)m -1(at)m -1(ory)m 17(variabl)m -1 r 101 c 303 761 p 99 c 118(==>)m 18(np)m 137(number)m 17(of)m 19(paramet)m -1(er)m -1 r 115 c 303 807 p 99 c 118(==>)m 18(nq)m 137(number)m 17(of)m 19(respons)m -1(es)m 17(per)m 18(observat)m -1(ion)m 303 852 p 99 c 118(==>)m 18(ldn)m 117(leadin)m -1 r 103 c 18(dimens)m -1(ion)m 17(declar)m -1(ato)m -1 r 114 c 17(equal)m 18(or)m 19(exceedi)m -1(ng)m 17 r 110 c 303 898 p 99 c 118(==>)m 18(ldm)m 117(leadin)m -1 r 103 c 18(dimens)m -1(ion)m 17(declar)m -1(ato)m -1 r 114 c 17(equal)m 18(or)m 19(exceedi)m -1(ng)m 17 r 109 c 303 944 p 99 c 118(==>)m 18(ldnp)m 97(leadin)m -1 r 103 c 18(dimens)m -1(ion)m 17(declar)m -1(ato)m -1 r 114 c 17(equal)m 18(or)m 19(exceedi)m -1(ng)m 17(np)m 303 989 p 99 c 118(==>)m 18(beta)m 97(curren)m -1 r 116 c 18(values)m 17(of)m 19(parame)m -1(ter)m -1 r 115 c 303 1035 p 99 c 118(==>)m 18(xplusd)m 57(curren)m -1 r 116 c 18(value)m 17(of)m 19(explana)m -1(tor)m -1 r 121 c 17(variable)m -1 r 44 c 18(i.e.,)m 17 r 120 c 20 r 43 c 19(delta)m 303 1080 p 99 c 118(==>)m 18(ifixb)m 77(indica)m -1(tor)m -1 r 115 c 17(for)m 19("fixing)m -1 r 34 c 17(paramete)m -1(rs)m 17(\(beta\))m 303 1126 p 99 c 118(==>)m 18(ifixx)m 77(indica)m -1(tor)m -1 r 115 c 17(for)m 19("fixing)m -1 r 34 c 17(explanat)m -1(ory)m 17(variab)m -1(le)m 17(\(x\))m 303 1172 p 99 c 118(==>)m 18(ldifx)m 77(leadin)m -1 r 103 c 18(dimens)m -1(ion)m 17(of)m 19(array)m 17(ifixx)m 303 1217 p 99 c 118(==>)m 18(ideval)m 57(indica)m -1(tor)m 17(for)m 18(selectin)m -1 r 103 c 17(computat)m -1(ion)m 17(to)m 19(be)m 18(performe)m -1 r 100 c 303 1263 p 99 c 98(<==)m 38 r 102 c 157(predic)m -1(ted)m 17(functio)m -1 r 110 c 17(values)m 303 1309 p 99 c 98(<==)m 38(fjacb)m 77(Jacobi)m -1(an)m 17(with)m 18(respect)m 17(to)m 19(beta)m 303 1354 p 99 c 98(<==)m 38(fjacd)m 77(Jacobi)m -1(an)m 17(with)m 18(respect)m 17(to)m 19(errors)m 17(delta)m 303 1400 p 99 c 98(<==)m 38(istop)m 77(stoppi)m -1(ng)m 17(conditio)m -1(n,)m 17(where)m 303 1446 p 99 c 412 r 48 c 19(means)m 18(current)m 17(beta)m 18(and)m 18(x+delta)m 17(were)m 303 1491 p 99 c 451(accepta)m -1(ble)m 17(and)m 18(values)m 18(were)m 18(comput)m -1(ed)m 17(successf)m -1(ul)m -1(ly)m 303 1537 p 99 c 412 r 49 c 19(means)m 18(current)m 17(beta)m 18(and)m 18(x+delta)m 17(are)m 303 1583 p 99 c 451(not)m 19(accept)m -1(abl)m -1(e;)m 37(ODRPAC)m -1 r 75 c 17(should)m 18(select)m 17(values)m 303 1628 p 99 c 451(closer)m 17(to)m 19(most)m 18(recently)m 17(used)m 18(values)m 17(if)m 19(possibl)m -1 r 101 c 303 1674 p 99 c 392(-1)m 19(means)m 18(current)m 17(beta)m 18(and)m 18(x+delta)m 17(are)m 303 1720 p 99 c 451(not)m 19(accept)m -1(abl)m -1(e;)m 37(ODRPAC)m -1 r 75 c 17(should)m 18(stop)m 303 1811 p 99 c 39(Input)m 18(argumen)m -1(ts)m -1 r 44 c 18(not)m 18(to)m 19(be)m 19(changed)m 17(by)m 19(this)m 18(routin)m -1(e:)m 421 1857 p (INTEGER)s 194(i,idev)m -1(al)m -1(,is)m -1(top)m -1(,l)m -1(,ld)m -1(if)m -1(x,l)m -1(dm)m -1(,ld)m -1(n,l)m -1(dn)m -1(p,m)m -1(,n)m -1(,np)m -1(,nq)m 421 1902 p (DOUBLE)s 17(PRECISIO)m -1 r 78 c 18(beta\(n)m -1(p\))m -1(,xp)m -1(lus)m -1(d\()m -1(ldn)m -1(,m)m -1 r 41 c 421 1948 p (INTEGER)s 194(ifixb\()m -1(np)m -1(\),i)m -1(fix)m -1(x\()m -1(ldi)m -1(fx)m -1(,m\))m 303 1994 p 99 c 39(Output)m 18(argume)m -1(nt)m -1(s:)m 421 2039 p (DOUBLE)s 17(PRECISIO)m -1 r 78 c 18(f\(ldn,)m -1(nq)m -1(\),f)m -1(jac)m -1(b\()m -1(ldn)m -1(,l)m -1(dnp)m -1(,n)m -1(q\),)m -1(fja)m -1(cd)m -1(\(ld)m -1(n,)m -1(ldm)m -1(,nq)m -1 r 41 c 303 2085 p 99 c 39(Local)m 18(variabl)m -1(es)m 421 2131 p (INTRINS)s -1(IC)m 155(exp)m 303 2268 p 99 c 39(Check)m 18(for)m 18(unaccept)m -1(abl)m -1 r 101 c 17(values)m 18(for)m 18(this)m 18(problem)m 421 2313 p (IF)s 19(\(beta\(1)m -1 r 41 c 17(.LT.)m 19(0.0d0\))m 17(THEN)m 480 2359 p (istop)s 18 r 61 c 19 r 49 c 480 2405 p (return)s 421 2450 p (ELSE)s @eop %%Page: 44 58 44 @bop0 cmtt9.300 @sf [ 16 29 -2 3 19.613] 47 @dc 44 @bop1 cmr10.329 @sf 0 114 p (44)s 1319(Using)m 15(ODRP)m -3 r 65 c (CK)s 0 134 p 1725 2 ru cmtt9.300 @sf 255 259 p (istop)s 18 r 61 c 19 r 48 c 196 304 p (END)s 19(IF)m 78 396 p 99 c 39(Compute)m 17(predict)m -1(ed)m 17(values)m 196 441 p (IF)s 19(\(MOD\(id)m -1(ev)m -1(al,)m -1(10\))m -1(.G)m -1(E.1)m -1 r 41 c 17(THEN)m 255 487 p (DO)s 19(110)m 18 r 108 c 19 r 61 c 20(1,nq)m 314 533 p (DO)s 19(100)m 18 r 105 c 19 r 61 c 20(1,n)m 373 578 p (f\(i,l\))s 17 r 61 c 19(beta\(1\))m 17 r 43 c 177 624 p 43 c 352(beta\(2\))m -1(*\(e)m -1(xp\()m -1(be)m -1(ta\()m -1(3\))m -1(*xp)m -1(lus)m -1(d\()m -1(i,1)m -1(\)\))m 17 r 45 c 19(1.0d0\)**)m -1 r 50 c 118 670 p (100)s 136(CONTIN)m -1(UE)m 118 715 p (110)s 77(CONTINU)m -1 r 69 c 196 761 p (END)s 19(IF)m 78 852 p 99 c 39(Compute)m 17(derivat)m -1(ive)m -1 r 115 c 18(with)m 18(respec)m -1 r 116 c 18(to)m 18(beta)m 196 898 p (IF)s 19(\(MOD\(id)m -1(ev)m -1(al/)m -1(10,)m -1(10)m -1(\).G)m -1(E.)m -1(1\))m 17(THEN)m 255 944 p (DO)s 19(210)m 18 r 108 c 19 r 61 c 20(1,nq)m 314 989 p (DO)s 19(200)m 18 r 105 c 19 r 61 c 20(1,n)m 373 1035 p (fjacb\()s -1(i,1)m -1(,l)m -1 r 41 c 18 r 61 c 19(1.0d0)m 373 1080 p (fjacb\()s -1(i,2)m -1(,l)m -1 r 41 c 18 r 61 c 19(\(exp\(be)m -1(ta)m -1(\(3\))m -1(*x)m -1(plu)m -1(sd\()m -1(i,)m -1(1\)\))m 17 r 45 c 19(1.0d0\)*)m -1(*2)m 373 1126 p (fjacb\()s -1(i,3)m -1(,l)m -1 r 41 c 18 r 61 c 19(beta\(2\))m -1(*2)m -1 r 42 c 177 1172 p 43 c 470(\(exp\(be)m -1(ta)m -1(\(3\))m -1(*x)m -1(plu)m -1(sd\()m -1(i,)m -1(1\)\))m 17 r 45 c 19(1.0d0\)*)m 177 1217 p 43 c 470(exp\(bet)m -1(a\()m -1(3\)*)m -1(xp)m -1(lus)m -1(d\(i)m -1(,1)m -1(\)\)*)m -1(xp)m -1(lus)m -1(d\()m -1(i,1)m -1 r 41 c 118 1263 p (200)s 136(CONTIN)m -1(UE)m 118 1309 p (210)s 77(CONTINU)m -1 r 69 c 196 1354 p (END)s 19(IF)m 78 1446 p 99 c 39(Compute)m 17(derivat)m -1(ive)m -1 r 115 c 18(with)m 18(respec)m -1 r 116 c 18(to)m 18(delta)m 196 1491 p (IF)s 19(\(MOD\(id)m -1(ev)m -1(al/)m -1(100)m -1(,1)m -1(0\).)m -1(GE)m -1(.1\))m 17(THEN)m 255 1537 p (DO)s 19(310)m 18 r 108 c 19 r 61 c 20(1,nq)m 314 1583 p (DO)s 19(300)m 18 r 105 c 19 r 61 c 20(1,n)m 373 1628 p (fjacd\()s -1(i,1)m -1(,l)m -1 r 41 c 18 r 61 c 19(beta\(2\))m -1(*2)m -1 r 42 c 177 1674 p 43 c 470(\(exp\(be)m -1(ta)m -1(\(3\))m -1(*x)m -1(plu)m -1(sd\()m -1(i,)m -1(1\)\))m 17 r 45 c 19(1.0d0\)*)m 177 1720 p 43 c 470(exp\(bet)m -1(a\()m -1(3\)*)m -1(xp)m -1(lus)m -1(d\(i)m -1(,1)m -1(\)\)*)m -1(be)m -1(ta\()m -1(3\))m 118 1765 p (300)s 136(CONTIN)m -1(UE)m 118 1811 p (310)s 77(CONTINU)m -1 r 69 c 196 1857 p (END)s 19(IF)m 196 1948 p (RETURN)s 196 1994 p (END)s @eop %%Page: 45 59 45 @bop0 cmbx10.329 @sf [<0038007000E001C003C0078007000F001E001E003C003C003C007800780078007800F800F000F0 00F000F000F000F000F000F000F000F80078007800780078003C003C003C001E001E000F000700 078003C001C000E000700038> 16 45 -3 11 20.328] 40 @dc [ 16 45 -3 11 20.328] 41 @dc cmtt10.329 @sf [<07F8001FFE007FFF007C0F80F007C0F003E0F001E0F000E06000E00000E00001E00001E03803C0 3E07C03FFF803FFF003BFC003800003800003800003800003800003800003800003800003FFF80 3FFF803FFF80> 24 28 -2 0 23.863] 53 @dc [<01F00007FC000FFE001F1F001C07003803807803C07001C07001C0F001E0E000E0E000E0E000E0 E000E0E000E0E000E0E000E0E000E0E000E07001C07001C07803C03803801C07001F1F000FFE00 07FC0001F000> 24 28 -2 0 23.863] 48 @dc [<78FCFCFCFC78> 8 6 -9 0 23.863] 46 @dc [<03F8000FFE001FFF003E0F803C07C07803E07801E07000E0F000E0F000E0F000E0F001E0F803E0 FC03C0FE0F80FFFF80EFFE00F3F800F000007800007800003C03C03E03C01F03C00FC3C007FFC0 03FF80007E00> 24 28 -2 0 23.863] 54 @dc [<03F8000FFE001FFF003E0F807803C07001C0E000E0E000E0E000E0E000E0F001E07001C03C0780 1F1F000FFE0007FC001FFF003C07803803807001C07001C07001C07001C03803803E0F801FFF00 0FFE0003F800> 24 28 -2 0 23.863] 56 @dc [<03800003800003800003800003800003800003C00003C00003C00001C00001C00001E00001E000 00E00000F00000F000007800007800003C00003C00001E00001F00000F00E00780E007C0FFFFE0 FFFFE0FFFFE0E00000> 24 29 -2 0 23.863] 55 @dc [<00FFF800FFF800FFF8000700000700000700000700000700000700FFFFF8FFFFF8FFFFF8F00700 7807003807003C07001E07000E070007070007870003C70001C70001E70000F700007700007F00 003F00001F00> 24 28 -1 0 23.863] 52 @dc [<0FE0003FF8007FFC00783F00781F007807807807C00003C00001C00001E00001E003F8E00FFEE0 3FFFE07E0FE07803E0F001E0F001E0E001E0E001E0E001C0F003C0F003C07807807E0F803FFF00 0FFE0003F800> 24 28 -2 0 23.863] 57 @dc 45 @bop1 cmr10.329 @sf 225 114 p (Using)s 15(ODRP)m -3 r 65 c (CK)s 1318(45)m 225 134 p 1725 2 ru cmbx10.329 @sf 225 259 p (2.C.i.b.)s 15(User)m 17(Supplied)m 16(Data)m 19(\(\014le)m cmtt10.329 @sf 17(data1)m cmbx10.329 @sf 41 c cmtt10.329 @sf 392 364 p (12)s 95 r 49 c 96 r 51 c 95 r 49 c 320 420 p (1500.0)s 47(-50.0)m 47(-0.1)m 416 477 p (0.0)s 71(1265.0)m 416 533 p (0.0)s 71(1263.6)m 416 590 p (5.0)s 71(1258.0)m 416 646 p (7.0)s 71(1254.0)m 416 703 p (7.5)s 71(1253.0)m 392 759 p (10.0)s 71(1249.8)m 392 816 p (16.0)s 71(1237.0)m 392 872 p (26.0)s 71(1218.0)m 392 929 p (30.0)s 71(1220.6)m 392 985 p (34.0)s 71(1213.8)m 392 1041 p (34.5)s 71(1215.5)m 368 1098 p (100.0)s 71(1212.0)m @eop %%Page: 46 60 46 @bop0 46 @bop1 cmr10.329 @sf 0 114 p (46)s 1319(Using)m 15(ODRP)m -3 r 65 c (CK)s 0 134 p 1725 2 ru cmbx10.329 @sf 0 259 p (2.C.i.c.)s 15(Rep)m 1(ort)m 18(Generated)m 18 r 98 c 121 c 16(ODRP)m -3 r 65 c -1(C)m -1 r 75 c 16(\(\014le)m cmtt10.329 @sf 17(report1)m cmbx10.329 @sf 41 c cmtt9.300 @sf 78 353 p (********)s -1(***)m -1(**)m -1(***)m -1(**)m -1(***)m -1(***)m -1(**)m -1(***)m -1(**)m -1(***)m -1(***)m -1(**)m -1(***)m -1(**)m -1(***)m -1(***)m -1(**)m -1(***)m 78 399 p 42 c 20(odrpac)m -1 r 107 c 18(versio)m -1 r 110 c 17(2.01)m 19(of)m 18(06-19-92)m 17(\(double)m 17(precisi)m -1(on)m -1 r 41 c 18 r 42 c 78 445 p (********)s -1(***)m -1(**)m -1(***)m 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115 c 18(in)m 19(explan)m -1(at)m -1(ory)m 17(variabl)m -1 r 101 c 78 624 p 99 c 98(maxnp)m 175(maximu)m -1 r 109 c 18(number)m 17(of)m 19(functi)m -1(on)m 17(paramete)m -1(rs)m 78 670 p 99 c 98(maxnq)m 175(maximu)m -1 r 109 c 18(number)m 17(of)m 19(respon)m -1(ses)m 17(per)m 18(observat)m -1(io)m -1 r 110 c 78 761 p 99 c 39(Paramete)m -1 r 114 c 17(Declarat)m -1(ion)m -1 r 115 c 17(and)m 19(Specifi)m -1(ca)m -1(tio)m -1(ns)m 196 807 p (INTEGER)s 76(ldwd,ld)m -1(we)m -1(,ld)m -1(x,)m -1(ldy)m -1(,ld)m -1(2w)m -1(d,l)m -1(d2)m -1(we,)m 177 852 p 43 c 215(liwork,)m -1(lw)m -1(ork)m -1(,m)m -1(axm)m -1(,ma)m -1(xn)m -1(,ma)m -1(xn)m -1(p,m)m -1(axn)m -1 r 113 c 196 898 p (PARAMET)s -1(ER)m 17(\(maxm=5,)m -1(ma)m -1(xn=)m -1(25)m -1(,ma)m -1(xnp)m -1(=5)m -1(,ma)m -1(xn)m -1(q=2)m -1 r 44 c 177 944 p 43 c 215(ldy=max)m -1(n,)m -1(ldx)m -1(=m)m -1(axn)m -1 r 44 c 177 989 p 43 c 215(ldwe=1,)m -1(ld)m -1(2we)m -1(=1)m -1(,ld)m -1(wd=)m -1(1,)m -1(ld2)m -1(wd)m -1(=1,)m 177 1035 p 43 c 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196 1446 p (DOUBLE)s 17(PRECISIO)m -1 r 78 c 18(beta\(m)m -1(ax)m -1(np\))m -1 r 44 c 177 1491 p 43 c 333(wd\(ldw)m -1(d,)m -1(ld2)m -1(wd,)m -1(ma)m -1(xm\))m -1(,w)m -1(e\(l)m -1(dwe)m -1(,l)m -1(d2w)m -1(e,)m -1(max)m -1(nq)m -1(\),)m 177 1537 p 43 c 333(work\(l)m -1(wo)m -1(rk\))m -1(,x\()m -1(ld)m -1(x,m)m -1(ax)m -1(m\),)m -1(y\(l)m -1(dy)m -1(,ma)m -1(xn)m -1(q\))m 196 1583 p (EXTERNA)s -1 r 76 c 175(fcn)m 78 1720 p 99 c 39(Specify)m 17(default)m 17(values)m 17(for)m 19(dodr)m 18(argumen)m -1(ts)m 196 1765 p (we\(1,1,)s -1(1\))m 37 r 61 c 19(-1.0d0)m 196 1811 p (wd\(1,1,)s -1(1\))m 37 r 61 c 19(-1.0d0)m 196 1857 p (job)s 156 r 61 c 19(-1)m 196 1902 p (iprint)s 96 r 61 c 19(-1)m 196 1948 p (lunerr)s 96 r 61 c 19(-1)m 196 1994 p (lunrpt)s 96 r 61 c 19(-1)m 78 2085 p 99 c 39(Set)m 19(up)m 19(ODRPAC)m -1 r 75 c 17(report)m 18(files)m 196 2131 p (lunerr)s 37 r 61 c 58 r 57 c 196 2176 p (lunrpt)s 37 r 61 c 58 r 57 c 196 2222 p (OPEN)s 18(\(unit=9)m -1(,fi)m -1(le=)m -1('r)m -1(epo)m -1(rt)m -1(2'\))m 78 2313 p 99 c 39(Read)m 18(problem)m 17(data)m 196 2359 p (OPEN)s 18(\(unit=5)m -1(,fi)m -1(le=)m -1('d)m -1(ata)m -1(2')m -1 r 41 c 196 2405 p (READ)s 18(\(5,FMT=)m -1(*\))m 17(n,m,np,n)m -1 r 113 c 196 2450 p (READ)s 18(\(5,FMT=)m -1(*\))m 17(\(beta\(i\))m -1(,i)m -1(=1,)m -1(np\))m @eop %%Page: 51 65 51 @bop0 51 @bop1 cmr10.329 @sf 225 114 p (Using)s 15(ODRP)m -3 r 65 c (CK)s 1318(51)m 225 134 p 1725 2 ru cmtt9.300 @sf 421 259 p (DO)s 19(10)m 19(i=1,n)m 480 304 p (READ)s 18(\(5,FMT=)m -1(*\))m 17(\(x\(i,j\))m -1(,j=)m -1(1,m)m -1 r 41 c 362 350 p (10)s 19(CONTINU)m -1 r 69 c 303 441 p 99 c 39(Specify)m 17(task:)m 18(implici)m -1 r 116 c 17(orthogon)m -1(al)m 17(distanc)m -1 r 101 c 18(regres)m -1(sio)m -1 r 110 c 303 487 p 99 c 314(with)m 18(forward)m 17(finite)m 17(differe)m -1(nce)m 17(derivat)m -1(iv)m -1(es)m 303 533 p 99 c 314(covaria)m -1(nc)m -1 r 101 c 18(matrix)m 17(constru)m -1(ct)m -1(ed)m 17(with)m 18(recomput)m -1(ed)m 17(derivat)m -1(ive)m -1 r 115 c 303 578 p 99 c 314(delta)m 18(initia)m -1(li)m -1(zed)m 17(to)m 19(zero)m 303 624 p 99 c 314(not)m 18 r 97 c 20(restar)m -1 r 116 c 421 670 p (job)s 97 r 61 c 19(00001)m 303 761 p 99 c 39(Compute)m 17(solutio)m -1 r 110 c 421 807 p (CALL)s 18(dodr\(fc)m -1(n,)m 402 852 p 43 c 215(n,m,np,)m -1(nq)m -1 r 44 c 402 898 p 43 c 215(beta,)m 402 944 p 43 c 215(y,ldy,x)m -1(,l)m -1(dx,)m 402 989 p 43 c 215(we,ldwe)m -1(,l)m -1(d2w)m -1(e,)m -1(wd,)m -1(ldw)m -1(d,)m -1(ld2)m -1(wd)m -1 r 44 c 402 1035 p 43 c 215(job,)m 402 1080 p 43 c 215(iprint,)m -1(lu)m -1(ner)m -1(r,)m -1(lun)m -1(rpt)m -1 r 44 c 402 1126 p 43 c 215(work,lw)m -1(or)m -1(k,i)m -1(wo)m -1(rk,)m -1(liw)m -1(or)m -1(k,)m 402 1172 p 43 c 215(info\))m 421 1217 p (END)s 421 1354 p (SUBROUT)s -1(INE)m 17(fcn\(n,m)m -1(,n)m -1(p,n)m -1(q,)m 402 1400 p 43 c 293(ldn,ldm,)m -1(ld)m -1(np,)m 402 1446 p 43 c 293(beta,xpl)m -1(us)m -1(d,)m 402 1491 p 43 c 293(ifixb,if)m -1(ix)m -1(x,l)m -1(dif)m -1(x,)m 402 1537 p 43 c 293(ideval,f)m -1(,f)m -1(jac)m -1(b,f)m -1(ja)m -1(cd,)m 402 1583 p 43 c 293(istop\))m 303 1674 p 99 c 39(Subrouti)m -1(ne)m 17(Argumen)m -1(ts)m 303 1720 p 99 c 118(==>)m 18 r 110 c 157(number)m 17(of)m 19(observa)m -1(ti)m -1(ons)m 303 1765 p 99 c 118(==>)m 18 r 109 c 157(number)m 17(of)m 19(columns)m 17(in)m 19(explan)m -1(at)m -1(ory)m 17(variabl)m -1 r 101 c 303 1811 p 99 c 118(==>)m 18(np)m 137(number)m 17(of)m 19(paramet)m -1(er)m -1 r 115 c 303 1857 p 99 c 118(==>)m 18(nq)m 137(number)m 17(of)m 19(respons)m -1(es)m 17(per)m 18(observat)m -1(ion)m 303 1902 p 99 c 118(==>)m 18(ldn)m 117(leadin)m -1 r 103 c 18(dimens)m -1(ion)m 17(declar)m -1(ato)m -1 r 114 c 17(equal)m 18(or)m 19(exceedi)m -1(ng)m 17 r 110 c 303 1948 p 99 c 118(==>)m 18(ldm)m 117(leadin)m -1 r 103 c 18(dimens)m -1(ion)m 17(declar)m -1(ato)m -1 r 114 c 17(equal)m 18(or)m 19(exceedi)m -1(ng)m 17 r 109 c 303 1994 p 99 c 118(==>)m 18(ldnp)m 97(leadin)m -1 r 103 c 18(dimens)m -1(ion)m 17(declar)m -1(ato)m -1 r 114 c 17(equal)m 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98(<==)m 38(fjacb)m 77(Jacobi)m -1(an)m 17(with)m 18(respect)m 17(to)m 19(beta)m 303 2405 p 99 c 98(<==)m 38(fjacd)m 77(Jacobi)m -1(an)m 17(with)m 18(respect)m 17(to)m 19(errors)m 17(delta)m 303 2450 p 99 c 98(<==)m 38(istop)m 77(stoppi)m -1(ng)m 17(conditio)m -1(n,)m 17(where)m @eop %%Page: 52 66 52 @bop0 52 @bop1 cmr10.329 @sf 0 114 p (52)s 1319(Using)m 15(ODRP)m -3 r 65 c (CK)s 0 134 p 1725 2 ru cmtt9.300 @sf 78 259 p 99 c 412 r 48 c 19(means)m 18(current)m 17(beta)m 18(and)m 18(x+delta)m 17(were)m 78 304 p 99 c 451(accepta)m -1(ble)m 17(and)m 18(values)m 18(were)m 18(comput)m -1(ed)m 17(successf)m -1(ul)m -1(ly)m 78 350 p 99 c 412 r 49 c 19(means)m 18(current)m 17(beta)m 18(and)m 18(x+delta)m 17(are)m 78 396 p 99 c 451(not)m 19(accept)m -1(abl)m -1(e;)m 37(ODRPAC)m -1 r 75 c 18(should)m 17(select)m 17(values)m 78 441 p 99 c 451(closer)m 17(to)m 19(most)m 18(recently)m 17(used)m 18(values)m 17(if)m 19(possibl)m -1 r 101 c 78 487 p 99 c 392(-1)m 19(means)m 18(current)m 17(beta)m 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18(problem)m 196 1035 p (IF)s 19(\(beta\(1)m -1 r 41 c 17(.GT.)m 19(0.0d0\))m 17(THEN)m 255 1080 p (istop)s 18 r 61 c 19 r 49 c 255 1126 p (return)s 196 1172 p (ELSE)s 255 1217 p (istop)s 18 r 61 c 19 r 48 c 196 1263 p (END)s 19(IF)m 78 1354 p 99 c 39(Compute)m 17(predict)m -1(ed)m 17(values)m 196 1400 p (IF)s 19(\(MOD\(id)m -1(ev)m -1(al,)m -1(10\))m -1(.G)m -1(E.1)m -1 r 41 c 17(THEN)m 255 1446 p (DO)s 19(110)m 18 r 108 c 19 r 61 c 20(1,nq)m 314 1491 p (DO)s 19(100)m 18 r 105 c 19 r 61 c 20(1,n)m 373 1537 p (f\(i,l\))s 17 r 61 c 19(beta\(3\))m -1(*\(x)m -1(plu)m -1(sd)m -1(\(i,)m -1(1\))m -1(-be)m -1(ta\()m -1(1\))m -1(\)**)m -1 r 50 c 17 r 43 c 177 1583 p 43 c 352(2*beta\()m -1(4\)*)m -1(\(xp)m -1(lu)m -1(sd\()m -1(i,)m -1(1\)-)m -1(bet)m -1(a\()m -1(1\)\))m -1 r 42 c 177 1628 p 43 c 548(\(xplusd\()m -1(i,)m -1(2\)-)m -1(bet)m -1(a\()m -1(2\)\))m 17 r 43 c 177 1674 p 43 c 352(beta\(5\))m -1(*\(x)m -1(plu)m -1(sd)m -1(\(i,)m -1(2\))m -1(-be)m -1(ta\()m -1(2\))m -1(\)**)m -1 r 50 c 17 r 45 c 20(1.0d0)m 118 1720 p (100)s 136(CONTIN)m -1(UE)m 118 1765 p (110)s 77(CONTINU)m -1 r 69 c 196 1811 p (END)s 19(IF)m 196 1902 p (RETURN)s 196 1948 p (END)s @eop %%Page: 53 67 53 @bop0 53 @bop1 cmr10.329 @sf 225 114 p (Using)s 15(ODRP)m -3 r 65 c (CK)s 1318(53)m 225 134 p 1725 2 ru cmbx10.329 @sf 225 259 p (2.C.ii.)s -1(b.)m 15(User)m 17(Supplied)m 17(Data)m 18(\(\014le)m cmtt10.329 @sf 18(data2)m cmbx10.329 @sf 41 c cmtt10.329 @sf 368 364 p (20)s 48 r 50 c 47 r 53 c 48 r 49 c 368 420 p (-1.0)s 23(-3.0)m 24(0.09)m 23(0.02)m 23(0.08)m 368 477 p (0.50)s 47(-0.12)m 368 533 p (1.20)s 47(-0.60)m 368 590 p (1.60)s 47(-1.00)m 368 646 p (1.86)s 47(-1.40)m 368 703 p (2.12)s 47(-2.54)m 368 759 p (2.36)s 47(-3.36)m 368 816 p (2.44)s 47(-4.00)m 368 872 p (2.36)s 47(-4.75)m 368 929 p (2.06)s 47(-5.25)m 368 985 p (1.74)s 47(-5.64)m 368 1041 p (1.34)s 47(-5.97)m 368 1098 p (0.90)s 47(-6.32)m 344 1154 p (-0.28)s 47(-6.44)m 344 1211 p (-0.78)s 47(-6.44)m 344 1267 p (-1.36)s 47(-6.41)m 344 1324 p (-1.90)s 47(-6.25)m 344 1380 p (-2.50)s 47(-5.88)m 344 1437 p (-2.88)s 47(-5.50)m 344 1493 p (-3.18)s 47(-5.24)m 344 1550 p (-3.44)s 47(-4.86)m @eop %%Page: 54 68 54 @bop0 54 @bop1 cmr10.329 @sf 0 114 p (54)s 1319(Using)m 15(ODRP)m -3 r 65 c (CK)s 0 134 p 1725 2 ru cmbx10.329 @sf 0 259 p (2.C.ii.)s -1(c.)m 16(Rep)m 1(ort)m 18(Generated)m 17 r 98 c 121 c 16(ODRP)m -3 r 65 c -1(CK)m 15(\(\014le)m cmtt10.329 @sf 17(report2)m cmbx10.329 @sf 41 c cmtt9.300 @sf 78 353 p (********)s -1(***)m -1(**)m -1(***)m -1(**)m -1(***)m -1(***)m -1(**)m -1(***)m -1(**)m -1(***)m -1(***)m -1(**)m -1(***)m -1(**)m -1(***)m -1(***)m -1(**)m -1(***)m 78 399 p 42 c 20(odrpac)m -1 r 107 c 18(versio)m -1 r 110 c 17(2.01)m 19(of)m 18(06-19-92)m 17(\(double)m 17(precisi)m -1(on)m -1 r 41 c 18 r 42 c 78 445 p (********)s -1(***)m -1(**)m -1(***)m -1(**)m -1(***)m -1(***)m -1(**)m -1(***)m -1(**)m -1(***)m -1(***)m -1(**)m -1(***)m -1(**)m -1(***)m -1(***)m -1(**)m -1(***)m 78 581 p (***)s 19(initial)m 17(summar)m 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-1(D-1)m -1 r 48 c 275 2408 p 53 c 38(8.000000)m -1(00D)m -1(-0)m -1 r 50 c 135(no)m 39(1.2500)m -1(000)m -1(0D+)m -1(01)m 56(3.16228)m -1(D-1)m -1 r 48 c @eop %%Page: 55 69 55 @bop0 55 @bop1 cmr10.329 @sf 225 114 p (Using)s 15(ODRP)m -3 r 65 c (CK)s 1318(55)m 225 134 p 1725 2 ru cmtt9.300 @sf 303 259 p (---)s 19(explana)m -1(to)m -1(ry)m 17(variable)m 17(and)m 18(delta)m 18(weight)m 17(summary)m -1 r 58 c 421 350 p (index)s 116(x\(i,j\))m 37(delta\()m -1(i,j)m -1 r 41 c 76(fixed)m 96(scale)m 77(weight)m 76(derivat)m -1(ive)m 1657 396 p (step)s 18(size)m 421 441 p (\(i,j\))s 508(\(ifixx\))m 76(\(scld\))m 115(\(wd\))m 156(\(stpd\))m 460 533 p (1,1)s 58(5.000D-)m -1(01)m 56(0.000D+0)m -1 r 48 c 135(no)m 39(2.00D+)m -1(00)m 37(1.00D+)m -1(00)m 57(3.1622)m -1(8D)m -1(-10)m 460 578 p (n,1)s 38(-3.440D+)m -1(00)m 56(0.000D+0)m -1 r 48 c 135(no)m 39(2.91D-)m -1(01)m 37(1.00D+)m -1(00)m 57(3.1622)m -1(8D)m -1(-10)m 460 670 p (1,2)s 38(-1.200D-)m -1(01)m 56(0.000D+0)m -1 r 48 c 135(no)m 39(8.33D+)m -1(00)m 37(1.00D+)m -1(00)m 57(3.1622)m -1(8D)m -1(-10)m 460 715 p (n,2)s 38(-4.860D+)m -1(00)m 56(0.000D+0)m -1 r 48 c 135(no)m 39(2.06D-)m -1(01)m 37(1.00D+)m -1(00)m 57(3.1622)m -1(8D)m -1(-10)m 303 807 p (***)s 19(final)m 18(summar)m -1 r 121 c 17(for)m 19(fit)m 18(by)m 19(method)m 18(of)m 18(odr)m 19(***)m 303 898 p (---)s 19(stoppin)m -1 r 103 c 17(conditio)m -1(ns:)m 460 944 p (info)s 18 r 61 c 98 r 50 c 19(==>)m 19(parame)m -1(ter)m 17(converg)m -1(en)m -1(ce.)m 441 989 p (niter)s 17 r 61 c 78(18)m 196(\(number)m 17(of)m 19(iterat)m -1(io)m -1(ns\))m 460 1035 p (nfev)s 18 r 61 c 59(217)m 195(\(number)m 17(of)m 19(functi)m -1(on)m 17(evaluat)m -1(ion)m -1(s\))m 441 1080 p (irank)s 17 r 61 c 98 r 48 c 196(\(rank)m 18(defici)m -1(en)m -1(cy\))m 441 1126 p (rcond)s 17 r 61 c 98(3.18D-0)m -1 r 50 c 57(\(invers)m -1 r 101 c 17(conditio)m -1 r 110 c 17(number\))m 441 1172 p (istop)s 17 r 61 c 98 r 48 c 196(\(return)m -1(ed)m 17(by)m 19(user)m 18(from)m 18(subrout)m -1(in)m -1 r 101 c 18(fcn\))m 303 1263 p (---)s 19(final)m 18(sum)m 18(of)m 19(squared)m 17(weight)m -1(ed)m 17(deltas)m 18 r 61 c 411(8.82420)m -1(346)m -1(D-)m -1(02)m 460 1309 p (final)s 18(penalty)m 17(functio)m -1 r 110 c 17(value)m 97 r 61 c 78(8.8244)m -1(561)m -1(6D)m -1(-02)m 578 1354 p (penalty)s 17(term)m 293 r 61 c 78(2.5270)m -1(089)m -1(7D)m -1(-06)m 578 1400 p (penalty)s 17(paramet)m -1(er)m 194 r 61 c 78(1.0D+0)m -1 r 53 c 303 1491 p (---)s 19(residua)m -1 r 108 c 17(standard)m 17(deviati)m -1(on)m 194 r 61 c 411(7.66994)m -1(283)m -1(D-)m -1(02)m 460 1537 p (degrees)s 17(of)m 19(freedom)m 292 r 61 c 58(15)m 303 1628 p (---)s 19(estimat)m -1(ed)m 17(beta\(j\))m -1 r 44 c 18 r 106 c 19 r 61 c 19(1,)m 19(...,)m 18(np:)m 696 1720 p (beta)s 116(s.d.)m 18(beta)m 77(----)m 18(95%)m 38(confide)m -1(nc)m -1 r 101 c 18(interv)m -1(al)m 17(----)m 421 1811 p 49 c 39(-9.9938)m -1(09)m -1(72D)m -1(-01)m 95(1.1138D-)m -1(01)m 76(-1.236)m -1(822)m -1(06D)m -1(+0)m -1 r 48 c 18(to)m 18(-7.61939)m -1(883)m -1(D-)m -1(01)m 421 1857 p 50 c 39(-2.9310)m -1(48)m -1(48D)m -1(+00)m 95(1.0977D-)m -1(01)m 76(-3.165)m -1(043)m -1(51D)m -1(+0)m -1 r 48 c 18(to)m 18(-2.69705)m -1(344)m -1(D+)m -1(00)m 421 1902 p 51 c 59(8.7573)m -1(04)m -1(79D)m -1(-02)m 95(4.1061D-)m -1(03)m 95(7.881999)m -1(15D)m -1(-0)m -1 r 50 c 18(to)m 38(9.63261)m -1(044)m -1(D-)m -1(02)m 421 1948 p 52 c 59(1.6229)m -1(97)m -1(39D)m -1(-02)m 95(2.7500D-)m -1(03)m 95(1.036763)m -1(38D)m -1(-0)m -1 r 50 c 18(to)m 38(2.20923)m -1(140)m -1(D-)m -1(02)m 421 1994 p 53 c 59(7.9753)m -1(80)m -1(08D)m -1(-02)m 95(3.4963D-)m -1(03)m 95(7.230070)m -1(73D)m -1(-0)m -1 r 50 c 18(to)m 38(8.72068)m -1(944)m -1(D-)m -1(02)m @eop %%Page: 56 70 56 @bop0 cmmi10.329 @sf [<000007F0FFFC0FF87FFC1F1C07C03F0E03C03F0603C03E0603E03E0001E03E0001E01E0001E01E 0001F01E0000F01E0000F00E0000F00E0000F81E0000783C00007FFC00007FFF00007C0F80003C 03E0003C01F0003C00F8003E00F8001E007C001E007C001E007C001F007C000F007C000F007800 0F01F000FFFFE000FFFF80> 32 32 -2 1 34.512] 82 @dc [<03800003800001800001800001C00001C00000C00000C00000E0000FFE001FFF803C63E07870F0 707078F0303CE0301CE0381EE0380EF0180F70180F701C07781C07380C073C0C0F1E0E0E0F0E1E 07C63C01FFF8007FF00007000003000003000003800003800001800001800001C00001C00000C0 0000C00000C0> 24 41 -2 9 27.083] 30 @dc cmex10.300 @sf [ 8 74 -10 72 19.602] 104 @dc [ 8 74 -1 72 19.602] 105 @dc [ 16 124 -11 122 24.214] 34 @dc [ 16 124 0 122 24.214] 35 @dc 56 @bop1 cmr10.329 @sf 0 114 p (56)s 1319(Using)m 15(ODRP)m -3 r 65 c (CK)s 0 134 p 1725 2 ru cmbx10.329 @sf 0 259 p (2.C.iii)s -1 r 46 c 15(Example)m 17(Problem)m 16(for)m 17(an)m 18(Explicit)m 17(Mo)m 1(del)m 17(with)m 17(Multiresp)m 1(onse)m 16(Data)m cmr10.329 @sf 0 364 p (The)s 12(problem)m 11(sho)m (wn)s 10(here)m 12(is)m 10(an)m 12(example)m 11(of)m 11 r 109 c (ultir)s -1(esp)m 1(onse)m 10(data)m 11(that)m 11(originates)m 9 r 98 c 1(ecause)m 13(the)m 0 420 p (underlying)s 13(data)m 12(are)m 12(complex.)m 19(The)m 13(problem)m 12(is)m 13(describ)m 1(ed)m 13(in)m 13(Chapter)m 12(4,)m 13(and)m 12(on)m 13(pages)m 13(280-)m 0 477 p (281,)s 12(of)m 11([Bates)m 12(and)m 12 r 87 c -3(atts,)m 10(1988].)m 18(In)m 12(this)m 12(case,)m 12(the)m 13(dep)m 1(enden)m 116 c 12 r 118 c -2(ariable)m 11(is)m 11(the)m 13(pair)m 11(of)m 12 r 118 c -2(alues)m 0 533 p (represen)s (ting)s 14(the)m 16(real)m 15(and)m 16(imaginary)m 14(parts)m 15(of)m 16(complex-v)m -2(alued)m 15(imp)m 1(edance)m 16(measuremen)m (ts)s 0 590 p (of)s 19 r 97 c 19 r 112 c 1(olymer,)m cmmi10.329 @sf 20 r 122 c cmmi8.300 @sf 314 597 p 105 c cmmi10.329 @sf 328 590 p 59 c 26 r 105 c cmr10.329 @sf 19 r 61 c 20 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 8 r 58 c 5 r 59 c 8 r 110 c cmr10.329 @sf 44 c 19(and)m 20(the)m 19(explanatory)m 18 r 118 c -2(ariable,)m cmmi10.329 @sf 19 r 120 c cmmi8.300 @sf 1285 597 p 105 c cmmi10.329 @sf 1299 590 p 59 c 26 r 105 c cmr10.329 @sf 19 r 61 c 20 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 7 r 58 c 6 r 59 c 8 r 110 c cmr10.329 @sf 44 c 19(is)m 19(the)m 0 646 p (\(real-v)s -2(alued\))m 12(frequency)m -3 r 46 c 19(The)m 14(data)m 13(are)m 13(sho)m (wn)s 12(in)m cmsy10.329 @sf 14 r 120 c cmr10.329 @sf (2.C.iii.)s -1(b.)m 18(The)m 14(function)m 13(form)m 13(is)m 13(explicit,)m 0 703 p (represen)s (ting)s 17(the)m 19(dielectric)m 18(constan)m 116 c 17 r 98 c 121 c 18(the)m 19(general)m 18(mo)m 1(del)m 19(prop)m 1(osed)m 19 r 98 c 121 c 17([Ha)m (vrili)s -1(ak)m 17(and)m 0 759 p (Negami,)s 14(1967])m 432 837 p 91 c cmsy10.329 @sf 60 c cmr10.329 @sf 40 c cmmi10.329 @sf 122 c cmmi8.300 @sf 517 844 p 105 c cmr10.329 @sf 530 837 p 41 c cmmi10.329 @sf 59 c cmsy10.329 @sf 8 r 61 c cmr10.329 @sf 40 c cmmi10.329 @sf 122 c cmmi8.300 @sf 641 844 p 105 c cmr10.329 @sf 654 837 p (\)])s cmsy10.329 @sf 12 r 25 c cmmi10.329 @sf 13 r 12 c cmr8.300 @sf 771 844 p 50 c cmr10.329 @sf 800 837 p 43 c cmmi10.329 @sf 996 806 p 12 c cmr8.300 @sf 1022 813 p 49 c cmsy10.329 @sf 1052 806 p 0 c cmmi10.329 @sf 10 r 12 c cmr8.300 @sf 1123 813 p 50 c 851 826 p 438 2 ru cmex10.300 @sf 851 843 p 16 c cmr10.329 @sf 876 890 p 49 c 9 r 43 c 11 r 40 c cmmi10.329 @sf 124 c cmr10.329 @sf 50 c cmmi10.329 @sf 25 c 2 r 120 c cmmi8.300 @sf 1066 897 p 105 c cmmi10.329 @sf 1079 890 p 101 c cmsy8.300 @sf 1100 878 p 0 c cmmi8.300 @sf 12 c cmr6.300 @sf 1147 883 p 51 c cmr10.329 @sf 1167 890 p 41 c cmmi8.300 @sf 1185 868 p 12 c cmr6.300 @sf 1205 873 p 52 c cmex10.300 @sf 1224 843 p 17 c cmmi8.300 @sf 1249 854 p 12 c cmr6.300 @sf 1269 859 p 53 c cmr10.329 @sf 0 985 p (for)s cmmi10.329 @sf 22 r 105 c cmr10.329 @sf 24 r 61 c 24 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 8 r 58 c 5 r 59 c 8 r 110 c cmr10.329 @sf 44 c 23(where)m cmmi10.329 @sf 23 r 124 c cmr10.329 @sf 24 r 61 c cmsy10.329 @sf 604 949 p 112 c 59 2 ru 642 985 p 0 c cmr10.329 @sf 49 c 46 c 41 r 70 c -3(or)m 21(ODRP)m -3 r 65 c (CK,)s 20(this)m 22 r 109 c (ust)s 21 r 98 c 1 r 101 c 23(enco)m 1(ded)m 23(as)m 22 r 116 c 119 c -1(o-)m 0 1041 p (term)s 14 r 109 c 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-1(wd=)m -1(1,)m 177 1217 p 43 c 215(ldifx=m)m -1(ax)m -1(n,l)m -1(ds)m -1(cld)m -1(=1,)m -1(ld)m -1(stp)m -1(d=)m -1(1,)m 177 1263 p 43 c 215(lwork=1)m -1 r 56 c 17 r 43 c 20(11*max)m -1(np)m 17 r 43 c 19(maxnp**2)m 17 r 43 c 19(maxm)m 18 r 43 c 19(maxm**2)m 17 r 43 c 177 1309 p 43 c 333(4*maxn)m -1(*m)m -1(axn)m -1 r 113 c 18 r 43 c 19(6*maxn)m -1(*ma)m -1(xm)m 17 r 43 c 19(2*maxn*m)m -1(ax)m -1(nq*)m -1(max)m -1(np)m 17 r 43 c 177 1354 p 43 c 333(2*maxn)m -1(*m)m -1(axn)m -1(q*m)m -1(ax)m -1 r 109 c 18 r 43 c 19(maxnq**)m -1 r 50 c 17 r 43 c 177 1400 p 43 c 333(5*maxn)m -1 r 113 c 17 r 43 c 20(maxnq*)m -1(\(ma)m -1(xn)m -1(p+m)m -1(axm)m -1 r 41 c 17 r 43 c 20(ldwe*l)m -1(d2)m -1(we*)m -1(max)m -1(nq)m -1 r 44 c 177 1446 p 43 c 215(liwork=)m -1(20)m -1(+ma)m -1(xn)m -1(p+m)m -1(axn)m -1(q*)m -1(\(ma)m -1(xn)m -1(p+m)m -1(axm)m -1(\)\))m 78 1537 p 99 c 39(Variable)m 17(Declar)m -1(ati)m -1(ons)m 196 1583 p (INTEGER)s 194(i,info)m -1(,i)m -1(pri)m -1(nt,)m -1(j,)m -1(job)m -1(,l)m -1(,lu)m -1(ner)m -1(r,)m -1(lun)m -1(rp)m -1(t,m)m -1(,m)m -1(axi)m -1(t,n)m -1 r 44 c 177 1628 p 43 c 333(ndigit)m -1(,n)m -1(p,n)m -1 r 113 c 196 1674 p (INTEGER)s 194(ifixb\()m -1(ma)m -1(xnp)m -1(\),i)m -1(fi)m -1(xx\()m -1(ld)m -1(ifx)m -1(,ma)m -1(xm)m -1(\),i)m -1(wo)m -1(rk\()m -1(li)m -1(wor)m -1(k\))m 196 1720 p (DOUBLE)s 17(PRECISIO)m -1 r 78 c 18(partol)m -1(,s)m -1(sto)m -1(l,t)m -1(au)m -1(fac)m 196 1765 p (DOUBLE)s 17(PRECISIO)m -1 r 78 c 18(beta\(m)m -1(ax)m -1(np\))m -1(,sc)m -1(lb)m -1(\(ma)m -1(xn)m -1(p\),)m -1(scl)m -1(d\()m -1(lds)m -1(cl)m -1(d,m)m -1(ax)m -1(m\),)m 177 1811 p 43 c 333(stpb\(m)m -1(ax)m -1(np\))m -1(,st)m -1(pd)m -1(\(ld)m -1(st)m -1(pd,)m -1(max)m -1(m\))m -1 r 44 c 177 1857 p 43 c 333(wd\(ldw)m -1(d,)m -1(ld2)m -1(wd,)m -1(ma)m -1(xm\))m -1(,w)m -1(e\(l)m -1(dwe)m -1(,l)m -1(d2w)m -1(e,)m -1(max)m -1(nq)m -1(\),)m 177 1902 p 43 c 333(work\(l)m -1(wo)m -1(rk\))m -1(,x\()m -1(ld)m -1(x,m)m -1(ax)m -1(m\),)m -1(y\(l)m -1(dy)m -1(,ma)m -1(xn)m -1(q\))m 196 1948 p (EXTERNA)s -1 r 76 c 175(fcn)m 78 2085 p 99 c 39(Specify)m 17(default)m 17(values)m 17(for)m 19(dodrc)m 18(argume)m -1(nt)m -1 r 115 c 196 2131 p (we\(1,1,)s -1(1\))m 37 r 61 c 19(-1.0d0)m 196 2176 p (wd\(1,1,)s -1(1\))m 37 r 61 c 19(-1.0d0)m 196 2222 p (ifixb\(1)s -1 r 41 c 57 r 61 c 19(-1)m 196 2268 p (ifixx\(1)s -1(,1\))m 17 r 61 c 19(-1)m 196 2313 p (job)s 156 r 61 c 19(-1)m 196 2359 p (ndigit)s 96 r 61 c 19(-1)m 196 2405 p (taufac)s 96 r 61 c 19(-1.0d0)m 196 2450 p (sstol)s 116 r 61 c 19(-1.0d0)m @eop %%Page: 59 73 59 @bop0 59 @bop1 cmr10.329 @sf 225 114 p (Using)s 15(ODRP)m -3 r 65 c (CK)s 1318(59)m 225 134 p 1725 2 ru cmtt9.300 @sf 421 259 p (partol)s 96 r 61 c 19(-1.0d0)m 421 304 p (maxit)s 116 r 61 c 19(-1)m 421 350 p (iprint)s 96 r 61 c 19(-1)m 421 396 p (lunerr)s 96 r 61 c 19(-1)m 421 441 p (lunrpt)s 96 r 61 c 19(-1)m 421 487 p (stpb\(1\))s 76 r 61 c 19(-1.0d0)m 421 533 p (stpd\(1,)s -1(1\))m 37 r 61 c 19(-1.0d0)m 421 578 p (sclb\(1\))s 76 r 61 c 19(-1.0d0)m 421 624 p (scld\(1,)s -1(1\))m 37 r 61 c 19(-1.0d0)m 303 715 p 99 c 39(Set)m 19(up)m 19(ODRPAC)m -1 r 75 c 17(report)m 18(files)m 421 761 p (lunerr)s 37 r 61 c 58 r 57 c 421 807 p (lunrpt)s 37 r 61 c 58 r 57 c 421 852 p (OPEN)s 18(\(unit=9)m -1(,fi)m -1(le=)m -1('r)m -1(epo)m -1(rt)m -1(3'\))m 303 944 p 99 c 39(Read)m 18(problem)m 17(data)m 421 989 p (OPEN)s 18(\(unit=5)m -1(,fi)m -1(le=)m -1('d)m -1(ata)m -1(3')m -1 r 41 c 421 1035 p (READ)s 18(\(5,FMT=)m -1(*\))m 17(n,m,np,n)m -1 r 113 c 421 1080 p (READ)s 18(\(5,FMT=)m -1(*\))m 17(\(beta\(i\))m -1(,i)m -1(=1,)m -1(np\))m 421 1126 p (DO)s 19(10)m 19(i=1,n)m 480 1172 p (READ)s 18(\(5,FMT=)m -1(*\))m 17(\(x\(i,j\))m -1(,j=)m -1(1,m)m -1(\),)m -1(\(y\()m -1(i,)m -1(l\),)m -1(l=)m -1(1,n)m -1(q\))m 362 1217 p (10)s 19(CONTINU)m -1 r 69 c 303 1309 p 99 c 39(Specify)m 17(task)m 18(as)m 19(explici)m -1 r 116 c 18(orthog)m -1(ona)m -1 r 108 c 17(distance)m 17(regress)m -1(io)m -1 r 110 c 303 1354 p 99 c 353(with)m 18(central)m 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480 2039 p (else)s 18(if)m 19(\(x\(i,1\))m -1(.l)m -1(e.1)m -1(50)m -1(.0d)m -1(0\))m 17(then)m 539 2085 p (work\(i)s -1 r 41 c 77 r 61 c 19(0.0d0)m 539 2131 p (ifixx\()s -1(i,1)m -1 r 41 c 18 r 61 c 19 r 49 c 480 2176 p (else)s 18(if)m 19(\(x\(i,1\))m -1(.l)m -1(e.1)m -1(00)m -1(0.0)m -1(d0\))m 17(then)m 539 2222 p (work\(i)s -1 r 41 c 77 r 61 c 19(25.0d0)m 539 2268 p (ifixx\()s -1(i,1)m -1 r 41 c 18 r 61 c 19 r 49 c 480 2313 p (else)s 18(if)m 19(\(x\(i,1\))m -1(.l)m -1(e.1)m -1(00)m -1(00.)m -1(0d0)m -1 r 41 c 17(then)m 539 2359 p (work\(i)s -1 r 41 c 77 r 61 c 19(560.0d)m -1 r 48 c 539 2405 p (ifixx\()s -1(i,1)m -1 r 41 c 18 r 61 c 19 r 49 c 480 2450 p (else)s 18(if)m 19(\(x\(i,1\))m -1(.l)m -1(e.1)m -1(00)m -1(000)m -1(.0d)m -1(0\))m 17(then)m @eop %%Page: 60 74 60 @bop0 60 @bop1 cmr10.329 @sf 0 114 p (60)s 1319(Using)m 15(ODRP)m -3 r 65 c (CK)s 0 134 p 1725 2 ru cmtt9.300 @sf 314 259 p (work\(i)s -1 r 41 c 77 r 61 c 19(9500.0)m -1(d0)m 314 304 p (ifixx\()s -1(i,1)m -1 r 41 c 18 r 61 c 19 r 49 c 255 350 p (else)s 314 396 p (work\(i)s -1 r 41 c 18 r 61 c 19(144000.)m -1(0d)m -1 r 48 c 314 441 p (ifixx\()s -1(i,1)m -1 r 41 c 18 r 61 c 19 r 49 c 255 487 p (end)s 18(if)m 137 533 p (20)s 19(CONTINU)m -1 r 69 c 78 624 p 99 c 39(Set)m 19(weight)m -1 r 115 c 196 670 p (DO)s 19(30)m 19(i=1,n)m 255 715 p (if)s 19(\(x\(i,1)m -1(\).e)m -1(q.1)m -1(00)m -1(.0d)m -1 r 48 c 17(.or.)m 19(x\(i,1\))m -1(.e)m -1(q.1)m -1(50.)m -1(0d)m -1(0\))m 17(then)m 314 761 p (we\(i,1)s -1(,1\))m 17 r 61 c 19(0.0d0)m 314 807 p (we\(i,1)s -1(,2\))m 17 r 61 c 19(0.0d0)m 314 852 p (we\(i,2)s -1(,1\))m 17 r 61 c 19(0.0d0)m 314 898 p (we\(i,2)s -1(,2\))m 17 r 61 c 19(0.0d0)m 255 944 p (else)s 314 989 p (we\(i,1)s -1(,1\))m 17 r 61 c 58(559.6d0)m 314 1035 p (we\(i,1)s -1(,2\))m 17 r 61 c 19(-1634.0)m -1(d0)m 314 1080 p (we\(i,2)s -1(,1\))m 17 r 61 c 19(-1634.0)m -1(d0)m 314 1126 p (we\(i,2)s -1(,2\))m 17 r 61 c 39(8397.0)m -1(d0)m 255 1172 p (end)s 18(if)m 255 1217 p (wd\(i,1,)s -1(1\))m 76 r 61 c 39(\(1.0d-)m -1(4\)/)m -1(\(x\()m -1(i,)m -1(1\)*)m -1(*2)m -1 r 41 c 137 1263 p (30)s 19(CONTINU)m -1 r 69 c 78 1354 p 99 c 39(Compute)m 17(solutio)m -1 r 110 c 196 1400 p (CALL)s 18(dodrc\(f)m -1(cn,)m 177 1446 p 43 c 215(n,m,np,)m -1(nq)m -1 r 44 c 177 1491 p 43 c 215(beta,)m 177 1537 p 43 c 215(y,ldy,x)m -1(,l)m -1(dx,)m 177 1583 p 43 c 215(we,ldwe)m -1(,l)m -1(d2w)m -1(e,)m -1(wd,)m -1(ldw)m -1(d,)m -1(ld2)m -1(wd)m -1 r 44 c 177 1628 p 43 c 215(ifixb,i)m -1(fi)m -1(xx,)m -1(ld)m -1(ifx)m -1 r 44 c 177 1674 p 43 c 215(job,ndi)m -1(gi)m -1(t,t)m -1(au)m -1(fac)m -1 r 44 c 177 1720 p 43 c 215(sstol,p)m -1(ar)m -1(tol)m -1(,m)m -1(axi)m -1(t,)m 177 1765 p 43 c 215(iprint,)m -1(lu)m -1(ner)m -1(r,)m -1(lun)m -1(rpt)m -1 r 44 c 177 1811 p 43 c 215(stpb,st)m -1(pd)m -1(,ld)m -1(st)m -1(pd,)m 177 1857 p 43 c 215(sclb,sc)m -1(ld)m -1(,ld)m -1(sc)m -1(ld,)m 177 1902 p 43 c 215(work,lw)m -1(or)m -1(k,i)m -1(wo)m -1(rk,)m -1(liw)m -1(or)m -1(k,)m 177 1948 p 43 c 215(info\))m 196 1994 p (END)s 196 2131 p (SUBROUT)s -1(INE)m 17(fcn\(n,m)m -1(,n)m -1(p,n)m -1(q,)m 177 2176 p 43 c 293(ldn,ldm,)m -1(ld)m -1(np,)m 177 2222 p 43 c 293(beta,xpl)m -1(us)m -1(d,)m 177 2268 p 43 c 293(ifixb,if)m -1(ix)m -1(x,l)m -1(dif)m -1(x,)m 177 2313 p 43 c 293(ideval,f)m -1(,f)m -1(jac)m -1(b,f)m -1(ja)m -1(cd,)m 177 2359 p 43 c 293(istop\))m 78 2450 p 99 c 39(Subrouti)m -1(ne)m 17(Argumen)m -1(ts)m @eop %%Page: 61 75 61 @bop0 61 @bop1 cmr10.329 @sf 225 114 p (Using)s 15(ODRP)m -3 r 65 c (CK)s 1318(61)m 225 134 p 1725 2 ru cmtt9.300 @sf 303 259 p 99 c 118(==>)m 18 r 110 c 157(number)m 17(of)m 19(observa)m -1(ti)m -1(ons)m 303 304 p 99 c 118(==>)m 18 r 109 c 157(number)m 17(of)m 19(columns)m 17(in)m 19(explan)m -1(at)m -1(ory)m 17(variabl)m -1 r 101 c 303 350 p 99 c 118(==>)m 18(np)m 137(number)m 17(of)m 19(paramet)m -1(er)m -1 r 115 c 303 396 p 99 c 118(==>)m 18(nq)m 137(number)m 17(of)m 19(respons)m -1(es)m 17(per)m 18(observat)m -1(ion)m 303 441 p 99 c 118(==>)m 18(ldn)m 117(leadin)m -1 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18(of)m 19(squares)m 135 r 61 c 411(4.20538)m -1(922)m -1(D-)m -1(01)m 460 1628 p (sum)s 19(of)m 19(square)m -1 r 100 c 18(weight)m -1(ed)m 17(deltas)m 57 r 61 c 78(5.5402)m -1(189)m -1(7D)m -1(-04)m 460 1674 p (sum)s 19(of)m 19(square)m -1 r 100 c 18(weight)m -1(ed)m 17(epsilon)m -1 r 115 c 18 r 61 c 78(4.1998)m -1(490)m -1(0D)m -1(-01)m 303 1765 p (---)s 19(residua)m -1 r 108 c 17(standard)m 17(deviati)m -1(on)m 194 r 61 c 411(1.62122)m -1(431)m -1(D-)m -1(01)m 460 1811 p (degrees)s 17(of)m 19(freedom)m 292 r 61 c 58(16)m 303 1902 p (---)s 19(estimat)m -1(ed)m 17(beta\(j\))m -1 r 44 c 18 r 106 c 19 r 61 c 19(1,)m 19(...,)m 18(np:)m 696 1994 p (beta)s 116(s.d.)m 18(beta)m 77(----)m 18(95%)m 38(confide)m -1(nc)m -1 r 101 c 18(interv)m -1(al)m 17(----)m 421 2085 p 49 c 59(4.3799)m -1(88)m -1(03D)m -1(+00)m 95(1.3063D-)m -1(02)m 95(4.352293)m -1(88D)m -1(+0)m -1 r 48 c 18(to)m 38(4.40768)m -1(218)m -1(D+)m -1(00)m 421 2131 p 50 c 59(2.4333)m -1(05)m -1(76D)m -1(+00)m 95(1.3050D-)m -1(02)m 95(2.405638)m -1(20D)m -1(+0)m -1 r 48 c 18(to)m 38(2.46097)m -1(332)m -1(D+)m -1(00)m 421 2176 p 51 c 59(8.0028)m -1(84)m -1(59D)m -1(+00)m 95(1.1671D-)m -1(01)m 95(7.755448)m -1(03D)m -1(+0)m -1 r 48 c 18(to)m 38(8.25032)m -1(115)m -1(D+)m -1(00)m 421 2222 p 52 c 59(5.1011)m -1(47)m -1(16D)m -1(-01)m 95(1.3264D-)m -1(02)m 95(4.819928)m -1(24D)m -1(-0)m -1 r 49 c 18(to)m 38(5.38236)m -1(609)m -1(D-)m -1(01)m 421 2268 p 53 c 59(5.1739)m -1(02)m -1(33D)m -1(-01)m 95(2.8853D-)m -1(02)m 95(4.562184)m -1(98D)m -1(-0)m -1 r 49 c 18(to)m 38(5.78561)m -1(968)m -1(D-)m -1(01)m 303 2359 p (---)s 19(estimat)m -1(ed)m 17(epsilon)m -1(\(i\))m 17(and)m 18(delta\(i,)m -1(*\))m -1 r 44 c 18 r 105 c 19 r 61 c 19(1,)m 19(...,)m 18(n:)m 460 2450 p 105 c 78(epsilon\()m -1(i,1)m -1 r 41 c 76(epsilon\()m -1(i,)m -1(2\))m 115(delta\(i,)m -1(1\))m @eop %%Page: 66 80 66 @bop0 66 @bop1 cmr10.329 @sf 0 114 p (66)s 1319(Using)m 15(ODRP)m -3 r 65 c (CK)s 0 134 p 1725 2 ru cmtt9.300 @sf 235 304 p 49 c 20(-7.385)m -1(58)m -1(795)m -1(D-0)m -1 r 51 c 37(1.25939)m -1(187)m -1(D-)m -1(03)m 37(0.00000)m -1(00)m -1(0D+)m -1(00)m 235 350 p 50 c 20(-1.056)m -1(14)m -1(733)m -1(D-0)m -1 r 51 c 17(-1.22846)m -1(292)m -1(D-)m -1(03)m 37(0.00000)m -1(00)m -1(0D+)m -1(00)m 235 396 p 51 c 20(-2.708)m -1(63)m -1(920)m -1(D-0)m -1 r 51 c 17(-2.14347)m -1(329)m -1(D-)m -1(03)m 37(0.00000)m -1(00)m -1(0D+)m -1(00)m 235 441 p 52 c 39(4.68593)m -1(517)m -1(D-0)m -1 r 50 c 17(-4.25940)m -1(138)m -1(D-)m -1(03)m 37(0.00000)m -1(00)m -1(0D+)m -1(00)m 235 487 p 53 c 39(8.08102)m -1(389)m -1(D-0)m -1 r 51 c 17(-3.47539)m -1(194)m -1(D-)m -1(03)m 37(0.00000)m -1(00)m -1(0D+)m -1(00)m 235 533 p 54 c 39(1.53882)m -1(522)m -1(D-0)m -1 r 51 c 37(3.85293)m -1(713)m -1(D-)m -1(04)m 37(3.03694)m -1(40)m -1(0D+)m -1(01)m 235 578 p 55 c 39(4.60535)m -1(703)m -1(D-0)m -1 r 51 c 37(1.19118)m -1(896)m -1(D-)m -1(03)m 37(3.78986)m -1(75)m -1(0D+)m -1(01)m 235 624 p 56 c 39(4.50906)m -1(164)m -1(D-0)m -1 r 51 c 37(1.23570)m -1(892)m -1(D-)m -1(03)m 37(6.22630)m -1(48)m -1(7D+)m -1(01)m 235 670 p 57 c 20(-1.006)m -1(21)m -1(895)m -1(D-0)m -1 r 51 c 17(-2.91865)m -1(043)m -1(D-)m -1(04)m 37(1.11186)m -1(98)m -1(0D+)m -1(02)m 216 715 p (10)s 38(1.05810)m -1(802)m -1(D-0)m -1 r 50 c 37(3.27284)m -1(194)m -1(D-)m -1(03)m 37(1.15709)m -1(87)m -1(7D+)m -1(02)m 216 761 p (11)s 38(6.93622)m -1(739)m -1(D-0)m -1 r 51 c 37(2.43482)m -1(106)m -1(D-)m -1(03)m 37(2.41436)m -1(59)m -1(1D+)m -1(02)m 216 807 p (12)s 38(3.95828)m -1(011)m -1(D-0)m -1 r 53 c 37(1.75905)m -1(014)m -1(D-)m -1(05)m 37(9.61344)m -1(53)m -1(2D+)m -1(02)m 216 852 p (13)s 19(-3.776)m -1(17)m -1(796)m -1(D-0)m -1 r 51 c 17(-2.42907)m -1(814)m -1(D-)m -1(03)m 37(1.33029)m -1(84)m -1(5D+)m -1(03)m 216 898 p (14)s 19(-5.567)m -1(34)m -1(978)m -1(D-0)m -1 r 52 c 17(-1.70123)m -1(784)m -1(D-)m -1(03)m 37(2.07511)m -1(56)m -1(6D+)m -1(03)m 216 944 p (15)s 38(2.08263)m -1(807)m -1(D-0)m -1 r 51 c 17(-2.23723)m -1(233)m -1(D-)m -1(03)m 37(2.90289)m -1(53)m -1(2D+)m -1(03)m 216 989 p (16)s 19(-7.506)m -1(89)m -1(916)m -1(D-0)m -1 r 51 c 37(2.16462)m -1(893)m -1(D-)m -1(03)m 37(5.21815)m -1(81)m -1(8D+)m -1(03)m 216 1035 p (17)s 19(-1.567)m -1(31)m -1(844)m -1(D-0)m -1 r 51 c 37(2.03367)m -1(085)m -1(D-)m -1(04)m 37(7.54564)m -1(63)m -1(6D+)m -1(03)m 216 1080 p (18)s 19(-5.932)m -1(23)m -1(183)m -1(D-0)m -1 r 52 c 37(2.72069)m -1(171)m -1(D-)m -1(05)m 37(1.74201)m -1(02)m -1(1D+)m -1(04)m 216 1126 p (19)s 38(1.15260)m -1(099)m -1(D-0)m -1 r 52 c 17(-2.42126)m -1(131)m -1(D-)m -1(07)m 37(2.42745)m -1(47)m -1(2D+)m -1(04)m 216 1172 p (20)s 38(2.63641)m -1(111)m -1(D-0)m -1 r 52 c 37(5.18510)m -1(319)m -1(D-)m -1(06)m 37(3.78492)m -1(05)m -1(2D+)m -1(04)m 216 1217 p (21)s 19(-3.810)m -1(11)m -1(180)m -1(D-0)m -1 r 52 c 17(-1.03963)m -1(850)m -1(D-)m -1(05)m 37(5.53493)m -1(28)m -1(0D+)m -1(04)m 216 1263 p (22)s 19(-3.368)m -1(22)m -1(611)m -1(D-0)m -1 r 52 c 17(-1.26141)m -1(391)m -1(D-)m -1(05)m 37(8.75791)m -1(43)m -1(2D+)m -1(04)m 216 1309 p (23)s 38(2.87173)m -1(883)m -1(D-0)m -1 r 51 c 37(1.41199)m -1(841)m -1(D-)m -1(04)m 37(1.29496)m -1(30)m -1(0D+)m -1(05)m @eop %%Page: 67 81 67 @bop0 cmcsc10.518 @sf [<003FE00001FFFC0007C03F000E000FC0180007E0300007F07E0003F87F0003F8FF8001FCFF8001 FCFF8001FEFF8001FE7F0001FE7F0001FE1C0001FE000001FE000001FE000001FC000003FC0000 03F8000003F0000007E0000007C000000F8000003E00003FF000003FF0000000FC0000003E0000 001F8000000FC000000FE0000007E0000007F0060003F01F8003F83FC003F83FC003F83FC003F8 3FC003F83F8003F81F0003F0180007F00C0007E007000FC003E03F0000FFFE00001FF000> 32 48 -4 1 39.650] 51 @dc [<000003000000300000000000038000007000000000000780000078000000000007C00000F80000 00000007C00000F800000000000FC00000FC00000000000FE00001FC00000000000FE00001FC00 000000001FE00001FE00000000001FF00003FE00000000001FF00003FE00000000003FB00003FB 00000000003FB80007FB00000000003F980007F300000000007F180007F180000000007F1C000F F180000000007F0C000FE18000000000FE0C000FE0C000000000FE0E001FE0C000000000FE0600 1FC0C000000001FC06001FC06000000001FC03003FC06000000001FC03003F806000000003F803 003F803000000003F801807F803000000003F801807F003000000007F001807F001800000007F0 00C0FF001800000007F000C0FE00180000000FE000C0FE000C0000000FE00061FC000C0000001F E00061FC000E0000001FC00061FC00060000001FC00033F800060000003FC00033F80007000000 3F800033F800030000003F80001FF000030000007F80001FF000038000007F00001FF000018000 007F00000FE00001800000FF00000FE00001C00000FE00000FE00000C00000FE00001FC00000C0 0001FE00001FC00000E00001FC00001FC00000E00001FC00003F800000F00003FC00003FC00001 F80007FF00007FE00007FC00FFFFF00FFFFF003FFFC0FFFFF00FFFFF003FFFC0> 80 50 -2 1 79.300] 87 @dc [ 40 37 -3 0 43.994] 104 @dc [ 64 49 -5 0 70.932] 77 @dc [ 32 37 -3 0 36.821] 108 @dc [ 24 49 -3 0 29.090] 73 @dc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dc [<003FFFFFF800003FFFFFF80000003FF8000000000FE0000000000FE0000000000FE0000000000F E0000000000FE0000000000FE0000000000FE0000000000FE0000000000FE0000000000FE00000 00000FE0000000000FE0000000000FE0000000000FE0000000000FE0000000000FE0000000000F E0000000000FE0000000000FE0000000000FE0000000000FE0000000000FE0000000000FE00000 00000FE0000000000FE0000000000FE0000000000FE0000000000FE0000000000FE0000000000F E00000C0000FE00006C0000FE00006C0000FE00006C0000FE00006C0000FE00006C0000FE00006 E0000FE0000EE0000FE0000E60000FE0000C60000FE0000C70000FE0001C78000FE0003C7C000F E0007C7F001FF001FC7FFFFFFFFFFC7FFFFFFFFFFC> 48 49 -4 0 56.387] 84 @dc [ 48 37 -4 0 53.558] 109 @dc [<0001FC00000007FF0000001F03C000003C00E000007800300000F000300001E000180001E0000C 0003E0000C0003C0000C0007C000060007C000060007C000060007C000060007C000060007C000 060007C000060007C000060007C000060007C000060007C000060007C000060007C000060007C0 00060007C000060007C000060007C000060007C000060007C000060007C000060007C000060007 C000060007C000060007C000060007C0000F000FE0001F80FFFE00FFF0FFFE00FFF0> 40 38 -3 1 43.994] 117 @dc cmmi10.329 @sf [<0380000003800000038000000380000001C0000001C0000001C0000001C0000000E0000000E000 0001FF000007FFC0001FFFF0003FF1F8003C703C0078301E007030070060300380E0180380E018 0180601C01C0600C00C0600E00C0700600C0300700C0300381C03803E3C01C01FF800C00FF800E 003F00> 32 30 -2 10 29.734] 39 @dc cmr10.329 @sf [ 48 2 0 -11 45.454] 124 @dc cmr9.300 @sf [<0380E0000380E0000380E00007C1F00007C1F00007C1B0000763B0000E6398000E6318000E3718 001C370C001C360C001C3E0C003C1E0E00FF3F9F80FF3F9F80> 32 16 -1 0 27.731] 119 @dc [<7F0FF07F0FF00E07000E07000E07000E07000E07000E07000E07000E07000E07000E07000E0700 0E0700FFFFF0FFFFF00E07000E07000E07000E07000E07000F0F0F070F8F07CFCF01FFFF007E7E> 24 26 0 0 22.398] 11 @dc [<007FC0007FC0000E00000E00000E00000E00000E000FCE001FFE003C7E00781E00700E00F00E00 E00E00E00E00E00E00E00E00F00E00700E00781E003E3E001FF60007C600> 24 23 -1 7 20.265] 113 @dc cmmi9.300 @sf [<3FF03FF00380038003C001C001C03FC07FE0E3E0E1E0C0E0E0F0E070E070E070F0787038703838 781C7C0FFC07CC> 16 23 -2 7 17.156] 113 @dc cmr9.300 @sf [<4180E7C07FE03E701820> 16 5 -3 -20 19.198] 126 @dc cmmi9.300 @sf [ 24 23 1 7 19.275] 112 @dc cmr9.300 @sf [<000C0000000C0000000C0000000C0000000C0000000C0000000C0000000C0000000C0000000C00 00000C0000000C0000FFFFFF80FFFFFF80000C0000000C0000000C0000000C0000000C0000000C 0000000C0000000C0000000C0000000C0000000C0000000C0000> 32 26 -2 4 29.864] 43 @dc cmmi9.300 @sf [<0C00000E00000E00000E00000E000007000007000007F8001FFE003FFF007F8F80F383C0E180E0 C18070C1C070C0C030E0E030606030607030703C70301FF0380FF01807C0> 24 23 -2 7 25.073] 39 @dc [<380E01F03C0F03F83C0F03DC1C07038E1C0703C61E0781C61E0781E00E0380E00E0380E00F03C0 E0CF03C0F0C781E070C7C1F07067E3F8F07F7F9FE03E3F0FC0> 32 16 -1 0 33.828] 109 @dc cmr9.300 @sf [ 16 24 -2 0 19.198] 50 @dc cmsy9.300 @sf [<3E007F80F380E3C0E1C0E1C001C001C003C003800F001F003F8073C0F1C0E1C0E1C0E1C0E3C0F3 807F003E003C007000F000E000E000E1C0E1C0F1C073C07F801F00> 16 33 -3 7 17.065] 120 @dc cmr9.300 @sf [<07FF07FF00700070007000700070FFFFFFFFE07060703070387018700C700E7006700770037001 F001F000F000700070> 16 24 -1 0 19.198] 52 @dc 67 @bop1 cmcsc10.518 @sf 225 519 p (3.)s 35(When)m 27(the)m 28(Model)m 26(Is)m 27(Ver)m -4 r 121 c 27(Time)m 27(Consuming)m cmr10.329 @sf 225 746 p (ODRP)s -3 r 65 c (CK)s 14(executes)m 15(user)m 16(supplied)m 15(subroutine)m cmtt10.329 @sf 15(FCN)m cmr10.329 @sf 15(not)m 14(only)m 15(to)m 14(compute)m 16(the)m 15(initial)m 13(sum)m 225 802 p (of)s 11(the)m 11(squared)m 12(errors)m cmmi10.329 @sf 11 r 83 c cmr10.329 @sf 3 r 40 c cmmi10.329 @sf 12 c 2 r 59 c 8 r 14 c cmr10.329 @sf 2 r 41 c 9(and)m 12(to)m 10(obtain)m 11(function)m 11(and)m 12(deriv)m -2(ativ)m -1 r 101 c 10 r 118 c -2(alues)m 10(within)m 11(its)m 10(main)m 225 858 p (iterativ)s -1 r 101 c 9(pro)m 1(cedure,)m 13(but)m 11(also)m 11(when)m 11(setting)m 11(the)m 11(default)m 11 r 118 c -2(alue)m 10(for)m 11(the)m 11 r 110 c (um)s 98 c 1(er)m 10(of)m 11(go)m 1 r 111 c 1 r 100 c 11(digits)m 225 915 p (in)s 12(the)m 13(function)m 13(results,)m 12(when)m 13 r 112 c 1(erforming)m 12(deriv)m -2(ativ)m -1 r 101 c 10 r 99 c (hec)s (king,)s 11(and)m 13(when)m 13(constructing)m 12(the)m 225 971 p (co)s 118 c -2(ari)m -1(ance)m 16(matrix)m 17(and)m 18(standard)m 17(deviations)m 17(of)m 17(the)m 18(estimated)m 17(parameters)m 1689 960 p 94 c cmmi10.329 @sf 1683 972 p 12 c cmr10.329 @sf 1711 971 p 46 c 28(When)m 18(the)m 225 1028 p (time)s 17(required)m 17(for)m 17(\014nding)m 18(the)m 17(solution)m 16(is)m 17(dominated)m 17 r 98 c 121 c 16(the)m 18(ev)m -2(aluation)m 15(of)m cmtt10.329 @sf 17(FCN)m cmr10.329 @sf 44 c 17(the)m 18(user)m 225 1084 p (will)s 16 r 119 c (an)s -1 r 116 c 15(to)m 16(mak)m 101 c 16(judicious)m 17(use)m 17(of)m 17(these)m 17(options)m 17(in)m 17(ligh)m 116 c 15(of)m 16(their)m 17(\\cost.")m 25(Let)m 21 r 126 c cmmi10.329 @sf -27 r 112 c cmr10.329 @sf 17 r 98 c 1 r 101 c 18(the)m 225 1141 p 110 c (um)s 98 c 1(er)m 19(of)m 20(un\014xed)m 22(parameters)m cmmi10.329 @sf 20 r 12 c cmr10.329 @sf 2 r 44 c 22(and)m 21(let)m cmmi10.329 @sf 20 r 39 c cmr10.329 @sf 22 r 61 c 22 r 49 c 20(if)m 21(the)m 21(\014t)m 20(is)m 20 r 98 c 121 c 20(orthogonal)m 19(distance)m 225 1197 p (regression)s 15(and)m cmmi10.329 @sf 17 r 39 c cmr10.329 @sf 14 r 61 c 15 r 48 c 16(if)m 16(the)m 16(\014t)m 16(is)m 16 r 98 c 121 c 15(ordinary)m 16(least)m 15(squares.)m 23(Then)m 17(the)m 16 r 110 c (um)s 98 c 1(er)m 15(of)m 16(times)m 225 1254 p (the)s 17(function)m 16(and)m 17(deriv)m -2(ativ)m -1(es)m 14(are)m 17(ev)m -2(aluated)m 15(in)m 16(eac)m 104 c 16(of)m 16(these)m 17(instances)m 16(is)m 16(summarized)m 16(as)m 225 1310 p (follo)s -1(ws:)m 510 1389 p (Computation)s 313 r 70 c -3(unction)m 112(Deriv)m -2(ativ)m -1 r 101 c 72(Con)m (troll)s -1(ing)m 1059 1446 p (Ev)s -2(aluatio)m -1(ns)m 59(Ev)m -2(aluations)m cmr8.300 @sf 1585 1431 p 49 c cmr10.329 @sf 1682 1446 p 86 c -3(ariable)m cmsy10.329 @sf 284 1514 p 15 c cmr10.329 @sf 15(Initial)m cmmi10.329 @sf 14 r 83 c cmr10.329 @sf 3 r 40 c cmmi10.329 @sf 12 c 2 r 59 c 8 r 14 c cmr10.329 @sf 2(\):)m 555 r 49 c 279 r 48 c 254 r 124 c cmsy10.329 @sf 284 1582 p 15 c cmr10.329 @sf 15 r 80 c (er)s 13(Iteration:)m cmsy10.329 @sf 547 r 21 c cmr10.329 @sf 15 r 49 c 254 r 49 c 254 r 124 c cmsy10.329 @sf 284 1650 p 15 c cmr10.329 @sf 15(Default)m 14 r 110 c (um)s 98 c 1(er)m 13(of)m 390 1707 p (go)s 1 r 111 c 1 r 100 c 15(digits)m 14(in)m 15(function)m 15(results:)m 164 r 52 c 279 r 48 c cmtt10.329 @sf 205(NDIGIT)m cmsy10.329 @sf 284 1775 p 15 c cmr10.329 @sf 15(Deriv)m -2(ati)m -1 r 118 c -1 r 101 c 14 r 99 c (hec)s (king)s -1 r 58 c cmsy10.329 @sf 326 r 21 c cmmi10.329 @sf 13 r 113 c cmr10.329 @sf 2 r 40 c 4 r 126 c cmmi10.329 @sf -27 r 112 c cmr10.329 @sf 9 r 43 c cmmi10.329 @sf 11('m)m cmr10.329 @sf 41 c 163 r 49 c cmtt10.329 @sf 240(JOB)m cmsy10.329 @sf 284 1843 p 15 c cmr10.329 @sf 15(Default)m 14(co)m 118 c -2(ari)m -1(ance)m 14(matrix:)m 312 r 48 c 279 r 49 c cmtt10.329 @sf 240(JOB)m cmr10.329 @sf 225 1927 p (Users)s 14(with)m 14 r 97 c 14 r 118 c (ery)s 13(time)m 13(consuming)m 14(subroutine)m cmtt10.329 @sf 14(FCN)m cmr10.329 @sf 14(should)m 15(also)m 13 r 98 c 1 r 101 c 15 r 97 c 119 c -1(a)m -1(re)m 13(of)m 14 r 116 c 119 c -2 r 111 c 12(of)m 14(ODR-)m 225 1984 p 80 c -3 r 65 c (CK's)s 14(options)m 15(that)m 16(are)m 16(sp)m 1(eci\014cally)m 16(designed)m 17(for)m 15(suc)m 104 c 16(problems.)m 22(The)m 17(most)m 15(imp)m 1(ortan)m 116 c 225 2040 p (of)s 18(these)m 18(is)m 18(the)m 18(restart)m 17(facilit)m 121 c -4 r 46 c 27(The)m 18(other)m 18(is)m 18(the)m 18(option)m 18(of)m 17(constructing)m 18(the)m 18(co)m 118 c -2(aria)m -1(nce)m 225 2097 p (matrix)s 12(without)m 11(recomputing)m 13(the)m 13(deriv)m -2(ativ)m -1 r 101 c 11(matrices)m 12(at)m 12(the)m 13(solution.)m 18(This)m 12(second)m 14(option)m 225 2153 p (is)s 18(discussed)m 18(in)m cmsy10.329 @sf 18 r 120 c cmr10.329 @sf (2.B.ii,)s 17(under)m 19(the)m 18(description)m 17(of)m 18(subroutine)m 18(argumen)m 116 c cmtt10.329 @sf 16(JOB)m cmr10.329 @sf 44 c 18(and)m 18(also)m 17(in)m cmsy10.329 @sf 225 2210 p 120 c cmr10.329 @sf (4.B.)s 22(The)m 16(remainder)m 16(of)m 15(this)m 16(section)m 15(describ)m 1(es)m 17(ho)m 119 c 14(ODRP)m -3 r 65 c (CK's)s 14(restart)m 15(facilit)m -1 r 121 c 14(can)m 16 r 98 c 1 r 101 c 225 2266 p (used)s 12(to)m 11(minimize)m 11(the)m 12(risk)m 11(of)m 11(losing)m 10(imp)m 1(ortan)m 116 c 9(results)m 11 r 98 c 1(ecause)m 13(system)m 11(imp)m 1(osed)m 12(time)m 11(limits)m 225 2323 p (are)s 15(reac)m (hed)s 14 r 98 c 1(efore)m 16(the)m 15(solution)m 14(is)m 15(found.)m 225 2353 p 690 2 ru cmr6.300 @sf 277 2381 p 49 c cmr9.300 @sf 294 2396 p 65 c 11(forw)m (ard)s 11(\014nite)m 12(di\013erence)m 12(appro)m (ximation)s 12(to)m 11(the)m 12(deriv)m -1(ativ)m 101 c 10(requires)m cmmi9.300 @sf 12 r 113 c cmr9.300 @sf 1 r 40 c 3 r 126 c cmmi9.300 @sf -22 r 112 c cmr9.300 @sf 6 r 43 c cmmi9.300 @sf 6('m)m cmr9.300 @sf 41 c 11(function)m 12(ev)m -1(aluations,)m 225 2442 p (and)s 14 r 97 c 13(cen)m (tral)s 12(\014nite)m 13(di\013erence)m 14(appro)m (ximation)s 13(requires)m 13 r 50 c cmmi9.300 @sf 113 c cmr9.300 @sf 1 r 40 c 3 r 126 c cmmi9.300 @sf -22 r 112 c cmr9.300 @sf 10 r 43 c cmmi9.300 @sf 8('m)m cmr9.300 @sf 41 c 13(function)m 13(ev)m -1(aluations.)m 17(\(See)m cmsy9.300 @sf 13 r 120 c cmr9.300 @sf (4.A.\))s cmr10.329 @sf 1065 2581 p (67)s @eop %%Page: 68 82 68 @bop0 68 @bop1 cmr10.329 @sf 0 114 p (68)s 831(When)m 16(the)m 15(Mo)m 1(del)m 15(Is)m 15 r 86 c -3(ery)m 15(Time)m 14(Consuming)m 0 134 p 1725 2 ru 0 259 p (The)s 14(restart)m 12(facilit)m -1 r 121 c 12(enables)m 14(the)m 13(user)m 14(to)m 13(step)m 14(through)m 13(the)m 14(solution)m 12(pro)m 1(cedure)m 15(one)m 13(or)m 13(more)m 0 315 p (iterations)s 13(at)m 15 r 97 c 14(time)m 15(without)m 14(incurring)m 14(an)m 121 c 14(additional)m 13(function)m 15(or)m 14(deriv)m -2(ativ)m 101 c 13(ev)m -2(aluations)m 0 372 p 111 c 118 c -1(er)m 10(what)m 11 r 119 c (ould)s 10 r 98 c 1 r 101 c 12(required)m 12(if)m 11(the)m 11(pro)m 1(cedure)m 13 r 119 c (ere)s 10(allo)m 119 c -2(ed)m 10(to)m 11(run)m 12(to)m 11(con)m 118 c -1(ergence.)m 18(Figure)m 0 428 p (3.1)s 14(sho)m (ws)s 13(an)m 14(example)m 15(of)m 14(ho)m 119 c 13(the)m 15(restart)m 13(facilit)m -1 r 121 c 13(can)m 15 r 98 c 1 r 101 c 15(emplo)m 121 c -1(ed.)m 18(This)m 14(example)m 15(allo)m -1(ws)m 0 484 p (up)s 17(to)m 16 r 97 c 16(total)m 14(of)m 16(30)m 16(iterations,)m 15(and)m 16(writes)m 15(the)m 17(con)m (ten)s (t)s -1 r 115 c 15(of)m 16(arra)m -1(ys)m cmtt10.329 @sf 15(BETA)m cmr10.329 @sf -1 r 44 c cmtt10.329 @sf 16(WORK)m cmr10.329 @sf 16(and)m cmtt10.329 @sf 17(IWORK)m cmr10.329 @sf 0 541 p (to)s 20 r 97 c 21(\014le)m 21 r 98 c 1(et)m 119 c (een)s 20(ev)m (ery)s 20(iteration,)m 20(alternating)m 19 r 98 c 1(et)m 119 c (een)s 20 r 116 c 119 c -1 r 111 c 18(\014les.)m 38(This)m 21(minimizes)m 20(the)m 0 597 p 99 c (hance)s 17(of)m 18(losing)m 16(signi\014can)m 116 c 16(amoun)m (ts)s 16(of)m 17(imp)m 1(ortan)m 116 c 16(information)m 16(due)m 18(to)m 17(system)m 18(imp)m 1(osed)m 0 654 p (limits:)s 20(if)m 16(suc)m 104 c 16 r 97 c 16(limit)m 14(is)m 16(reac)m (hed)s 16 r 98 c 1(efore)m 16(con)m 118 c (ergence,)s 15(arra)m -1(ys)m cmtt10.329 @sf 15(BETA)m cmr10.329 @sf -1 r 44 c cmtt10.329 @sf 16(WORK)m cmr10.329 @sf 16(and)m cmtt10.329 @sf 16(IWORK)m cmr10.329 @sf 16(can)m 0 710 p 98 c 1 r 101 c 22(restored)m 21(using)m 21(the)m 21(sa)m 118 c -1(ed)m 20(data)m 20(and)m 22(the)m 21(computations)m 20(restarted.)m 37(In)m 22(this)m 20(example,)m 0 767 p (the)s 19(initial)m 17(computation)m 19(rep)m 1(ort)m 18(is)m 19(only)m 19(generated)m 19(at)m 18(the)m 20(\014rst)m 18(iteration,)m 18(while)m 19(the)m 19(\014nal)m 0 823 p (computation)s 20(rep)m 1(ort)m 22(is)m 21(generated)m 21(after)m 21(ev)m (ery)s 20(iteration.)m 37(The)m 22(options)m 21(selected)m 22(include)m 0 880 p (constructing)s 12(the)m 14(co)m 118 c -2(a)m -1(riance)m 11(matrix)m 12(using)m 13(the)m 13(deriv)m -2(ativ)m -1 r 101 c 11(matrices)m 12(from)m 13(the)m 13(last)m 12(iteration,)m 0 936 p (and)s 21(th)m (us)s 20(no)m 21(additional)m 20(calls)m 20(to)m 20(subroutine)m cmtt10.329 @sf 21(FCN)m cmr10.329 @sf 21(are)m 21(incurred)m 21(in)m 21(order)m 21(to)m 20(pro)m (vide)s 20(the)m 0 992 p (standard)s 15(deviations)m 14(of)m 15(the)m 15(parameters)m 14(prin)m (ted)s 14(in)m 15(eac)m 104 c 15(of)m 14(the)m 16(rep)m 1(orts.)m 0 1069 p (Users)s 18(with)m 17 r 118 c (ery)s 16(time)m 18(consuming)m 17(problems)m 18(should)m 18 r 98 c 1 r 101 c 18 r 97 c 119 c -1(are)m 16(that,)m 17(dep)m 1(ending)m 19(on)m 18(whic)m 104 c 0 1125 p (options)s 21(are)m 22(selected,)m 24(ODRP)m -3 r 65 c (CK)s 21(will)m 21(mak)m 101 c 20(at)m 22(least)m 21(one)m 22(and)m 23 r 112 c 1(ossibly)m 22(more)m 21(calls)m 22(to)m 0 1181 p (subroutine)s cmtt10.329 @sf 14(FCN)m cmr10.329 @sf 14 r 98 c 1(efore)m 15(attempting)m 13(to)m 14(generate)m 14(an)m 121 c 14(computation)m 13(rep)m 1(orts.)m 19(Also,)m 14(on)m 14(man)m 121 c 0 1238 p (systems)s 16(the)m 16(output)m 17(generated)m 16 r 98 c 121 c 15 r 97 c 17(program)m 15(is)m 16(not)m 16(written)m 15(directly)m 16(in)m 16 r 97 c 16(\014le)m 17(but)m 16(rather)m 0 1294 p (is)s 19(stored)m 20(in)m 19 r 97 c 20(\\bu\013er")m 19(un)m (til)s 18(the)m 20(bu\013er)m 19(is)m 20(full,)m 19(and)m 20(is)m 20(only)m 19(written)m 19(to)m 19(the)m 20(\014le)m 20(at)m 19(that)m 0 1351 p 112 c 1(oin)m (t.)s 18(If)m 16 r 97 c 15(run)m 15(is)m 15(ab)m 1(orted)m 15(prematurely)m -3 r 44 c 14(either)m 14 r 98 c 121 c 15(the)m 15(user)m 15(or)m 15 r 98 c 1(ecause)m 16 r 97 c 15(system)m 15(imp)m 1(osed)m 0 1407 p (limit)s 16(is)m 17(reac)m (hed,)s 18(then)m 18(the)m 18(con)m (ten)s 116 c 15(of)m 17(these)m 18(bu\013ers)m 18(migh)m 116 c 16(not)m 17 r 98 c 1 r 101 c 19(emptied)m 17(in)m (to)s 16(the)m 18(\014les)m 0 1464 p (asso)s 1(ciated)m 21(with)m 20(them.)m 39(Th)m (us,)s 22(the)m 21(\014les)m 22(asso)m 1(ciated)m 20(with)m 21(the)m 22(logical)m 19(units)m 21(sp)m 1(eci\014ed)m 23 r 98 c 121 c 0 1520 p (argumen)s (ts)s cmtt10.329 @sf 13(LUNERR)m cmr10.329 @sf 13(and)m cmtt10.329 @sf 15(LUNRPT)m cmr10.329 @sf 14(migh)m 116 c 12(not)m 15(include)m 15(all)m 13(information)m 13(actually)m 13(generated)m 15 r 98 c 121 c 0 1577 p (ODRP)s -3 r 65 c (CK)s 15(at)m 15(the)m 16(time)m 15(it)m 15(stopp)m 1(ed.)m 22(When)m 17(the)m 16(user)m 16(is)m 15(not)m 16(getting)m 14(the)m 16(exp)m 1(ected)m 17(rep)m 1(orts)m 0 1633 p (from)s 15(ODRP)m -3 r 65 c (CK,)s 14(it)m 15(ma)m 121 c 15 r 98 c 1 r 101 c 16(necessary)m 16(to)m 15(ha)m 118 c 101 c 14(ODRP)m -3 r 65 c (CK)s 14(generate)m 16(rep)m 1(orts)m cmti10.329 @sf 15(dir)m -1 r 101 c -1(ctly)m cmr10.329 @sf 14(to)m 0 1690 p (\\standard)s 16(output,")m 16(whic)m 104 c 15(is)m 16(usually)m 16(not)m 16(bu\013ered,)m 16(in)m 17(order)m 16(to)m 15(determine)m 17(exactly)m 16(where)m 0 1746 p (the)s 14(computations)m 12(are)m 13(stopping.)m 19(\(See)m cmsy10.329 @sf 14 r 120 c cmr10.329 @sf (2.B.ii,)s 12(subroutine)m 13(argumen)m (ts)s cmtt10.329 @sf 12(IPRINT)m cmr10.329 @sf -1 r 44 c cmtt10.329 @sf 13(LUNERR)m cmr10.329 @sf 13(and)m cmtt10.329 @sf 0 1802 p (LUNRPT)s cmr10.329 @sf -1(.\))m @eop %%Page: 69 83 69 @bop0 1.000000 /cmtt8.300 @newfont cmtt8.300 @sf [ 8 26 -7 3 17.642] 124 @dc [<0FE01FF03C787038F000E000E000E000E000F00070103C381FF80FF0> 16 14 -2 0 17.642] 99 @dc [ 16 14 -2 0 17.642] 115 @dc [<0FE01FF03C787038F000E000FFF8FFF8E038F03870783CF01FE00FC0> 16 14 -2 0 17.642] 101 @dc [<03E007F00E780E380E380E000E000E000E000E000E000E00FFF8FFF80E000E000E000E00> 16 18 -1 0 17.642] 116 @dc [<07FF800FFF801C3C001C1C001C1C001C1C001C1C001C1C001C1C001C1C001C1C001C1C00FCFC00 FCFC00> 24 14 0 0 17.642] 117 @dc [ 16 21 0 7 17.642] 112 @dc [<7FFC7FFC0380038003800380038003800380038003800380FFFEFFFE03800380038203C701FF00 7E> 16 20 0 0 17.642] 102 @dc [ 16 21 -3 0 17.642] 105 @dc [ 16 20 -1 0 17.642] 108 @dc [<0F803FE038E07070F078E038E038E038E038E038707038E03FE00F80> 16 14 -2 0 17.642] 111 @dc [<1FBE7FFEF0F0E070E070F07078703FF00FF00070207070F07FE03F80> 16 14 -2 0 17.642] 97 @dc [<038007C007C006C00EE00EE00EE01C701C701C703C783838FEFEFEFE> 16 14 -1 0 17.642] 118 @dc [ 24 14 1 0 17.642] 109 @dc [ 24 14 0 0 17.642] 110 @dc [ 16 14 -1 0 17.642] 114 @dc [<7FF07FF0070007000700070007000700070007000700070007000700F700FF001F000F00070003 00> 16 20 -2 0 17.642] 49 @dc [ 16 9 -1 -6 17.642] 61 @dc [<3FE07FF07070E038E038E038E038E038E038E038E038E038E038E038E038E038E03870707FF03F E0> 16 20 -2 0 17.642] 79 @dc [ 16 20 -1 0 17.642] 80 @dc [ 16 20 -1 0 17.642] 69 @dc [ 16 20 -1 0 17.642] 78 @dc [<018007800F001E003C00380078007000F000E000E000E000E000E000E000E000F0007000780038 003C001E000F0007800180> 16 25 -5 2 17.642] 40 @dc [ 8 10 -6 5 17.642] 44 @dc [ 8 12 -6 -8 17.642] 39 @dc [<70F8F8F870> 8 5 -6 0 17.642] 46 @dc [<0FBF3FFF78F87078F038E038E038E038E038F038707838F81FF80FB8003800380038003801F801 F8> 16 20 -1 0 17.642] 100 @dc [ 16 25 -3 2 17.642] 41 @dc [ 16 20 -2 0 17.642] 50 @dc [ 24 20 0 0 17.642] 104 @dc [ 16 14 -1 0 17.642] 120 @dc [<1DF01FF81F1C1E0E1C0F1C071C071C071C071C0F1E0E1F1E1FFC1DF01C001C001C001C00FC00FC 00> 16 20 0 0 17.642] 98 @dc [ 16 20 -1 0 17.642] 68 @dc [ 16 20 -1 0 17.642] 82 @dc [ 16 20 -1 0 17.642] 65 @dc [<07E00FF81E3C381E780E700EF00EE000E000E000E000E000E000F00E700E781E381E1E3E0FFE07 E6> 16 20 -1 0 17.642] 67 @dc [ 16 20 -1 0 17.642] 75 @dc [<1CF01CF01CF038B83AB83FF83FF83BB838383018701C701CFEFEFEFE> 16 14 -1 0 17.642] 119 @dc [<0FE03FF8783CF01EE00EE00EE00EF03E7FFC3FF83FF070007F803FE038E0707070707070707038 E73FFF0FBE> 16 22 -1 8 17.642] 103 @dc [<3C007E007700778003800380038003C003C003C006E006E00E600E600E701C701C701C383C38FE FEFEFE> 16 21 -1 7 17.642] 121 @dc [ 24 20 0 0 17.642] 107 @dc [<7F00FF80E3C0E1E000E000E000E000E000E000E000E000E000E000E000E000E000E000E000E03F E03FE000000000000000C001E001E000C0> 16 28 -2 7 17.642] 106 @dc [<07C00FE01C703838701C701CE01EE00EE00EE00EE00EE00EE00EE00E701C701C38381C700FE007 C0> 16 20 -1 0 17.642] 48 @dc [<1FE07FF8F83CE01CE00EE00E000E000E001C003C07F807F00078003C001C701C701C787C3FF81F E0> 16 20 -1 0 17.642] 51 @dc [ 16 20 0 0 17.642] 76 @dc [ 16 20 -2 0 17.642] 73 @dc [ 16 20 -1 0 17.642] 70 @dc [<00FF8000FF80001C00001C00001C00001C00001C000FDC001FFC003C7C00703C00F01C00E01C00 E01C00E01C00E01C00F01C00703C003C7C001FFC000FDC00> 24 21 -1 7 17.642] 113 @dc [<1FF01FF00380038003800380038003800380038003800380038003800380E38EE38EE38EFFFEFF FE> 16 20 -1 0 17.642] 84 @dc [ 16 20 -1 0 17.642] 72 @dc [ 16 20 -2 0 17.642] 83 @dc [<03E0000FF8001E3C001C1C003C1E00380E00380E00380E00380E00380E00380E00380E00380E00 380E00380E00380E00380E00380E00FE3F80FE3F80> 24 20 0 0 17.642] 85 @dc [<0E38001E3C001F7C001B6C001B6C001B6C001B6C001B6C001B6C001BEC003BEE003BEE00380E00 380E00380E00380E00380E00380E00FE3F80FE3F80> 24 20 0 0 17.642] 87 @dc [<070007000700E738FFF87FF01FC01FC07FF0FFF8E738070007000700> 16 14 -2 -3 17.642] 42 @dc 69 @bop1 cmr10.329 @sf 225 114 p (When)s 16(the)m 15(Mo)m 1(del)m 15(Is)m 15 r 86 c -3(ery)m 15(Time)m 14(Consuming)m 831(69)m 225 134 p 1725 2 ru 605 343 p (Figure)s 15(3.1:)m 19(Using)m 14(ODRP)m -3 r 65 c (CK's)s 14(Restart)m 14 r 70 c -3(acilit)m -1 r 121 c cmtt8.300 @sf 408 429 p 124 c 408 469 p 99 c 35(set)m 17(up)m 17(files)m 16(to)m 16(save)m 17(computa)m -1(ti)m -1(ons)m 15(for)m 17(future)m 15(restarts)m 514 508 p (lun1)s 16 r 61 c 18(11)m 514 547 p (OPEN)s 16(\(unit=lu)m -1(n1,)m -1(fil)m -1(e=')m -1(sav)m -1(e1)m -1(.da)m -1(t'\))m 514 587 p (lun2)s 16 r 61 c 18(12)m 514 626 p (OPEN)s 16(\(unit=lu)m -1(n2,)m -1(fil)m -1(e=')m -1(sav)m -1(e2)m -1(.da)m -1(t'\))m 408 705 p 99 c 35(set)m 17(the)m 16(maximum)m 15(number)m 16(of)m 17(iterati)m -1(ons)m 15(for)m 17(each)m 16(call)m 16(to)m 17(ODRPACK)m 15(to)m 17(one)m 408 745 p 99 c 35(so)m 17(results)m 15(can)m 17(be)m 17(stored)m 15(between)m 15(iteration)m -1 r 115 c 514 784 p (maxit)s 16 r 61 c 17 r 49 c 408 863 p 99 c 35(set)m 17(argumen)m -1 r 116 c 16(approp)m -1(ria)m -1(tel)m -1(y,)m 15(making)m 16(sure)m 16(for)m 16(first)m 16(iteratio)m -1 r 110 c 16(that)m 408 902 p 99 c 159(fit)m 16(is)m 17(not)m 17 r 97 c 17(restart)m 15(and)m 408 942 p 99 c 159(covaria)m -1(nc)m -1 r 101 c 16(matrix)m 15(is)m 17(construc)m -1(ted)m 15(without)m 15(recompu)m -1(tin)m -1 r 103 c 16(derivat)m -1(iv)m -1(es)m 514 981 p (job)s 17 r 61 c 17(00100)m 408 1060 p 99 c 35(set)m 17(iprint)m 15(to)m 17(indicate)m 15 r 97 c 17(long)m 16(initial)m 16(report)m -1 r 44 c 408 1099 p 99 c 441 r 97 c 17(short)m 16(iteratio)m -1 r 110 c 16(report)m -1 r 44 c 16(and)m 408 1139 p 99 c 441 r 97 c 17(long)m 16(final)m 16(report)m 514 1178 p (iprint)s 16 r 61 c 17(2112)m 408 1257 p 99 c 35(step)m 16(through)m 16(up)m 16(to)m 17(30)m 17(iteratio)m -1(ns)m 514 1297 p (DO)s 17(100)m 17(niter)m 15 r 61 c 18(1,)m 17(30)m 567 1376 p (CALL)s 16(dodrc\(fc)m -1(n,)m 15(...)m 17(,info\))m 408 1454 p 99 c 35(save)m 16(the)m 17(content)m -1 r 115 c 16(of)m 17(beta,)m 16(work)m 16(and)m 16(iwork)m 16(for)m 17(future)m 15(referenc)m -1 r 101 c 567 1494 p (IF)s 17(\(mod\(ni)m -1(ter)m -1(,2\))m -1(.eq)m -1(.1\))m 15(THEN)m 620 1533 p (lun)s 17 r 61 c 17(lun1)m 567 1573 p (ELSE)s 620 1612 p (lun)s 17 r 61 c 17(lun2)m 567 1652 p (END)s 17(IF)m 567 1691 p (OPEN)s 34(\(UNIT=l)m -1(un\))m 567 1730 p (WRITE)s 16(\(lun,*\))m 15(\(beta\(k\))m -1(,k)m -1(=1,)m -1(np\))m 567 1770 p (WRITE)s 16(\(lun,*\))m 15(\(work\(i\))m -1(,i)m -1(=1,)m -1(lwo)m -1(rk\))m 567 1809 p (WRITE)s 16(\(lun,*\))m 15(\(iwork\(i)m -1(\),)m -1(i=1)m -1(,li)m -1(wor)m -1(k\))m 567 1849 p (CLOSE)s 16(\(UNIT=l)m -1(un\))m 567 1928 p (IF)s 17(\(info.g)m -1(e.1)m -1(000)m -1 r 48 c 16(.or.)m 16(mod\(inf)m -1(o,1)m -1(0\).)m -1(le)m -1(.3\))m 15(then)m 408 1967 p 99 c 35(stop)m 16(because)m 16(either)m 15 r 97 c 17(fatal)m 16(error)m 16(was)m 17(detect)m -1(ed,)m 15(or)m 17(the)m 16(problem)m 16(conver)m -1(ged)m 620 2006 p (stop)s 567 2046 p (ELSE)s 408 2085 p 99 c 35(set)m 17(job)m 16(to)m 17(indicate)m 15(the)m 17(next)m 16(iterati)m -1(on)m 15(is)m 17 r 97 c 17(restart)m 16(and)m 408 2125 p 99 c 35(set)m 17(iprint)m 15(to)m 17(suppress)m 15(the)m 17(initia)m -1 r 108 c 16(report)m 15(for)m 17(future)m 15(iteratio)m -1(ns.)m 620 2164 p (job)s 17 r 61 c 17(10100)m 620 2204 p (iprint)s 15 r 61 c 18(0112)m 567 2243 p (END)s 17(IF)m 444 2283 p (100)s 16(CONTINUE)m 408 2322 p 99 c 408 2361 p 124 c @eop %%Page: 70 84 70 @bop0 70 @bop1 cmr10.329 @sf 0 114 p (70)s 831(When)m 16(the)m 15(Mo)m 1(del)m 15(Is)m 15 r 86 c -3(ery)m 15(Time)m 14(Consuming)m 0 134 p 1725 2 ru @eop %%Page: 71 85 71 @bop0 cmcsc10.518 @sf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dc [ 32 37 -3 0 40.009] 112 @dc cmbx12.300 @sf [<00FFFE00FFFE0007E00007E00007E00007E00007E00007E00007E0FFFFFEFFFFFEE007E07007E0 3807E01807E00C07E00E07E00707E00307E00187E001C7E000E7E00077E00037E0001FE0001FE0 000FE00007E00003E00003E00001E00000E0> 24 32 -2 0 28.019] 52 @dc [<0FF8003FFF00783F80FE1FC0FE1FE0FE0FE0FE0FE0FE0FE07C0FE0000FE0000FE0000FE0000FE0 000FE0000FE0000FE0000FE0000FE0000FE0000FE0000FE0000FE0000FE0000FE0000FE0000FE0 000FE0000FE0000FE0000FE0000FE0000FE007FFFE07FFFE> 24 34 -2 0 28.942] 74 @dc [ 48 34 -2 0 53.156] 77 @dc cmmi8.300 @sf [<1FC0007FF000707800E01C00E00E00E00700E00700E00380E00380F003807807C03C0FC01FFFC0 0FFDC00081C00001C00001C01E01C00E01C00E03800F0F0007FE0001FC00> 24 23 -1 0 18.587] 64 @dc [<7800FE00EE00E700070007000380038003800380038003C001C001C001C001C001E000E00FFE0F FE00E000E000F0007000700077003F003F001F> 16 29 -2 6 16.950] 102 @dc cmmi6.300 @sf [ 8 17 -2 0 10.003] 108 @dc cmr8.300 @sf [ 8 20 -3 6 9.801] 59 @dc cmmi6.300 @sf [ 16 17 -2 0 16.460] 107 @dc cmr10.329 @sf [<07F00F801FFC3FE03E1EF8707C07F0307803C018F807C018F00FE000F00F7000F01E3000F03C38 00F03C180078781C0038F00C001CF00E000FE0070007E0030003C0038003C0038003E007E003F0 1FFC03B81FFC071C0000070E0000070E0000070700000707000007030000070300000703000007 0300000387000003CE000001FE0000007C0000> 32 34 -2 1 35.353] 38 @dc cmmi6.300 @sf [<7800FE00EE00670003000300038003800180018001C001C018C01CC00FC0078000000000000000 0000E000E000E0> 16 23 0 5 12.741] 106 @dc cmbx10.329 @sf [<3E07C07F0FE07F0FE0FF1FE0FF1FE0FF1FE0FE1FC0C01800E01C00E01C00600C00700E00380700 3C07801E03C00E01C0> 24 16 -5 -16 27.398] 92 @dc [<700E00780F003C07801C03800E01C00600C00700E00700E00300607F0FE0FF1FE0FF1FE0FF1FE0 FE1FC0FE1FC07C0F80> 24 16 -2 -16 27.398] 34 @dc 71 @bop1 cmcsc10.518 @sf 225 519 p (4.)s 35(Comput)m -4 r 97 c -4(tional)m 25(Det)m -4(ails)m cmbx12.300 @sf 225 747 p (4.A.)s 18(Computing)m 19(the)m 18(Jacobian)m 19(Matrices)m cmr10.329 @sf 225 868 p (As)s 12 r 119 c (as)s 11(noted)m 12(in)m cmsy10.329 @sf 12 r 120 c cmr10.329 @sf (1.A,)s 12(the)m 13(matrices)m 11(of)m 12(\014rst)m 12(partial)m 10(deriv)m -2(ativ)m -1(es,)m 11(i.e.,)m 11(the)m 13(Jacobian)m 12(matrices)m cmmi8.300 @sf 518 944 p 64 c 2 r 102 c cmmi6.300 @sf 556 950 p (il)s cmr8.300 @sf 578 944 p 40 c cmmi8.300 @sf 120 c cmmi6.300 @sf 612 949 p 105 c cmr8.300 @sf 625 944 p 43 c cmmi8.300 @sf 14 c cmmi6.300 @sf 668 949 p 105 c cmr8.300 @sf 681 944 p 59 c cmmi8.300 @sf 12 c cmr8.300 @sf 2 r 41 c 518 956 p 209 2 ru cmmi8.300 @sf 592 980 p 64 c 2 r 12 c cmmi6.300 @sf 633 986 p 107 c cmmi10.329 @sf 731 965 p 59 c 53 r 105 c cmr10.329 @sf 12 r 61 c 13 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 8 r 58 c 5 r 59 c 8(n;)m 47 r 107 c cmr10.329 @sf 14 r 61 c 13 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 7 r 58 c 5 r 59 c 8(p;)m cmr10.329 @sf 47 r 38 c cmmi10.329 @sf 16 r 108 c cmr10.329 @sf 13 r 61 c 13 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 7 r 58 c 5 r 59 c 8 r 113 c 2 r 59 c cmmi8.300 @sf 518 1069 p 64 c 2 r 102 c cmmi6.300 @sf 556 1075 p (il)s cmr8.300 @sf 578 1069 p 40 c cmmi8.300 @sf 120 c cmmi6.300 @sf 612 1074 p 105 c cmr8.300 @sf 625 1069 p 43 c cmmi8.300 @sf 14 c cmmi6.300 @sf 668 1074 p 105 c cmr8.300 @sf 681 1069 p 59 c cmmi8.300 @sf 12 c cmr8.300 @sf 2 r 41 c 518 1081 p 209 2 ru cmmi8.300 @sf 584 1106 p 64 c cmr8.300 @sf 2 r 1 c cmmi6.300 @sf 634 1111 p (ij)s cmmi10.329 @sf 731 1090 p 59 c 53 r 105 c cmr10.329 @sf 12 r 61 c 13 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 8 r 58 c 5 r 59 c 8(n;)m 41 r 106 c cmr10.329 @sf 15 r 61 c 12 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 8 r 58 c 5 r 59 c 8(m;)m cmr10.329 @sf 40 r 38 c cmmi10.329 @sf 16 r 108 c cmr10.329 @sf 13 r 61 c 13 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 7 r 58 c 5 r 59 c 8 r 113 c 2 r 59 c cmr10.329 @sf 1857 1028 p (\(4)s cmmi10.329 @sf 58 c cmr10.329 @sf (1\))s 225 1188 p (are)s 20(required)m 20(at)m 20(ev)m (ery)s 19(iteration.)m 33(These)m 21(can)m 20 r 98 c 1 r 101 c 21(pro)m (vided)s 19 r 98 c 121 c 19(the)m 20(user)m 21(as)m 19(describ)m 1(ed)m 22(for)m 225 1244 p (subroutine)s 19(argumen)m 116 c cmtt10.329 @sf 18(FCN)m cmr10.329 @sf 19(in)m cmsy10.329 @sf 19 r 120 c cmr10.329 @sf (2.B.ii,)s 18(or)m 19(can)m 19 r 98 c 1 r 101 c 20(appro)m (ximated)s 17(automatically)m 17 r 98 c 121 c 18(ODR-)m 225 1301 p 80 c -3 r 65 c (CK.)s 16(User)m 19(supplied)m 19(deriv)m -2(ativ)m -1(es)m 17(are)m 18(generally)m 18(either)m 18(\\hand)m 19(co)m 1(ded")m 19(as)m 18(is)m 18(done)m 19(in)m 19(the)m 225 1357 p (example)s 15(program)m 14(sho)m (wn)s 14(in)m cmsy10.329 @sf 15 r 120 c cmr10.329 @sf (2.C.i,)s 13(or)m 15(are)m 15(the)m 15(pro)m 1(duct)m 15(of)m 15(an)m 15(\\automatic)m 13(di\013eren)m (tiati)s -1(on")m 225 1414 p (to)s 1(ol.)m 35(ODRP)m -3 r 65 c (CK's)s 19(appro)m (ximati)s -1(ons)m 19(are)m 20(formed)m 21(using)m 20(either)m 20(forw)m (ard)s 19(or)m 20(cen)m (tral)s 19(\014nite)m 225 1470 p (di\013erences.)s cmbx10.329 @sf 225 1608 p (4.A.i.)s 15(\\Hand)m 18(Co)m 1(ded")m 19(Deriv)m -3(ativ)m -1(es)m cmr10.329 @sf 225 1714 p (Hand)s 16(co)m 1(ded)m 17(deriv)m -2(ativ)m -1(es)m 14(are)m 16(those)m 15(pro)m 1(duced)m 17 r 98 c 121 c 15(the)m 16(user)m 16(without)m 15(the)m 16(aid)m 16(of)m 15 r 97 c 16(di\013eren)m (ti-)s 225 1770 p (ation)s 15(to)m 1(ol.)m 20(Because)m 16(co)m 1(ding)m 16(errors)m 15(are)m 15 r 97 c 16(common)m 15(problem)m 15(with)m 15(hand)m 17(co)m 1(ded)m 16(deriv)m -2(ativ)m -1(es,)m 225 1826 p (ODRP)s -3 r 65 c (CK)s 14(has)m 16(an)m 15(option)m 15(to)m 15 r 99 c (hec)s 107 c 14(the)m 16 r 118 c -2(alidit)m -1 r 121 c 13(of)m 15(the)m 16(user)m 16(supplied)m 16(deriv)m -2(ativ)m -1 r 101 c 14(co)m 1(de)m 16 r 98 c 121 c 225 1883 p (comparing)s 13(its)m 13(results)m 14(to)m 13(\014nite)m 14(di\013erence)m 14 r 118 c -2(alues)m 13(for)m 13(the)m 14(deriv)m -2(ativ)m -1(e.)m 18(The)m 14(deriv)m -2(ativ)m -1 r 101 c 12 r 99 c (hec)s (k-)s 225 1939 p (ing)s 17(pro)m 1(cedure)m 18(examines)m 16(the)m 17(un\014xed)m 19 r 118 c -2(ariables)m 15(at)m 16(only)m 17(one)m 17(ro)m 119 c 15(of)m 17(the)m 17(Jacobian)m 17(matrix,)m 225 1996 p (and)s 14(is)m 13(therefore)m 14(quite)m 13(e\016cien)m (t.)s 18(Chec)m (king)s 13(only)m 13(one)m 14(ro)m 119 c 11(is)m 14(reasonable)m 13(for)m 13(regression)m 13(mo)m 1(d-)m 225 2052 p (els)s 12(since)m 12(the)m 12(same)m 12(co)m 1(de)m 12(is)m 12(frequen)m (tly)s 10(used)m 13(to)m 11(compute)m 13(the)m 12(mo)m 1(del)m 12(function)m 12(and)m 12(deriv)m -2(ativ)m -1(es)m 225 2109 p (for)s 15(eac)m 104 c 14(ro)m (w,)s 13(as)m 15(is)m 14(the)m 15(case)m 16(for)m 14(eac)m 104 c 15(of)m 14(the)m 16(examples)m 15(sho)m (wn)s 13(in)m cmsy10.329 @sf 15 r 120 c cmr10.329 @sf 1(2.C.)m 225 2185 p (When)s 17(the)m 16 r 118 c -2(alue)m 16(of)m 16(the)m 16(user)m 17(supplied)m 17(deriv)m -2(ativ)m -1 r 101 c 14(disagrees)m 16(with)m 16(the)m 17(corresp)m 1(onding)m 16(\014nite)m 225 2241 p (di\013erence)s 19 r 118 c -2(alue,)m 17(the)m 19 r 99 c (hec)s (king)s 16(pro)m 1(cedure)m 19(attempts)m 17(to)m 18(determine)m 18(whether)m 19(the)m 18(disagree-)m 225 2298 p (men)s 116 c 19(is)m 20(due)m 21(to)m 20(an)m 20(error)m 20(in)m 20(the)m 20(user's)m 20(co)m 1(de,)m 22(or)m 20(is)m 20(due)m 21(to)m 20(the)m 20(inaccuracy)m 21(of)m 19(the)m 21(\014nite)m 225 2354 p (di\013erence)s 17(appro)m (xima)s -1(tio)m -1(n.)m 22(The)m 16 r 99 c (hec)s (king)s 15(pro)m 1(cedure)m 17(generates)m 16(an)m 16(error)m 16(rep)m 1(ort)m 16(when)m 17(one)m 225 2411 p (or)s 10(more)m 11(of)m 10(the)m 11(deriv)m -2(ativ)m -1(es)m 9(are)m 11(found)m 11(to)m 10 r 98 c 1 r 101 c 12(questionable.)m 18(This)m 10(information)m 9(is)m 11(also)m 10(returned)m 225 2467 p (to)s 15(the)m 15(user)m 15(in)m 15(subroutine)m 15(argumen)m 116 c cmtt10.329 @sf 14(IWORK)m cmr10.329 @sf -1 r 46 c 20(\(See)m cmsy10.329 @sf 15 r 120 c cmr10.329 @sf 1(5.B.\))m 1065 2581 p (71)s @eop %%Page: 72 86 72 @bop0 cmbx10.329 @sf [<3FF8FFF0003FF8FFF00007C01F000007C01F000007C01F000007C01F000007C01F000007C01F00 0007C01F000007C01F000007C01F000007C01F000007C01F000007C01F000007C01F000007C01F 000007C01F000007C01F0000FFFFFFF800FFFFFFF80007C01F000007C01F000007C01F000007C0 1F000007C03F000007C07F078007C07F0FC007E07F8FC003F07F8FC001FC3FEFC0007FFFFF8000 0FF07F00> 40 32 0 0 30.492] 11 @dc 72 @bop1 cmr10.329 @sf 0 114 p (72)s 1227(Computational)m 13(Details)m 0 134 p 1725 2 ru 0 259 p (Questionable)s 15(deriv)m -2(ativ)m -1(es)m 13(can)m 15 r 111 c 1(ccur)m 16(when)m 16(the)m 15(deriv)m -2(ativ)m -1 r 101 c 13(is)m 15(exactly)m 14(zero)m 15(or)m 15(when)m 15(the)m 16 r 110 c (u-)s 0 315 p (merical)s 16(deriv)m -2(ativ)m -1 r 101 c 14(used)m 18(in)m 16(the)m 17 r 99 c (hec)s (king)s 14(pro)m 1(cedure)m 18(is)m 16 r 98 c 1(eliev)m (ed)s 16(to)m 15 r 98 c 1 r 101 c 18(inaccurate)m 16 r 98 c 1(ecause)m 0 372 p (of)s 14(the)m 14(prop)m 1(erties)m 14(of)m 14(the)m 14(function.)m 20(Zero)m 14 r 118 c -2(alued)m 13(deriv)m -2(ativ)m -1(es)m 13(are)m 14(questionable)m 14 r 98 c 1(ecause)m 15(they)m 0 428 p (could)s 17(indicate)m 16(that)m 16(the)m 17(initial)m 15 r 118 c -2(alues)m 16(of)m 17(the)m 17(function)m 16(parameters)m cmmi10.329 @sf 16 r 12 c cmr10.329 @sf 19(migh)m 116 c 15 r 98 c 1 r 101 c 17(hiding)m 17(an)m 0 484 p (error)s 15(in)m 15(the)m 16(deriv)m -2(ativ)m -1(e,)m 13(suc)m 104 c 15(as)m 15(could)m 16 r 111 c 1(ccur)m 16(if)m 14(the)m 16(initial)m 14 r 118 c -2(alue)m 14(of)m 15(one)m 16(of)m 15(the)m 16(parameters)m 0 541 p 119 c (as)s 13(zero.)m 19(Users)m 14(should)m 15(examine)m 14(the)m 15(ODRP)m -3 r 65 c (CK)s 13(error)m 13(rep)m 1(orts,)m 14(or)m 14(the)m 15(enco)m 1(ded)m 15 r 118 c -2(alues)m 14(in)m 0 597 p (subroutine)s 18(argumen)m 116 c cmtt10.329 @sf 16(IWORK)m cmr10.329 @sf 17(as)m 18(describ)m 1(ed)m 19(in)m cmsy10.329 @sf 17 r 120 c cmr10.329 @sf 1(5.B,)m 17(to)m 18(determine)m 18(the)m 18(cause)m 18(of)m 17(the)m 18(ques-)m 0 654 p (tionable)s 12(results,)m 13(and)m 13(then)m 13(examine)m 13(subroutine)m cmtt10.329 @sf 13(FCN)m cmr10.329 @sf 13(to)m 12(insure)m 13(that)m 12(there)m 14(is)m 12(not)m 13(an)m 13(error)m 12(in)m 0 710 p (the)s 15(user)m 15(supplied)m 15(deriv)m -2(ativ)m -1(es)m 12(that)m 14(could)m 15 r 98 c 1 r 101 c 15(adv)m (ersely)s 13(a\013ecting)m 14(the)m 15(least)m 13(squares)m 15(results.)m cmbx10.329 @sf 0 850 p (4.A.ii.)s 15(Automatic)m 17(Di\013eren)m (tiation)s cmr10.329 @sf 0 955 p (Automatic)s 19(di\013eren)m (tia)s -1(tio)m -1 r 110 c 18(to)m 1(ols)m 19(pro)m 1(duce)m 21(co)m 1(de)m 21(to)m 19(calculate)m 19 r 97 c 20(function's)m 19(deriv)m -2(ativ)m -1(es)m 18(di-)m 0 1012 p (rectly)s 13(from)m 13(the)m 14(co)m 1(de)m 14(used)m 14(to)m 13(compute)m 14(the)m 14(function)m 13 r 118 c -2(alues.)m 18(Suc)m 104 c 14(to)m 1(ols)m 12(enable)m 14(the)m 14(user)m 14(to)m 0 1068 p (generate)s 15(the)m 15(deriv)m -2(ativ)m -1(es)m 14(required)m 15 r 98 c 121 c 14(ODRP)m -3 r 65 c (CK)s 14(without)m 14(the)m 16(tedium)m 15(and)m 15(errors)m 14(asso)m 1(ci-)m 0 1125 p (ated)s 13(with)m 12(hand)m 14(co)m 1(ded)m 14(deriv)m -2(ativ)m -1(es.)m 17(An)m 13 r 111 c 118 c -1(erview)m 11(of)m 13(automatic)m 11(di\013eren)m (tiat)s -1(ion)m 11(is)m 12(presen)m (ted)s 0 1181 p (in)s 18([Griew)m -1(ank,)m 16(1989],)m 17(and)m 18 r 97 c 17(surv)m (ey)s 17(of)m 17(automatic)m 16(di\013eren)m (tiati)s -1(on)m 16(soft)m 119 c -1(a)m -1(re)m 16(is)m 17(pro)m (vided)s 17(in)m 0 1238 p ([Juedes,)s 14(1991].)m 17 r 87 c -3 r 101 c 12(ha)m 118 c 101 c 11(found)m 13(to)m 1(ols)m 11(suc)m 104 c 13(as)m 12(ADIF)m (OR)s 12([Bisc)m (hof)s cmti10.329 @sf 11(et)m 14(al.)m cmr10.329 @sf 44 c 13(1991])m 11(and)m 13 r 68 c (APRE)s 0 1294 p ([Stephens)s 13(and)m 12(Pryce,)m 13(1991],)m 10(whic)m 104 c 11(are)m 12(precompilers)m 12(that)m 11(transform)m 11 r 97 c 12 r 70 c -3(ortran)m 10(subroutine)m 0 1350 p (that)s 15(ev)m -2(aluates)m 15(the)m 16(function)m 16(in)m (to)s 15 r 97 c 15 r 70 c -3(ortran)m 14(subroutine)m 16(that)m 16(ev)m -2(aluates)m 15 r 98 c 1(oth)m 16(the)m 16(function)m 0 1407 p (and)s 15(its)m 15(deriv)m -2(ativ)m -1(es,)m 13(esp)m 1(ecially)m 15(suitable)m 14(for)m 15(use)m 15(with)m 15(ODRP)m -3 r 65 c (CK.)s 0 1483 p (Curren)s (tly)s -4 r 44 c 12(most)m 12(di\013eren)m (tiat)s -1(ion)m 11(to)m 1(ols,)m 12(including)m 13(ADIF)m (OR)s 13(and)m 13 r 68 c (APRE,)s 12(generate)m 13(co)m 1(de)m 14(to)m 0 1539 p (ev)s -2(aluate)m 16(the)m 18(function)m 18(and)m 17(deriv)m -2(ativ)m -1 r 101 c 16 r 118 c -2(alues)m 17(sim)m (ulta)s -1(neously)m -3 r 46 c 25(Least)m 17(squares)m 17(pro)m 1(cedures,)m 0 1596 p (ho)s 119 c -1(ev)m -1(er,)m 14(need)m 17(the)m 16(deriv)m -2(ativ)m -1(es)m 14(only)m 16(after)m 15(determining)m 15(that)m 16 r 97 c 15(satisfactory)m 14(new)m 17 r 112 c 1(oin)m 116 c 14(has)m 0 1652 p 98 c 1(een)m 21(found,)m 20(and)m 20(this)m 18(determination)m 19(requires)m 19(at)m 19(least)m 18(one)m 20(and)m 19 r 112 c 1(ossibly)m 19(more)m 19(function)m 0 1709 p (ev)s -2(aluations.)m 29(Th)m (us,)s 18(when)m 20(using)m 18 r 97 c 19(di\013eren)m (tiat)s -1(ion)m 17(to)m 1(ol,)m 18(one)m 19(has)m 19 r 116 c 119 c -1 r 111 c 16 r 99 c (hoices:)s 26(either)m 19(the)m 0 1765 p (function)s 15(and)m 16(deriv)m -2(ativ)m -1(es)m 13(can)m 16 r 98 c 1 r 101 c 16(alw)m 97 c -2(ys)m 13(ev)m -2(aluated)m 15(together)m 14(using)m 15(the)m 16(co)m 1(de)m 16(generated)m 15 r 98 c 121 c 0 1822 p (the)s 18(di\013eren)m (tiat)s -1(ion)m 16(to)m 1(ol;)m 18(or)m 18(the)m 18(hand)m 18(co)m 1(ded)m 19(function)m 18(can)m 18 r 98 c 1 r 101 c 19(ev)m -2(aluated)m 17 r 98 c 121 c 17(itself)m 17(un)m (til)s 16 r 97 c 0 1878 p (satisfactory)s 19(new)m 21 r 112 c 1(oin)m 116 c 19(has)m 21 r 98 c 1(een)m 22(found,)m 22(at)m 20(whic)m 104 c 19(time)m 21(the)m 20(deriv)m -2(ativ)m 101 c 19(co)m 1(de)m 21(generated)m 0 1935 p 98 c 121 c 18(the)m 19(di\013eren)m (tiat)s -1(ion)m 17(to)m 1(ol)m 18(co)m 1(de)m 20(can)m 19 r 98 c 1 r 101 c 19(ev)m -2(aluated.)m 31(The)m 19(\014rst)m 19 r 99 c (hoice)s 18(has)m 19(the)m 19(dra)m (wbac)s -1 r 107 c 0 1991 p (that)s 16(sometimes)m 16(the)m 18(computed)m 17(deriv)m -2(ativ)m -1 r 101 c 15 r 118 c -2(alues)m 17(will)m 15(not)m 17 r 98 c 1 r 101 c 18(used.)m 26(If)m 17(the)m 17(second)m 18(option)m 0 2047 p (is)s 15(selected,)m 16(the)m 16(function)m 16 r 118 c -2(alues)m 15(pro)m 1(duced)m 17 r 98 c 121 c 15(the)m 15(di\013eren)m (tiati)s -1(on)m 14(to)m 1(ol)m 15(generated)m 16(co)m 1(de)m 16(are)m 0 2104 p (used)s 17(only)m 15(for)m 16(the)m 16(ev)m -2(aluation)m 14(of)m 16(the)m 16(Jacobian)m 16(matrices)m 15(and)m 16(not)m 16(within)m 15(the)m 16(least)m 15(squares)m 0 2160 p (pro)s 1(cedure.)m 0 2236 p 70 c -3(or)m 15(the)m 16(di\013eren)m (tia)s -1(tio)m -1 r 110 c 15(to)m 1(ols)m 15(and)m 16(problems)m 16(examined)m 16 r 98 c 121 c 15(the)m 17(authors,)m 15(the)m 16(time)m 16(required)m 0 2293 p (to)s 20(ev)m -2(aluate)m 20(the)m 22(deriv)m -2(ativ)m -1 r 101 c 19(and)m 21(function)m 21(together)m 21(using)m 21(co)m 1(de)m 21(generated)m 21 r 98 c 121 c 20(automatic)m 0 2349 p (di\013eren)s (tiat)s -1(ion)m 15(is)m 17(frequen)m (tly)s 17(signi\014can)m (tl)s -1 r 121 c 16(more)m 17(than)m 17(that)m 17(required)m 18(to)m 16(ev)m -2(aluate)m 17(only)m 17(the)m 0 2406 p (hand)s 17(co)m 1(ded)m 17(function.)m 23 r 87 c -3 r 101 c 15(th)m (us)s 16 r 98 c 1(eliev)m 101 c 15(that)m 15(in)m 17(most)m 15(cases)m 16(it)m 16(will)m 15 r 98 c 1 r 101 c 17(more)m 16(cost)m 16(e\013ectiv)m 101 c 0 2462 p (for)s 18(users)m 19(to)m 18(emplo)m 121 c 17(the)m 19(second)m 19(of)m 18(the)m 19 r 116 c 119 c -1 r 111 c 16 r 99 c (hoices)s 18(men)m (tioned)s 17(ab)m 1 r 111 c 118 c (e.)s 28(Users)m 19 r 109 c (ust)s 17(also)m @eop %%Page: 73 87 73 @bop0 cmmi10.329 @sf [<01F0F803FDFC079FCC07078E0707860703C60703C70701C00701C00781E00381E00380E003C0E0 E1C0F061C0F061E07070E07039E0781FC0780F8038> 24 20 -1 0 26.020] 117 @dc cmsy10.329 @sf [ 8 45 -5 11 12.626] 106 @dc cmmi8.300 @sf [<00C00000C00000E00000600000600000600001FE0007FF800FB3C01E31E01E38701E18300E1838 0E18180F1C18E70C18670C1C770C3C3F0E3C1E0638000600000600000700000300000300000300 000380000180000180> 24 29 0 6 23.061] 32 @dc 73 @bop1 cmr10.329 @sf 225 114 p (Computational)s 13(Details)m 1226(73)m 225 134 p 1725 2 ru 225 259 p 98 c 1 r 101 c 22 r 97 c 119 c -1(are)m 20(that)m 20(ODRP)m -3 r 65 c (CK)s 21(nev)m (er)s 20(asks)m 21(that)m 21 r 98 c 1(oth)m 22(the)m 22(function)m 21(and)m 22(its)m 20(deriv)m -2(ativ)m (es)s 19 r 98 c 1 r 101 c 225 315 p (computed)s 17(in)m 16 r 97 c 16(single)m 16(call)m 16(to)m 16(subroutine)m cmtt10.329 @sf 16(FCN)m cmr10.329 @sf 44 c 16(and)m 17(that)m 15(it)m 16(is)m 16 r 112 c 1(ossible)m 16(that)m 16(an)m 16(in)m 118 c 111 c (cation)s 225 372 p (of)s cmtt10.329 @sf 14(FCN)m cmr10.329 @sf 14(for)m 14(ev)m -2(aluating)m 13(the)m 14(deriv)m -2(ativ)m -1 r 101 c 13(will)m 13(not)m 14 r 98 c 1 r 101 c cmti10.329 @sf 16(imme)m -1(diately)m cmr10.329 @sf 13(preceded)m 16(with)m 14 r 97 c 14(call)m 14(to)m cmtt10.329 @sf 13(FCN)m cmr10.329 @sf 225 428 p (to)s 18(ev)m -2(aluate)m 18(the)m 18(function)m 19(for)m 18(the)m 19(same)m 18(parameter)m 18 r 118 c -2(alues.)m 30(Th)m (us,)s 18(if)m 18(the)m 19(\014rst)m 18(of)m 18(the)m 19 r 116 c 119 c -1 r 111 c 225 484 p (options)s 9(is)m 10(emplo)m 121 c -1(ed,)m 10(the)m 10(user)m 10(will)m 9(need)m 11(to)m 10(construct)m 10 r 97 c 10(mec)m (hanism)s 8(for)m 10(sa)m (ving)s 8(the)m 11(computed)m 225 541 p (deriv)s -2(ativ)m -1(es)m 12(un)m (til)s 12(ODRP)m -3 r 65 c (CK)s 12(actually)m 13(requests)m 14(them,)m 13 r 112 c 1(ossibly)m 14(using)m 13(the)m 14 r 70 c -3(ortran)m cmtt10.329 @sf 12(COMMON)m cmr10.329 @sf 225 597 p (facilit)s -1 r 121 c -4 r 44 c 12(and)m 14(also)m 13 r 97 c 13(mec)m (hanism)s 13(for)m 13(determining)m 13(whether)m 14(the)m 14(sa)m 118 c -1(ed)m 12(deriv)m -2(ativ)m -1 r 101 c 12 r 118 c -2(alues)m 13 r 119 c (ere)s 225 654 p (in)s 15(fact)m 15(those)m 15(ev)m -2(aluated)m 14(at)m 14(the)m 16(selected)m 15(parameter)m 15 r 118 c -2(alues.)m cmbx10.329 @sf 225 793 p (4.A.iii)s -1 r 46 c 15(Finite)m 17(Di\013erence)m 17(Deriv)m -2(ativ)m -2(es)m cmr10.329 @sf 225 898 p (Finite)s 18(di\013erence)m 20(deriv)m -2(ativ)m -1(es)m 17(are)m 19(automatically)m 17(constructed)m 19 r 98 c 121 c 19(ODRP)m -3 r 65 c (CK)s 18(to)m 18(appro)m (x-)s 225 955 p (imate)s 20(the)m 21(Jacobian)m 21(matrices)m 20(when)m 22(the)m 21(user)m 21(do)m 1(es)m 21(not)m 21(supply)m 21(co)m 1(de)m 22(within)m 20(subroutine)m cmtt10.329 @sf 225 1011 p (FCN)s cmr10.329 @sf 16(to)m 15(compute)m 16(them.)m 23(Either)m 16(forw)m (a)s -1(rd)m 14(or)m 16(cen)m (tral)s 14(\014nite)m 17(di\013erences)m 16(can)m 16 r 98 c 1 r 101 c 17(emplo)m 121 c -1(ed)m 15(for)m 225 1068 p (the)s 16(appro)m (xima)s -1(tio)m -1(n.)m 20(\(See)m cmsy10.329 @sf 16 r 120 c cmr10.329 @sf (2.B.ii,)s 14(subroutine)m 15(argumen)m 116 c 14(JOB.\))m 16 r 65 c 15(cen)m (tral)s 14(\014nite)m 16(di\013erence)m 225 1124 p (deriv)s -2(ativ)m -1 r 101 c 16(giv)m (es)s 16 r 97 c 17(more)m 17(accurate)m 17(appro)m (ximati)s -1(on)m 16(than)m 17(the)m 18(corresp)m 1(onding)m 18(forw)m (a)s -1(rd)m 16(\014nite)m 225 1181 p (di\013erence)s 14(deriv)m -2(ativ)m -1(e,)m 11(but)m 14(at)m 13(the)m 14(exp)m 1(ense)m 14(of)m 13(an)m 14(additional)m 12(call)m 13(to)m 12(subroutine)m cmtt10.329 @sf 14(FCN)m cmr10.329 @sf 13(for)m 13(eac)m 104 c 225 1237 p (partial)s 13(deriv)m -2(ativ)m -1 r 101 c 12(computed.)m 20(The)m 15(in)m (terested)s 12(reader)m 15(is)m 13(referred)m 15(to)m 13([Dennis)m 14(and)m 15(Sc)m (hnab)s 1(el,)m 225 1293 p (1983])s 13(and)m 14([Gill)m cmti10.329 @sf 12(et)m 16(al.)m cmr10.329 @sf 44 c 13(1981])m 13(for)m 13 r 97 c 14(more)m 14(complete)m 14(discussion)m 14(of)m 13(forw)m (ard)s 12(and)m 15(cen)m (tral)s 12(\014nite)m 225 1350 p (di\013erence)s 15(appro)m (ximati)s -1(ons.)m cmbx10.329 @sf 225 1489 p (4.A.iii)s -1(.a.)m 15 r 70 c -3(orw)m -1(ard)m 15(Finite)m 17(Di\013erence)m 17(Deriv)m -2(ativ)m -2(es)m cmr10.329 @sf 225 1594 p (The)s 14(forw)m (ard)s 12(\014nite)m 15(di\013erence)m 14(deriv)m -2(ativ)m -1 r 101 c 13(with)m 13(resp)m 1(ect)m 15(to)m cmmi10.329 @sf 14 r 12 c cmr10.329 @sf 16(for)m 13(resp)m 1(onse)m cmmi10.329 @sf 15 r 108 c cmr10.329 @sf 15(of)m 14(observ)m -2(ation)m cmmi10.329 @sf 12 r 105 c cmr10.329 @sf 225 1651 p (is)s 15(computed)m 15(using)m cmmi10.329 @sf 692 1706 p 102 c cmmi8.300 @sf 714 1713 p (il)s cmr10.329 @sf 740 1706 p 40 c cmmi10.329 @sf 120 c cmmi8.300 @sf 784 1713 p 105 c cmr10.329 @sf 807 1706 p 43 c cmmi10.329 @sf 11 r 14 c cmmi8.300 @sf 873 1713 p 105 c cmr10.329 @sf 887 1706 p 59 c cmmi10.329 @sf 23 r 12 c cmr10.329 @sf 12 r 43 c 1007 1695 p 126 c cmmi10.329 @sf 1006 1707 p 104 c cmmi8.300 @sf 1032 1714 p 12 c cmmi6.300 @sf 1052 1720 p 107 c cmmi10.329 @sf 1073 1706 p 117 c cmmi8.300 @sf 1099 1713 p 107 c cmr10.329 @sf 1121 1706 p 41 c cmsy10.329 @sf 9 r 0 c cmmi10.329 @sf 11 r 102 c cmmi8.300 @sf 1216 1713 p (il)s cmr10.329 @sf 1241 1706 p 40 c cmmi10.329 @sf 120 c cmmi8.300 @sf 1285 1713 p 105 c cmr10.329 @sf 1309 1706 p 43 c cmmi10.329 @sf 11 r 14 c cmmi8.300 @sf 1375 1713 p 105 c cmr10.329 @sf 1389 1706 p 59 c cmmi10.329 @sf 8 r 12 c cmr10.329 @sf 2 r 41 c 692 1727 p 763 2 ru 1040 1763 p 126 c cmmi10.329 @sf 1040 1775 p 104 c cmmi8.300 @sf 1066 1782 p 12 c cmmi6.300 @sf 1086 1788 p 107 c cmmi10.329 @sf 1475 1737 p 59 c 225 1849 p 105 c cmr10.329 @sf 12 r 61 c 13 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 8 r 58 c 5 r 59 c 8(n;)m 14 r 107 c cmr10.329 @sf 13 r 61 c 13 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 8 r 58 c 5 r 59 c 8 r 112 c cmr10.329 @sf 44 c 13(and)m cmmi10.329 @sf 15 r 108 c cmr10.329 @sf 13 r 61 c 13 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 8 r 58 c 5 r 59 c 8 r 113 c 2 r 59 c cmr10.329 @sf 13(where)m cmmi10.329 @sf 15 r 117 c cmmi8.300 @sf 1232 1856 p 107 c cmr10.329 @sf 1268 1849 p (is)s 15(the)m cmmi10.329 @sf 15 r 107 c cmr10.329 @sf 1(th)m 14(unit)m 15 r 118 c (ector,)s 13(i.e.,)m 13(the)m cmmi10.329 @sf 15 r 107 c cmr10.329 @sf 1(th)m 225 1905 p (column)s 15(of)m 15 r 97 c cmmi10.329 @sf 15 r 112 c cmsy10.329 @sf 10 r 2 c cmmi10.329 @sf 10 r 112 c cmr10.329 @sf 15(iden)m (tit)s -1 r 121 c 13(matrix,)m 14(and)m 15(where)m 1139 1894 p 126 c cmmi10.329 @sf 1138 1906 p 104 c cmmi8.300 @sf 1164 1913 p 12 c cmmi6.300 @sf 1184 1919 p 107 c cmr10.329 @sf 1221 1905 p (is)s 14(the)m 16(\014nite)m 15(di\013erence)m 15(step)m 15(size,)m 776 1993 p 126 c cmmi10.329 @sf 776 2005 p 104 c cmmi8.300 @sf 802 2012 p 12 c cmmi6.300 @sf 822 2018 p 107 c cmr10.329 @sf 856 2004 p 61 c cmmi10.329 @sf 13 r 104 c cmmi8.300 @sf 930 2011 p 12 c cmmi6.300 @sf 950 2017 p 107 c cmsy10.329 @sf 971 2004 p 106 c cmmi10.329 @sf 12 c cmmi8.300 @sf 1010 2011 p 107 c cmsy10.329 @sf 1030 2004 p 106 c cmmi10.329 @sf 59 c 98 r 107 c cmr10.329 @sf 14 r 61 c 13 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 7 r 58 c 5 r 59 c 8(p;)m cmr10.329 @sf 457(\(4)m cmmi10.329 @sf 58 c cmr10.329 @sf (2\))s 225 2103 p (with)s cmmi10.329 @sf 14 r 104 c cmmi8.300 @sf 354 2110 p 12 c cmmi6.300 @sf 374 2116 p 107 c cmr10.329 @sf 409 2103 p (the)s cmti10.329 @sf 14 r 114 c -1(elative)m cmr10.329 @sf 13(step)m 14(size)m 14(for)m 14(parameter)m cmmi10.329 @sf 13 r 12 c cmmi8.300 @sf 1135 2110 p 107 c cmr10.329 @sf 1171 2103 p (sp)s 1(eci\014ed)m 15 r 98 c 121 c 13(subroutine)m 14(argumen)m 116 c cmtt10.329 @sf 13(STPB)m cmr10.329 @sf -1 r 46 c 225 2159 p (\(See)s cmsy10.329 @sf 22 r 120 c cmr10.329 @sf (2.B.ii.\))s 39(The)m 22(default)m 22 r 118 c -2(alue)m 21(for)m 21(the)m 22(relativ)m 101 c 20(step)m 22(for)m 21 r 97 c 22(forw)m (ard)s 20(\014nite)m 22(di\013erence)m 225 2216 p (deriv)s -2(ativ)m -1 r 101 c 13(is)m cmmi10.329 @sf 933 2272 p 104 c cmr10.329 @sf 13 r 61 c cmr7.300 @sf 1041 2257 p 49 c 1025 2264 p 50 2 ru 1025 2287 p (100)s cmr10.329 @sf 1080 2272 p (10)s cmsy8.300 @sf 1126 2254 p 0 c cmmi8.300 @sf 32 c 1 r 61 c cmr8.300 @sf 50 c cmmi10.329 @sf 1229 2272 p 59 c cmr10.329 @sf 225 2354 p (where)s cmmi10.329 @sf 11 r 32 c cmr10.329 @sf 12(indicates)m 10(the)m 11 r 110 c (um)s 98 c 1(er)m 10(of)m 10(go)m 1 r 111 c 1 r 100 c 11(digits)m 9(in)m 11(the)m 11(results)m 10(of)m 11(the)m 11(user)m 11(supplied)m 11(subroutine)m cmtt10.329 @sf 225 2411 p (FCN)s cmr10.329 @sf 46 c 19(\(See)m cmsy10.329 @sf 14 r 120 c cmr10.329 @sf (2.B.ii,)s 12(subroutine)m 13(argumen)m 116 c cmtt10.329 @sf 12(NDIGIT)m cmr10.329 @sf -1(.\))m 19(This)m 13(default)m 13 r 118 c -2(alue)m 13(is)m 13(selected)m 14(based)m 14(on)m 225 2467 p (empirical)s 13(evidence)m 16(that)m 13(indicates)m 14(it)m 14(generally)m 13(outp)m 1(erforms)m 14(the)m 14(commonly)m 14(recommended)m @eop %%Page: 74 88 74 @bop0 cmbx12.300 @sf [<000E0000000E0000001F0000001F0000003F8000003F8000007FC000007EC000007EC00000FC60 0000FC600001F8300001F8300003F8180003F0180007F01C0007E00C000FE00E000FC006000FC0 0700FFF01FE0FFF01FE0> 32 22 -1 0 29.576] 118 @dc 74 @bop1 cmr10.329 @sf 0 114 p (74)s 1227(Computational)m 13(Details)m 0 134 p 1725 2 ru 0 259 p 118 c -2(alue)m cmmi10.329 @sf 16 r 104 c cmr10.329 @sf 16 r 61 c 16(10)m cmr8.300 @sf 258 244 p 40 c cmsy8.300 @sf 0 c cmmi8.300 @sf 32 c 1 r 61 c cmr8.300 @sf (2\))s cmr10.329 @sf 374 259 p 46 c 26(\(See,)m 17(e.g.,)m 17([Dennis)m 16(and)m 18(Sc)m (hnab)s 1(el,)m 17(1983].\))m 23(Pro)m 1(cedures)m 18(for)m 17(selecting)m 0 315 p (near)s 14(optimal)m 12(relativ)m -1 r 101 c 12(step)m 14(sizes)m 14(are)m 13(discussed)m 14(in)m 14([Gill)m cmti10.329 @sf 12(et)m 15(al.)m cmr10.329 @sf 44 c 13(1981])m 12(and)m 14([Sc)m (hnab)s 1(el,)m 13(1982].\))m 0 391 p (The)s 20(step)m 199 380 p 126 c cmmi10.329 @sf 198 392 p 104 c cmmi8.300 @sf 224 399 p 12 c cmmi6.300 @sf 244 405 p 107 c cmr10.329 @sf 285 391 p 109 c (ust)s 18 r 98 c 1 r 101 c 20(large)m 19(enough)m 20(so)m 19(that)m 19(appro)m (ximat)s -1(ely)m 18(half)m 19(of)m 19(the)m 19(go)m 1 r 111 c 1 r 100 c 20(digits)m 18(of)m cmmi10.329 @sf 0 448 p 102 c cmmi8.300 @sf 22 455 p (il)s cmr10.329 @sf 47 448 p 40 c cmmi10.329 @sf 120 c cmmi8.300 @sf 91 455 p 105 c cmr10.329 @sf 113 448 p 43 c cmmi10.329 @sf 8 r 14 c cmmi8.300 @sf 176 455 p 105 c cmr10.329 @sf 191 448 p 59 c cmmi10.329 @sf 21 r 12 c cmr10.329 @sf 10 r 43 c 305 437 p 126 c cmmi10.329 @sf 305 449 p 104 c cmmi8.300 @sf 331 456 p 12 c cmmi6.300 @sf 351 462 p 107 c cmmi10.329 @sf 372 448 p 117 c cmmi8.300 @sf 398 455 p 107 c cmr10.329 @sf 419 448 p 41 c 14(and)m cmmi10.329 @sf 14 r 102 c cmmi8.300 @sf 560 455 p (il)s cmr10.329 @sf 586 448 p 40 c cmmi10.329 @sf 120 c cmmi8.300 @sf 630 455 p 105 c cmr10.329 @sf 651 448 p 43 c cmmi10.329 @sf 9 r 14 c cmmi8.300 @sf 715 455 p 105 c cmr10.329 @sf 729 448 p 59 c cmmi10.329 @sf 8 r 12 c cmr10.329 @sf 2 r 41 c 13(will)m 13 r 98 c 1 r 101 c 15(the)m 14(same.)m 19(The)m 15(forw)m (a)s -1(rd)m 13(\014nite)m 14(di\013erence)m 0 504 p (appro)s (ximat)s -1(ion)m 13(to)m 14(the)m 15(deriv)m -2(ativ)m -1 r 101 c 14(can)m 15(then)m 15 r 98 c 1 r 101 c 16(exp)m 1(ected)m 16(to)m 14(ha)m 118 c 101 c 13(roughly)m 14(half)m 15(the)m 15 r 110 c (um)s -1 r 98 c 1(er)m 0 560 p (of)s 14(go)m 1 r 111 c 1 r 100 c 15(digits)m 13(as)m 14(are)m 15(in)m 14(the)m 15(computed)m 15 r 118 c -2(alue)m 14(of)m cmmi10.329 @sf 14 r 102 c cmmi8.300 @sf 945 567 p (il)s cmr10.329 @sf 970 560 p 40 c cmmi10.329 @sf 120 c cmmi8.300 @sf 1014 567 p 105 c cmr10.329 @sf 1037 560 p 43 c cmmi10.329 @sf 9 r 14 c cmmi8.300 @sf 1101 567 p 105 c cmr10.329 @sf 1115 560 p 59 c cmmi10.329 @sf 8 r 12 c cmr10.329 @sf 2(\).)m 19(When)m 15(the)m 15(computation)m 13(of)m cmmi10.329 @sf 0 617 p 102 c cmmi8.300 @sf 22 624 p (il)s cmr10.329 @sf 47 617 p 40 c cmmi10.329 @sf 120 c cmmi8.300 @sf 91 624 p 105 c cmr10.329 @sf 110 617 p 43 c cmmi10.329 @sf 5 r 14 c cmmi8.300 @sf 170 624 p 105 c cmr10.329 @sf 185 617 p 59 c cmmi10.329 @sf 8 r 12 c cmr10.329 @sf 2 r 41 c 12(has)m 12(su\016cien)m 116 c 12(precision,)m 12(then)m 13(forw)m (ard)s 11(\014nite)m 12(di\013erence)m 13(deriv)m -2(ativ)m -1(es)m 11(will)m 12(cause)m 0 673 p 118 c (ery)s 13(little)m 12 r 99 c (hange)s 13(in)m 14(the)m 14(results)m 13(from)m 13(those)m 14(that)m 13 r 119 c (ould)s 12 r 98 c 1 r 101 c 15(obtained)m 14(using)m 13(hand)m 15(co)m 1(ded)m 14(or)m 0 730 p (automatic)s 14(di\013eren)m (tia)s -1(tio)m -1 r 110 c 14(deriv)m -2(ativ)m -1(es.)m 0 806 p (The)s 18(forw)m (ard)s 16(\014nite)m 18(di\013erence)m 19(deriv)m -2(ativ)m -1(es)m 16(with)m 17(resp)m 1(ect)m 19(to)m 18 r 1 c 18(are)m 17(formed)m 18(analogously)m 17(to)m 0 862 p (those)s 14(with)m 13(resp)m 1(ect)m 14(to)m cmmi10.329 @sf 13 r 12 c cmr10.329 @sf 2 r 46 c 20(\(See)m cmsy10.329 @sf 14 r 120 c cmr10.329 @sf (2.B.ii,)s 12(subroutine)m 14(argumen)m 116 c cmtt10.329 @sf 12(STPD)m cmr10.329 @sf -1 r 44 c 14(for)m 13(sp)m 1(eci\014cation)m 13(of)m 14(the)m 0 919 p (relativ)s -1 r 101 c 14(stepsize.\))m cmbx10.329 @sf 0 1058 p (4.A.iii)s -1(.b.)m 15(Cen)m (tral)s 15(Finite)m 17(Di\013erence)m 17(Deriv)m -2(ativ)m -2(es)m cmr10.329 @sf 0 1164 p (When)s 12(the)m 12(user)m 12(susp)m 1(ects)m 12(that)m 12(the)m 11(forw)m (ard)s 10(\014nite)m 12(di\013erence)m 12(appro)m (xima)s -1(tio)m -1 r 110 c 10(will)m 11(not)m 11(pro)m (vide)s 0 1220 p (su\016cien)s 116 c 19(precision,)m 21(then)m 20 r 97 c 20(cen)m (tral)s 19(\014nite)m 20(di\013erence)m 20(appro)m (ximati)s -1(on)m 19(can)m 20 r 98 c 1 r 101 c 21(used.)m 36(\(See)m cmsy10.329 @sf 0 1277 p 120 c cmr10.329 @sf (2.B.ii,)s 17(subroutine)m 18(argumen)m 116 c cmtt10.329 @sf 16(JOB)m cmr10.329 @sf (.\))s 28(The)m 19(cen)m (tral)s 16(\014nite)m 18(di\013erence)m 18(appro)m (ximati)s -1(on)m 16(to)m 18(the)m 0 1333 p (partial)s 14(deriv)m -2(ativ)m -1 r 101 c 13(with)m 15(resp)m 1(ect)m 15(to)m cmmi10.329 @sf 15 r 12 c cmmi8.300 @sf 696 1340 p 107 c cmr10.329 @sf 732 1333 p (for)s 15(resp)m 1(onse)m cmmi10.329 @sf 15 r 108 c cmr10.329 @sf 16(of)m 15(observ)m -2(ation)m cmmi10.329 @sf 13 r 105 c cmr10.329 @sf 15(is)m 15(giv)m (en)s 13 r 98 c 121 c cmmi10.329 @sf 410 1434 p 102 c cmmi8.300 @sf 432 1441 p (il)s cmr10.329 @sf 457 1434 p 40 c cmmi10.329 @sf 120 c cmmi8.300 @sf 501 1441 p 105 c cmr10.329 @sf 525 1434 p 43 c cmmi10.329 @sf 10 r 14 c cmmi8.300 @sf 590 1441 p 105 c cmr10.329 @sf 604 1434 p 59 c cmmi10.329 @sf 8 r 12 c cmr10.329 @sf 12 r 43 c 709 1423 p 126 c cmmi10.329 @sf 708 1435 p 104 c cmmi8.300 @sf 734 1442 p 107 c cmmi10.329 @sf 756 1434 p 117 c cmmi8.300 @sf 782 1441 p 107 c cmr10.329 @sf 803 1434 p 41 c cmsy10.329 @sf 10 r 0 c cmmi10.329 @sf 10 r 102 c cmmi8.300 @sf 898 1441 p (il)s cmr10.329 @sf 924 1434 p 40 c cmmi10.329 @sf 120 c cmmi8.300 @sf 968 1441 p 105 c cmr10.329 @sf 991 1434 p 43 c cmmi10.329 @sf 11 r 14 c cmmi8.300 @sf 1057 1441 p 105 c cmr10.329 @sf 1071 1434 p 59 c cmmi10.329 @sf 8 r 12 c cmsy10.329 @sf 12 r 0 c cmr10.329 @sf 1176 1423 p 126 c cmmi10.329 @sf 1175 1435 p 104 c cmmi8.300 @sf 1201 1442 p 107 c cmmi10.329 @sf 1223 1434 p 117 c cmmi8.300 @sf 1249 1441 p 107 c cmr10.329 @sf 1270 1434 p 41 c 410 1454 p 879 2 ru 825 1491 p 126 c cmmi10.329 @sf 825 1503 p 104 c cmmi8.300 @sf 851 1510 p 107 c cmmi10.329 @sf 1308 1465 p 59 c 0 1601 p 105 c cmr10.329 @sf 12 r 61 c 13 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 8 r 58 c 5 r 59 c 8(n;)m 14 r 107 c cmr10.329 @sf 14 r 61 c 13 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 7 r 58 c 5 r 59 c 8 r 112 c cmr10.329 @sf 44 c 14(and)m cmmi10.329 @sf 15 r 108 c cmr10.329 @sf 13 r 61 c 13 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 7 r 58 c 6 r 59 c 8 r 113 c 2 r 58 c cmr10.329 @sf 13(The)m 15(step)m 1041 1590 p 126 c cmmi10.329 @sf 1040 1602 p 104 c cmmi8.300 @sf 1066 1609 p 107 c cmr10.329 @sf 1103 1601 p (is)s 14(formed)m 15(as)m 15(in)m 15(\(4.2\),)m 13(where)m 15(the)m 0 1658 p (default)s 15 r 118 c -2(alue)m 14(for)m 15(the)m 15(relativ)m -1 r 101 c 14(step)m 15(for)m 15 r 97 c 14(cen)m (tral)s 14(\014nite)m 15(di\013erence)m 15(deriv)m -2(ativ)m -1 r 101 c 14(is)m cmmi10.329 @sf 738 1760 p 104 c cmr10.329 @sf 13 r 61 c 13(10)m cmsy8.300 @sf 871 1742 p 0 c cmmi8.300 @sf 32 c 1 r 61 c cmr8.300 @sf 51 c cmmi10.329 @sf 974 1760 p 58 c cmr10.329 @sf 0 1862 p (The)s 14(cen)m (tral)s 11(\014nite)m 13(di\013erence)m 14(deriv)m -2(ativ)m -1(es)m 11(with)m 13(resp)m 1(ect)m 14(to)m 12 r 1 c 14(are)m 12(again)m 13(formed)m 13(analogously)m -4 r 46 c cmbx12.300 @sf 0 2008 p (4.B.)s 18(Co)m -1 r 118 c -2(ariance)m 16(Matrix)m cmr10.329 @sf 0 2129 p (The)s 19(linearized)m 19(con\014dence)m 20(regions)m 18(and)m 19(in)m (terv)s -2(als)m 16(for)m 19(the)m 19(unkno)m (wns)s cmmi10.329 @sf 18 r 12 c cmr10.329 @sf 21(and)m 19 r 1 c 19(estimated)m 0 2186 p 98 c 121 c 17(orthogonal)m 16(distance)m 17(regression)m 17(are)m 17(the)m 18(same)m 18(as)m 17(the)m 18(linearized)m 17(regions)m 17(and)m 18(in)m (terv)s -2(a)m -1(ls)m 0 2242 p (that)s 16 r 119 c (ould)s 14 r 98 c 1 r 101 c 17(obtained)m 16(if)m 16(the)m 16(orthogonal)m 14(distance)m 16(regression)m 16(problem)m 16 r 119 c (ere)s 15(solv)m (ed)s 14(as)m 16 r 97 c cmmi10.329 @sf 0 2298 p 112 c cmr10.329 @sf 2 r 43 c cmmi10.329 @sf 2(nm)m cmr10.329 @sf 11(parameter)m 10(nonlinear)m 11(ordinary)m 10(least)m 10(squares)m 11(problem.)m 18(If)m 11 r 119 c 101 c 10(express)m 12(the)m 11(orthogonal)m 0 2355 p (distance)s 15(regression)m 14(problem)m 15(de\014ned)m 16 r 98 c 121 c 14(\(1.8\))m 14(or)m 14(\(1.9\))m 13(as)m 15(suc)m 104 c 14 r 97 c 15(nonlinear)m 15(ordinary)m 14(least)m 0 2411 p (squares)s 17(problem)m 16(with)m cmmi10.329 @sf 17(nq)m cmr10.329 @sf 13 r 43 c cmmi10.329 @sf 12(nm)m cmr10.329 @sf 17(observ)m -2(ations)m 15(and)m cmmi10.329 @sf 17 r 112 c cmr10.329 @sf 12 r 43 c cmmi10.329 @sf 11(nm)m cmr10.329 @sf 17(unkno)m (wns,)s 17(and)m 17 r 119 c 101 c 15(designate)m @eop %%Page: 75 89 75 @bop0 cmmi10.329 @sf [<0007000007000007000007800007800003800003800003C00003C00001C01C01C01E01E01E01E0 0E00E00E00E00F00F00F00F007007007007007807807807803803803C038E3C03863E03C61F01C 71F83C33FC383F8FF81F07F0> 24 30 -1 10 22.569] 17 @dc [<00FF800003FFE1000FE0FB001F801F801F000F803E0007807C0007C07C0007C0780003C0780003 C0F80003E0F80003E0F8007FFCF8007FFCFC0000007C0000007C0000007C0000007E0000003E00 00003E0000181F0000181F0000180F80001C0FC0001C07C0001C03E0003C01F0003E00FC007E00 3E007E001FC1EE0007FFC70000FF03> 32 33 -2 1 35.738] 71 @dc cmr10.329 @sf [<3FC03FC03FC03FC07FC03FE061C0386061C03860C1C03830C3801C3003801C0007801E0007000E 000F000F000F000F001F000F801E0007803E0007C03E0007C03E0007C07C0003E07C0003E07C00 03E07C0003E07C0003E07C0003E07C0003E03E0007C03E0007C01F000F801F801F800FC03F0003 F0FC0001FFF800003FC000> 32 32 -2 0 32.828] 10 @dc cmmi10.329 @sf [<7FC000FFF000F87800783C00701E00000E00000F00000F0000070003E70007FF800F1F800E0F80 1E07801E03C01E03C01E01C01E01C01F01E00F01E00F00E00F00E00780F00780F003C0F001E1F0 00F1F8007FF8001F38> 24 29 0 9 21.680] 103 @dc cmex10.300 @sf [<00001C00007C0000F80001F00003C0000780000F80001F00001E00003E00003C00003C00007800 007800007800007800007800007800007800007800007800007800007800007800007800007800 007800007800007800007800007800007800007800007800007800007800007800007800007800 00780000780000780000780000780000780000780000780000780000780000780000F80000F000 00F00001E00001E00003C00007C0000F80001F00003E0000780000F00000F000007800003E0000 1F00000F800007C00003C00001E00001E00000F00000F00000F800007800007800007800007800 007800007800007800007800007800007800007800007800007800007800007800007800007800 007800007800007800007800007800007800007800007800007800007800007800007800007800 007800007800007800007800007800007800007800007800003C00003C00003E00001E00001F00 000F800007800003C00001F00000F800007C00001C> 24 124 -5 122 33.439] 40 @dc [ 16 74 -13 73 27.673] 50 @dc [ 8 27 -13 26 27.673] 54 @dc [ 16 74 -13 72 27.673] 52 @dc cmmi6.300 @sf [<301E00383F003833801839801C18001C18001E1C00CE0C00EF9C007FFC0078F800> 24 11 -1 0 19.169] 110 @dc cmex10.300 @sf [<001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C00 1C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C 001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C001C00 1C001C001C001C001C001C001C001C001C001C001C001C001CFFFCFFFCFFFC> 16 74 0 73 27.673] 51 @dc [ 8 27 -11 26 27.673] 55 @dc [ 16 74 0 72 27.673] 53 @dc cmmi8.300 @sf [<001C00001C00001C00001E00001E00000E00380E003C0F003C0F001C07001C07001E07801E0780 0E03800F0380CF8380EF83806FE3807FFF803E3F00> 24 20 0 6 17.705] 17 @dc cmsy8.300 @sf [<60E0F0707878783C3C3C1E1E1E1F0F0F0F> 8 17 -1 -1 9.570] 48 @dc cmmi10.329 @sf [ 24 20 -2 0 22.453] 23 @dc cmmi8.300 @sf [ 24 14 -1 0 17.344] 23 @dc cmmi10.329 @sf [ 32 30 -1 10 27.388] 22 @dc 75 @bop1 cmr10.329 @sf 225 114 p (Computational)s 13(Details)m 1226(75)m 225 134 p 1725 2 ru 225 259 p (the)s 16(unkno)m (wns)s 15(of)m 15(this)m 15(ordinary)m 15(least)m 15(squares)m 15(problem)m 16(as)m cmmi10.329 @sf 15 r 17 c cmr6.300 @sf 1369 244 p 84 c cmr10.329 @sf 1406 259 p 61 c 14 r 40 c cmmi10.329 @sf 12 c cmr6.300 @sf 1501 244 p 84 c cmmi10.329 @sf 1524 259 p 59 c 8 r 14 c cmr6.300 @sf 1567 244 p 84 c cmr8.300 @sf 1565 270 p 49 c cmmi10.329 @sf 1590 259 p 59 c 8 r 58 c 8 r 58 c 8 r 58 c 5 r 59 c 8 r 14 c cmr6.300 @sf 1714 244 p 84 c cmmi8.300 @sf 1712 270 p 110 c cmr10.329 @sf 1737 259 p 41 c -1 r 44 c 16(then)m 16(the)m 225 315 p (sum)s 15(of)m 15(squares)m 15(to)m 15 r 98 c 1 r 101 c 15(minimized)m 15(is)m cmmi10.329 @sf 889 404 p 83 c cmr10.329 @sf 3 r 40 c cmmi10.329 @sf 17 c cmr10.329 @sf 2 r 41 c cmsy10.329 @sf 10 r 17 c cmmi10.329 @sf 13 r 71 c cmr10.329 @sf 40 c cmmi10.329 @sf 17 c cmr10.329 @sf 2 r 41 c cmr6.300 @sf 1136 386 p 84 c cmr10.329 @sf 1158 404 p 10 c cmmi10.329 @sf 71 c cmr10.329 @sf 40 c cmmi10.329 @sf 17 c cmr10.329 @sf 2 r 41 c 225 493 p (where)s cmmi10.329 @sf 15 r 71 c cmr10.329 @sf 40 c cmmi10.329 @sf 17 c cmr10.329 @sf 2 r 41 c 14(is)m 15(the)m 15 r 118 c (ector)s 13 r 118 c -2(alued)m 15(function)m 15(whose)m cmmi10.329 @sf 15 r 105 c cmr10.329 @sf (th)s 15(\\elemen)m (t")s 13(is)m 15(de\014ned)m 17 r 98 c 121 c cmmi10.329 @sf 560 614 p 103 c cmmi8.300 @sf 582 621 p 105 c cmr10.329 @sf 595 614 p 40 c cmmi10.329 @sf 17 c cmr10.329 @sf 2 r 41 c 12 r 61 c cmex10.300 @sf 716 542 p 40 c cmmi10.329 @sf 770 586 p 102 c cmmi8.300 @sf 792 593 p 105 c cmr10.329 @sf 806 586 p 40 c cmmi10.329 @sf 120 c cmmi8.300 @sf 850 593 p 105 c cmr10.329 @sf 874 586 p 43 c cmmi10.329 @sf 10 r 14 c cmmi8.300 @sf 939 593 p 105 c cmr10.329 @sf 954 586 p 59 c cmmi10.329 @sf 8 r 12 c cmr10.329 @sf 2 r 41 c cmsy10.329 @sf 9 r 0 c cmmi10.329 @sf 10 r 121 c cmmi8.300 @sf 1097 593 p 105 c cmmi10.329 @sf 1244 586 p 105 c cmr10.329 @sf 12 r 61 c 13 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 8 r 58 c 5 r 59 c 8(n;)m 770 642 p 14 c cmmi8.300 @sf 790 649 p 105 c cmsy8.300 @sf 0 c cmmi8.300 @sf 110 c cmmi10.329 @sf 1244 642 p 105 c cmr10.329 @sf 12 r 61 c cmmi10.329 @sf 13 r 110 c cmr10.329 @sf 11 r 43 c 10 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 7 r 58 c 6 r 59 c cmr10.329 @sf 8 r 50 c cmmi10.329 @sf (n;)s cmr10.329 @sf 225 743 p (and)s 15 r 10 c cmsy10.329 @sf 13 r 50 c 13 r 60 c cmr8.300 @sf 435 728 p 40 c cmmi8.300 @sf (nq)s cmr8.300 @sf 1 r 43 c cmmi8.300 @sf (nm)s cmr8.300 @sf 41 c cmsy8.300 @sf 2 c cmr8.300 @sf 40 c cmmi8.300 @sf (nq)s cmr8.300 @sf 1 r 43 c cmmi8.300 @sf (nm)s cmr8.300 @sf 41 c cmr10.329 @sf 771 743 p (is)s 15(the)m 15(blo)m 1 r 99 c 107 c 14(diagonal)m 14 r 119 c (eigh)s -1(ti)m -1(ng)m 13(matrix)m 14(giv)m (en)s 14 r 98 c 121 c 692 992 p 10 c 12 r 61 c cmex10.300 @sf 785 796 p 50 c 785 869 p 54 c 785 894 p 54 c 785 919 p 54 c 785 944 p 54 c 785 969 p 54 c 785 994 p 54 c 785 1019 p 54 c 785 1044 p 54 c 785 1069 p 54 c 785 1096 p 52 c cmmi10.329 @sf 834 828 p 119 c cmmi8.300 @sf 862 835 p 15 c cmr6.300 @sf 876 840 p 49 c cmr10.329 @sf 938 879 p 46 c 956 892 p 46 c 974 905 p 46 c cmmi10.329 @sf 1030 964 p 119 c cmmi8.300 @sf 1058 971 p 15 c cmmi6.300 @sf 1072 975 p 110 c cmmi10.329 @sf 1136 1021 p 119 c cmmi8.300 @sf 1164 1028 p 14 c cmr6.300 @sf 1180 1033 p 49 c cmr10.329 @sf 1242 1071 p 46 c 1259 1084 p 46 c 1277 1097 p 46 c cmmi10.329 @sf 1334 1157 p 119 c cmmi8.300 @sf 1362 1164 p 14 c cmmi6.300 @sf 1378 1168 p 110 c cmex10.300 @sf 1420 796 p 51 c 1420 869 p 55 c 1420 894 p 55 c 1420 919 p 55 c 1420 944 p 55 c 1420 969 p 55 c 1420 994 p 55 c 1420 1019 p 55 c 1420 1044 p 55 c 1420 1069 p 55 c 1420 1096 p 53 c cmmi10.329 @sf 1470 992 p 58 c cmr10.329 @sf 225 1244 p (The)s 15(ordinary)m 15(least)m 14(squares)m 15(represen)m (tation)s 13(of)m 15(\(1.8\))m 14(or)m 14(\(1.9\))m 14(is)m 15(th)m (us)s 762 1371 p (min)s cmmi8.300 @sf 791 1396 p 17 c cmmi10.329 @sf 846 1371 p 83 c cmr10.329 @sf 3 r 40 c cmmi10.329 @sf 17 c cmr10.329 @sf 2 r 41 c 10 r 61 c 13(min)m cmmi8.300 @sf 1025 1396 p 17 c cmr8.300 @sf 1090 1318 p 50 c cmmi8.300 @sf 110 c cmex10.300 @sf 1079 1330 p 88 c cmmi8.300 @sf 1081 1422 p 105 c cmr8.300 @sf (=1)s cmmi10.329 @sf 1147 1371 p 103 c cmmi8.300 @sf 1169 1378 p 105 c cmr10.329 @sf 1183 1371 p 40 c cmmi10.329 @sf 17 c cmr10.329 @sf 2 r 41 c cmr6.300 @sf 1244 1353 p 84 c cmr10.329 @sf 1266 1371 p 10 c cmmi8.300 @sf 1299 1378 p (ii)s cmmi10.329 @sf 1325 1371 p 103 c cmmi8.300 @sf 1347 1378 p 105 c cmr10.329 @sf 1361 1371 p 40 c cmmi10.329 @sf 17 c cmr10.329 @sf 2 r 41 c 435(\(4)m cmmi10.329 @sf 58 c cmr10.329 @sf (3\))s 225 1496 p (where)s 15 r 10 c cmmi8.300 @sf 389 1503 p (ii)s cmr10.329 @sf 431 1496 p (denotes)s 15(the)m 15 r 40 c cmmi10.329 @sf (i;)s 8 r 105 c cmr10.329 @sf (\)th)s 13(\\elemen)m (t")s 14(of)m 14(\012.)m 225 1572 p (Let)s cmmi10.329 @sf 19 r 71 c cmsy8.300 @sf 346 1557 p 48 c cmr10.329 @sf 357 1572 p 40 c 3 r 94 c cmmi10.329 @sf -26 r 17 c cmr10.329 @sf 1 r 41 c cmsy10.329 @sf 13 r 50 c 12 r 60 c cmr8.300 @sf 505 1557 p 40 c cmmi8.300 @sf (nq)s cmr8.300 @sf 1 r 43 c cmmi8.300 @sf (nm)s cmr8.300 @sf 41 c cmsy8.300 @sf 2 c cmr8.300 @sf 40 c cmmi8.300 @sf 112 c cmr8.300 @sf 43 c cmmi8.300 @sf (nm)s cmr8.300 @sf 41 c cmr10.329 @sf 825 1572 p (denote)s 19(the)m 19(Jacobian)m 18(matrix)m 17(with)m 19 r 40 c cmmi10.329 @sf 23 c 59 c 8 r 107 c cmr10.329 @sf 1(\)th)m 18(elemen)m 116 c 17(equal)m 225 1629 p (to)s cmmi10.329 @sf 19 r 64 c 3 r 103 c cmmi8.300 @sf 334 1636 p 23 c cmr10.329 @sf 355 1629 p 40 c cmmi10.329 @sf 17 c cmr10.329 @sf 2 r 41 c cmmi10.329 @sf (=@)s 3 r 17 c cmmi8.300 @sf 488 1636 p 107 c cmr10.329 @sf 527 1629 p (ev)s -2(aluated)m 18(at)m 22 r 94 c cmmi10.329 @sf -26 r 17 c cmr10.329 @sf 1 r 46 c 33(If)m 20 r 119 c 101 c 18(assume)m 19(that)m cmmi10.329 @sf 19 r 71 c cmsy8.300 @sf 1285 1614 p 48 c cmr10.329 @sf 1296 1629 p 40 c 3 r 94 c cmmi10.329 @sf -26 r 17 c cmr10.329 @sf 1 r 41 c 19(and)m 20 r 10 c 19(are)m 19(full)m 19(rank,)m 20(so)m 19(that)m 225 1685 p 91 c cmmi10.329 @sf 71 c cmsy8.300 @sf 274 1670 p 48 c cmr10.329 @sf 285 1685 p 40 c 3 r 94 c cmmi10.329 @sf -26 r 17 c cmr10.329 @sf 1 r 41 c cmr6.300 @sf 345 1670 p 84 c cmr10.329 @sf 368 1685 p 10 c cmmi10.329 @sf 71 c cmsy8.300 @sf 437 1670 p 48 c cmr10.329 @sf 449 1685 p 40 c 3 r 94 c cmmi10.329 @sf -26 r 17 c cmr10.329 @sf (\)])s 15(is)m 15(nonsingular,)m 15(then)m 15(the)m 16(linearized)m 15(co)m 118 c -2(ari)m -1(ance)m 14(matrix)m 14(for)m 15(the)m 16(estimators)m 228 1742 p 94 c cmmi10.329 @sf -26 r 17 c cmr10.329 @sf 16(is)m 15(the)m 15 r 40 c cmmi10.329 @sf 112 c cmr10.329 @sf 10 r 43 c cmmi10.329 @sf 10(nm)m cmr10.329 @sf 41 c cmsy10.329 @sf 10 r 2 c cmr10.329 @sf 11 r 40 c cmmi10.329 @sf 112 c cmr10.329 @sf 9 r 43 c cmmi10.329 @sf 11(nm)m cmr10.329 @sf 41 c 15(matrix)m 816 1820 p 94 c cmmi10.329 @sf 809 1831 p 86 c cmr10.329 @sf 887 1830 p 61 c 44 r 94 c cmmi10.329 @sf -25 r 27 c cmr8.300 @sf 992 1812 p 50 c cmr10.329 @sf 1011 1830 p 91 c cmmi10.329 @sf 71 c cmsy8.300 @sf 1060 1812 p 48 c cmr10.329 @sf 1071 1830 p 40 c 3 r 94 c cmmi10.329 @sf -26 r 17 c cmr10.329 @sf 1 r 41 c cmr6.300 @sf 1131 1812 p 84 c cmr10.329 @sf 1154 1830 p 10 c cmmi10.329 @sf 71 c cmsy8.300 @sf 1223 1812 p 48 c cmr10.329 @sf 1234 1830 p 40 c 3 r 94 c cmmi10.329 @sf -26 r 17 c cmr10.329 @sf 1(\)])m cmsy8.300 @sf 1307 1812 p 0 c cmr8.300 @sf 49 c cmmi10.329 @sf 1354 1830 p 59 c cmr10.329 @sf 225 1919 p (where)s 23 r 94 c cmmi10.329 @sf -26 r 27 c cmr10.329 @sf 23 r 61 c cmmi10.329 @sf 21 r 83 c cmr10.329 @sf 3 r 40 c 3 r 94 c cmmi10.329 @sf -26 r 17 c cmr10.329 @sf 41 c cmmi10.329 @sf (=\026)s cmr10.329 @sf 21 r 61 c cmmi10.329 @sf 21 r 83 c cmr10.329 @sf 3 r 40 c 738 1908 p 94 c cmmi10.329 @sf 732 1920 p 12 c 759 1919 p 59 c cmr10.329 @sf 782 1908 p 94 c cmmi10.329 @sf 780 1920 p 14 c cmr10.329 @sf 802 1919 p 41 c cmmi10.329 @sf -1(=\026)m cmr10.329 @sf 20(is)m 20(the)m 20(estimated)m 19(residual)m 20 r 118 c -2(ariance)m 19(with)m cmmi10.329 @sf 19 r 22 c cmr10.329 @sf 21(degrees)m 20(of)m 225 1976 p (freedom.)s 24(\(The)m 16(degrees)m 17(of)m 16(freedom)m 16(is)m 16(the)m 17 r 110 c (um)s 98 c 1(er)m 15(of)m 16(observ)m -2(ations)m 15(with)m 16(nonzero)m 16 r 119 c (eigh)s -1(ts)m 225 2032 p (min)s (us)s 21(the)m 23 r 110 c (um)s 98 c 1(er)m 21(of)m 22(parameters)m 22(actually)m 21 r 98 c 1(eing)m 23(estimated,)m 23(i.e.,)m cmmi10.329 @sf 23 r 22 c cmr10.329 @sf 26 r 61 c 27 r 126 c cmmi10.329 @sf -25 r 110 c cmsy10.329 @sf 15 r 0 c cmr10.329 @sf 20 r 126 c cmmi10.329 @sf -27 r 112 c cmr10.329 @sf (.\))s 41(This)m 225 2089 p (co)s 118 c -2(ari)m -1(ance)m 14(matrix)m 600 2079 p 94 c cmmi10.329 @sf 593 2090 p 86 c cmr10.329 @sf 644 2089 p (can)s 16 r 98 c 1 r 101 c 16(partitioned)m 913 2198 p 94 c cmmi10.329 @sf 906 2209 p 86 c cmr10.329 @sf 955 2208 p 61 c cmex10.300 @sf 1003 2136 p 34 c cmr10.329 @sf 1064 2169 p 94 c cmmi10.329 @sf 1057 2180 p 86 c cmmi8.300 @sf 1084 2187 p 12 c cmr10.329 @sf 1164 2169 p 94 c cmmi10.329 @sf 1157 2180 p 86 c cmmi8.300 @sf 1184 2187 p 12 c 2 r 14 c cmr10.329 @sf 1055 2229 p 94 c cmmi10.329 @sf 1048 2240 p 86 c cmmi8.300 @sf 1075 2247 p 14 c 1 r 12 c cmr10.329 @sf 1175 2229 p 94 c cmmi10.329 @sf 1168 2240 p 86 c cmmi8.300 @sf 1195 2247 p 14 c cmex10.300 @sf 1245 2136 p 35 c cmr10.329 @sf 225 2339 p (where)s 369 2329 p 94 c cmmi10.329 @sf 362 2340 p 86 c cmmi8.300 @sf 389 2347 p 12 c cmsy10.329 @sf 425 2339 p 50 c 13 r 60 c cmmi8.300 @sf 501 2324 p 112 c cmsy8.300 @sf 2 c cmmi8.300 @sf 112 c cmr10.329 @sf 586 2339 p (is)s 20(the)m 21(co)m 118 c -2(ar)m -1(iance)m 19(matrix)m 19(for)m 20(the)m 21(estimators)m 1490 2328 p 94 c cmmi10.329 @sf 1484 2340 p 12 c cmr10.329 @sf 1512 2339 p 44 c 1553 2329 p 94 c cmmi10.329 @sf 1547 2340 p 86 c cmmi8.300 @sf 1574 2347 p 14 c cmsy10.329 @sf 1605 2339 p 50 c 13 r 60 c cmmi8.300 @sf 1681 2324 p (nm)s cmsy8.300 @sf 2 c cmmi8.300 @sf (nm)s cmr10.329 @sf 1836 2339 p (is)s 20(the)m 225 2400 p (co)s 118 c -2(ari)m -1(ance)m 16(matrix)m 17(for)m 17(the)m 18(estimators)m 981 2390 p 94 c 974 2401 p 1 c 1011 2400 p 44 c 18(and)m 1140 2390 p 94 c cmmi10.329 @sf 1133 2401 p 86 c cmmi8.300 @sf 1160 2408 p 12 c 2 r 14 c cmr10.329 @sf 1213 2400 p 61 c 1268 2390 p 94 c cmmi10.329 @sf 1261 2401 p 86 c cmr6.300 @sf 1298 2385 p 84 c cmmi8.300 @sf 1288 2413 p 14 c 1 r 12 c cmsy10.329 @sf 1341 2400 p 50 c 12 r 60 c cmmi8.300 @sf 1416 2385 p 112 c cmsy8.300 @sf 2 c cmmi8.300 @sf (nm)s cmr10.329 @sf 1534 2400 p (giv)s (es)s 16(co)m 118 c -2(ar)m -1(iances)m 16 r 98 c 1(e-)m 225 2467 p 116 c 119 c -1(een)m cmmi10.329 @sf 12 r 12 c cmr10.329 @sf 16(and)m 14(\001.)m 19(It)m 14(is)m 14(the)m 13(co)m 118 c -2(aria)m -1(nce)m 13(matrix)m 1092 2457 p 94 c cmmi10.329 @sf 1085 2468 p 86 c cmmi8.300 @sf 1112 2475 p 12 c cmr10.329 @sf 1149 2467 p (of)s 13(the)m 14(estimators)m 1502 2456 p 94 c cmmi10.329 @sf 1495 2468 p 12 c cmr10.329 @sf 1537 2467 p (that)s 13(is)m 13(automatically)m @eop %%Page: 76 90 76 @bop0 cmsy10.329 @sf [ 32 32 -3 1 35.353] 6 @dc cmmi8.300 @sf [ 8 4 -3 0 9.801] 58 @dc cmr8.300 @sf [<1F803FE070F07038703C001C001C020E1FEE3FFE703EF01EE00EE00EE00EE00EE01C701C78781F F00FE0> 16 21 -1 0 17.642] 57 @dc [<0E000E000E000E000E000E0006000700070003000380018001C000E00060C070C038E01C7FFE7F FE7FFE6000> 16 22 -2 0 17.642] 55 @dc cmmi8.300 @sf [ 24 20 -1 6 21.226] 22 @dc 76 @bop1 cmr10.329 @sf 0 114 p (76)s 1227(Computational)m 13(Details)m 0 134 p 1725 2 ru 0 259 p (pro)s (vided)s 17 r 98 c 121 c 16(ODRP)m -3 r 65 c (CK.)s 17(The)m 18(actual)m 17(computational)m 16(tec)m (hnique)s 17(used)m 18 r 98 c 121 c 17(ODRP)m -3 r 65 c (CK)s 17(to)m 0 315 p (compute)s 191 305 p 94 c cmmi10.329 @sf 184 316 p 86 c cmmi8.300 @sf 211 323 p 12 c cmr10.329 @sf 250 315 p (is)s 14(describ)m 1(ed)m 16(in)m 15(detail)m 15(in)m 15([Boggs)m 14(and)m 15(Rogers,)m 15(1990b].)m 0 391 p (By)s 11(default,)m 12(ODRP)m -3 r 65 c (CK)s 10(will)m 10(recompute)m 11(the)m 12(Jacobian)m 11(matrices)m 10(at)m 11(the)m 11(\014nal)m 12(solution)m 10 r 98 c 1(efore)m 0 448 p (constructing)s 17(the)m 18(co)m 118 c -2(ar)m -1(iance)m 16(matrix.)m 26(Ho)m 119 c -1(ev)m -1(er,)m 16(ODRP)m -3 r 65 c (CK)s 17(also)m 16(pro)m (vides)s 17(the)m 17(option)m 17(of)m 0 504 p (constructing)s 14(the)m 15(co)m 118 c -2(ari)m -1(ance)m 13(matrix)m 14(using)m 14(the)m 15(Jacobian)m 15(matrices)m 13(from)m 14(the)m 15(last)m 14(iteration.)m 0 560 p (\(See)s cmsy10.329 @sf 22 r 120 c cmr10.329 @sf (2.B.ii,)s 21(subroutine)m 21(argumen)m 116 c cmtt10.329 @sf 20(JOB)m cmr10.329 @sf -1(.\))m 38(The)m 22(option)m 20(of)m 21(using)m 21(the)m 22(Jacobian)m 21(matrices)m 0 617 p (from)s 15(the)m 15(last)m 15(iteration)m 14(to)m 15(construct)m 15(the)m 16(co)m 118 c -2(a)m -1(riance)m 14(matrix)m 14(is)m 15(esp)m 1(ecially)m 15(useful)m 16(when)m 16(the)m 0 673 p (ev)s -2(aluation)m 14(of)m 15(user)m 16(supplied)m 15(subroutine)m cmtt10.329 @sf 16(FCN)m cmr10.329 @sf 15(is)m 15 r 118 c (ery)s 14(time)m 15(consuming.)m 21(Assuming)m 15(that)m 15(the)m 0 730 p (algorithm)s 16(has)m 18(actually)m 16(con)m 118 c (erg)s -1(ed,)m 17(using)m 18(the)m 17(Jacobian)m 18(matrices)m 17(from)m 17(the)m 18(last)m 17(iteration)m 0 786 p (should)s 20(giv)m 101 c 19(essen)m (tial)s -1(ly)m 18(the)m 20(same)m 20(co)m 118 c -2(ari)m -1(ance)m 19(matrix)m 19(as)m 19(that)m 20(whic)m 104 c 19 r 119 c (ould)s 18 r 98 c 1 r 101 c 21(obtained)m 0 843 p (using)s 17(the)m 17(Jacobian)m 17(matrices)m 16(recomputed)m 18(at)m 17(the)m 17(solution.)m 25(Once)m 18(the)m 17(user)m 17(con\014rms)m 18(that)m 0 899 p (the)s 15(solution)m 14(is)m 14(satisfactory)m -4 r 44 c 13(the)m 15(co)m 118 c -2(ar)m -1(iance)m 13(matrix)m 14(can)m 15(easily)m 14 r 98 c 1 r 101 c 15(computed)m 16(at)m 14(the)m 15(actual)m 0 956 p (solution)s 19 r 98 c 121 c 19(calling)m 19(ODRP)m -3 r 65 c (CK)s 19(with)m 20(the)m 20(\014nal)m 21 r 118 c -2(alues)m 19(of)m cmmi10.329 @sf 20 r 12 c cmr10.329 @sf 22(and)m 21 r 1 c 20(as)m 20(input,)m 21(and)m 21(with)m 0 1012 p (argumen)s 116 c cmtt10.329 @sf 13(MAXIT)m cmr10.329 @sf 12 r 61 c 13 r 48 c 15(and)m 16(the)m 15(third)m 15(digit)m 14(of)m 14(argumen)m 116 c cmtt10.329 @sf 14(JOB)m cmr10.329 @sf 15(set)m 15(to)m 14(0.)m 0 1088 p (The)s 13(standard)m 11(deviations,)m 14 r 94 c cmmi10.329 @sf -25 r 27 c cmmi8.300 @sf 530 1095 p 12 c cmr10.329 @sf 553 1088 p 44 c 13(of)m 12(the)m 12(function)m 12(parameters)m 1117 1077 p 94 c cmmi10.329 @sf 1111 1089 p 12 c cmr10.329 @sf 1151 1088 p (listed)s 12(in)m 12(the)m 12(ODRP)m -3 r 65 c (CK)s 11(\014nal)m 0 1149 p (rep)s 1(ort)m 15(are)m 15(the)m 15(square)m 15(ro)m 1(ots)m 14(of)m 15(the)m 15(diagonal)m 14(elemen)m (ts)s 14(of)m 1107 1139 p 94 c cmmi10.329 @sf 1100 1150 p 86 c cmmi8.300 @sf 1127 1157 p 12 c cmr10.329 @sf 1150 1149 p 44 c 15(i.e.,)m 689 1262 p 94 c cmmi10.329 @sf -26 r 27 c cmmi8.300 @sf 712 1269 p 12 c cmmi6.300 @sf 732 1275 p 107 c cmr10.329 @sf 766 1262 p 61 c 821 1252 p 94 c cmmi10.329 @sf 814 1263 p 86 c cmr8.300 @sf 850 1240 p 49 c cmmi8.300 @sf 61 c cmr8.300 @sf 50 c cmmi8.300 @sf 841 1276 p 12 c cmr10.329 @sf 905 1262 p 40 c cmmi10.329 @sf 107 c 1 r 59 c 8 r 107 c cmr10.329 @sf 1 r 41 c cmmi10.329 @sf 14 r 58 c cmr10.329 @sf 0 1364 p (The)s 15(95%)m 15(con\014dence)m 17(in)m (terv)s -3(als)m 13(are)m 15(computed)m 15(using)m 728 1455 p 94 c cmmi10.329 @sf 722 1467 p 12 c cmmi8.300 @sf 748 1474 p 107 c cmsy10.329 @sf 779 1466 p 6 c cmmi10.329 @sf 10 r 116 c cmmi8.300 @sf 840 1473 p 58 c cmr8.300 @sf (975)s cmmi8.300 @sf (;\026)s cmr10.329 @sf 939 1466 p 94 c cmmi10.329 @sf -26 r 27 c cmmi8.300 @sf 962 1473 p 12 c cmmi6.300 @sf 982 1479 p 107 c cmr10.329 @sf 0 1568 p (where)s cmmi10.329 @sf 11 r 116 c cmmi8.300 @sf 143 1575 p 58 c cmr8.300 @sf (975)s cmmi8.300 @sf (;\026)s cmr10.329 @sf 249 1568 p (is)s 10(the)m 11(appropriate)m 9 r 118 c -2(alue)m 9(for)m 10(constructing)m 10 r 97 c 10 r 116 c 119 c -1(o-si)m -1(ded)m 9(95%)m 10(con\014dence)m 12(in)m (terv)s -2(a)m -1 r 108 c 0 1624 p (using)s 17(the)m 17(Studen)m (t's)s cmmi10.329 @sf 16 r 116 c cmr10.329 @sf 18 r 118 c -2(alue)m 16(for)m cmmi10.329 @sf 17 r 22 c cmr10.329 @sf 17(degrees)m 17(of)m 17(freedom.)m 26(When)m cmmi10.329 @sf 17 r 22 c 17 r 62 c cmr10.329 @sf 16(20,)m cmmi10.329 @sf 17 r 116 c cmmi8.300 @sf 1406 1631 p 58 c cmr8.300 @sf (975)s cmmi8.300 @sf (;\026)s cmsy10.329 @sf 1518 1624 p 25 c cmr10.329 @sf 16(2;)m 16(when)m cmmi10.329 @sf 0 1681 p 22 c 13 r 60 c cmr10.329 @sf 13(5,)m cmmi10.329 @sf 14 r 116 c cmmi8.300 @sf 154 1688 p 58 c cmr8.300 @sf (975)s cmmi8.300 @sf (;\026)s cmmi10.329 @sf 263 1681 p 62 c cmr10.329 @sf 13 r 50 c cmmi10.329 @sf 58 c cmr10.329 @sf 53 c 15 r 46 c 0 1757 p (If)s 17(necessary)m -3 r 44 c 17(the)m 17(full)m 17(co)m 118 c -2(ari)m -1(ance)m 16(matrix)m 800 1747 p 94 c cmmi10.329 @sf 793 1758 p 86 c cmr10.329 @sf 847 1757 p (for)s 17(all)m 16(of)m 17(the)m 17(estimators)m 18 r 94 c cmmi10.329 @sf -26 r 17 c cmr10.329 @sf 18(can)m 18 r 98 c 1 r 101 c 18(computed)m 0 1813 p (using)s 21(the)m 22(equations)m 21(giv)m (en)s 20(in)m 22([Boggs)m 20(and)m 22(Rogers,)m 23(1990b],)m 22(or)m 21(can)m 22 r 98 c 1 r 101 c 22(\\automaticall)m -1(y")m 0 1870 p (obtained)s 16(from)m 15(most)m 16(ordinary)m 15(least)m 15(squares)m 16(soft)m 119 c -1(ar)m -1 r 101 c 15(\(including)m 15(ODRP)m -3 r 65 c (CK\))s 15 r 98 c 121 c 15(solving)m 0 1926 p (the)s 11(orthogonal)m 9(distance)m 11(regression)m 10(problem)m 10(as)m 11(the)m 10(ordinary)m 10(least)m 10(squares)m 11(problem)m 11(de\014ned)m 0 1983 p 98 c 121 c 14(\(4.3\).)m 0 2059 p (Note)s 20(that)m 19(for)m 19(nonlinear)m 20(ordinary)m 19(least)m 19(squares,)m 21(the)m 20(linearized)m 19(con\014dence)m 22(regions)m 19(and)m 0 2115 p (in)s (terv)s -2(a)m -1(ls)m 18(are)m 20(asymptotically)m 18(correct)m 20(as)m cmmi10.329 @sf 19 r 110 c cmsy10.329 @sf 21 r 33 c 22 r 49 c cmr10.329 @sf 20([Jennric)m (h,)s 21(1969].)m 33 r 70 c -3(or)m 18(the)m 21(orthogonal)m 0 2172 p (distance)s 12(regression)m 11(problem,)m 11(they)m 12(ha)m 118 c 101 c 10 r 98 c 1(een)m 12(sho)m (wn)s 11(to)m 11 r 98 c 1 r 101 c 12(asymptotically)m 10(correct)m 11(as)m cmmi10.329 @sf 12 r 27 c cmsy8.300 @sf 1648 2157 p 3 c cmsy10.329 @sf 1680 2172 p 33 c cmr10.329 @sf 0 2228 p 48 c 13([F)m -3(uller,)m 11(1987].)m 18(The)m 14(di\013erence)m 13 r 98 c 1(et)m 119 c (een)s 12(the)m 13(conditions)m 13(of)m 13(asymptotic)m 12(correctness)m 13(can)m 13 r 98 c 1 r 101 c 0 2285 p (explained)s 18 r 98 c 121 c 17(the)m 18(fact)m 17(that,)m 17(as)m 18(the)m 18 r 110 c (um)s 98 c 1(er)m 16(of)m 17(observ)m -2(ations)m 16(increases)m 18(in)m 18(the)m 18(orthogonal)m 0 2341 p (distance)s 12(regression)m 11(problem)m 12(one)m 12(do)m 1(es)m 13(not)m 12(obtain)m 11(additional)m 11(information)m 10(for)m 11(\001.)m 19(Note)m 12(also)m 0 2398 p (that)s 106 2388 p 94 c cmmi10.329 @sf 99 2399 p 86 c cmr10.329 @sf 152 2398 p (is)s 15(dep)m 1(enden)m 116 c 16(up)m 1(on)m 17(the)m 16 r 119 c (eigh)s -1 r 116 c 13(matrix)m 15(\012,)m 15(whic)m 104 c 15 r 109 c (ust)s 14 r 98 c 1 r 101 c 17(assumed)m 16(to)m 15 r 98 c 1 r 101 c 17(correct,)m 0 2454 p (and)s 15(cannot)m 15 r 98 c 1 r 101 c 15(con\014rmed)m 16(from)m 14(the)m 15(orthogonal)m 13(distance)m 15(regression)m 14(results.)m 19(Errors)m 14(in)m 15(the)m @eop %%Page: 77 91 77 @bop0 cmmi10.329 @sf [ 32 32 -2 0 34.090] 65 @dc [ 24 20 -2 0 26.188] 20 @dc cmsy10.329 @sf [ 16 46 -5 12 22.727] 107 @dc cmex10.300 @sf [ 16 27 -6 26 23.061] 13 @dc cmsy8.300 @sf [<0E000E000E000E000E000E000E000E000E000E000E000E000E000E000E000E000E000E00FFE0FF E0FFE00E000E000E000E000E000E000E000E00> 16 29 -2 6 15.682] 121 @dc cmmi8.300 @sf [<3FE0003FF00007800003800003800003800001C00001C00001C00001C00001E00003F000039800 038C00078E000707000703800F01800E00C00E00601E0078FF80FFFF80FF> 24 23 -1 0 20.450] 89 @dc [ 24 23 -1 0 26.428] 65 @dc cmr10.329 @sf [ 16 2 -3 -25 22.727] 22 @dc cmmi8.300 @sf [<0000300000F00003E0000F80003E0000780001E00007C0001F00007C0000F00000F000007C0000 1F000007C00001E000007800003E00000F800003E00000F0000030> 24 22 -3 3 27.443] 60 @dc cmex10.300 @sf [<0000700000F00001E00001C0000380000700000E00001E00001C0000380000780000700000F000 00E00001E00001C00003C0000380000780000780000700000F00000F00000E00001E00001E0000 1E00003C00003C00003C00003C0000380000780000780000780000780000780000780000780000 F00000F00000F00000F00000F00000F00000F00000F00000F00000F00000F00000F00000F00000 F00000F00000F00000F00000F00000F00000F00000F00000780000780000780000780000780000 7800007800003800003C00003C00003C00003C00001E00001E00001E00000E00000F00000F0000 07000007800007800003800003C00001C00001E00000E00000F000007000007800003800001C00 001E00000E000007000003800001C00001E00000F0000070> 24 99 -9 97 30.556] 18 @dc [ 24 99 -1 97 30.556] 19 @dc 77 @bop1 cmr10.329 @sf 225 114 p (Computational)s 13(Details)m 1226(77)m 225 134 p 1725 2 ru 225 260 p 118 c -2(alues)m 15(of)m cmmi10.329 @sf 15 r 119 c cmmi8.300 @sf 441 267 p 15 c cmmi6.300 @sf 455 272 p 105 c cmr10.329 @sf 485 260 p (and)s cmmi10.329 @sf 15 r 119 c cmmi8.300 @sf 601 267 p 14 c cmmi6.300 @sf 617 272 p 105 c cmr10.329 @sf 646 260 p (that)s 15(form)m 15 r 10 c 15(will)m 15(ha)m 118 c -1 r 101 c 14(an)m 15(adv)m (erse)s 15(a\013ect)m 15(on)m 15(the)m 16(accuracy)m 15(of)m 1832 250 p 94 c cmmi10.329 @sf 1825 261 p 86 c cmr10.329 @sf 1877 260 p (and)s 225 317 p (its)s 14(comp)m 1(onen)m 116 c 14(parts.)m 19(The)m 15(results)m 14(of)m 15 r 97 c 14(Mon)m (te)s 13(Carlo)m 14(exp)m 1(erimen)m 116 c 14(examining)m 14(the)m 15(accuracy)m 225 373 p (of)s 21(the)m 22(linearized)m 22(con\014dence)m 23(in)m (terv)s -2(a)m -1(ls)m 20(for)m 21(four)m 21(di\013eren)m 116 c 20(measuremen)m 116 c 21(error)m 21(mo)m 1(dels)m 21(is)m 225 430 p (presen)s (ted)s 21(in)m 20([Boggs)m 20(and)m 22(Rogers,)m 22(1990b].)m 36(Those)m 21(results)m 20(indicate)m 21(that)m 20(the)m 21(con\014dence)m 225 486 p (regions)s 14(and)m 16(in)m (terv)s -2(a)m -1(ls)m 13(for)m 15 r 1 c 15(are)m 14(not)m 15(as)m 15(accurate)m 15(as)m 15(those)m 15(for)m cmmi10.329 @sf 14 r 12 c cmr10.329 @sf 2 r 46 c 225 562 p (Despite)s 17(its)m 16 r 112 c 1(oten)m (tial)s 15(inaccuracy)m -3 r 44 c 16(the)m 17(co)m 118 c -2(ari)m -1(ance)m 15(matrix)m 16(is)m 17(frequen)m (tly)s 15(used)m 18(to)m 16(construct)m 225 618 p (con\014dence)s 23(regions)m 21(and)m 21(in)m (terv)s -2(al)m -1 r 115 c 20(for)m 21 r 98 c 1(oth)m 21(nonlinear)m 21(ordinary)m 21(least)m 20(squares)m 21(and)m 22(mea-)m 225 675 p (suremen)s 116 c 18(error)m 19(mo)m 1(dels)m 19 r 98 c 1(ecause)m 21(the)m 19(resulting)m 19(regions)m 18(and)m 20(in)m (terv)s -2(al)m -1 r 115 c 18(are)m 19(inexp)m 1(ensiv)m 101 c 19(to)m 225 731 p (compute,)s 13(often)m 13(adequate,)m 13(and)m 13(familiar)m 11(to)m 13(practitioners.)m cmti10.329 @sf 17(Caution)m 14(must)m 15 r 98 c -1 r 101 c 13(exer)m -1(cise)m -2 r 100 c 12(when)m 225 788 p (using)s 18(such)m 18 r 114 c -1 r 101 c -2(gions)m 16(and)m 18(intervals,)m 18(however,)m 19(sinc)m -2 r 101 c 17(the)m 18(validity)m 18(of)m 19(the)m 18(appr)m -1(oximation)m 18(wil)m 2 r 108 c 225 844 p (dep)s -1(end)m 19(on)m 21(the)m 20(nonline)m -2(arity)m 20(of)m 20(the)m 21(mo)m -1(del,)m 20(the)m 21(varianc)m -1 r 101 c 19(and)m 21(distribution)m 21(of)m 20(the)m 21(err)m -1(ors,)m 225 901 p (and)s 17(the)m 18(data)m 18(itself.)m cmr10.329 @sf 23(When)m 16(more)m 16(reliable)m 16(in)m (terv)s -3(als)m 14(and)m 16(regions)m 16(are)m 16(required,)m 16(other)m 16(more)m 225 957 p (accurate)s 16(metho)m 1(ds)m 16(should)m 15 r 98 c 1 r 101 c 17(used.)m 22(\(See,)m 16(e.g.,)m 15([Bates)m 15(and)m 16 r 87 c -3(atts,)m 14(1988],)m 14([Donaldson)m 15(and)m 225 1014 p (Sc)s (hnab)s 1(el,)m 15(1987],)m 13(and)m 15([Efron,)m 14(1985].\))m cmbx12.300 @sf 225 1158 p (4.C.)s 18(Condition)m 19(Num)m -1 r 98 c 2(er)m cmr10.329 @sf 225 1279 p 70 c -3(or)m 14 r 97 c cmti10.329 @sf 14(line)m -1(ar)m cmr10.329 @sf 14(least)m 14(squares)m 15(system)m 15(of)m 14(equations)m cmmi10.329 @sf 984 1371 p (A\014)s cmr10.329 @sf 15 r 61 c cmr8.300 @sf 1094 1378 p 50 c cmmi10.329 @sf 1127 1371 p 89 c 25 r 59 c cmr10.329 @sf 666(\(4)m cmmi10.329 @sf 58 c cmr10.329 @sf (4\))s 225 1463 p (with)s cmmi10.329 @sf 15 r 65 c cmsy10.329 @sf 13 r 50 c 13 r 60 c cmmi8.300 @sf 452 1448 p 110 c cmsy8.300 @sf 2 c cmmi8.300 @sf 112 c cmr10.329 @sf 536 1463 p (assumed)s 15(to)m 15(ha)m 118 c 101 c 13(full)m 15(column)m 16(rank)m 15(and)m 16 r 61 c cmr8.300 @sf 1348 1470 p 50 c cmr10.329 @sf 1384 1463 p (meaning)s 15(\\equals)m 15(in)m 15(the)m 16(least)m 225 1520 p (squares)s 15(sense,")m 15(the)m cmti10.329 @sf 15 r 99 c -1(ondition)m 15(numb)m -1(er)m cmr10.329 @sf 14(of)m cmmi10.329 @sf 15 r 65 c cmr10.329 @sf 15(is)m 15(de\014ned)m 16(as)m cmmi10.329 @sf 899 1617 p 20 c cmr10.329 @sf 40 c cmmi10.329 @sf 65 c cmr10.329 @sf 41 c cmsy10.329 @sf 12 r 17 c 13 r 107 c cmmi10.329 @sf 65 c cmsy10.329 @sf 107 c cmex10.300 @sf 1142 1569 p 13 c 1142 1594 p 13 c 1142 1619 p 13 c cmmi10.329 @sf 1166 1617 p 65 c cmsy8.300 @sf 1200 1599 p 121 c cmex10.300 @sf 1217 1569 p 13 c 1217 1594 p 13 c 1217 1619 p 13 c cmmi10.329 @sf 1263 1617 p 59 c cmr10.329 @sf 225 1723 p (where)s cmmi10.329 @sf 16 r 65 c cmsy8.300 @sf 391 1708 p 121 c cmsy10.329 @sf 423 1723 p 17 c cmr10.329 @sf 14 r 40 c cmmi10.329 @sf 65 c cmr6.300 @sf 524 1708 p 84 c cmmi10.329 @sf 548 1723 p 65 c cmr10.329 @sf 41 c cmsy8.300 @sf 600 1708 p 0 c cmr8.300 @sf 49 c cmmi10.329 @sf 647 1723 p 65 c cmr6.300 @sf 681 1708 p 84 c cmr10.329 @sf 720 1723 p (is)s 16(kno)m (wn)s 15(as)m 15(the)m 16(pseudo)m 17(in)m 118 c -1(erse)m 14(of)m cmmi10.329 @sf 16 r 65 c cmr10.329 @sf 46 c 22 r 70 c -3(rom)m 14(this)m 16(de\014nition,)m 15 r 119 c 101 c 225 1779 p (can)s 15(sho)m 119 c 14(that)m cmmi10.329 @sf 14 r 20 c cmr10.329 @sf 40 c cmmi10.329 @sf 65 c cmr10.329 @sf 41 c cmsy10.329 @sf 13 r 21 c cmr10.329 @sf 13(1,)m 14(and)m 16(that)m cmmi10.329 @sf 14 r 20 c cmr10.329 @sf 40 c cmmi10.329 @sf 65 c cmr10.329 @sf 41 c cmsy10.329 @sf 12 r 33 c 13 r 49 c cmr10.329 @sf 16(as)m 15(the)m 15(columns)m 15(of)m cmmi10.329 @sf 15 r 65 c cmr10.329 @sf 15 r 98 c 1(ecome)m 16(dep)m 1(enden)m (t.)s 225 1855 p (Using)s cmmi10.329 @sf 17 r 20 c cmr10.329 @sf 40 c cmmi10.329 @sf 65 c cmr10.329 @sf (\),)s 17 r 98 c 1(ounds)m 18(can)m 18 r 98 c 1 r 101 c 18(constructed)m 17(on)m 18(the)m 17(relativ)m 101 c 15(error)m 17(in)m 17(the)m 17(true)m 18(least)m 16(squares)m 225 1912 p (solution)s cmmi10.329 @sf 20 r 12 c cmsy8.300 @sf 431 1897 p 3 c cmr10.329 @sf 473 1912 p 61 c cmmi10.329 @sf 23 r 65 c cmsy8.300 @sf 565 1897 p 121 c cmmi10.329 @sf 583 1912 p 89 c cmr10.329 @sf 31(due)m 22(to)m 20 r 97 c 21 r 112 c 1(erturbation)m cmmi10.329 @sf 20 r 69 c cmmi8.300 @sf 1143 1919 p 89 c cmr10.329 @sf 1194 1912 p (of)s cmmi10.329 @sf 21 r 89 c cmr10.329 @sf 10 r 44 c 22(or)m 21(to)m 20 r 97 c 21 r 112 c 1(erturbation)m cmmi10.329 @sf 21 r 69 c cmmi8.300 @sf 1797 1919 p 65 c cmr10.329 @sf 1846 1912 p (of)s cmmi10.329 @sf 20 r 65 c cmr10.329 @sf 46 c 225 1968 p (While)s 15(the)m 17(actual)m 15 r 98 c 1(ounds,)m 17(discussed)m 16(in)m 16(detail)m 16(in)m 15([Stew)m (art,)s 14(1973],)m 14(are)m 16(quite)m 16(complicated,)m 225 2024 p 119 c 101 c 17(can)m 18(roughly)m 17(appro)m (xima)s -1(te)m 16(them)m 18(as)m 17(follo)m (w)s -1(s.)m 26(Let)m 1257 2013 p 22 c cmmi10.329 @sf 1250 2025 p 12 c cmmi8.300 @sf 1276 2032 p 89 c cmr10.329 @sf 1324 2024 p (and)s 1422 2013 p 22 c cmmi10.329 @sf 1415 2025 p 12 c cmmi8.300 @sf 1441 2032 p 65 c cmr10.329 @sf 1487 2024 p (denote)s 18(the)m 18(solutions)m 17(to)m 225 2081 p (the)s 16 r 112 c 1(erturb)m 1(ed)m 18(systems,)m 707 2070 p 22 c cmmi10.329 @sf 701 2082 p 12 c cmmi8.300 @sf 727 2089 p 89 c cmr10.329 @sf 769 2081 p 61 c cmmi10.329 @sf 13 r 65 c cmsy8.300 @sf 851 2066 p 121 c cmr10.329 @sf 869 2081 p 40 c cmmi10.329 @sf 89 c cmr10.329 @sf 21 r 43 c cmmi10.329 @sf 10 r 69 c cmmi8.300 @sf 1013 2088 p 89 c cmr10.329 @sf 1043 2081 p 41 c 16(and)m 1173 2070 p 22 c cmmi10.329 @sf 1166 2082 p 12 c cmmi8.300 @sf 1192 2089 p 65 c cmr10.329 @sf 1233 2081 p 61 c 13 r 40 c cmmi10.329 @sf 65 c cmr10.329 @sf 10 r 43 c cmmi10.329 @sf 11 r 69 c cmmi8.300 @sf 1423 2088 p 65 c cmr10.329 @sf 1451 2081 p 41 c cmsy8.300 @sf 1469 2066 p 121 c cmmi10.329 @sf 1486 2081 p 89 c cmr10.329 @sf 11 r 44 c 16(resp)m 1(ectiv)m (ely)s -3 r 44 c 14(and)m 16(let)m cmmi10.329 @sf 225 2137 p 82 c cmr10.329 @sf 12 r 61 c cmmi10.329 @sf 13(A\014)m cmsy8.300 @sf 382 2122 p 3 c cmsy10.329 @sf 412 2137 p 0 c cmmi10.329 @sf 11 r 89 c cmr10.329 @sf 26(denote)m 15(the)m 15(residual)m 15(at)m cmmi10.329 @sf 14 r 12 c cmsy8.300 @sf 987 2122 p 3 c cmr10.329 @sf 1007 2137 p 46 c 20(Then)m cmex10.300 @sf 832 2187 p 13 c 832 2212 p 13 c cmmi10.329 @sf 855 2224 p 12 c cmsy8.300 @sf 883 2209 p 3 c cmsy10.329 @sf 913 2224 p 0 c cmr10.329 @sf 965 2213 p 22 c cmmi10.329 @sf 958 2225 p 12 c cmmi8.300 @sf 984 2232 p 89 c cmex10.300 @sf 1014 2187 p 13 c 1014 2212 p 13 c 832 2244 p 206 2 ru cmsy10.329 @sf 888 2286 p 107 c cmmi10.329 @sf 12 c cmsy8.300 @sf 939 2274 p 3 c cmsy10.329 @sf 959 2286 p 107 c cmmi8.300 @sf 1066 2236 p 60 c cmsy10.329 @sf 1063 2265 p 25 c cmmi10.329 @sf 1118 2255 p 20 c cmr10.329 @sf 40 c cmmi10.329 @sf 65 c cmr10.329 @sf 41 c cmsy10.329 @sf 1234 2224 p 107 c cmmi10.329 @sf -1 r 69 c cmmi8.300 @sf 1290 2231 p 89 c cmsy10.329 @sf 1320 2224 p 107 c 1234 2244 p 110 2 ru 1247 2286 p 107 c cmmi10.329 @sf 89 c cmsy10.329 @sf 11 r 107 c cmr10.329 @sf 1857 2255 p (\(4)s cmmi10.329 @sf 58 c cmr10.329 @sf (5\))s 225 2368 p (and)s cmex10.300 @sf 650 2374 p 13 c 650 2399 p 13 c cmmi10.329 @sf 673 2410 p 12 c cmsy8.300 @sf 701 2395 p 3 c cmsy10.329 @sf 731 2410 p 0 c cmr10.329 @sf 783 2399 p 22 c cmmi10.329 @sf 777 2411 p 12 c cmmi8.300 @sf 803 2418 p 65 c cmex10.300 @sf 831 2374 p 13 c 831 2399 p 13 c 650 2430 p 204 2 ru cmsy10.329 @sf 705 2472 p 107 c cmmi10.329 @sf 12 c cmsy8.300 @sf 756 2460 p 3 c cmsy10.329 @sf 776 2472 p 107 c cmmi8.300 @sf 883 2422 p 60 c cmsy10.329 @sf 879 2451 p 25 c cmex10.300 @sf 942 2382 p 18 c cmmi10.329 @sf 973 2441 p 20 c cmr10.329 @sf 40 c cmmi10.329 @sf 65 c cmr10.329 @sf 41 c 9 r 43 c cmmi10.329 @sf 11 r 20 c cmr8.300 @sf 1150 2423 p 50 c cmr10.329 @sf 1170 2441 p 40 c cmmi10.329 @sf 65 c cmr10.329 @sf 41 c cmsy10.329 @sf 1260 2410 p 107 c cmmi10.329 @sf 82 c cmsy10.329 @sf 107 c 1259 2430 p 82 2 ru 1259 2472 p 107 c cmmi10.329 @sf 89 c cmsy10.329 @sf 11 r 107 c cmex10.300 @sf 1346 2382 p 19 c cmsy10.329 @sf 1389 2410 p 107 c cmmi10.329 @sf 69 c cmmi8.300 @sf 1446 2417 p 65 c cmsy10.329 @sf 1474 2410 p 107 c 1389 2430 p 108 2 ru 1403 2472 p 107 c cmmi10.329 @sf 65 c cmsy10.329 @sf 107 c cmmi10.329 @sf 1517 2441 p 58 c cmr10.329 @sf 327(\(4)m cmmi10.329 @sf 58 c cmr10.329 @sf (6\))s @eop %%Page: 78 92 78 @bop0 cmsy8.300 @sf [ 24 23 -1 0 26.814] 75 @dc cmsy10.329 @sf [ 32 33 -1 1 34.633] 75 @dc cmti10.329 @sf [ 32 31 -8 0 32.524] 84 @dc [<7E07E00000007F0FF0000000FF1F380000007B8F1C00000071CE0E00000001C00E00000001C007 00000001E00700000000E00700000000E007800F0000E003801F8000E003803DC000F0038038C0 0070038038C0007003C038E0007001C03C60007001C01C00007801C01C00003801C01C00003801 E01E00003800E00E00003800E00E00003C00E00E00001C00E00F00001C00F00700001C00700700 001C0070070001FFFFFFFF8000FFFFFFFF80000E00780000000E00380000000E00380000000F00 3800000007003800000007003C00000007001C01C0000781FC01E0000381EE01E00001C1EF00E0 0000FFE3FFE000003FC0FF80> 48 41 2 9 40.075] 14 @dc cmmi10.329 @sf [ 48 31 -2 0 44.096] 77 @dc [<1F80007FE00071F000E0F800F87C00F83C00F83C00783E00381E00001E00001E00001F00000F00 000F00000F00000F800007800007800007800007C00003C00003C00003C00003E00001E00001E0 0001E00001F00000F00000F8003FFF003FFF> 24 32 -3 1 25.205] 74 @dc cmti10.329 @sf [ 32 31 -3 0 28.509] 76 @dc [ 8 14 -9 -18 13.939] 39 @dc [<01FE000007FFC4000FC1EC001F007E003E003E003C001E0078001F0078001F0070000F00F0000F 00F0000F80F0000F80F000FFF0F000FFF0F80000007800000078000000780000007C0000003C00 00003C0000601E0000601E0000600F0000700F8000700780007003C0007001E000F800F800F800 7C01F8001F8798000FFF1C0001FC0C> 32 33 -6 1 35.163] 71 @dc 78 @bop1 cmr10.329 @sf 0 114 p (78)s 1227(Computational)m 13(Details)m 0 134 p 1725 2 ru 0 259 p 70 c -3(or)m 10(\(4.5\))m 10 r 119 c 101 c 11(th)m (us)s 10(observ)m 101 c 11(that)m 11(the)m 12(relativ)m -1 r 101 c 10(error)m 11(in)m 11(the)m 12(solution)m 11(could)m 11 r 98 c 1 r 101 c 13(as)m 11 r 109 c (uc)s 104 c 10(as)m cmmi10.329 @sf 11 r 20 c cmr10.329 @sf 40 c cmmi10.329 @sf 65 c cmr10.329 @sf 41 c 0 315 p (larger)s 16(than)m 17(the)m 17(relativ)m 101 c 15(error)m 16(in)m cmmi10.329 @sf 17 r 89 c cmr10.329 @sf 11 r 46 c 26(Similarly)m -4 r 44 c 15(for)m 17(\(4.6\))m 15 r 119 c 101 c 16(observ)m 101 c 16(that)m 17(if)m 16(the)m 18(residual)m cmmi10.329 @sf 0 372 p 82 c cmr10.329 @sf 15(is)m 15(small,)m 13(then)m 16(the)m 15(relativ)m 101 c 13(error)m 14(in)m cmmi10.329 @sf 15 r 65 c cmr10.329 @sf 16(is)m 14 r 109 c (ultiplied)s 13 r 98 c 121 c cmmi10.329 @sf 14 r 20 c cmr10.329 @sf 40 c cmmi10.329 @sf 65 c cmr10.329 @sf (\),)s 15(whereas)m 15(if)m 15(the)m 15(residual)m 14(is)m 0 428 p (not)s 14(small,)m 12(then)m 14(the)m 14(second)m 15(term)m 13(in)m 14(\(4.6\))m 12(will)m 13(dominate)m 13(and)m 14(the)m 14(relativ)m 101 c 12(error)m 13(in)m cmmi10.329 @sf 14 r 65 c cmr10.329 @sf 14(could)m 0 484 p 98 c 1 r 101 c 16 r 109 c (ultipli)s -1(ed)m 14 r 98 c 121 c 14(as)m 15 r 109 c (uc)s 104 c 13(as)m cmmi10.329 @sf 15 r 20 c cmr8.300 @sf 600 469 p 50 c cmr10.329 @sf 620 484 p 40 c cmmi10.329 @sf 65 c cmr10.329 @sf 41 c cmmi10.329 @sf 58 c cmr10.329 @sf 0 560 p (If)s 16 r 119 c 101 c 14(express)m 16(the)m 16(condition)m 15 r 110 c (um)s -1 r 98 c 1(er)m cmmi10.329 @sf 14 r 20 c cmr10.329 @sf 40 c cmmi10.329 @sf 65 c cmr10.329 @sf 41 c 16(as)m 15 r 97 c 15 r 112 c 1 r 111 c 119 c (er)s 13(of)m 15(10,)m 15(i.e.,)m cmmi10.329 @sf 14 r 20 c cmr10.329 @sf 40 c cmmi10.329 @sf 65 c cmr10.329 @sf 41 c 13 r 61 c 14(10)m cmsy8.300 @sf 1471 545 p 75 c cmr10.329 @sf 1499 560 p 44 c 16(then)m 16(\(4.5\))m 0 617 p (implies)s 18(that)m 17(the)m 19(elemen)m (ts)s 17(of)m 18(the)m 19(least)m 17(squares)m 18(solution)m 18(could)m 18(ha)m 118 c 101 c cmsy10.329 @sf 16 r 75 c cmr10.329 @sf 19(few)m (er)s 17(signi\014can)m 116 c 0 673 p (digits)s 18(of)m 20(accuracy)m 20(than)m 19(the)m 20(elemen)m (ts)s 18(of)m cmmi10.329 @sf 20 r 89 c cmr10.329 @sf 10 r 44 c 20(while)m 20(\(4.6\))m 18(implies)m 19(that)m 19(the)m 19(least)m 19(squares)m 0 730 p (solution)s 11(could)m 13(ha)m 118 c 101 c 10(as)m 13(man)m 121 c 11(as)m 12 r 50 c cmsy10.329 @sf 75 c cmr10.329 @sf 13(few)m (er)s 11(signi\014can)m 116 c 11(digits)m 11(of)m 12(accuracy)m 13(than)m 13(the)m 12(elemen)m (ts)s 0 786 p (of)s cmmi10.329 @sf 13 r 65 c cmr10.329 @sf 46 c cmti10.329 @sf 19(Ther)m -1(efor)m -1(e,)m cmmi10.329 @sf 12 r 20 c cmr10.329 @sf 40 c cmmi10.329 @sf 65 c cmr10.329 @sf 41 c cmti10.329 @sf 15(su\016ciently)m 13(lar)m -1(ge)m 13 r 99 c -1(ould)m 14(indic)m -1(ate)m 13(that)m 15(the)m 15(le)m -1(ast)m 13(squar)m -1(es)m 13(solution)m 14(has)m 0 843 p (no)s 16(signi\014c)m -2(ant)m 15(digits.)m cmr10.329 @sf 20 r 70 c -3(or)m 14(the)m 15(condition)m 15 r 110 c (um)s 98 c 1(er)m 13(to)m 15(pro)m (vide)s 14 r 97 c 15(meaningful)m 15(estimate)m 14(of)m 15(ill-)m 0 899 p (conditioning,)s 14(ho)m 119 c -1(ev)m -1(er,)m 13(the)m 15(user's)m 15(problem)m 15 r 109 c (ust)s 14 r 98 c 1 r 101 c 16(form)m (ula)s -1(ted)m 14(so)m 14(that)m 15(the)m 15(errors)m 15(in)m 15(the)m 0 956 p (columns)s 13(of)m cmmi10.329 @sf 12 r 65 c cmr10.329 @sf 13(are)m 12(equilibrated.)m 19(This)m 12(requires)m 13(an)m 12(in)m (timate)s 11(kno)m (wledge)s 11(of)m 12(the)m 13(problem,)m 13(and)m 0 1012 p (cannot)s 10 r 98 c 1 r 101 c 11(done)m 11(as)m 9(part)m 10(of)m 10(ODRP)m -3 r 65 c (CK's)s 8(automatic)m 9(scaling)m 9(pro)m 1(cedure.)m 19(If)m 11(this)m 10(equilibration)m 0 1069 p (has)s 15(not)m 14 r 98 c 1(een)m 16(done)m 15 r 98 c 121 c 14(the)m 15(user,)m 15(the)m 14(condition)m 15 r 110 c (um)s -1 r 98 c 1(er)m 14(returned)m 15 r 98 c 121 c 14(ODRP)m -3 r 65 c (CK)s 13(ma)m 121 c 13(not)m 0 1125 p (re\015ect)s 15(the)m 16(true)m 15(conditioning)m 14(of)m 15(the)m 15(problem.)m 0 1201 p (ODRP)s -3 r 65 c (CK)s 12(returns)m 14(an)m 14(appro)m (ximat)s -1(ion)m 12(to)m 13(the)m cmti10.329 @sf 14(inverse)m cmr10.329 @sf 12(of)m 14(the)m 14(condition)m 13 r 110 c (um)s 98 c 1(er)m cmmi10.329 @sf 12 r 20 c cmr10.329 @sf 40 c cmmi10.329 @sf 77 c cmmi8.300 @sf 1627 1208 p 14 c cmmi10.329 @sf 1646 1201 p 74 c cmmi8.300 @sf 1671 1208 p 12 c cmr10.329 @sf 1695 1201 p (\),)s 0 1257 p (where)s cmmi10.329 @sf 18 r 74 c cmmi8.300 @sf 159 1264 p 12 c cmr10.329 @sf 200 1257 p (is)s 17(the)m 18(Jacobian)m 17(matrix)m 16(of)m 17(partial)m 16(deriv)m -2(ativ)m -1(es)m 16(with)m 16(resp)m 1(ect)m 18(to)m cmmi10.329 @sf 17 r 12 c cmr10.329 @sf 2 r 44 c 18(and)m cmmi10.329 @sf 18 r 77 c cmmi8.300 @sf 1618 1264 p 14 c cmr10.329 @sf 1654 1257 p (is)s 17 r 97 c 0 1314 p (blo)s 1 r 99 c 107 c 10(diagonal)m 9(matrix)m 9(formed)m 11(using)m 10(the)m 11(partial)m 9(deriv)m -2(ativ)m (es)s 8(with)m 11(resp)m 1(ect)m 11(to)m 10 r 1 c 11(as)m 10(describ)m 1(ed)m 0 1370 p (in)s 14([Boggs)m cmti10.329 @sf 13(et)m 16(al.)m cmr10.329 @sf 44 c 14(1987].)m 18(The)m 14(matrix)m cmmi10.329 @sf 13 r 77 c cmmi8.300 @sf 744 1377 p 14 c cmmi10.329 @sf 763 1370 p 74 c cmmi8.300 @sf 788 1377 p 12 c cmr10.329 @sf 826 1370 p (is)s 14(used)m 15 r 98 c 121 c 13(ODRP)m -3 r 65 c (CK)s 13(to)m 13(form)m 14 r 97 c 14(linearization)m 0 1427 p (of)s 16(the)m 16(user's)m 16(problem)m 16(at)m 16(the)m 16(solution,)m 15(and)m 17(can)m 16(th)m (us)s 16 r 98 c 1 r 101 c 17(substituted)m 16(for)m 15(the)m 17(matrix)m cmmi10.329 @sf 15 r 65 c cmr10.329 @sf 16(in)m 0 1483 p (in)s 18(the)m 19(ab)m 1 r 111 c 118 c -1 r 101 c 17(discussions.)m 30(The)m 18(appro)m (ximate)s 17(in)m 118 c -1(erse)m 17(condition)m 17 r 110 c (um)s 98 c 1(er)m 17(is)m 18(calculated)m 18(as)m 0 1540 p (describ)s 1(ed)m 16(in)m 15(the)m cmti10.329 @sf 15(Linp)m -1(ack)m 15(Users')m 15(Guide)m cmr10.329 @sf 16([Dongarra)m cmti10.329 @sf 13(et)m 16(al.)m cmr10.329 @sf 44 c 15(1980].)m cmbx12.300 @sf 0 1686 p (4.D.)s 18(Scaling)m 18(Algorithms)m cmr10.329 @sf 0 1807 p 80 c 111 c 1(orly)m 10(scaled)m 13(problems,)m 12(i.e.,)m 12(problems)m 13(in)m 12(whic)m 104 c 12(the)m 12(unkno)m (wns)s cmmi10.329 @sf 12 r 12 c cmr10.329 @sf 15(and)m 13 r 1 c 12 r 118 c -2(ary)m 12 r 111 c 118 c -1(er)m 11(sev)m (eral)s 0 1863 p (orders)s 20(of)m 19(magnitude,)m 21(can)m 20(cause)m 20(di\016cult)m 121 c 18(for)m 20(least)m 19(squares)m 20(pro)m 1(cedures.)m 35(ODRP)m -3 r 65 c (CK's)s 0 1920 p (scaling)s 18(algorithms)m 17(\(discussed)m 19 r 98 c 1(elo)m (w\))s 17(attempt)m 17(to)m 19 r 111 c 118 c -1(ercome)m 17(these)m 19(di\016culties)m 18(automati-)m 0 1976 p (cally)s -3 r 44 c 13(although)m 14(it)m 14(is)m 15(preferable)m 15(for)m 14(the)m 15(user)m 16(to)m 14 r 99 c (ho)s 1(ose)m 14(the)m 15(units)m 15(of)m cmmi10.329 @sf 14 r 12 c cmr10.329 @sf 17(and)m 16 r 1 c 14(so)m 15(that)m 14(their)m 0 2033 p (estimated)s 16 r 118 c -2(alues)m 16(will)m 15(ha)m 118 c 101 c 15(roughly)m 16(the)m 16(same)m 17(magnitude.)m 24(\(See,)m 17(e.g.,)m 16([Dennis)m 16(and)m 17(Sc)m (hn-)s 0 2089 p (ab)s 1(el,)m 20(1983].\))m 29(When)m 20(the)m 19 r 118 c -2(ariables)m 17(ha)m 118 c 101 c 17(roughly)m 18(the)m 19(same)m 19(magnitude,)m 19(the)m 19(ODRP)m -3 r 65 c (CK)s 0 2146 p (scaling)s 14(algorithm)m 12(will)m 13(select)m 15(scale)m 14 r 118 c -2(alues)m 14(that)m 14(are)m 14(roughly)m 14(equal,)m 14(and)m 15(the)m 14(resulting)m 14(com-)m 0 2202 p (putations)s 18(will)m 18 r 98 c 1 r 101 c 20(the)m 19(same)m 19(\(except)m 19(for)m 19(the)m 19(e\013ect)m 19(of)m 19(\014nite)m 19(precision)m 19(arithmetic\))m 17(as)m 19(an)m 0 2259 p (unscaled)s 16(analysis,)m 14(i.e.,)m 14(an)m 15(analysis)m 14(in)m 16(whic)m 104 c 14(all)m 14(of)m 15(the)m 16(scale)m 15 r 118 c -2(alues)m 14(are)m 15(set)m 16(to)m 14(one.)m 21(If)m 16(the)m 0 2315 p (user)s 14(do)m 1(es)m 15(not)m 13(do)m 14(this,)m 14(the)m 14(ODRP)m -3 r 65 c (CK)s 13(scaling)m 13(algorithm)m 12(will)m 13(select)m 14 r 118 c -2(arying)m 12(scale)m 14 r 118 c -2(alues.)m 0 2371 p (This)s 18(will)m 17(not)m 17 r 99 c (hange)s 18(the)m 18(optimal)m 16(solution,)m 18(but)m 18(it)m 17(ma)m 121 c 17(a\013ect)m 17(the)m 19 r 110 c (um)s -1 r 98 c 1(er)m 17(of)m 18(iterations)m 0 2428 p (required,)s 15(or,)m 14(in)m 15(some)m 15(cases,)m 15(whether)m 15(the)m 16(algorit)m -1(hm)m 14(is)m 14(or)m 15(is)m 15(not)m 15(successful.)m @eop %%Page: 79 93 79 @bop0 79 @bop1 cmr10.329 @sf 225 114 p (Computational)s 13(Details)m 1226(79)m 225 134 p 1725 2 ru 225 259 p (The)s 15(scale)m 15 r 118 c -2(alue)m 14(times)m 14(the)m 15(corresp)m 1(onding)m 15(absolute)m 14 r 118 c -2(alue)m 14(of)m 14(the)m 15(exp)m 1(ected)m 16(solution)m 14(should)m 225 315 p 98 c 1 r 101 c 11(appro)m (ximately)s 8(one.)m 19 r 70 c -3(or)m 9(example,)m 11(if)m cmmi10.329 @sf 10 r 12 c cmr6.300 @sf 1004 322 p 75 c cmr10.329 @sf 1040 315 p (is)s 10(exp)m 1(ected)m 12(to)m 10 r 98 c 1 r 101 c 12(of)m 10(order)m 11(10)m cmr8.300 @sf 1583 300 p (10)s cmr10.329 @sf 1630 315 p (then)s cmcsc10.329 @sf 11(scale)m cmsy10.329 @sf 1 r 102 c cmmi10.329 @sf 12 c cmr6.300 @sf 1903 322 p 75 c cmsy10.329 @sf 1927 315 p 103 c cmr10.329 @sf 225 372 p (should)s 18 r 98 c 1 r 101 c 18(set)m 17(to)m 17(10)m cmsy8.300 @sf 613 357 p 0 c cmr8.300 @sf (10)s cmr10.329 @sf 677 372 p 44 c 18(while)m 17(if)m cmmi10.329 @sf 17 r 12 c cmr6.300 @sf 899 379 p 75 c cmr10.329 @sf 941 372 p (is)s 17(exp)m 1(ected)m 19(to)m 17(lie)m 17 r 98 c 1(et)m 119 c (een)s cmsy10.329 @sf 16 r 0 c cmr10.329 @sf (10)s cmsy8.300 @sf 1561 357 p 0 c cmr8.300 @sf 50 c cmr10.329 @sf 1625 372 p (and)s cmsy10.329 @sf 18 r 0 c cmr10.329 @sf (10)s cmsy8.300 @sf 1797 357 p 0 c cmr8.300 @sf 52 c cmr10.329 @sf 1862 372 p (then)s cmcsc10.329 @sf 225 428 p (scale)s cmsy10.329 @sf 102 c cmmi10.329 @sf 12 c cmr6.300 @sf 398 435 p 75 c cmsy10.329 @sf 423 428 p 103 c cmr10.329 @sf 19(should)m 19 r 98 c 1 r 101 c 19(set)m 19(to)m 19(10)m cmr8.300 @sf 859 413 p 51 c cmr10.329 @sf 878 428 p 46 c 31(Scaling)m 19(should)m 19(not)m 19 r 98 c 1 r 101 c 19(confused)m 20(with)m 18(the)m 20 r 119 c (eigh)s -1(t)m -1(ing)m 225 484 p (matrices)s cmmi10.329 @sf 15 r 119 c cmmi8.300 @sf 436 491 p 15 c cmmi6.300 @sf 450 496 p 105 c cmr10.329 @sf 481 484 p (and)s cmmi10.329 @sf 16 r 119 c cmmi8.300 @sf 598 491 p 14 c cmmi6.300 @sf 614 496 p 105 c cmr10.329 @sf 644 484 p (sp)s 1(eci\014ed)m 18 r 98 c 121 c 15(subroutine)m 16(argumen)m (ts)s cmtt10.329 @sf 14(WE)m cmr10.329 @sf 16(and)m cmtt10.329 @sf 17(WD)m cmr10.329 @sf 46 c 23(\(See)m 17(also)m cmsy10.329 @sf 15 r 120 c cmr10.329 @sf (1.A)s 16(and)m cmsy10.329 @sf 225 541 p 120 c cmr10.329 @sf (1.F.\))s @eop %%Page: 80 94 80 @bop0 cmr8.300 @sf [ 32 14 0 0 29.403] 109 @dc [<3F9C7FFEF8FBE03BE03BF038F8387FF81FF80078103838F83FF01FC0> 16 14 -1 0 17.642] 97 @dc [ 16 14 -1 0 18.622] 120 @dc [ 8 23 0 0 9.801] 105 @dc [ 24 14 0 0 19.602] 110 @dc 80 @bop1 cmr10.329 @sf 0 114 p (80)s 1227(Computational)m 13(Details)m 0 134 p 1725 2 ru cmbx10.329 @sf 0 259 p (4.D.i.)s 16(Scaling)m cmmi10.329 @sf 17 r 12 c cmr10.329 @sf 0 364 p (ODRP)s -3 r 65 c (CK)s 14 r 99 c (ho)s 1(oses)m 14(the)m 15(default)m 15(scale)m 15 r 118 c -2(alues)m 14(for)m 15(the)m 15(estimated)m 14 r 118 c -2(alues)m 15(of)m cmmi10.329 @sf 14 r 12 c cmr10.329 @sf 18(as)m 15(follo)m -1(ws.)m 93 443 p (If)s 23(some)m 15(of)m 15(the)m 15 r 118 c -2(alues)m 14(of)m cmmi10.329 @sf 15 r 12 c cmr10.329 @sf 17(are)m 15(nonzero)m 16(then)m 203 509 p (Let)s cmmi10.329 @sf 23 r 12 c cmr8.300 @sf 318 516 p (max)s cmr10.329 @sf 398 509 p 61 c 16(the)m 15(largest)m 14(nonzero)m 15(absolute)m 15 r 118 c -2(alue)m 14(in)m cmmi10.329 @sf 15 r 12 c cmr10.329 @sf 2 r 44 c 15(and)m 203 575 p (Let)s cmmi10.329 @sf 23 r 12 c cmr8.300 @sf 318 582 p (min)s cmr10.329 @sf 391 575 p 61 c 16(the)m 15(smallest)m 14(nonzero)m 15(absolute)m 15 r 118 c -2(alue)m 14(in)m cmmi10.329 @sf 15 r 12 c cmr10.329 @sf 2 r 46 c 203 641 p 70 c -3(or)m cmtt10.329 @sf 21 r 75 c cmr10.329 @sf 13 r 61 c 13 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 7 r 58 c 5 r 59 c 8 r 112 c cmr10.329 @sf 14(do)m 385 708 p (If)s cmmi10.329 @sf 23 r 12 c cmr6.300 @sf 464 715 p 75 c cmr10.329 @sf 502 708 p 61 c 13 r 48 c 15(then)m cmcsc10.329 @sf 438 764 p (scale)s cmsy10.329 @sf 102 c cmmi10.329 @sf 12 c cmr6.300 @sf 611 771 p 75 c cmsy10.329 @sf 636 764 p 103 c cmr10.329 @sf 12 r 61 c 13(10)m cmmi10.329 @sf (=\014)s cmr8.300 @sf 814 771 p (min)s cmr10.329 @sf 292 830 p (Else)s 15(if)m 22(log)m 40 c cmmi10.329 @sf 12 c cmr8.300 @sf 541 837 p (max)s cmr10.329 @sf 608 830 p 41 c cmsy10.329 @sf 10 r 0 c cmr10.329 @sf 10(log)m 40 c cmmi10.329 @sf 12 c cmr8.300 @sf 784 837 p (min)s cmr10.329 @sf 844 830 p 41 c cmmi10.329 @sf 13 r 62 c cmr10.329 @sf 13 r 49 c 14(then)m cmcsc10.329 @sf 438 887 p (scale)s cmsy10.329 @sf 102 c cmmi10.329 @sf 12 c cmr6.300 @sf 611 894 p 75 c cmsy10.329 @sf 636 887 p 103 c cmr10.329 @sf 12 r 61 c 13 r 49 c cmmi10.329 @sf 61 c cmsy10.329 @sf 106 c cmmi10.329 @sf 12 c cmr6.300 @sf 804 894 p 75 c cmsy10.329 @sf 828 887 p 106 c cmr10.329 @sf 334 953 p (Else)s cmcsc10.329 @sf 438 1009 p (scale)s cmsy10.329 @sf 102 c cmmi10.329 @sf 12 c cmr6.300 @sf 611 1016 p 75 c cmsy10.329 @sf 636 1009 p 103 c cmr10.329 @sf 12 r 61 c 13 r 49 c cmmi10.329 @sf (=\014)s cmr8.300 @sf 791 1016 p (max)s cmr10.329 @sf 42 1076 p (Else)s 22(if)m 15(all)m 14(of)m 15(the)m 15 r 118 c -2(alues)m 14(of)m cmmi10.329 @sf 15 r 12 c cmr10.329 @sf 17(are)m 15(zero)m 15(then)m 203 1142 p 70 c -3(or)m cmtt10.329 @sf 21 r 75 c cmr10.329 @sf 13 r 61 c 13 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 7 r 58 c 5 r 59 c 8 r 112 c cmr10.329 @sf 14(do)m cmcsc10.329 @sf 292 1198 p (scale)s cmsy10.329 @sf 102 c cmmi10.329 @sf 12 c cmr6.300 @sf 465 1205 p 75 c cmsy10.329 @sf 490 1198 p 103 c cmr10.329 @sf 12 r 61 c 13 r 49 c 0 1287 p (Users)s 15(ma)m 121 c 14(also)m 14(substitute)m 14(their)m 15 r 111 c (wn)s 14(scaling)m 14 r 118 c -2(alues)m 15(for)m cmmi10.329 @sf 14 r 12 c cmr10.329 @sf 2 r 46 c 20(\(See)m cmsy10.329 @sf 16 r 120 c cmr10.329 @sf (2.B.ii,)s 13(subroutine)m 15(argu-)m 0 1343 p (men)s 116 c cmtt10.329 @sf 14(SCLB)m cmr10.329 @sf -1(.\))m @eop %%Page: 81 95 81 @bop0 81 @bop1 cmr10.329 @sf 225 114 p (Computational)s 13(Details)m 1226(81)m 225 134 p 1725 2 ru cmbx10.329 @sf 225 259 p (4.D.ii.)s 15(Scaling)m cmr10.329 @sf 18 r 1 c 225 364 p (ODRP)s -3 r 65 c (CK)s 13 r 99 c (ho)s 1(oses)m 13(default)m 13(scale)m 14 r 118 c -2(alues)m 13(for)m 14(the)m 14(estimated)m 13(errors)m 13 r 1 c cmr6.300 @sf 1543 371 p 73 c 74 c cmr10.329 @sf 1586 364 p (in)s 14(the)m 14(explanatory)m 225 420 p 118 c -2(ariables)m 14(as)m 14(follo)m (w)s -1(s.)m 282 499 p 70 c -3(or)m cmtt10.329 @sf 21 r 74 c cmr10.329 @sf 13 r 61 c 13 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 7 r 58 c 5 r 59 c 8 r 109 c cmr10.329 @sf 14(do)m 464 565 p (If)s 23(some)m 15 r 118 c -2(alues)m 14(in)m 15(column)m cmtt10.329 @sf 16 r 74 c cmr10.329 @sf 15(of)m cmmi10.329 @sf 14 r 88 c cmr10.329 @sf 19(are)m 15(nonzero)m 15(then)m 574 632 p (Let)s cmmi10.329 @sf 23 r 88 c cmr8.300 @sf 701 639 p (max)s cmr10.329 @sf 781 632 p 61 c 16(the)m 15(largest)m 14(nonzero)m 15(absolute)m 15 r 118 c -2(alue)m 14(in)m 15(column)m cmtt10.329 @sf 15 r 74 c cmr10.329 @sf 574 698 p (Let)s cmmi10.329 @sf 23 r 88 c cmr8.300 @sf 701 705 p (min)s cmr10.329 @sf 774 698 p 61 c 16(the)m 15(smallest)m 14(nonzero)m 15(absolute)m 15 r 118 c -2(alue)m 14(in)m 15(column)m cmtt10.329 @sf 15 r 74 c cmr10.329 @sf 574 764 p 70 c -3(or)m cmtt10.329 @sf 21 r 73 c cmr10.329 @sf 13 r 61 c 13 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 7 r 58 c 5 r 59 c 8 r 110 c cmr10.329 @sf 15(do)m 756 830 p (If)s cmmi10.329 @sf 23 r 88 c cmr6.300 @sf 847 837 p 73 c 74 c cmr10.329 @sf 888 830 p 61 c 13 r 48 c 15(then)m cmcsc10.329 @sf 809 887 p (scale)s cmsy10.329 @sf 1 r 102 c cmr10.329 @sf 1 c cmr6.300 @sf 995 894 p 73 c -1 r 74 c cmsy10.329 @sf 1023 887 p 103 c cmr10.329 @sf 12 r 61 c 13(10)m cmmi10.329 @sf (=X)s cmr8.300 @sf 1213 894 p (min)s cmr10.329 @sf 663 953 p (Else)s 15(if)m 22(log)m 40 c cmmi10.329 @sf 88 c cmr8.300 @sf 924 960 p (max)s cmr10.329 @sf 991 953 p 41 c cmsy10.329 @sf 10 r 0 c cmr10.329 @sf 10(log)m 40 c cmmi10.329 @sf 88 c cmr8.300 @sf 1179 960 p (min)s cmr10.329 @sf 1239 953 p 41 c cmmi10.329 @sf 13 r 62 c cmr10.329 @sf 13 r 49 c 14(then)m cmcsc10.329 @sf 809 1009 p (scale)s cmsy10.329 @sf 1 r 102 c cmr10.329 @sf 1 c cmr6.300 @sf 995 1016 p 73 c -1 r 74 c cmsy10.329 @sf 1023 1009 p 103 c cmr10.329 @sf 12 r 61 c 13 r 49 c cmmi10.329 @sf 61 c cmsy10.329 @sf 106 c cmmi10.329 @sf 88 c cmr6.300 @sf 1203 1016 p 73 c -1 r 74 c cmsy10.329 @sf 1231 1009 p 106 c cmr10.329 @sf 705 1076 p (Else)s cmcsc10.329 @sf 809 1132 p (scale)s cmsy10.329 @sf 1 r 102 c cmr10.329 @sf 1 c cmr6.300 @sf 995 1139 p 73 c -1 r 74 c cmsy10.329 @sf 1023 1132 p 103 c cmr10.329 @sf 12 r 61 c 13 r 49 c cmmi10.329 @sf (=X)s cmr8.300 @sf 1190 1139 p (max)s cmr10.329 @sf 413 1198 p (Else)s 22(if)m 15(all)m 14 r 118 c -2(alues)m 14(in)m 15(column)m cmtt10.329 @sf 15 r 74 c cmr10.329 @sf 15(of)m cmmi10.329 @sf 15 r 88 c cmr10.329 @sf 19(are)m 14(zero)m 16(then)m 574 1265 p 70 c -3(or)m cmtt10.329 @sf 21 r 73 c cmr10.329 @sf 13 r 61 c 13 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 7 r 58 c 5 r 59 c 8 r 110 c cmr10.329 @sf 15(do)m cmcsc10.329 @sf 663 1321 p (scale)s cmsy10.329 @sf 102 c cmr10.329 @sf 1 c cmr6.300 @sf 848 1328 p 73 c 74 c cmsy10.329 @sf 877 1321 p 103 c cmr10.329 @sf 12 r 61 c 13 r 49 c 225 1410 p (Users)s 14(ma)m 121 c 13(also)m 13(substitute)m 14(their)m 14 r 111 c (wn)s 13(scaling)m 14 r 118 c -2(alues)m 13(for)m 14(\001.)m 19(\(See)m cmsy10.329 @sf 15 r 120 c cmr10.329 @sf (2.B.ii,)s 13(subroutine)m 14(argu-)m 225 1466 p (men)s 116 c cmtt10.329 @sf 14(SCLD)m cmr10.329 @sf -1(.\))m @eop %%Page: 82 96 82 @bop0 82 @bop1 cmr10.329 @sf 0 114 p (82)s 1227(Computational)m 13(Details)m 0 134 p 1725 2 ru @eop %%Page: 83 97 83 @bop0 cmcsc10.518 @sf [<007F800001FFF0000780FC000E003E001C001F0038000F80300007C0600007E0600007E0FC0003 F0FE0003F0FF0003F8FF0003F8FF0003F87E0003F83C0003F8000003F8000003F8000003F80000 03F0000003F0000003F0000007E0080007C00C0007C00E000F800F801F000DE03E000C7FF8000C 1FE0000C0000000C0000000C0000000C0000000C0000000C0000000C0000000C0000000C000000 0C0000000FFF80000FFFF0000FFFFC000FFFFE000FFFFF000FFFFF800FC00FC00C0000C0> 32 48 -5 1 39.650] 53 @dc [ 40 37 -3 0 45.588] 107 @dc cmbx12.300 @sf [<07FC001FFF003C1FC0780FE06007F0FC03F0FC03F8FC03F8FC03F8FC03F87803F80003F80003F8 0003F80003F01803F01C07E01F0FC01FFF8019FE001800001800001800001800001BE0001FFC00 1FFF001FFF801FFFC01FFFE01E03E0180060> 24 32 -3 0 28.019] 53 @dc [ 24 34 -1 0 20.870] 73 @dc cmtt10.329 @sf [ 24 28 -1 0 23.863] 72 @dc [<0707000F8F800F8F800D8D800DDD800DDD800DDD801CD9C01CD9C01CF9C01CF9C01C71C01C01C0 1C01C03800E03800E03800E0FF8FF8FF8FF8FF8FF8> 24 20 -1 0 23.863] 119 @dc [ 24 29 -4 0 23.863] 105 @dc [ 24 20 0 0 23.863] 110 @dc [<7FFF007FFF007FFF0001C00001C00001C00001C00001C00001C00001C00001C00001C00001C000 01C00001C00001C00001C000FFFFC0FFFFC0FFFFC001C00001C00001C00001E0C001F1E000FFE0 007FE0001FC0> 24 28 -1 0 23.863] 102 @dc 83 @bop1 cmcsc10.518 @sf 225 519 p (5.)s 35 r 87 c -1(ork)m 26(Vectors)m cmbx12.300 @sf 225 747 p (5.A.)s 18(Extracting)m 18(Information)m 18(from)m 18 r 86 c -4(ector)m cmtt12.300 @sf 18(WORK)m cmr10.329 @sf 225 868 p (Up)s 1(on)m 13(return)m 12(from)m 12 r 97 c 12(call)m 11(to)m 12(ODRP)m -3 r 65 c (CK,)s 11(arra)m -1 r 121 c cmtt10.329 @sf 11(WORK)m cmr10.329 @sf 11(con)m (tains)s 11 r 118 c -2(alues)m 11(that)m 12(ma)m 121 c 11 r 98 c 1 r 101 c 13(of)m 12(in)m (ter-)s 225 925 p (est)s 15(to)m 15(the)m 16(user.)m 21 r 84 c -3 r 111 c 15(extract)m 14(information)m 14(from)m cmtt10.329 @sf 15(WORK)m cmr10.329 @sf -1 r 44 c 16(the)m 15(follo)m (w)s -1(ing)m 14(declaration)m 14(statemen)m 116 c 225 981 p 109 c (ust)s 14 r 98 c 1 r 101 c 15(added)m 16(to)m 15(the)m 15(user's)m 15(program:)m cmtt10.329 @sf 368 1094 p (LOGICAL)s 344 1150 p 43 c 72(ISODR)m 368 1206 p (INTEGER)s 344 1263 p 43 c 72(DELTAI,EPSI,XPLUS)m -1(I,FNI,S)m -1(DI,VCVI,)m 344 1319 p 43 c 72(RVARI,WSSI,WSSDEI)m -1(,WSSEPI)m -1(,RCONDI,)m -1(ETAI,)m 344 1376 p 43 c 72(OLMAVI,TAUI,ALPHA)m -1(I,ACTRS)m -1(I,PNORMI)m -1(,RNORSI)m -1(,PRERSI)m -1 r 44 c 344 1432 p 43 c 72(PARTLI,SSTOLI,TAU)m -1(FCI,EPS)m -1(MAI,)m 344 1489 p 43 c 72(BETA0I,BETACI,BET)m -1(ASI,BET)m -1(ANI,SI,S)m -1(SI,SSFI)m -1(,QRAUXI)m -1(,UI,)m 344 1545 p 43 c 72(FSI,FJACBI,WE1I,D)m -1(IFFI,)m 344 1602 p 43 c 72(DELTSI,DELTNI,TI,)m -1(TTI,OME)m -1(GAI,FJAC)m -1(DI,)m 344 1658 p 43 c 72(WRK1I,WRK2I,WRK3I)m -1(,WRK4I,)m -1(WRK5I,WR)m -1(K6I,WRK)m -1(7I,)m 344 1715 p 43 c 72(LWKMN)m cmr10.329 @sf 225 1827 p (where)s cmtt10.329 @sf 18(DELTAI)m cmr10.329 @sf 17(through)m cmtt10.329 @sf 18(WRK7I)m cmr10.329 @sf 17(are)m 17 r 118 c -2(ariables)m 16(that)m 18(indicate)m 17(the)m 18(starting)m 16(lo)m 1(cations)m 17(within)m cmtt10.329 @sf 225 1883 p (WORK)s cmr10.329 @sf 15(of)m 14(the)m 16(stored)m 14 r 118 c -2(alues,)m 14(and)m cmtt10.329 @sf 16(LWKMN)m cmr10.329 @sf 14(is)m 15(the)m 15(minim)m (um)s 13(acceptable)m 16(length)m 15(of)m 14(arra)m 121 c cmtt10.329 @sf 13(WORK)m cmr10.329 @sf 46 c 225 1959 p (The)s 17(appropriate)m 16 r 118 c -2(alues)m 16(of)m cmtt10.329 @sf 16(DELTAI)m cmr10.329 @sf 16(through)m cmtt10.329 @sf 16(WRK7I)m cmr10.329 @sf 16(are)m 17(obtained)m 16 r 98 c 121 c 16(in)m 118 c -1(oki)m -1(ng)m 15(subroutine)m cmtt10.329 @sf 225 2016 p (SWINF)s cmr10.329 @sf 14(when)m 14(using)m 14(either)m 14(of)m 14(the)m 15(single)m 13(precision)m 14(ODRP)m -3 r 65 c (CK)s 13(subroutines)m cmtt10.329 @sf 14(SODR)m cmr10.329 @sf 14(or)m cmtt10.329 @sf 14(SODRC)m cmr10.329 @sf -1 r 44 c 225 2072 p (and)s 18 r 98 c 121 c 16(in)m 118 c -1(oking)m cmtt10.329 @sf 15(DWINF)m cmr10.329 @sf 17(when)m 18(using)m 17(either)m 18(of)m 17(the)m 17(double)m 18(precision)m 17(subroutines)m cmtt10.329 @sf 18(DODR)m cmr10.329 @sf 16(or)m cmtt10.329 @sf 225 2129 p (DODRC)s cmr10.329 @sf -1 r 46 c 34(The)m 20(call)m 18(statemen)m (ts)s 18(for)m cmtt10.329 @sf 19(SWINF)m cmr10.329 @sf 19(and)m cmtt10.329 @sf 20(DWINF)m cmr10.329 @sf 19(ha)m 118 c -1 r 101 c 18(the)m 20(same)m 19(argumen)m 116 c 18(lists.)m 32 r 84 c -3 r 111 c 225 2185 p (in)s 118 c -1(ok)m -1 r 101 c 13(either)m 15(subroutine,)m 15(use)m cmtt10.329 @sf 368 2298 p (CALL)s 23()m 344 2354 p 43 c 72(\(N,M,NP,NQ,LDWE,L)m -1(D2WE,IS)m -1(ODR,)m 344 2411 p 43 c 72(DELTAI,EPSI,XPLUS)m -1(I,FNI,S)m -1(DI,VCVI,)m 344 2467 p 43 c 72(RVARI,WSSI,WSSDEI)m -1(,WSSEPI)m -1(,RCONDI,)m -1(ETAI,)m cmr10.329 @sf 1065 2581 p (83)s @eop %%Page: 84 98 84 @bop0 84 @bop1 cmr10.329 @sf 0 123 p (84)s 1410 r 87 c -3(ork)m 13 r 86 c -3(ectors)m 0 134 p 1725 2 ru cmtt10.329 @sf 119 259 p 43 c 72(OLMAVI,TAUI,ALPHA)m -1(I,ACTRS)m -1(I,PNORMI)m -1(,RNORSI)m -1(,PRERSI)m -1 r 44 c 119 315 p 43 c 72(PARTLI,SSTOLI,TAU)m -1(FCI,EPS)m -1(MAI,)m 119 372 p 43 c 72(BETA0I,BETACI,BET)m -1(ASI,BET)m -1(ANI,SI,S)m -1(SI,SSFI)m -1(,QRAUXI)m -1(,UI,)m 119 428 p 43 c 72(FSI,FJACBI,WE1I,D)m -1(IFFI,)m 119 484 p 43 c 72(DELTSI,DELTNI,TI,)m -1(TTI,OME)m -1(GAI,FJAC)m -1(DI,)m 119 541 p 43 c 72(WRK1I,WRK2I,WRK3I)m -1(,WRK4I,)m -1(WRK5I,WR)m -1(K6I,WRK)m -1(7I,)m 119 597 p 43 c 72(LWKMN\))m cmr10.329 @sf 0 711 p (where)s cmtt10.329 @sf 15(SWINF)m cmr10.329 @sf 14(should)m 15 r 98 c 1 r 101 c 16(substituted)m 14(for)m cmtt10.329 @sf 14()m cmr10.329 @sf 14(when)m 16(using)m cmtt10.329 @sf 14(SODR)m cmr10.329 @sf 15(and)m cmtt10.329 @sf 15(SODRC)m cmr10.329 @sf -1 r 44 c 15(and)m cmtt10.329 @sf 15(DWINF)m cmr10.329 @sf 0 767 p (should)s 17 r 98 c 1 r 101 c 17(substituted)m 16(for)m cmtt10.329 @sf 16()m cmr10.329 @sf 16(when)m 17(using)m cmtt10.329 @sf 17(DODR)m cmr10.329 @sf 16(and)m cmtt10.329 @sf 17(DODRC)m cmr10.329 @sf -1 r 46 c 24(The)m 17 r 118 c -2(ariables)m cmtt10.329 @sf 15 r 78 c cmr10.329 @sf 44 c cmtt10.329 @sf 17 r 77 c 24(NP)m cmr10.329 @sf -1 r 44 c cmtt10.329 @sf 0 824 p (NQ)s cmr10.329 @sf 44 c cmtt10.329 @sf 13(LDWE)m cmr10.329 @sf 44 c 13(and)m cmtt10.329 @sf 14(LD2WE)m cmr10.329 @sf 12 r 109 c (ust)s 12 r 98 c 1 r 101 c 14(input)m 14(to)m cmtt10.329 @sf 13(SIWINF)m cmr10.329 @sf 12(and)m cmtt10.329 @sf 14(DIWINF)m cmr10.329 @sf 12(with)m 13(exactly)m 13(the)m 14(same)m 13 r 118 c -2(alues)m 0 880 p (as)s 15 r 119 c (ere)s 14(used)m 16(in)m 15(the)m 15(original)m 13(call)m 15(to)m 14(ODRP)m -3 r 65 c (CK,)s 14(and)m cmtt10.329 @sf 15(ISODR)m cmr10.329 @sf 14 r 109 c (ust)s 14 r 98 c 1 r 101 c 16(input)m 15(set)m 15(to)m cmti10.329 @sf 15(true)m cmr10.329 @sf 15(if)m 0 937 p (the)s 15(\014t)m 15 r 119 c (as)s 13 r 98 c 121 c 14(orthogonal)m 13(distance)m 15(regression,)m 14(and)m 15 r 98 c 1 r 101 c 15(input)m 15(set)m 15(to)m cmti10.329 @sf 14(false)m cmr10.329 @sf 15(if)m 14(the)m 15(\014t)m 15 r 119 c (as)s 13 r 98 c 121 c 0 993 p (ordinary)s 13(least)m 13(squares.)m cmti10.329 @sf 19(Note)m 15(that)m 16(when)m cmtt10.329 @sf 15(ISODR)m cmti10.329 @sf 14(is)m cmr10.329 @sf 15(false)m cmti10.329 @sf 44 c 15(the)m 15(lo)m -1 r 99 c -2(ations)m 13(that)m 16(ar)m -1 r 101 c 14(sp)m -1 r 101 c -2(ci\014)m -1 r 101 c -2 r 100 c 13(by)m cmtt10.329 @sf 0 1049 p (DELTASI)s cmti10.329 @sf 15(thr)m -1(ough)m cmtt10.329 @sf 17(WRK1I)m cmti10.329 @sf 15(ar)m -1 r 101 c 15(the)m 17(same)m 16(as)m 16(the)m 17(lo)m -1 r 99 c -2(ation)m 14(sp)m -1 r 101 c -2(ci\014)m -1 r 101 c -2 r 100 c 15(by)m cmtt10.329 @sf 16(DELTAI)m cmti10.329 @sf 46 c cmr10.329 @sf 0 1125 p (In)s 19(the)m 19(follo)m -1(wi)m -1(ng)m 17(descriptions)m 18(of)m 18(the)m 18(information)m 17(returned)m 19(in)m cmtt10.329 @sf 18(WORK)m cmr10.329 @sf 44 c 1362 1127 p 3 28 ru cmmi10.329 @sf 1358 1125 p 62 c cmr10.329 @sf 19(indicates)m 18 r 118 c -2(alues)m 0 1182 p (that)s 14(are)m 15(most)m 15(lik)m (ely)s 13(to)m 14 r 98 c 1 r 101 c 16(of)m 15(in)m (terest.)s 14 1302 p 3 28 ru cmmi10.329 @sf 10 1300 p 62 c cmtt10.329 @sf 39(WORK\(DELTAI\))m cmr10.329 @sf 21(is)m 11(the)m 12(\014rst)m 12(elemen)m 116 c 10(of)m 11(an)m cmmi10.329 @sf 12 r 110 c cmsy10.329 @sf 3 r 2 c cmmi10.329 @sf 3 r 109 c cmr10.329 @sf 13(arra)m 121 c cmtt10.329 @sf 9(DELTA)m cmr10.329 @sf 11(con)m (taining)s 10(the)m 12(estimated)m 393 1356 p (errors)s 530 1346 p 94 c 523 1357 p 1 c 576 1356 p (in)s 15(the)m 15(explanatory)m 14 r 118 c -2(ariables)m 14(at)m 14(the)m 15(solution,)m 14(where)m cmtt10.329 @sf 393 1422 p (WORK\(DELTAI-1+)s 73 c -2(+\()m 74 c (-1\)*N\))s cmr10.329 @sf 14 r 61 c cmtt10.329 @sf 15(DELTA\()m 73 c 44 c 74 c -1 r 41 c cmr10.329 @sf 15 r 61 c 1343 1412 p 94 c 1336 1423 p 1 c cmr6.300 @sf 1374 1430 p 73 c 74 c cmr10.329 @sf 393 1489 p (for)s cmtt10.329 @sf 15 r 73 c cmr10.329 @sf 12 r 61 c 13 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 7 r 58 c 6 r 59 c 8 r 110 c cmr10.329 @sf 44 c 14(and)m cmtt10.329 @sf 15 r 74 c cmr10.329 @sf 13 r 61 c 13 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 7 r 58 c 5 r 59 c 8 r 109 c cmr10.329 @sf 46 c cmtt10.329 @sf 393 1555 p (DELTAI)s cmr10.329 @sf 14 r 61 c 16 r 49 c 30 r 46 c 14 1682 p 3 28 ru cmmi10.329 @sf 10 1680 p 62 c cmtt10.329 @sf 87(WORK\(EPSI\))m cmr10.329 @sf 21(is)m 16(the)m 16(\014rst)m 16(elemen)m 116 c 15(of)m 16(an)m cmmi10.329 @sf 17 r 110 c cmsy10.329 @sf 11 r 2 c cmmi10.329 @sf 11 r 113 c cmr10.329 @sf 18(arra)m 121 c cmtt10.329 @sf 14(EPS)m cmr10.329 @sf 16(con)m (taining)s 14(the)m 17(estimated)m 393 1737 p (errors)s 533 1727 p 94 c cmmi10.329 @sf 523 1738 p 69 c cmr10.329 @sf 574 1737 p (in)s 15(the)m 15(resp)m 1(onse)m 16 r 118 c -2(ariables)m 13(at)m 15(the)m 15(solution,)m 14(where)m cmtt10.329 @sf 393 1803 p (WORK\(EPSI-1+)s 73 c -2(+\()m 76 c (-1\)*N\))s cmr10.329 @sf 14 r 61 c cmtt10.329 @sf 16(EPS\()m 73 c -1 r 44 c 76 c 41 c cmr10.329 @sf 15 r 61 c 1251 1793 p 94 c cmmi10.329 @sf 1240 1804 p 69 c cmr6.300 @sf 1274 1811 p 73 c 76 c cmr10.329 @sf 393 1869 p (for)s cmtt10.329 @sf 15 r 73 c cmr10.329 @sf 12 r 61 c 13 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 7 r 58 c 6 r 59 c 8 r 110 c cmr10.329 @sf 44 c 14(and)m cmtt10.329 @sf 15 r 76 c cmr10.329 @sf 13 r 61 c 13 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 7 r 58 c 5 r 59 c 8 r 113 c cmr10.329 @sf 2 r 46 c cmtt10.329 @sf 393 1935 p (EPSI)s cmr10.329 @sf 27 r 61 c cmmi10.329 @sf 13(nm)m cmr10.329 @sf 11 r 43 c 10 r 49 c 30 r 46 c 14 2063 p 3 28 ru cmmi10.329 @sf 10 2061 p 62 c cmtt10.329 @sf 39(WORK\(XPLUSI\))m cmr10.329 @sf 21(is)m 17(the)m 18(\014rst)m 17(elemen)m 116 c 17(of)m 17(an)m cmmi10.329 @sf 18 r 110 c cmsy10.329 @sf 12 r 2 c cmmi10.329 @sf 12 r 109 c cmr10.329 @sf 18(arra)m -1 r 121 c cmtt10.329 @sf 16(XPLUSD)m cmr10.329 @sf 17(con)m (taining)s 15(the)m 18(\014nal)m 393 2117 p (estimates)s 14(of)m 15(the)m 15(explanatory)m 14 r 118 c -2(ariable)m 1157 2107 p 94 c cmmi10.329 @sf 1144 2118 p 88 c cmr10.329 @sf 1185 2117 p 44 c 15(where)m cmtt10.329 @sf 393 2183 p (WORK\(XPLUSI-1+)s 73 c -2(+\()m 74 c (-1\)*N\))s cmr10.329 @sf 14 r 61 c cmtt10.329 @sf 15(XPLUSD\()m 73 c -1 r 44 c 74 c 41 c cmr10.329 @sf 15 r 61 c 1373 2173 p 94 c cmmi10.329 @sf 1360 2184 p 88 c cmr6.300 @sf 1398 2191 p 73 c -1 r 74 c cmr10.329 @sf 1439 2183 p 61 c cmmi10.329 @sf 13 r 88 c cmr6.300 @sf 1525 2190 p 73 c -1 r 74 c cmr10.329 @sf 1563 2183 p 43 c 1616 2173 p 94 c 1608 2184 p 1 c cmr6.300 @sf 1646 2191 p 73 c 74 c cmr10.329 @sf 393 2250 p (for)s cmtt10.329 @sf 15 r 73 c cmr10.329 @sf 12 r 61 c 13 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 7 r 58 c 6 r 59 c 8 r 110 c cmr10.329 @sf 44 c 14(and)m cmtt10.329 @sf 15 r 74 c cmr10.329 @sf 13 r 61 c 13 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 7 r 58 c 5 r 59 c 8 r 109 c cmr10.329 @sf 46 c cmtt10.329 @sf 393 2316 p (XPLUSI)s cmr10.329 @sf 27 r 61 c cmmi10.329 @sf 13(nm)m cmr10.329 @sf 10 r 43 c cmmi10.329 @sf 11(nq)m cmr10.329 @sf 12 r 43 c 11 r 49 c 30 r 46 c @eop %%Page: 85 99 85 @bop0 85 @bop1 cmr10.329 @sf 225 123 p 87 c -3(ork)m 14 r 86 c -3(ectors)m 1408(85)m 225 134 p 1725 2 ru 239 261 p 3 28 ru cmmi10.329 @sf 235 259 p 62 c cmtt10.329 @sf 111(WORK\(FNI\))m cmr10.329 @sf 21(is)m 11(the)m 12(\014rst)m 11(elemen)m 116 c 11(of)m 11(an)m cmmi10.329 @sf 12 r 110 c cmsy10.329 @sf 3 r 2 c cmmi10.329 @sf 3 r 113 c cmr10.329 @sf 14(arra)m 121 c cmtt10.329 @sf 10(FN)m cmr10.329 @sf 11(con)m (taining)s 10(the)m 12(\014nal)m 11(estimates)m 618 315 p (of)s 15(the)m 15(resp)m 1(onse)m 16 r 118 c -2(ariable)m 1109 305 p 94 c cmmi10.329 @sf 1102 316 p 89 c cmr10.329 @sf 1139 315 p 44 c 15(where)m cmtt10.329 @sf 618 381 p (WORK\(FNI-1+)s 73 c -2(+\()m 76 c (-1\)*N\))s cmr10.329 @sf 14 r 61 c cmtt10.329 @sf 16(FN\()m 73 c -1 r 44 c 76 c 41 c cmr10.329 @sf 15 r 61 c 1424 371 p 94 c cmmi10.329 @sf 1418 382 p 89 c cmr6.300 @sf 1444 389 p 73 c 76 c cmr10.329 @sf 1488 381 p 61 c cmmi10.329 @sf 13 r 102 c cmr6.300 @sf 1558 388 p 73 c 1 r 76 c cmr10.329 @sf 1591 381 p 40 c cmmi10.329 @sf 120 c cmr6.300 @sf 1635 388 p 73 c cmr10.329 @sf 1657 381 p 43 c 1705 370 p 94 c cmmi10.329 @sf 1703 382 p 14 c cmr6.300 @sf 1723 389 p 73 c cmr10.329 @sf 1736 381 p 59 c 1763 370 p 94 c cmmi10.329 @sf 1757 382 p 12 c cmr10.329 @sf 1784 381 p 41 c 618 448 p (for)s cmtt10.329 @sf 15 r 73 c cmr10.329 @sf 12 r 61 c 13 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 7 r 58 c 6 r 59 c 8 r 110 c cmr10.329 @sf 44 c 14(and)m cmtt10.329 @sf 15 r 76 c cmr10.329 @sf 13 r 61 c 13 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 7 r 58 c 5 r 59 c 8 r 113 c cmr10.329 @sf 2 r 46 c cmtt10.329 @sf 618 514 p (FNI)s cmr10.329 @sf 27 r 61 c 13 r 50 c cmmi10.329 @sf (nm)s cmr10.329 @sf 10 r 43 c cmmi10.329 @sf 11(nq)m cmr10.329 @sf 12 r 43 c 11 r 49 c 30 r 46 c 239 641 p 3 28 ru cmmi10.329 @sf 235 639 p 62 c cmtt10.329 @sf 111(WORK\(SDI\))m cmr10.329 @sf 21(is)m 22(the)m 22(\014rst)m 21(elemen)m 116 c 21(of)m 22 r 97 c cmmi10.329 @sf 22 r 112 c cmsy10.329 @sf 14 r 2 c cmr10.329 @sf 15 r 49 c 22(arra)m 121 c cmtt10.329 @sf 20(SD)m cmr10.329 @sf 21(con)m (taining)s 20(the)m 22(standard)m 618 696 p (deviations)s 19 r 94 c cmmi10.329 @sf -26 r 27 c cmmi8.300 @sf 862 703 p 12 c cmr6.300 @sf 882 709 p 75 c cmr10.329 @sf 926 696 p (of)s 17(the)m 17(function)m 17(parameters)m cmmi10.329 @sf 17 r 12 c cmr10.329 @sf 2 r 44 c 17(i.e.,)m 17(the)m 17(square)m 17(ro)m 1(ots)m 618 752 p (of)s 15(the)m 15(diagonal)m 14(en)m (tries)s 14(of)m 14(the)m 16(co)m 118 c -2(a)m -1(riance)m 13(matrix,)m 14(where)m cmtt10.329 @sf 618 824 p (WORK\(SDI-1+)s 75 c -2 r 41 c cmr10.329 @sf 15 r 61 c cmtt10.329 @sf 16(SD\()m 75 c -1 r 41 c cmr10.329 @sf 15 r 61 c 1186 814 p 94 c cmmi10.329 @sf 1179 825 p 86 c cmr8.300 @sf 1216 802 p 49 c cmmi8.300 @sf 61 c cmr8.300 @sf 50 c cmmi8.300 @sf 1206 838 p 12 c cmr10.329 @sf 1271 824 p 40 c cmtt10.329 @sf 75 c cmmi10.329 @sf -1 r 59 c cmtt10.329 @sf 8 r 75 c cmr10.329 @sf -1 r 41 c 15 r 61 c 18 r 94 c cmmi10.329 @sf -25 r 27 c cmmi8.300 @sf 1466 831 p 12 c cmr6.300 @sf 1486 837 p 75 c cmr10.329 @sf 618 890 p (for)s cmtt10.329 @sf 16 r 75 c cmr10.329 @sf 15 r 61 c 15 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 7 r 58 c 6 r 59 c 8(p:)m cmr10.329 @sf 15(The)m 17(standard)m 16(deviations)m 15(are)m 16(only)m 16(computed)m 17(when)m 618 946 p (the)s 13(third)m 13(digit)m 12(of)m cmtt10.329 @sf 12(JOB)m cmr10.329 @sf 13(is)m 12(less)m 13(than)m 13(or)m 13(equal)m 12(to)m 13(1.)m 19(\(See)m cmsy10.329 @sf 13 r 120 c cmr10.329 @sf (2.B.ii,)s 12(subrou-)m 618 1003 p (tine)s 18(argumen)m 116 c cmtt10.329 @sf 16(JOB)m cmr10.329 @sf 44 c 18(and)m cmsy10.329 @sf 18 r 120 c cmr10.329 @sf (4.B.\))s 27(Ro)m (ws)s 17(of)m cmtt10.329 @sf 17(SD)m cmr10.329 @sf 18(corresp)m 1(onding)m 18(to)m 17(\014xed)m 618 1059 p (elemen)s (ts)s 14(of)m cmmi10.329 @sf 15 r 12 c cmr10.329 @sf 2 r 44 c 15(and)m 15(to)m 15(elemen)m (ts)s 14(dropp)m 1(ed)m 16 r 98 c 1(ecause)m 17(they)m 15(induced)m 16(rank)m 618 1116 p (de\014ciency)s -3 r 44 c 15(are)m 15(set)m 15(to)m 15(zero.)m cmtt10.329 @sf 618 1182 p (SDI)s cmr10.329 @sf 27 r 61 c 13 r 50 c cmmi10.329 @sf (nm)s cmr10.329 @sf 10 r 43 c 11 r 50 c cmmi10.329 @sf (nq)s cmr10.329 @sf 12 r 43 c 10 r 49 c 30 r 46 c 239 1309 p 3 28 ru cmmi10.329 @sf 235 1307 p 62 c cmtt10.329 @sf 87(WORK\(VCVI\))m cmr10.329 @sf 21(is)m 20(the)m 20(\014rst)m 19(elemen)m 116 c 19(of)m 19 r 97 c cmmi10.329 @sf 20 r 112 c cmsy10.329 @sf 13 r 2 c cmmi10.329 @sf 14 r 112 c cmr10.329 @sf 19(arra)m 121 c cmtt10.329 @sf 18(VCV)m cmr10.329 @sf 20(con)m (tai)s -1(ning)m 18(the)m 20 r 118 c -2(alues)m 19(of)m 618 1364 p (the)s 19(co)m 118 c -2(a)m -1(riance)m 17(matrix)m 17(of)m 17(the)m 19(parameters)m cmmi10.329 @sf 17 r 12 c cmr10.329 @sf 21(prior)m 17(to)m 18(scaling)m 18 r 98 c 121 c 17(the)m 618 1420 p (residual)s 15 r 118 c -2(ariance,)m 13(where)m cmtt10.329 @sf 618 1486 p (WORK\(VCVI-1+I+\(J-1\)*)s -1(\(NP\)\))m cmr10.329 @sf 13 r 61 c cmtt10.329 @sf 15(VCV\()m 73 c 44 c 74 c -1 r 41 c cmr10.329 @sf 15 r 61 c 18 r 94 c cmmi10.329 @sf -25 r 27 c cmsy8.300 @sf 1565 1471 p 0 c cmr8.300 @sf 50 c cmr10.329 @sf 1619 1476 p 94 c cmmi10.329 @sf 1612 1487 p 86 c cmmi8.300 @sf 1639 1494 p 12 c cmr10.329 @sf 1662 1486 p 40 c cmtt10.329 @sf 73 c cmmi10.329 @sf -1 r 59 c cmtt10.329 @sf 8 r 74 c cmr10.329 @sf -1 r 41 c 618 1553 p (for)s cmtt10.329 @sf 19 r 73 c cmr10.329 @sf 20 r 61 c 20 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 7 r 58 c 5 r 59 c 8 r 112 c cmr10.329 @sf 19(and)m cmtt10.329 @sf 20 r 74 c cmr10.329 @sf 20 r 61 c 20 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 7 r 58 c 5 r 59 c 8 r 112 c cmr10.329 @sf 46 c 32(The)m 20(co)m 118 c -2(ari)m -1(ance)m 18(matrix)m 18(is)m 19(only)m 618 1609 p (computed)s 13(when)m 13(the)m 12(third)m 12(digit)m 11(of)m cmtt10.329 @sf 12(JOB)m cmr10.329 @sf 12(is)m 11(less)m 12(than)m 13(or)m 11(equal)m 12(to)m 12(1.)m 19(\(See)m cmsy10.329 @sf 618 1665 p 120 c cmr10.329 @sf (2.B.ii,)s 14(subroutine)m 15(argumen)m 116 c cmtt10.329 @sf 13(JOB)m cmr10.329 @sf 44 c 15(and)m cmsy10.329 @sf 15 r 120 c cmr10.329 @sf 1(4.B.\))m 19(Ro)m (ws)s 14(and)m 15(columns)m 15(of)m cmtt10.329 @sf 618 1722 p (VCV)s cmr10.329 @sf 15(corresp)m 1(onding)m 15(to)m 15(\014xed)m 16(elemen)m (ts)s 14(of)m cmmi10.329 @sf 15 r 12 c cmr10.329 @sf 2 r 44 c 15(and)m 15(to)m 15(elemen)m (ts)s 14(dropp)m 1(ed)m 618 1778 p 98 c 1(ecause)m 16(they)m 16(induced)m 16(rank)m 15(de\014ciency)m -3 r 44 c 15(are)m 15(set)m 15(to)m 14(zero.)m cmtt10.329 @sf 618 1845 p (VCVI)s cmr10.329 @sf 27 r 61 c 13 r 50 c cmmi10.329 @sf (nm)s cmr10.329 @sf 10 r 43 c 11 r 50 c cmmi10.329 @sf (nq)s cmr10.329 @sf 12 r 43 c cmmi10.329 @sf 10 r 112 c cmr10.329 @sf 10 r 43 c 11 r 49 c 30 r 46 c 239 1972 p 3 28 ru cmmi10.329 @sf 235 1970 p 62 c cmtt10.329 @sf 63(WORK\(RVARI\))m cmr10.329 @sf 21(is)m 15(the)m 15(estimated)m 14(residual)m 15 r 118 c -2(ariance)m 17 r 94 c cmmi10.329 @sf -26 r 27 c cmr8.300 @sf 1325 1955 p 50 c cmr10.329 @sf 1357 1970 p 61 c cmmi10.329 @sf 13 r 83 c cmr10.329 @sf 3 r 40 c 1460 1959 p 94 c cmmi10.329 @sf 1454 1971 p 12 c 1481 1970 p 59 c cmr10.329 @sf 1504 1959 p 94 c cmmi10.329 @sf 1502 1971 p 14 c cmr10.329 @sf 1523 1970 p 41 c cmmi10.329 @sf (=\026)s cmr10.329 @sf 46 c 20(\(See)m cmsy10.329 @sf 16 r 120 c cmr10.329 @sf (4.B.\))s cmtt10.329 @sf 618 2036 p (RVARI)s cmr10.329 @sf 27 r 61 c 13 r 50 c cmmi10.329 @sf (nm)s cmr10.329 @sf 10 r 43 c 11 r 50 c cmmi10.329 @sf (nq)s cmr10.329 @sf 12 r 43 c cmmi10.329 @sf 10 r 112 c cmr10.329 @sf 10 r 43 c cmmi10.329 @sf 11 r 112 c cmr8.300 @sf 1188 2021 p 50 c cmr10.329 @sf 1217 2036 p 43 c 11 r 49 c 30 r 46 c 239 2163 p 3 28 ru cmmi10.329 @sf 235 2161 p 62 c cmtt10.329 @sf 87(WORK\(WSSI\))m cmr10.329 @sf 21(is)m cmmi10.329 @sf 15 r 83 c cmr10.329 @sf 3 r 40 c 719 2150 p 94 c cmmi10.329 @sf 713 2162 p 12 c 740 2161 p 59 c cmr10.329 @sf 762 2150 p 94 c cmmi10.329 @sf 761 2162 p 14 c cmr10.329 @sf 782 2161 p (\).)s 20(\(See)m cmsy10.329 @sf 15 r 120 c cmr10.329 @sf (1.A.\))s cmtt10.329 @sf 618 2228 p (WSSI)s cmr10.329 @sf 27 r 61 c 13 r 50 c cmmi10.329 @sf (nm)s cmr10.329 @sf 10 r 43 c 11 r 50 c cmmi10.329 @sf (nq)s cmr10.329 @sf 12 r 43 c cmmi10.329 @sf 10 r 112 c cmr10.329 @sf 10 r 43 c cmmi10.329 @sf 11 r 112 c cmr8.300 @sf 1164 2213 p 50 c cmr10.329 @sf 1193 2228 p 43 c 11 r 50 c 30 r 46 c 239 2355 p 3 28 ru cmmi10.329 @sf 235 2353 p 62 c cmtt10.329 @sf 39(WORK\(WSSDEI\))m cmr10.329 @sf 21(is)m cmmi10.329 @sf 15 r 83 c cmmi8.300 @sf 692 2360 p 14 c cmr10.329 @sf 711 2353 p 40 c 735 2342 p 94 c cmmi10.329 @sf 729 2354 p 12 c 756 2353 p 59 c cmr10.329 @sf 779 2342 p 94 c cmmi10.329 @sf 777 2354 p 14 c cmr10.329 @sf 799 2353 p (\).)s 19(\(See)m cmsy10.329 @sf 16 r 120 c cmr10.329 @sf (1.A.\))s cmtt10.329 @sf 618 2419 p (WSSDEI)s cmr10.329 @sf 27 r 61 c 13 r 50 c cmmi10.329 @sf (nm)s cmr10.329 @sf 10 r 43 c 11 r 50 c cmmi10.329 @sf (nq)s cmr10.329 @sf 12 r 43 c cmmi10.329 @sf 10 r 112 c cmr10.329 @sf 10 r 43 c cmmi10.329 @sf 10 r 112 c cmr8.300 @sf 1211 2404 p 50 c cmr10.329 @sf 1241 2419 p 43 c 11 r 51 c 30 r 46 c @eop %%Page: 86 100 86 @bop0 86 @bop1 cmr10.329 @sf 0 123 p (86)s 1410 r 87 c -3(ork)m 13 r 86 c -3(ectors)m 0 134 p 1725 2 ru 14 263 p 3 28 ru cmmi10.329 @sf 10 261 p 62 c cmtt10.329 @sf 39(WORK\(WSSEPI\))m cmr10.329 @sf 21(is)m cmmi10.329 @sf 15 r 83 c cmmi8.300 @sf 467 268 p 15 c cmr10.329 @sf 483 261 p 40 c 507 250 p 94 c cmmi10.329 @sf 501 262 p 12 c 529 261 p 59 c cmr10.329 @sf 551 250 p 94 c cmmi10.329 @sf 550 262 p 14 c cmr10.329 @sf 571 261 p (\).)s 19(\(See)m cmsy10.329 @sf 16 r 120 c cmr10.329 @sf (1.A.\))s cmtt10.329 @sf 393 327 p (WSSEPI)s cmr10.329 @sf 27 r 61 c 13 r 50 c cmmi10.329 @sf (nm)s cmr10.329 @sf 10 r 43 c 11 r 50 c cmmi10.329 @sf (nq)s cmr10.329 @sf 12 r 43 c cmmi10.329 @sf 10 r 112 c cmr10.329 @sf 10 r 43 c cmmi10.329 @sf 10 r 112 c cmr8.300 @sf 986 312 p 50 c cmr10.329 @sf 1016 327 p 43 c 11 r 52 c 30 r 46 c 14 454 p 3 28 ru cmmi10.329 @sf 10 452 p 62 c cmtt10.329 @sf 39(WORK\(RCONDI\))m cmr10.329 @sf 21(is)m cmmi10.329 @sf 15 r 20 c cmsy8.300 @sf 465 437 p 0 c cmr8.300 @sf 49 c cmr10.329 @sf 512 452 p 40 c cmmi10.329 @sf 77 c cmmi8.300 @sf 574 459 p 14 c cmmi10.329 @sf 593 452 p 74 c cmmi8.300 @sf 618 459 p 12 c cmr10.329 @sf 642 452 p 41 c 14(at)m 15(the)m 15(solution.)m 19(\(See)m cmsy10.329 @sf 15 r 120 c cmr10.329 @sf 1(4.C.\))m cmtt10.329 @sf 393 518 p (RCONDI)s cmr10.329 @sf 27 r 61 c 13 r 50 c cmmi10.329 @sf (nm)s cmr10.329 @sf 10 r 43 c 11 r 50 c cmmi10.329 @sf (nq)s cmr10.329 @sf 12 r 43 c cmmi10.329 @sf 10 r 112 c cmr10.329 @sf 10 r 43 c cmmi10.329 @sf 10 r 112 c cmr8.300 @sf 986 503 p 50 c cmr10.329 @sf 1016 518 p 43 c 11 r 53 c 30 r 46 c 14 646 p 3 28 ru cmmi10.329 @sf 10 644 p 62 c cmtt10.329 @sf 87(WORK\(ETAI\))m cmr10.329 @sf 21(is)m 15(the)m 15(relativ)m -1 r 101 c 14(error)m 14(in)m 15(the)m 16(function)m 15 r 118 c -2(alues)m 14(computed)m 16(within)m cmtt10.329 @sf 14(FCN)m cmr10.329 @sf 46 c cmtt10.329 @sf 393 710 p (ETAI)s cmr10.329 @sf 27 r 61 c 13 r 50 c cmmi10.329 @sf (nm)s cmr10.329 @sf 10 r 43 c 11 r 50 c cmmi10.329 @sf (nq)s cmr10.329 @sf 12 r 43 c cmmi10.329 @sf 10 r 112 c cmr10.329 @sf 10 r 43 c cmmi10.329 @sf 11 r 112 c cmr8.300 @sf 939 695 p 50 c cmr10.329 @sf 968 710 p 43 c 11 r 54 c 30 r 46 c cmtt10.329 @sf 84 835 p (WORK\(OLMAVI\))s cmr10.329 @sf 21(is)m 19(the)m 20 r 97 c 118 c -1(era)m -1(ge)m 18 r 110 c (um)s 98 c 1(er)m 17(of)m 19(steps)m 20(required)m 19(to)m 19(obtain)m 19(the)m 19(Lev)m (en)s 98 c 1(erg-)m 393 892 p (Marquardt)s 14(parameter.)m cmtt10.329 @sf 132 1017 p (WORK\(TAUI\))s cmr10.329 @sf 21(is)m 15(the)m 15(trust)m 15(region)m 14(radius)m 15(at)m 14(the)m 16(time)m 14(the)m 15(computations)m 15(stopp)m 1(ed.)m cmtt10.329 @sf 84 1142 p (WORK\(ALPHAI\))s cmr10.329 @sf 21(is)m 20(the)m 20(Lev)m (en)s 98 c 1(erg-Marquardt)m 18(parameter)m 19(at)m 20(the)m 20(time)m 20(the)m 20(computa-)m 393 1199 p (tions)s 14(stopp)m 1(ed.)m cmtt10.329 @sf 84 1324 p (WORK\(ACTRSI\))s cmr10.329 @sf 21(is)m 15(the)m 15(actual)m 14(relativ)m 101 c 13(reduction)m 15(in)m cmmi10.329 @sf 15 r 83 c cmr10.329 @sf 3 r 40 c cmmi10.329 @sf 12 c 2 r 59 c 8 r 14 c cmr10.329 @sf 2 r 41 c 14(from)m 14(the)m 15(last)m 14(iteration.)m cmtt10.329 @sf 84 1449 p (WORK\(PNROMI\))s cmr10.329 @sf 21(is)m 15(the)m 15(norm)m 15(of)m 15(the)m 15(scaled)m 15 r 118 c -2(alues)m 14(of)m 1094 1438 p 94 c cmmi10.329 @sf 1087 1450 p 12 c cmr10.329 @sf 1130 1449 p (and)s 1221 1438 p 94 c cmmi10.329 @sf 1219 1450 p 14 c cmr10.329 @sf 1241 1449 p 46 c cmtt10.329 @sf 84 1575 p (WORK\(RNORSI\))s cmr10.329 @sf 21(is)m cmmi10.329 @sf 15 r 83 c cmr10.329 @sf 3 r 40 c 494 1564 p 94 c cmmi10.329 @sf 488 1576 p 12 c 515 1575 p 59 c cmr10.329 @sf 537 1564 p 94 c cmmi10.329 @sf 536 1576 p 14 c cmr10.329 @sf 557 1575 p 41 c cmr8.300 @sf 575 1560 p 49 c cmmi8.300 @sf 61 c cmr8.300 @sf 50 c cmr10.329 @sf 630 1575 p 46 c cmtt10.329 @sf 84 1700 p (WORK\(PRERSI\))s cmr10.329 @sf 21(is)m 13(the)m 14(predicted)m 15(relativ)m -1 r 101 c 12(reduction)m 14(in)m cmmi10.329 @sf 13 r 83 c cmr10.329 @sf 3 r 40 c cmmi10.329 @sf 12 c 2 r 59 c 8 r 14 c cmr10.329 @sf 2 r 41 c 12(from)m 13(the)m 14(last)m 13(iteration.)m cmtt10.329 @sf 84 1825 p (WORK\(PARTLI\))s cmr10.329 @sf 21(is)m 15(the)m 15(stopping)m 15(tolerance)m 14(used)m 16(to)m 15(detect)m 15(parameter)m 14(con)m 118 c (ergence.)s cmtt10.329 @sf 84 1950 p (WORK\(SSTOLI\))s cmr10.329 @sf 21(is)m 12(the)m 13(stopping)m 12(tolerance)m 12(used)m 14(to)m 12(detect)m 13(sum)m 12(of)m 13(squares)m 12(con)m 118 c (erg)s -1(ence.)m cmtt10.329 @sf 84 2076 p (WORK\(TAUFCI\))s cmr10.329 @sf 21(is)m 15(the)m 15(factor)m 14(used)m 16(to)m 15(compute)m 15(the)m 15(initial)m 14(trust)m 14(region)m 15(radius.)m cmtt10.329 @sf 84 2201 p (WORK\(EPSMAI\))s cmr10.329 @sf 21(is)m 15(mac)m (hine)s 14(precision,)m 14(i.e.,)m 14(the)m 15(smallest)m 14 r 118 c -2(alue)m cmmi10.329 @sf 15 r 24 c cmr10.329 @sf 17(suc)m 104 c 14(that)m 15 r 49 c 9 r 43 c cmmi10.329 @sf 11 r 24 c 14 r 62 c cmr10.329 @sf 13 r 49 c cmmi10.329 @sf 15 r 58 c cmtt10.329 @sf 84 2326 p (WORK\(BETA0I\))s cmr10.329 @sf 21(is)m 21(the)m 20(\014rst)m 21(elemen)m 116 c 20(of)m 20 r 97 c cmmi10.329 @sf 21 r 112 c cmsy10.329 @sf 13 r 2 c cmr10.329 @sf 15 r 49 c 20(arra)m 121 c cmtt10.329 @sf 19(BETA0)m cmr10.329 @sf 20(con)m (taining)s 19(the)m cmti10.329 @sf 21(initial)m cmr10.329 @sf 393 2383 p (estimates)s 14(of)m 15(the)m 15(function)m 15(parameters)m cmmi10.329 @sf 15 r 12 c cmr8.300 @sf 1165 2368 p 48 c cmr10.329 @sf 1184 2383 p 44 c 15(where)m cmtt10.329 @sf 393 2449 p (WORK\(BETAI0-1+)s 75 c -2 r 41 c cmr10.329 @sf 15 r 61 c cmtt10.329 @sf 16(BETA0\()m 75 c -1 r 41 c cmr10.329 @sf 15 r 61 c cmmi10.329 @sf 15 r 12 c cmr8.300 @sf 1125 2434 p 48 c cmr6.300 @sf 1123 2460 p 75 c @eop %%Page: 87 101 87 @bop0 cmmi8.300 @sf [<1FC07FF0F078E018E000E000E000E000E000700078383E380FF803F0> 16 14 -1 0 15.282] 99 @dc [<7F00FFC0E1C0E0E0E0E001E01FE01FE03F803C601C701E700FF007E0> 16 14 -2 0 16.316] 115 @dc 87 @bop1 cmr10.329 @sf 225 123 p 87 c -3(ork)m 14 r 86 c -3(ectors)m 1408(87)m 225 134 p 1725 2 ru 618 259 p (for)s cmtt10.329 @sf 14 r 75 c cmr10.329 @sf 13 r 61 c 13 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 7 r 58 c 5 r 59 c 8(p:)m cmr10.329 @sf 13 r 70 c -3(or)m 13(implicit)m 13(mo)m 1(dels,)m cmtt10.329 @sf 14(BETA0)m cmr10.329 @sf 14(is)m 14(the)m 15(initial)m 13 r 118 c -2(alue)m 13(used)m 618 315 p (for)s 15(the)m 15(last)m 14 r 118 c -2(alue)m 14(of)m 15(the)m 16 r 112 c 1(enalt)m 121 c 13(parameter.)m cmtt10.329 @sf 309 440 p (WORK\(BETACI\))s cmr10.329 @sf 21(is)m 18(the)m 19(\014rst)m 19(elemen)m 116 c 17(of)m 19 r 97 c cmmi10.329 @sf 18 r 112 c cmsy10.329 @sf 13 r 2 c cmr10.329 @sf 12 r 49 c 19(arra)m 121 c cmtt10.329 @sf 17(BETAC)m cmr10.329 @sf 18(con)m (taini)s -1(ng)m 17(the)m cmti10.329 @sf 19(curr)m -1(ent)m cmr10.329 @sf 618 497 p 119 c (orking)s 13(estimates)m 14(of)m 15(the)m 19 r 126 c cmmi10.329 @sf -27 r 112 c cmr10.329 @sf 15(un\014xed)m 16(function)m 15(parameters)m 1738 486 p 126 c cmmi10.329 @sf 1732 498 p 12 c cmmi8.300 @sf 1760 482 p 99 c cmr10.329 @sf 1777 497 p 44 c 15(where)m cmtt10.329 @sf 618 563 p (WORK\(BETACI-1+)s 75 c -2 r 41 c cmr10.329 @sf 15 r 61 c cmtt10.329 @sf 16(BETAC\()m 75 c -1 r 41 c cmr10.329 @sf 15 r 61 c 1329 552 p 126 c cmmi10.329 @sf 1322 564 p 12 c cmmi8.300 @sf 1350 549 p 99 c cmr6.300 @sf 1348 574 p 75 c cmr10.329 @sf 618 629 p (for)s cmtt10.329 @sf 15 r 75 c cmr10.329 @sf 12 r 61 c 13 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 7 r 58 c 6 r 59 c cmr10.329 @sf 11 r 126 c cmmi10.329 @sf -26 r 112 c -1 r 58 c cmtt10.329 @sf 309 755 p (WORK\(BETASI\))s cmr10.329 @sf 21(is)m 22(the)m 22(\014rst)m 21(elemen)m 116 c 21(of)m 21 r 97 c cmmi10.329 @sf 22 r 112 c cmsy10.329 @sf 14 r 2 c cmr10.329 @sf 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16(arra)m 121 c cmtt10.329 @sf 15(SSF)m cmr10.329 @sf 17(con)m (taining)s 15(the)m 17(scale)m 16(of)m 17(all)m 618 2068 p (of)s 15(the)m 15(function)m 15(parameters)m cmmi10.329 @sf 15 r 12 c cmr10.329 @sf 2 r 44 c 14(where)m cmtt10.329 @sf 618 2134 p (WORK\(SSFI-1+)s 75 c -2 r 41 c cmr10.329 @sf 15 r 61 c cmtt10.329 @sf 16(SSF\()m 75 c -1 r 41 c cmr10.329 @sf 15 r 61 c cmcsc10.329 @sf 16(scale)m cmsy10.329 @sf 102 c cmmi10.329 @sf 12 c cmr6.300 @sf 1400 2141 p 75 c cmsy10.329 @sf 1425 2134 p 103 c cmr10.329 @sf 618 2200 p (for)s cmtt10.329 @sf 15 r 75 c cmr10.329 @sf 12 r 61 c 13 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 7 r 58 c 6 r 59 c 8(p:)m cmtt10.329 @sf 309 2326 p (WORK\(QRAUXI\))s cmr10.329 @sf 21(is)m 16(the)m 16(\014rst)m 16(elemen)m 116 c 15(of)m 16 r 97 c cmmi10.329 @sf 16 r 112 c cmsy10.329 @sf 11 r 2 c cmr10.329 @sf 11 r 49 c 16(arra)m -1 r 121 c cmtt10.329 @sf 15(QRAUX)m cmr10.329 @sf 15(used)m 17(during)m 16(the)m 16(compu-)m 618 2382 p (tations,)s 14(where)m cmtt10.329 @sf 618 2448 p (WORK\(QRAUXI-1+)s 73 c -2 r 41 c cmr10.329 @sf 15 r 61 c cmtt10.329 @sf 16(QRAUX\()m 73 c -1 r 41 c @eop %%Page: 88 102 88 @bop0 cmsy10.329 @sf [<0C00000800000E00000C00000E00000E00000700001E00000780001F000007C0001F800007C000 1FC00007E0001EC00007F0001EE00007B8001E70000398001E3800039C001E180003CE001E1C00 03C6001E0C0003C3003E060003C3803E030003C1803C030003C0C03C018003C0C03C018003C060 3C00C003C0307C004003C0307C004003C01878006003C01878002007C00CF8002007C004F80030 078006F000300F8002F000700F8003F001F01F0001F001F03F0001E001F0FE0001E000F07C0000 E000E0> 48 33 -2 2 44.898] 87 @dc cmr8.300 @sf [<4300E7807FC03CE01840> 16 5 -3 -17 17.642] 126 @dc 88 @bop1 cmr10.329 @sf 0 123 p (88)s 1410 r 87 c -3(ork)m 13 r 86 c -3(ectors)m 0 134 p 1725 2 ru 393 259 p (for)s cmtt10.329 @sf 15 r 73 c cmr10.329 @sf 12 r 61 c 13 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 7 r 58 c 6 r 59 c 8(p:)m cmtt10.329 @sf 203 384 p (WORK\(U\))s cmr10.329 @sf 22(is)m 13(the)m 14(\014rst)m 13(elemen)m 116 c 13(of)m 13 r 97 c cmmi10.329 @sf 13 r 112 c cmsy10.329 @sf 7 r 2 c cmr10.329 @sf 7 r 49 c 14(arra)m 121 c cmtt10.329 @sf 11 r 85 c cmr10.329 @sf 14(used)m 14(during)m 14(the)m 13(computations,)m 393 440 p (where)s cmtt10.329 @sf 393 507 p (WORK\(UI-1+)s 73 c -1 r 41 c cmr10.329 @sf 15 r 61 c cmtt10.329 @sf 15(U\()m 73 c 41 c cmr10.329 @sf 393 573 p (for)s cmtt10.329 @sf 15 r 73 c cmr10.329 @sf 12 r 61 c 13 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 7 r 58 c 6 r 59 c 8(p:)m cmtt10.329 @sf 156 698 p (WORK\(FSI\))s cmr10.329 @sf 21(is)m 17(the)m 17(\014rst)m 17(elemen)m 116 c 16(of)m 17(an)m cmmi10.329 @sf 17 r 110 c cmsy10.329 @sf 12 r 2 c cmmi10.329 @sf 11 r 113 c cmr10.329 @sf 20(arra)m -1 r 121 c cmtt10.329 @sf 15(FS)m cmr10.329 @sf 17(con)m (taining)s 15(the)m cmti10.329 @sf 18(save)m -1 r 100 c cmr10.329 @sf 15(esti-)m 393 755 p (mated)s 15(errors)m cmmi10.329 @sf 14 r 69 c cmmi8.300 @sf 698 740 p 115 c cmr10.329 @sf 731 755 p (in)s 15(the)m 15(resp)m 1(onse)m 16 r 118 c 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cmtt10.329 @sf 21 r 73 c cmr10.329 @sf 24 r 61 c 24 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 7 r 58 c 5 r 59 c 8(n;)m cmtt10.329 @sf 21 r 75 c cmr10.329 @sf 24 r 61 c 24 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 7 r 58 c 5 r 59 c cmr10.329 @sf 11 r 126 c cmmi10.329 @sf -26 r 112 c cmr10.329 @sf -1 r 44 c cmtt10.329 @sf 24 r 76 c cmr10.329 @sf 23 r 61 c 24 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 7 r 58 c 6 r 59 c 8 r 113 c cmr10.329 @sf 2 r 44 c 22(and)m cmsy10.329 @sf 22 r 87 c cmr6.300 @sf 1479 1342 p 73 c 1492 1317 p 84 c cmsy10.329 @sf 1516 1335 p 87 c cmr6.300 @sf 1561 1342 p 73 c cmr10.329 @sf 1597 1335 p 61 c cmmi10.329 @sf 24 r 119 c cmmi8.300 @sf 1684 1342 p 15 c cmr6.300 @sf 1698 1348 p 73 c cmr10.329 @sf 1712 1335 p 46 c 393 1392 p (The)s 13(deriv)m -2(ativ)m -1(es)m 12(are)m 12(the)m 13 r 118 c -2(alues)m 13(ev)m -2(aluated)m 12(at)m 12(the)m 13 r 98 c 1(eginning)m 13(of)m 13(the)m 13(last)m 393 1448 p (iteration)s 18(unless)m 21(the)m 20(user)m 20(requested)m 20(that)m 20(the)m 20(co)m 118 c -2(ari)m -1(ance)m 19(matrix)m 18 r 98 c 1 r 101 c 393 1505 p (computed)s 14(using)m 14(the)m 13(\014nal)m 14(solution,)m 12(in)m 14(whic)m 104 c 12(case)m 14(they)m 14(are)m 13(the)m 14 r 118 c -2(alues)m 393 1561 p (obtained)s 20(at)m 20(the)m 21(\014nal)m 20(solution.)m 35(\(See)m cmsy10.329 @sf 21 r 120 c cmr10.329 @sf (2.B.ii,)s 20(subroutine)m 21(argumen)m 116 c cmtt10.329 @sf 393 1617 p (JOB)s cmr10.329 @sf (.\))s cmtt10.329 @sf 132 1743 p (WORK\(WE1I\))s cmr10.329 @sf 21(is)m 14(the)m 14(\014rst)m 13(elemen)m 116 c 13(of)m 14(an)m cmtt10.329 @sf 14(LDWE)m cmsy10.329 @sf 7 r 2 c cmtt10.329 @sf 8(LD2WE)m cmsy10.329 @sf 7 r 2 c cmmi10.329 @sf 8 r 113 c cmr10.329 @sf 16(arra)m 121 c cmtt10.329 @sf 12(WE1)m cmr10.329 @sf 13(con)m (taining)s 12(the)m 393 1799 p (Cholesky)s 15(factorizatio)m -1(ns)m 14(for)m 14(the)m 16 r 119 c (eigh)s -1(t)m -1 r 115 c cmmi10.329 @sf 13 r 119 c cmmi8.300 @sf 1207 1806 p 15 c cmr10.329 @sf 1238 1799 p (sp)s 1(eci\014ed)m 16(in)m cmtt10.329 @sf 15(WE)m cmr10.329 @sf 44 c 14(where)m cmtt10.329 @sf 393 1865 p (WORK\(WE1I-1+)s 73 c -2(+\()m 76 c 49 c (-1\)*LDWE+\()s 76 c -2 r 50 c (-1\)*LDWE*LD2WE\))s cmr10.329 @sf 526 1932 p 61 c cmtt10.329 @sf 16(WE1I\()m 73 c -1 r 44 c 76 c 49 c 44 c 76 c -1 r 50 c 41 c cmr10.329 @sf 393 1998 p (for)s cmtt10.329 @sf 20 r 73 c cmr10.329 @sf 20 r 61 c 21 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 7 r 58 c 6 r 59 c cmtt10.329 @sf 8(LDWE)m cmmi10.329 @sf -2 r 59 c cmtt10.329 @sf 20 r 76 c cmr10.329 @sf 49 c 20 r 61 c 21 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 7 r 58 c 6 r 59 c cmtt10.329 @sf 8(LD2WE)m cmr10.329 @sf -2 r 44 c 21(and)m cmtt10.329 @sf 20 r 76 c cmr10.329 @sf 50 c 21 r 61 c 21 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 7 r 58 c 5 r 59 c 8 r 113 c cmr10.329 @sf 2 r 46 c cmtt10.329 @sf 34(WE1I)m cmr10.329 @sf 393 2054 p (sp)s 1(eci\014es)m 19(the)m 18(factorization)m 16(in)m 17(the)m 19(same)m 17(manner)m 18(that)m 17(subroutine)m 18(ar-)m 393 2111 p (gumen)s 116 c cmtt10.329 @sf 14(WE)m cmr10.329 @sf 15(is)m 15(used)m 15(to)m 15(sp)m 1(ecify)m cmmi10.329 @sf 15 r 119 c cmmi8.300 @sf 1002 2118 p 15 c cmr10.329 @sf 1017 2111 p 46 c 20(\(See)m cmsy10.329 @sf 16 r 120 c cmr10.329 @sf (2.B.ii.\))s cmtt10.329 @sf 108 2236 p (WORK\(DIFFI\))s cmr10.329 @sf 21(is)m 20(the)m 21(\014rst)m 21(elemen)m 116 c 19(of)m 21(an)m cmmi10.329 @sf 21 r 113 c cmsy10.329 @sf 15 r 2 c cmr10.329 @sf 14 r 40 c cmmi10.329 @sf 112 c cmr10.329 @sf 14 r 43 c cmmi10.329 @sf 14 r 109 c cmr10.329 @sf 41 c 20(arra)m 121 c cmtt10.329 @sf 19(DIFF)m cmr10.329 @sf 20(con)m (taining)s 19(the)m 393 2293 p (relativ)s 101 c 18(di\013erences)m 20 r 98 c 1(et)m 119 c (een)s 19(the)m 21(user)m 20(supplied)m 21(deriv)m -2(ativ)m -1(es)m 18(and)m 21(the)m 393 2349 p (\014nite)s 15(di\013erence)m 16 r 118 c -2(alues)m 14(they)m 15 r 119 c (ere)s 14 r 99 c (hec)s 107 c -1(ed)m 14(against,)m 13(where)m cmtt10.329 @sf 393 2415 p (WORK\(DIFFI-1+)s 76 c -2(+\()m 74 c (-1\)*NQ\))s cmr10.329 @sf 14 r 61 c cmtt10.329 @sf 15(DIFF\()m 76 c 44 c 74 c -1 r 41 c @eop %%Page: 89 103 89 @bop0 89 @bop1 cmr10.329 @sf 225 123 p 87 c -3(ork)m 14 r 86 c -3(ectors)m 1408(89)m 225 134 p 1725 2 ru 618 259 p (for)s cmtt10.329 @sf 15 r 76 c cmr10.329 @sf 12 r 61 c 13 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 7 r 58 c 6 r 59 c 8 r 113 c 2 r 59 c cmr10.329 @sf 14(and)m cmtt10.329 @sf 15 r 74 c cmr10.329 @sf 12 r 61 c 13 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 8 r 58 c 5 r 59 c cmr10.329 @sf 8 r 40 c cmmi10.329 @sf 112 c cmr10.329 @sf 9 r 43 c cmmi10.329 @sf 10 r 109 c cmr10.329 @sf (\).)s cmtt10.329 @sf 309 384 p (WORK\(DELTSI\))s cmr10.329 @sf 21(is)m 16(the)m 16(\014rst)m 16(elemen)m 116 c 15(of)m 16(an)m cmmi10.329 @sf 16 r 110 c cmsy10.329 @sf 11 r 2 c cmmi10.329 @sf 11 r 109 c cmr10.329 @sf 16(arra)m 121 c cmtt10.329 @sf 14(DELTAS)m cmr10.329 @sf 15(con)m (taining)s 14(the)m cmti10.329 @sf 16(save)m -1 r 100 c cmr10.329 @sf 618 440 p 119 c (orking)s 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@sf 20 r 110 c cmsy10.329 @sf 13 r 2 c cmmi10.329 @sf 13 r 112 c cmsy10.329 @sf 13 r 2 c cmmi10.329 @sf 14 r 113 c cmr10.329 @sf 21(arra)m 121 c cmtt10.329 @sf 17(WRK6)m cmr10.329 @sf 19(required)m 20(for)m 19 r 119 c (ork)s 618 315 p (space,)s 15(where)m cmtt10.329 @sf 618 381 p (WORK\(WRK6I-1+)s 73 c -2(+\()m 75 c (-1\)*N+\()s 76 c -1(-1\)*N*NQ\))m cmr10.329 @sf 14 r 61 c cmtt10.329 @sf 15(WRK6\()m 73 c -1 r 44 c 75 c 44 c 76 c 41 c cmr10.329 @sf 618 448 p (for)s cmtt10.329 @sf 15 r 73 c cmr10.329 @sf 12 r 61 c 13 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 7 r 58 c 6 r 59 c 8 r 110 c cmr10.329 @sf 44 c cmtt10.329 @sf 14 r 75 c cmr10.329 @sf 12 r 61 c 13 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 8 r 58 c 5 r 59 c 8 r 112 c cmr10.329 @sf 44 c 14(and)m cmtt10.329 @sf 15 r 76 c cmr10.329 @sf 13 r 61 c 13 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 7 r 58 c 5 r 59 c 8 r 113 c cmr10.329 @sf 2 r 46 c cmtt10.329 @sf 333 573 p (WORK\(WRK7I\))s cmr10.329 @sf 21(is)m 20(the)m 21(\014rst)m 20(elemen)m 116 c 19(of)m 20(an)m 21 r 53 c cmmi10.329 @sf 113 c cmr10.329 @sf 22(arra)m 121 c cmtt10.329 @sf 18(WRK7)m cmr10.329 @sf 20(required)m 21(for)m 19 r 119 c (ork)s 19(space,)m 618 629 p (where)s cmtt10.329 @sf 618 696 p (WORK\(WRK7I-1+)s 74 c -2 r 41 c cmr10.329 @sf 15 r 61 c cmtt10.329 @sf 16(WRK7\()m 74 c -1 r 41 c cmr10.329 @sf 618 762 p (for)s cmtt10.329 @sf 15 r 74 c cmr10.329 @sf 12 r 61 c 13 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 7 r 58 c 6 r 59 c cmr10.329 @sf 8 r 53 c cmmi10.329 @sf 113 c 2 r 58 c cmbx12.300 @sf 225 908 p (5.B.)s 18(Extracting)m 17(Information)m 18(from)m 19 r 86 c -4(ector)m cmtt12.300 @sf 17(IWORK)m cmr10.329 @sf 225 1029 p (Up)s 1(on)m 20(return)m 19(from)m 18 r 97 c 19(call)m 19(to)m 18(ODRP)m -3 r 65 c (CK,)s 18(arra)m -1 r 121 c cmtt10.329 @sf 17(IWORK)m cmr10.329 @sf 19(con)m (tains)s 17 r 118 c -2(alues)m 19(that)m 18(ma)m 121 c 17 r 98 c 1 r 101 c 20(of)m 225 1085 p (in)s (terest)s 21(to)m 22(the)m 23(user.)m 43 r 84 c -3 r 111 c 21(extract)m 22(information)m 21(from)m cmtt10.329 @sf 22(IWORK)m cmr10.329 @sf -1 r 44 c 25(the)m 23(follo)m -1(wi)m -1(ng)m 21(declaration)m 225 1142 p (statemen)s 116 c 13 r 109 c (ust)s 14 r 98 c 1 r 101 c 16(added)m 15(to)m 15(the)m 15(user's)m 15(program)m cmtt10.329 @sf 368 1255 p (INTEGER)s 344 1312 p 43 c 72(MSGBI,MSGDI,IFIX2)m -1(I,ISTOP)m -1(I,)m 344 1368 p 43 c 72(NNZWI,NPPI,IDFI,)m 344 1425 p 43 c 72(JOBI,IPRINI,LUNER)m -1(I,LUNRP)m -1(I,)m 344 1481 p 43 c 72(NROWI,NTOLI,NETAI)m -1 r 44 c 344 1538 p 43 c 72(MAXITI,NITERI,NFE)m -1(VI,NJEV)m -1(I,INT2I,)m -1(IRANKI,)m -1(LDTTI,)m 344 1594 p 43 c 72(LIWKMN)m cmr10.329 @sf 225 1707 p (where)s cmtt10.329 @sf 20(MSGBI)m cmr10.329 @sf 20(through)m cmtt10.329 @sf 19(LDTTI)m cmr10.329 @sf 20(are)m 19 r 118 c -2(ariables)m 19(that)m 19(indicate)m 19(the)m 21(starting)m 18(lo)m 1(cations)m 19(within)m cmtt10.329 @sf 225 1764 p (IWORK)s cmr10.329 @sf 10(of)m 10(the)m 11(stored)m 10 r 118 c -2(alues,)m 11(and)m cmtt10.329 @sf 11(LIWKMN)m cmr10.329 @sf 9(is)m 11(the)m 10(minim)m (um)s 9(acceptable)m 11(length)m 10(of)m 11(arra)m -1 r 121 c cmtt10.329 @sf 9(IWORK)m cmr10.329 @sf -1 r 46 c 225 1820 p (The)s 19(appropriate)m 18 r 118 c -2(alues)m 18(of)m cmtt10.329 @sf 19(MSGBI)m cmr10.329 @sf 18(through)m cmtt10.329 @sf 18(LDTTI)m cmr10.329 @sf 18(are)m 19(obtained)m 19 r 98 c 121 c 17(in)m 118 c (oki)s -1(ng)m 17(subroutine)m cmtt10.329 @sf 225 1877 p (SIWINF)s cmr10.329 @sf 11(when)m 13(using)m 12(either)m 12(of)m 12(the)m 13(single)m 11(precision)m 12(ODRP)m -3 r 65 c (CK)s 11(subroutines)m cmtt10.329 @sf 12(SODR)m cmr10.329 @sf 12(or)m cmtt10.329 @sf 12(SODRC)m cmr10.329 @sf -1 r 44 c 225 1933 p (and)s 16 r 98 c 121 c 14(in)m 118 c (oki)s -1(ng)m cmtt10.329 @sf 14(DIWINF)m cmr10.329 @sf 15(when)m 16(using)m 15(either)m 16(of)m 15(the)m 16(double)m 16(precision)m 15(subroutines)m cmtt10.329 @sf 15(DODR)m cmr10.329 @sf 15(or)m cmtt10.329 @sf 225 1990 p (DODRC)s cmr10.329 @sf -1 r 46 c 25(The)m 17(call)m 16(statemen)m (ts)s 15(for)m cmtt10.329 @sf 16(SIWINF)m cmr10.329 @sf 16(and)m cmtt10.329 @sf 17(DIWINF)m cmr10.329 @sf 16(ha)m 118 c 101 c 15(the)m 17(same)m 16(argumen)m 116 c 16(lists.)m 23 r 84 c -3 r 111 c 225 2046 p (in)s 118 c -1(ok)m -1 r 101 c 13(either)m 15(subroutine,)m 15(use)m cmtt10.329 @sf 368 2159 p (CALL)s 23()m 344 2216 p 43 c 72(\(M,NP,NQ,)m 344 2272 p 43 c 72(MSGBI,MSGDI,IFIX2)m -1(I,ISTOP)m -1(I,)m 344 2329 p 43 c 72(NNZWI,NPPI,IDFI,)m 344 2385 p 43 c 72(JOBI,IPRINI,LUNER)m -1(I,LUNRP)m -1(I,)m 344 2442 p 43 c 72(NROWI,NTOLI,NETAI)m -1 r 44 c @eop %%Page: 92 106 92 @bop0 92 @bop1 cmr10.329 @sf 0 123 p (92)s 1410 r 87 c -3(ork)m 13 r 86 c -3(ectors)m 0 134 p 1725 2 ru cmtt10.329 @sf 119 259 p 43 c 72(MAXITI,NITERI,NFE)m -1(VI,NJEV)m -1(I,INT2I,)m -1(IRANKI,)m -1(LDTTI,)m 119 315 p 43 c 72(LIWKMN\))m cmr10.329 @sf 0 420 p (where)s cmtt10.329 @sf 22(SIWINF)m cmr10.329 @sf 21(should)m 22 r 98 c 1 r 101 c 23(substituted)m 21(for)m cmtt10.329 @sf 22()m cmr10.329 @sf 21(when)m 22(using)m cmtt10.329 @sf 22(SODR)m cmr10.329 @sf 21(and)m cmtt10.329 @sf 22(SODRC)m cmr10.329 @sf 44 c 23(and)m cmtt10.329 @sf 0 477 p (DIWINF)s cmr10.329 @sf 15(should)m 16 r 98 c 1 r 101 c 17(substituted)m 15(for)m cmtt10.329 @sf 15()m cmr10.329 @sf 15(when)m 17(using)m cmtt10.329 @sf 15(DODR)m cmr10.329 @sf 16(and)m cmtt10.329 @sf 16(DODRC)m cmr10.329 @sf -1 r 46 c 22(Note)m 16(that)m 15(the)m 0 533 p 118 c -2(alues)m 19(of)m cmtt10.329 @sf 19 r 77 c cmr10.329 @sf 44 c cmtt10.329 @sf 20(NP)m cmr10.329 @sf 44 c 20(and)m cmtt10.329 @sf 20(NQ)m cmr10.329 @sf 19 r 109 c (ust)s 18 r 98 c 1 r 101 c 20(input)m 20(to)m cmtt10.329 @sf 19(SIWINF)m cmr10.329 @sf 19(and)m cmtt10.329 @sf 19(DIWINF)m cmr10.329 @sf 19(with)m cmti10.329 @sf 19(exactly)m cmr10.329 @sf 20(the)m 19(same)m 0 590 p 118 c -2(alues)m 14(as)m 15 r 119 c (ere)s 14(used)m 16(in)m 15(the)m 15(original)m 13(call)m 15(to)m 14(ODRP)m -3 r 65 c (CK.)s 0 666 p (In)s 17(the)m 17(follo)m -1(wing)m 14(descriptions)m 16(of)m 16(the)m 17(information)m 14(returned)m 17(in)m cmtt10.329 @sf 17(IWORK)m cmr10.329 @sf -1 r 44 c 1366 668 p 3 28 ru cmmi10.329 @sf 1362 666 p 62 c cmr10.329 @sf 17(indicates)m 16 r 118 c -2(alues)m 0 722 p (that)s 14(are)m 15(most)m 15(lik)m (ely)s 13(to)m 14 r 98 c 1 r 101 c 16(of)m 15(in)m (terest.)s 14 839 p 3 28 ru cmmi10.329 @sf 10 837 p 62 c cmtt10.329 @sf 39(IWORK\(MSGBI\))m cmr10.329 @sf 21(is)m 21(the)m 21(\014rst)m 21(elemen)m 116 c 20(of)m 21 r 97 c 20 r 49 c 14 r 43 c 15 r 40 c cmmi10.329 @sf 113 c cmsy10.329 @sf 15 r 2 c cmmi10.329 @sf 15 r 112 c cmr10.329 @sf 41 c 21(arra)m -1 r 121 c cmtt10.329 @sf 19(MSGB)m cmr10.329 @sf 21(used)m 22(to)m 20(indicate)m 393 893 p (the)s 18(results)m 16(of)m 17 r 99 c (hec)s (king)s 16(the)m 17(partial)m 16(deriv)m -2(ativ)m -1(es)m 16(with)m 16(resp)m 1(ect)m 18(to)m cmmi10.329 @sf 17 r 12 c cmr10.329 @sf 20(at)m 393 950 p (observ)s -2(ation)m cmtt10.329 @sf 14(NROW)m cmr10.329 @sf 46 c 14(\(See)m cmtt10.329 @sf 15(IWORK\(NROWI\))m cmr10.329 @sf 14 r 98 c 1(elo)m (w.\))s 393 1016 p (The)s 16 r 118 c -2(alue)m 14(of)m cmtt10.329 @sf 15(IWORK\(MSGBI\))m cmr10.329 @sf 13(summarizes)m 15(the)m 15(results)m 15 r 111 c 118 c -1(er)m 13(all)m cmmi10.329 @sf 14 r 12 c cmr10.329 @sf 2 r 46 c cmsy10.329 @sf 393 1091 p 15 c cmr10.329 @sf 23(If)m cmtt10.329 @sf 15(IWORK\(MSGBI\))m cmmi10.329 @sf 11 r 60 c cmr10.329 @sf 13 r 48 c 15(then)m 439 1148 p (the)s 15(partial)m 13(deriv)m -2(ativ)m (es)s 13(with)m 14(resp)m 1(ect)m 16(to)m cmmi10.329 @sf 15 r 12 c cmr10.329 @sf 17 r 119 c (ere)s 14(not)m 15 r 99 c (hec)s 107 c -1(ed.)m cmsy10.329 @sf 393 1214 p 15 c cmr10.329 @sf 23(If)m cmtt10.329 @sf 15(IWORK\(MSGBI\))m cmr10.329 @sf 11 r 61 c 13 r 48 c 15(then)m 439 1271 p (the)s 11(partial)m 9(deriv)m -2(ativ)m -1(es)m 9(with)m 11(resp)m 1(ect)m 11(to)m 10(eac)m 104 c 11(of)m 10(the)m cmmi10.329 @sf 11 r 12 c cmr6.300 @sf 1425 1278 p 75 c cmmi10.329 @sf 1450 1271 p 59 c cmtt10.329 @sf 18 r 75 c cmr10.329 @sf 13 r 61 c 13 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 7 r 58 c 5 r 59 c 8(p;)m cmr10.329 @sf 439 1327 p (for)s 14(eac)m 104 c 14(of)m 15(the)m cmmi10.329 @sf 15 r 113 c cmr10.329 @sf 18(resp)m 1(onses)m 15(app)m 1(ear)m 16(to)m 14 r 98 c 1 r 101 c 16(correct.)m cmsy10.329 @sf 393 1393 p 15 c cmr10.329 @sf 23(If)m cmtt10.329 @sf 15(IWORK\(MSGBI\))m cmr10.329 @sf 11 r 61 c 13 r 49 c 15(then)m 439 1450 p (the)s 15(partial)m 14(deriv)m -2(ativ)m -1 r 101 c 14(with)m 15(resp)m 1(ect)m 16(to)m 15(at)m 15(least)m 14(one)m 16(of)m 15(the)m cmmi10.329 @sf 16 r 12 c cmr6.300 @sf 1592 1457 p 75 c cmmi10.329 @sf 1617 1450 p 59 c cmtt10.329 @sf 23 r 75 c cmr10.329 @sf 13 r 61 c 439 1506 p 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 7 r 58 c 5 r 59 c 8(p;)m cmr10.329 @sf 16(app)m 1(ears)m 18(to)m 17 r 98 c 1 r 101 c 19(questionable)m 17(for)m 17(at)m 17(least)m 16(one)m 18(of)m 18(the)m cmmi10.329 @sf 17 r 113 c cmr10.329 @sf 20(re-)m 439 1563 p (sp)s 1(onses.)m cmsy10.329 @sf 393 1629 p 15 c cmr10.329 @sf 23(If)m cmtt10.329 @sf 15(IWORK\(MSGBI\))m cmr10.329 @sf 11 r 61 c 13 r 50 c 15(then)m 439 1685 p (the)s 15(partial)m 14(deriv)m -2(ativ)m -1 r 101 c 14(with)m 15(resp)m 1(ect)m 16(to)m 15(at)m 15(least)m 14(one)m 16(of)m 15(the)m cmmi10.329 @sf 16 r 12 c cmr6.300 @sf 1592 1692 p 75 c cmmi10.329 @sf 1617 1685 p 59 c cmtt10.329 @sf 23 r 75 c cmr10.329 @sf 13 r 61 c 439 1742 p 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 7 r 58 c 5 r 59 c 8(p;)m cmr10.329 @sf 17(app)m 1(ears)m 18(to)m 17 r 98 c 1 r 101 c 19(seriously)m 16(questionable)m 18(for)m 17(at)m 17(least)m 17(one)m 18(of)m 439 1798 p (the)s cmmi10.329 @sf 15 r 113 c cmr10.329 @sf 17(resp)m 1(onses.)m 393 1874 p (The)s 11 r 118 c -2(alue)m 9(of)m cmtt10.329 @sf 10(IWORK\(MSGBI+)m 76 c -2(+\()m 75 c (-1\)*NQ\))s cmmi10.329 @sf -1 r 59 c cmtt10.329 @sf 18 r 76 c cmr10.329 @sf 12 r 61 c 13 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 7 r 58 c 6 r 59 c 8 r 113 c 2 r 59 c cmtt10.329 @sf 16 r 75 c cmr10.329 @sf 13 r 61 c 13 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 7 r 58 c 5 r 59 c 8 r 112 c cmr10.329 @sf 44 c 393 1930 p (indicates)s 15(the)m 15(individual)m 15(results)m 15(of)m 14 r 99 c (hec)s (king)s 14(the)m 15(partial)m 14(deriv)m -2(ativ)m -1 r 101 c 13(of)m 393 1987 p (the)s cmtt10.329 @sf 19 r 76 c cmr10.329 @sf (th)s 19(resp)m 1(onse)m 19(with)m 18(resp)m 1(ect)m 19(to)m 19(eac)m 104 c cmmi10.329 @sf 18 r 12 c cmr6.300 @sf 1206 1994 p 75 c cmmi10.329 @sf 1230 1987 p 59 c cmr10.329 @sf 19(where)m 19(for)m cmtt10.329 @sf 18 r 76 c cmr10.329 @sf 19 r 61 c 19 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 7 r 58 c 5 r 59 c 8 r 113 c 2 r 59 c cmr10.329 @sf 393 2043 p (and)s cmtt10.329 @sf 16 r 75 c cmr10.329 @sf 12 r 61 c 13 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 7 r 58 c 6 r 59 c 8 r 112 c cmr10.329 @sf 11 r 58 c cmsy10.329 @sf 393 2119 p 15 c cmr10.329 @sf 23(If)m cmtt10.329 @sf 15(IWORK\(MSGBI+)m 76 c -2(+\()m 75 c (-1\)*NQ\))s cmr10.329 @sf 11 r 61 c cmsy10.329 @sf 13 r 0 c cmr10.329 @sf 49 c 16(then)m 439 2175 p (the)s 15(partial)m 14(deriv)m -2(ativ)m -1 r 101 c 14(of)m 15(the)m cmtt10.329 @sf 16 r 76 c cmr10.329 @sf (th)s 15(resp)m 1(onse)m 16(with)m 15(resp)m 1(ect)m 16(to)m cmmi10.329 @sf 15 r 12 c cmr6.300 @sf 1612 2182 p 75 c cmr10.329 @sf 1653 2175 p 119 c (as)s 439 2231 p (not)s 14 r 99 c (hec)s 107 c -1(ed)m 14 r 98 c 1(ecause)m cmmi10.329 @sf 16 r 12 c cmr6.300 @sf 880 2238 p 75 c cmr10.329 @sf 920 2231 p 119 c (as)s 14(\014xed.)m cmsy10.329 @sf 393 2298 p 15 c cmr10.329 @sf 23(If)m cmtt10.329 @sf 15(IWORK\(MSGBI+)m 76 c -2(+\()m 75 c (-1\)*NQ\))s cmr10.329 @sf 11 r 61 c 13 r 48 c 15(then)m 439 2354 p (the)s 16(partial)m 15(deriv)m -2(ativ)m -1 r 101 c 15(of)m 16(the)m cmtt10.329 @sf 16 r 76 c cmr10.329 @sf (th)s 16(resp)m 1(onse)m 17(with)m 16(resp)m 1(ect)m 17(to)m cmmi10.329 @sf 16 r 12 c cmr6.300 @sf 1621 2361 p 75 c cmr10.329 @sf 1662 2354 p (ap-)s 439 2411 p 112 c 1(ears)m 16(to)m 16 r 98 c 1 r 101 c 17(correct,)m 16(i.e.,)m 16(the)m 16(relativ)m 101 c 14(di\013erence)m 17 r 98 c 1(et)m 119 c (een)s 15(its)m 16 r 118 c -2(alue)m 439 2467 p (and)s 21(the)m 21(\014nite)m 21(di\013erence)m 21(appro)m (ximat)s -1(ion)m 19(it)m 20(is)m 20 r 99 c (hec)s 107 c -1(ed)m 20(against)m 19(is)m @eop %%Page: 93 107 93 @bop0 93 @bop1 cmr10.329 @sf 225 123 p 87 c -3(ork)m 14 r 86 c -3(ectors)m 1408(93)m 225 134 p 1725 2 ru 664 259 p (within)s 14(the)m 15(required)m 16(tolerance.)m cmsy10.329 @sf 618 325 p 15 c cmr10.329 @sf 23(If)m cmtt10.329 @sf 15(IWORK\(MSGBI+)m 76 c -2(+\()m 75 c (-1\)*NQ\))s cmr10.329 @sf 11 r 61 c 13 r 49 c 15(then)m 664 381 p (the)s 19(partial)m 18(deriv)m -2(ativ)m -1 r 101 c 17(of)m 19(the)m cmtt10.329 @sf 20 r 76 c cmr10.329 @sf (th)s 19(resp)m 1(onse)m 20(with)m 19(resp)m 1(ect)m 19(to)m cmmi10.329 @sf 19 r 12 c cmr6.300 @sf 1875 388 p 75 c cmr10.329 @sf 1919 381 p (is)s 664 438 p (questionable)s 17 r 98 c 1(ecause)m 20(the)m 19(user)m 18(supplied)m 19(deriv)m -2(ativ)m -1 r 101 c 17(and)m 18(the)m 19(\014nite)m 664 494 p (di\013erence)s 15 r 118 c -2(alue)m 14(it)m 15(is)m 15 r 99 c (hec)s 107 c -1(ed)m 13(against)m 14(are)m 15 r 98 c 1(oth)m 15(zero.)m cmsy10.329 @sf 618 560 p 15 c cmr10.329 @sf 23(If)m cmtt10.329 @sf 15(IWORK\(MSGBI+)m 76 c -2(+\()m 75 c (-1\)*NQ\))s cmr10.329 @sf 11 r 61 c 13 r 50 c 15(then)m 664 617 p (the)s 19(partial)m 18(deriv)m -2(ativ)m -1 r 101 c 17(of)m 19(the)m cmtt10.329 @sf 20 r 76 c cmr10.329 @sf (th)s 19(resp)m 1(onse)m 20(with)m 19(resp)m 1(ect)m 19(to)m cmmi10.329 @sf 19 r 12 c cmr6.300 @sf 1875 624 p 75 c cmr10.329 @sf 1919 617 p (is)s 664 673 p (questionable)s 22 r 98 c 1(ecause)m 23(either)m 23(the)m 23(user)m 22(supplied)m 23(deriv)m -2(ativ)m 101 c 20(is)m 23(ex-)m 664 730 p (actly)s 17(zero)m 17(and)m 18(the)m 18(\014nite)m 18(di\013erence)m 18 r 118 c -2(alue)m 17(it)m 17(is)m 18 r 99 c (hec)s 107 c -1(ed)m 16(against)m 16(is)m 664 786 p (only)s 14(appro)m (ximat)s -1(ely)m 13(zero,)m 15(or)m 14(the)m 15(user)m 15(supplied)m 15(deriv)m -2(ativ)m -1 r 101 c 13(only)m 15(ap-)m 664 843 p (pro)s (xima)s -1(tely)m 13(zero)m 16(and)m 16(and)m 15(the)m 16(\014nite)m 16(di\013erence)m 16 r 118 c -2(alue)m 14(it)m 15(is)m 15 r 99 c (hec)s 107 c (ed)s 664 899 p (against)s 13(is)m 15(exactly)m 15(zero.)m cmsy10.329 @sf 618 965 p 15 c cmr10.329 @sf 23(If)m cmtt10.329 @sf 15(IWORK\(MSGBI+)m 76 c -2(+\()m 75 c (-1\)*NQ\))s cmr10.329 @sf 11 r 61 c 13 r 51 c 15(then)m 664 1022 p (the)s 19(partial)m 18(deriv)m -2(ativ)m -1 r 101 c 17(of)m 19(the)m cmtt10.329 @sf 20 r 76 c cmr10.329 @sf (th)s 19(resp)m 1(onse)m 20(with)m 19(resp)m 1(ect)m 19(to)m cmmi10.329 @sf 19 r 12 c cmr6.300 @sf 1875 1029 p 75 c cmr10.329 @sf 1919 1022 p (is)s 664 1078 p (questionable)s 11 r 98 c 1(ecause)m 14(either)m 12(the)m 13(user)m 12(supplied)m 13(deriv)m -2(ativ)m -1 r 101 c 11(is)m 12(exactly)m 664 1135 p (zero)s 20(and)m 21(the)m 21(\014nite)m 21(di\013erence)m 20 r 118 c -2(alue)m 20(it)m 20(is)m 21 r 99 c (hec)s 107 c -1(ed)m 19(against)m 19(is)m 20(not)m 664 1191 p (ev)s (en)s 13(appro)m (xima)s -1(tely)m 12(zero,)m 13(or)m 13(the)m 14(user)m 14(supplied)m 14(deriv)m -2(ativ)m -1 r 101 c 12(not)m 14(ev)m (en)s 664 1248 p (appro)s (xima)s -1(tely)m 9(zero)m 10(and)m 11(and)m 11(the)m 11(\014nite)m 11(di\013erence)m 11 r 118 c -2(alue)m 10(it)m 10(is)m 10 r 99 c (hec)s 107 c (ed)s 664 1304 p (against)s 13(is)m 15(exactly)m 15(zero.)m cmsy10.329 @sf 618 1370 p 15 c cmr10.329 @sf 23(If)m cmtt10.329 @sf 15(IWORK\(MSGBI+)m 76 c -2(+\()m 75 c (-1\)*NQ\))s cmr10.329 @sf 11 r 61 c 13 r 52 c 15(then)m 664 1427 p (the)s 19(partial)m 18(deriv)m -2(ativ)m -1 r 101 c 17(of)m 19(the)m cmtt10.329 @sf 20 r 76 c cmr10.329 @sf (th)s 19(resp)m 1(onse)m 20(with)m 19(resp)m 1(ect)m 19(to)m cmmi10.329 @sf 19 r 12 c cmr6.300 @sf 1875 1434 p 75 c cmr10.329 @sf 1919 1427 p (is)s 664 1483 p (questionable)s 12 r 98 c 1(ecause)m 13(the)m 13(\014nite)m 12(di\013erence)m 13 r 118 c -2(alue)m 12(it)m 12(is)m 12 r 98 c 1(eing)m 12 r 99 c (hec)s 107 c (ed)s 664 1540 p (against)s 17(is)m 17(questionable)m 18(due)m 19(to)m 18 r 97 c 18(high)m 18(ratio)m 17(of)m 18(relativ)m -1 r 101 c 17(curv)m -2(ature)m 664 1596 p (to)s 14(relativ)m 101 c 13(slop)m 1 r 101 c 15(or)m 15(to)m 14(an)m 15(incorrect)m 15(scale)m 15 r 118 c -2(alue.)m cmsy10.329 @sf 618 1662 p 15 c cmr10.329 @sf 23(If)m cmtt10.329 @sf 15(IWORK\(MSGBI+)m 76 c -2(+\()m 75 c (-1\)*NQ\))s cmr10.329 @sf 11 r 61 c 13 r 53 c 15(then)m 664 1719 p (the)s 19(partial)m 18(deriv)m -2(ativ)m -1 r 101 c 17(of)m 19(the)m cmtt10.329 @sf 20 r 76 c cmr10.329 @sf (th)s 19(resp)m 1(onse)m 20(with)m 19(resp)m 1(ect)m 19(to)m cmmi10.329 @sf 19 r 12 c cmr6.300 @sf 1875 1726 p 75 c cmr10.329 @sf 1919 1719 p (is)s 664 1775 p (questionable)s 12 r 98 c 1(ecause)m 13(the)m 13(\014nite)m 12(di\013erence)m 13 r 118 c -2(alue)m 12(it)m 12(is)m 12 r 98 c 1(eing)m 12 r 99 c (hec)s 107 c (ed)s 664 1832 p (against)s 17(is)m 17(questionable)m 18(due)m 19(to)m 18 r 97 c 18(high)m 18(ratio)m 17(of)m 18(relativ)m -1 r 101 c 17(curv)m -2(ature)m 664 1888 p (to)s 14(relativ)m 101 c 13(slop)m 1(e.)m cmsy10.329 @sf 618 1954 p 15 c cmr10.329 @sf 23(If)m cmtt10.329 @sf 15(IWORK\(MSGBI+)m 76 c -2(+\()m 75 c (-1\)*NQ\))s cmr10.329 @sf 11 r 61 c 13 r 54 c 15(then)m 664 2011 p (the)s 24(partial)m 23(deriv)m -2(ativ)m -1 r 101 c 22(of)m 24(the)m cmtt10.329 @sf 25 r 76 c cmr10.329 @sf (th)s 24(resp)m 1(onse)m 25(with)m 23(resp)m 1(ect)m 25(to)m cmmi10.329 @sf 24 r 12 c cmr6.300 @sf 1925 2018 p 75 c cmr10.329 @sf 664 2067 p (is)s 24(questionable)m 25 r 98 c 1(ecause)m 26(it)m 24(do)m 1(es)m 25(not)m 25(agree)m 25(with)m 24(the)m 25(\014nite)m 25(dif-)m 664 2124 p (ference)s 22 r 118 c -2(alue)m 20(it)m 21(is)m 20 r 98 c 1(eing)m 22 r 99 c (hec)s 107 c -1(ed)m 20(against)m 19(to)m 21(the)m 21(required)m 22(toler-)m 664 2180 p (ance,)s 17(although)m 15(the)m 17 r 118 c -2(alues)m 16(do)m 16(agree)m 17(in)m 16(their)m 16(\014rst)m 16 r 116 c 119 c -1 r 111 c 15(digits.)m 23(\(See)m cmtt10.329 @sf 664 2237 p (IWORK\(NTOLI\))s cmr10.329 @sf 13 r 98 c 1(elo)m (w.\))s cmsy10.329 @sf 618 2303 p 15 c cmr10.329 @sf 23(If)m cmtt10.329 @sf 15(IWORK\(MSGBI+)m 76 c -2(+\()m 75 c (-1\)*NQ\))s cmr10.329 @sf 11 r 61 c 13 r 55 c 15(then)m 664 2359 p (the)s 19(partial)m 18(deriv)m -2(ativ)m -1 r 101 c 17(of)m 19(the)m cmtt10.329 @sf 20 r 76 c cmr10.329 @sf (th)s 19(resp)m 1(onse)m 20(with)m 19(resp)m 1(ect)m 19(to)m cmmi10.329 @sf 19 r 12 c cmr6.300 @sf 1875 2366 p 75 c cmr10.329 @sf 1919 2359 p (is)s 664 2416 p (seriously)s 13(questionable)m 13 r 98 c 1(ecause)m 15(it)m 14(has)m 14(few)m (er)s 12(than)m 14 r 116 c 119 c -1 r 111 c 12(digits)m 13(agree-)m @eop %%Page: 94 108 94 @bop0 94 @bop1 cmr10.329 @sf 0 123 p (94)s 1410 r 87 c -3(ork)m 13 r 86 c -3(ectors)m 0 134 p 1725 2 ru 439 259 p (men)s 116 c 13(with)m 15(the)m 15(\014nite)m 15(di\013erence)m 16 r 118 c -2(alue)m 14(it)m 15(is)m 14 r 98 c 1(eing)m 16 r 99 c (hec)s 107 c -1(ed)m 14(against.)m cmtt10.329 @sf 393 337 p (MSGBI)s cmr10.329 @sf 12 r 61 c 13 r 49 c 30 r 46 c 14 465 p 3 28 ru cmmi10.329 @sf 10 463 p 62 c cmtt10.329 @sf 39(IWORK\(MSGDI\))m cmr10.329 @sf 21(is)m 20(the)m 20(\014rst)m 19(elemen)m 116 c 19(of)m 19 r 97 c 20 r 49 c 13 r 43 c 14 r 40 c cmmi10.329 @sf 113 c cmsy10.329 @sf 14 r 2 c cmmi10.329 @sf 14 r 109 c cmr10.329 @sf 41 c 20(arra)m -1 r 121 c cmtt10.329 @sf 18(MSGD)m cmr10.329 @sf 20(used)m 20(to)m 19(indicate)m 393 519 p (the)s 21(results)m 20(of)m 21 r 99 c (hec)s (king)s 19(the)m 21(partial)m 19(deriv)m -2(ativ)m -1(es)m 19(with)m 21(resp)m 1(ect)m 21(to)m 20(\001,)m 393 575 p (analagous)s 18(to)m cmtt10.329 @sf 19(MSGB)m cmr10.329 @sf 18(describ)m 1(ed)m 20(ab)m 1 r 111 c 118 c (e.)s 30(The)m 19 r 118 c -2(alues)m 18(in)m cmtt10.329 @sf 19(MSGD)m cmr10.329 @sf 19(ha)m 118 c -1 r 101 c 18(the)m 393 632 p (same)s 22(meanings)m 22(as)m 22(those)m 21(used)m 23(to)m 22(indicate)m 21(the)m 23(results)m 21(of)m 22 r 99 c (hec)s (king)s 393 688 p (the)s 19(partial)m 16(deriv)m -2(ativ)m (es)s 16(with)m 18(resp)m 1(ect)m 19(to)m cmmi10.329 @sf 18 r 12 c cmr10.329 @sf 2 r 44 c 19(except)m 18(that)m 18(the)m 19 r 118 c -2(alue)m 17(of)m cmtt10.329 @sf 393 745 p (IWORK\(MSGDI\))s cmr10.329 @sf 9(summarizes)m 10(the)m 11(results)m 10 r 111 c 118 c -1(er)m 9(all)m 9(columns)m 11(of)m 10(\001,)m 11(and)m 11(the)m 393 801 p 118 c -2(alues)m 18(of)m cmtt10.329 @sf 18(IWORK\(MSGDI+)m 76 c -2(+\()m 74 c -1(-1\)*NQ\))m cmmi10.329 @sf 59 c cmtt10.329 @sf 25 r 76 c cmr10.329 @sf 18 r 61 c 18 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 8 r 58 c 5 r 59 c 8 r 113 c 2 r 59 c cmtt10.329 @sf 25 r 74 c cmr10.329 @sf 17 r 61 c 19 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 7 r 58 c 5 r 59 c 8 r 109 c cmr10.329 @sf 44 c 393 858 p (indicates)s 13(the)m 13(individual)m 13(results)m 13(for)m 12 r 99 c (hec)s (king)s 12(the)m 13(partial)m 12(deriv)m -2(ativ)m -1 r 101 c 11(of)m 393 914 p (the)s cmtt10.329 @sf 13 r 76 c cmr10.329 @sf (th)s 12(resp)m 1(onse)m 13(with)m 12(resp)m 1(ect)m 13(to)m 11(the)m cmtt10.329 @sf 13 r 74 c cmr10.329 @sf (th)s 12(column)m 12(of)m 12 r 1 c 13(at)m 12(observ)m -2(ation)m cmtt10.329 @sf 393 971 p (NROW)s cmr10.329 @sf 46 c 14(\(See)m cmtt10.329 @sf 16(IWORK\(NROWI\))m cmr10.329 @sf 13 r 98 c 1(elo)m (w.\))s cmtt10.329 @sf 393 1037 p (MSGDI)s cmr10.329 @sf 12 r 61 c cmmi10.329 @sf 13 r 113 c 2 r 112 c cmr10.329 @sf 10 r 43 c 10 r 50 c 30 r 46 c 14 1164 p 3 28 ru cmmi10.329 @sf 10 1162 p 62 c cmtt10.329 @sf 15(IWORK\(IFIX2I\))m cmr10.329 @sf 21(is)m 18(the)m 19(\014rst)m 18(elemen)m 116 c 17(of)m 19 r 97 c cmmi10.329 @sf 18 r 112 c cmsy10.329 @sf 12 r 2 c cmr10.329 @sf 13 r 49 c 18(arra)m 121 c cmtt10.329 @sf 16(IFIX2)m cmr10.329 @sf 18(con)m (taining)s 17 r 118 c -2(alues)m 17(used)m 393 1219 p (to)s 16(indicate)m 15(whether)m 16 r 97 c 16(giv)m (en)s 15(parameter)m 15(is)m 16(un\014xed,)m 17(\014xed)m 16(or)m 16(dropp)m 1(ed)m 393 1275 p 98 c 1(ecause)m 16(it)m 15(induced)m 16(rank)m 15(de\014ciency)m -3 r 44 c 15(where)m cmtt10.329 @sf 393 1341 p (WORK\(IFIX2I-1+)s 75 c -2 r 41 c cmr10.329 @sf 15 r 61 c cmtt10.329 @sf 16(IFIX2\()m 75 c -1 r 41 c cmr10.329 @sf 393 1408 p (for)s cmtt10.329 @sf 15 r 75 c cmr10.329 @sf 12 r 61 c 13 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 7 r 58 c 6 r 59 c 8(p:)m cmr10.329 @sf 14(If)m cmsy10.329 @sf 393 1474 p 15 c cmtt10.329 @sf 23(IFIX2\()m 75 c -1 r 41 c cmr10.329 @sf 12 r 61 c 48 r 49 c 15(the)m 16(parameter)m 14 r 119 c (as)s 13(un\014xed,)m cmsy10.329 @sf 393 1540 p 15 c cmtt10.329 @sf 23(IFIX2\()m 75 c -1 r 41 c cmr10.329 @sf 12 r 61 c 48 r 48 c 15(the)m 16(parameter)m 14 r 119 c (as)s 13(\014xed,)m cmsy10.329 @sf 393 1606 p 15 c cmtt10.329 @sf 23(IFIX2\()m 75 c -1 r 41 c cmr10.329 @sf 12 r 61 c cmsy10.329 @sf 13 r 0 c cmr10.329 @sf 49 c 15(the)m 16(parameter)m 14 r 119 c (as)s 13(dropp)m 1(ed,)m 16(and)m cmsy10.329 @sf 393 1673 p 15 c cmtt10.329 @sf 23(IFIX2\()m 75 c -1 r 41 c cmr10.329 @sf 12 r 61 c cmsy10.329 @sf 13 r 0 c cmr10.329 @sf 50 c 15(no)m 15(parameters)m 15 r 119 c (ere)s 14(estimated.)m cmtt10.329 @sf 393 1739 p (IFIX2I)s cmr10.329 @sf 12 r 61 c cmmi10.329 @sf 13 r 113 c 2 r 112 c cmr10.329 @sf 10 r 43 c cmmi10.329 @sf 10 r 113 c 2 r 109 c cmr10.329 @sf 10 r 43 c 11 r 51 c 30 r 46 c 14 1866 p 3 28 ru cmmi10.329 @sf 10 1864 p 62 c cmtt10.329 @sf 15(IWORK\(ISTOPI\))m cmr10.329 @sf 21(is)m 15 r 118 c -2(alue)m 14(of)m cmtt10.329 @sf 15(ISTOP)m cmr10.329 @sf 14(returned)m 16(from)m 15(the)m 15(last)m 14(call)m 14(to)m 15(subroutine)m cmtt10.329 @sf 15(FCN)m cmr10.329 @sf 46 c cmtt10.329 @sf 393 1930 p (ISTOPI)s cmr10.329 @sf 12 r 61 c cmmi10.329 @sf 13 r 113 c 2 r 112 c cmr10.329 @sf 10 r 43 c cmmi10.329 @sf 10 r 113 c 2 r 109 c cmr10.329 @sf 10 r 43 c cmmi10.329 @sf 11 r 112 c cmr10.329 @sf 10 r 43 c 10 r 51 c 30 r 46 c cmtt10.329 @sf 84 2056 p (IWORK\(NNZWI\))s cmr10.329 @sf 21(is)m 15(the)m 15 r 110 c (um)s 98 c 1(er)m 14(of)m 14(nonzero)m cmmi10.329 @sf 16 r 15 c cmr10.329 @sf 15(error)m 15 r 119 c (eigh)s -1(ts,)m cmmi10.329 @sf 12 r 119 c cmmi8.300 @sf 1251 2063 p 15 c cmr6.300 @sf 1265 2069 p 73 c cmmi10.329 @sf 1279 2056 p 59 c cmtt10.329 @sf 23 r 73 c cmr10.329 @sf 12 r 61 c 13 r 49 c cmmi10.329 @sf 59 c 8 r 58 c 8 r 58 c 8 r 58 c 5 r 59 c 8 r 110 c cmr10.329 @sf 46 c cmtt10.329 @sf 108 2181 p (IWORK\(NPPI\))s cmr10.329 @sf 21(is)m 19(the)m 20 r 110 c (um)s 98 c 1(er)m 21 r 126 c cmmi10.329 @sf -26 r 112 c cmr10.329 @sf 19(of)m 19(function)m 19(parameters)m 19(actually)m 18 r 98 c 1(eing)m 20(estimated,)m 393 2237 p (i.e.,)s 14(the)m 15 r 110 c (um)s 98 c 1(er)m 14(of)m 15(un\014xed)m 16(parameters.)m cmtt10.329 @sf 108 2363 p (IWORK\(IDFI\))s cmr10.329 @sf 21(is)m 16(the)m 16(degrees)m 16(of)m 15(freedom,)m cmmi10.329 @sf 16 r 22 c cmr10.329 @sf 44 c 16(of)m 16(the)m 16(\014t,)m 15(i.e.,)m 15(the)m 16 r 110 c (um)s 98 c 1(er)m 14(of)m 16(observ)m -2(a-)m 393 2419 p (tions)s 11(with)m 10(nonzero)m 11 r 119 c (eigh)s (t)s -1 r 115 c 9(min)m (us)s 10(the)m 11 r 110 c (um)s 98 c 1(er)m 10(of)m 11(parameters)m 10(actually)m @eop %%Page: 95 109 95 @bop0 95 @bop1 cmr10.329 @sf 225 123 p 87 c -3(ork)m 14 r 86 c -3(ectors)m 1408(95)m 225 134 p 1725 2 ru 618 259 p 98 c 1(eing)m 16(estimated.)m cmtt10.329 @sf 333 384 p (IWORK\(JOBI\))s cmr10.329 @sf 21(is)m 11(the)m 11 r 118 c -2(alue)m 11(used)m 12(to)m 10(sp)m 1(ecify)m 12(problem)m 11(initializat)m -1(ion)m 9(and)m 12(computational)m 618 440 p (metho)s 1(ds.)m cmtt10.329 @sf 285 566 p (IWORK\(IPRINI\))s cmr10.329 @sf 21(is)m 15(the)m 15(prin)m 116 c 14(con)m (trol)s 12 r 118 c -2(alue)m 15(used.)m cmtt10.329 @sf 285 691 p (IWORK\(LUNERI\))s cmr10.329 @sf 21(is)m 15(the)m 15(logical)m 14(unit)m 14 r 110 c (um)s 98 c 1(er)m 14(used)m 16(for)m 14(error)m 15(rep)m 1(orts.)m cmtt10.329 @sf 285 816 p (IWORK\(LUNRPI\))s cmr10.329 @sf 21(is)m 15(the)m 15(logical)m 14(unit)m 14 r 110 c (um)s 98 c 1(er)m 14(used)m 16(for)m 14(computation)m 14(rep)m 1(orts.)m cmtt10.329 @sf 309 942 p (IWORK\(NROWI\))s cmr10.329 @sf 21(is)m 15(the)m 15(observ)m -2(ation)m cmtt10.329 @sf 14(NROW)m cmr10.329 @sf 14(at)m 15(whic)m 104 c 14(the)m 15(deriv)m -2(ativ)m -1(es)m 14 r 119 c (ere)s 13 r 99 c (hec)s 107 c -1(ed.)m cmtt10.329 @sf 309 1067 p (IWORK\(NTOLI\))s cmr10.329 @sf 21(is)m 12(the)m 12 r 110 c (um)s 98 c 1(er)m 11(of)m 12(digits)m 11(of)m 12(agreemen)m 116 c 10(required)m 13 r 98 c 1(et)m 119 c -1(een)m 11(the)m 13 r 110 c (umerical)s 618 1123 p (deriv)s -2(ativ)m -1(es)m 17(and)m 18(the)m 18(user)m 19(supplied)m 19(deriv)m -2(ativ)m -1(es)m 16(for)m 18(the)m 18(user)m 19(supplied)m 618 1180 p (deriv)s -2(ativ)m -1(es)m 13(to)m 15 r 98 c 1 r 101 c 16(considered)m 16(correct.)m cmtt10.329 @sf 309 1305 p (IWORK\(NETAI\))s cmr10.329 @sf 21(is)m 13(the)m 13 r 110 c (um)s -1 r 98 c 1(er)m 12(of)m 12(go)m 1 r 111 c 1 r 100 c 13(digits)m 12(in)m 13(the)m 13(function)m 12(results)m 13(returned)m 13 r 98 c 121 c 12(user)m 618 1361 p (supplied)s 16(subroutine)m cmtt10.329 @sf 15(FCN)m cmr10.329 @sf -1 r 46 c cmtt10.329 @sf 285 1487 p (IWORK\(MAXITI\))s cmr10.329 @sf 21(is)m 15(the)m 15(maxim)m (um)s 13 r 110 c (um)s 98 c 1(er)m 14(of)m 15(iterations)m 13(allo)m -1 r 119 c -1(ed.)m cmtt10.329 @sf 285 1612 p (IWORK\(NITERI\))s cmr10.329 @sf 21(is)m 15(the)m 15 r 110 c (um)s 98 c 1(er)m 14(of)m 14(iterations)m 14(tak)m (en.)s cmtt10.329 @sf 309 1737 p (IWORK\(NFEVI\))s cmr10.329 @sf 21(is)m 15(the)m 15 r 110 c (um)s 98 c 1(er)m 14(of)m 14(function)m 15(ev)m -2(aluations)m 14(made.)m cmtt10.329 @sf 309 1863 p (IWORK\(NJEVI\))s cmr10.329 @sf 21(is)m 15(the)m 15 r 110 c (um)s 98 c 1(er)m 14(of)m 14(Jacobian)m 15(matrix)m 14(ev)m -2(aluations)m 14(made.)m cmtt10.329 @sf 309 1988 p (IWORK\(INT2I\))s cmr10.329 @sf 21(is)m 14(the)m 14 r 110 c (um)s 98 c 1(er)m 12(of)m 14(in)m (ternal)s 12(doubling)m 13(steps)m 14(tak)m (en)s 13(at)m 13(the)m 14(time)m 14(the)m 14(com-)m 618 2044 p (putations)s 14(stopp)m 1(ed.)m cmtt10.329 @sf 285 2170 p (IWORK\(IRANKI\))s cmr10.329 @sf 21(is)m 15(the)m 15(rank)m 15(de\014ciency)m 16(at)m 15(the)m 15(solution.)m cmtt10.329 @sf 309 2295 p (IWORK\(LDTTI\))s cmr10.329 @sf 21(is)m 15(the)m 15(leading)m 15(dimension)m 15(of)m 14(the)m cmmi10.329 @sf 16 r 110 c cmsy10.329 @sf 10 r 2 c cmmi10.329 @sf 10 r 109 c cmr10.329 @sf 16(arra)m -1 r 121 c cmtt10.329 @sf 13(TT)m cmr10.329 @sf 46 c 15(\(See)m cmsy10.329 @sf 15 r 120 c cmr10.329 @sf 1(5.A.\))m @eop %%Page: 96 110 96 @bop0 96 @bop1 cmr10.329 @sf 0 123 p (96)s 1410 r 87 c -3(ork)m 13 r 86 c -3(ectors)m 0 134 p 1725 2 ru @eop %%Page: 97 111 97 @bop0 cmcsc10.518 @sf [ 48 49 -4 0 55.291] 66 @dc cmti10.329 @sf [ 32 33 -3 1 25.555] 83 @dc [ 32 31 -3 0 29.671] 70 @dc [ 40 31 -2 0 33.787] 88 @dc [<1F80003FF00070F800603C00E01E00E00F00F00F00780F80780780300780000780000780000780 000780000F0000FE0000FF000007800001C00000E007C0F007E070066070067078067038076038 03803803C07001F0F0007FE0001F80> 24 31 -4 1 23.232] 51 @dc [<7E0000FF8000E3C000E0E000F07000F07800703C00001E00001E00000F00010F000FFF800FFF80 1E1F801C0F801C07C03C07C03C03C03E03C01E03E01E01E01E01E01F01E00F01E00F00E00780E0 0780E003C1C001F3C0007F80003F00> 24 31 -5 1 23.232] 57 @dc [ 16 30 -5 0 23.232] 49 @dc [<03C00003C00003E00003E00003E00001E00001F00001F00000F00000F00000F800007800007800 003C00003C00001C00001E00000E00000F00000700000700C00380E003807001C07801C03C07E0 3F1FE01FFCF01FFC701FF8380CF818> 24 31 -6 1 23.232] 55 @dc cmr10.329 @sf [<007FFE00007FFE000003C0000003C0000003C0000003C0000003C0000003C0000003C0000003C0 000003C0000003C0000003C0000007C0000007E000000FF000001F3000001E3800003E1800003C 0C00007C0C0000F8060000F0070001F0030001E0038003E0018007C001C0078000E00F8001F0FF F007FFFFF007FF> 32 31 -1 0 34.090] 89 @dc cmti10.329 @sf [<1F80007FE00071F000E0F800F87C00F83C00F83C00783E00381E00001E00001E00001F00000F00 000F00000F00000F800007800007800007800007C00003C00003C00003C00003E00001E00001E0 0001E00001F00000F00000F0001FFF001FFF> 24 32 -3 1 23.863] 74 @dc cmr10.329 @sf [<0601800006018000060180000701C0000300C0000300C0000300C0000300C0000380E000018060 0001806000018060000180600001C07000FFFFFFFEFFFFFFFE0060180000601800006018000060 180000701C0000300C0000300C0000300C00FFFFFFFEFFFFFFFE00180600001C0700000C030000 0C0300000C0300000C0300000E038000060180000601800006018000060180000701C0000300C0 000300C0000300C0> 32 41 -3 9 37.878] 35 @dc [ 32 31 -1 0 34.090] 88 @dc cmti10.329 @sf [ 24 31 -3 0 17.525] 73 @dc [ 48 31 -3 0 40.756] 77 @dc [ 32 31 -3 0 30.832] 69 @dc 97 @bop1 cmcsc10.518 @sf 225 519 p (Bibliography)s cmr10.329 @sf 248 746 p ([1])s 21(American)m 12(National)m 11(Standards)m 12(Institute)m 11(\(1977\),)m cmti10.329 @sf 11(ANS)m 12 r 70 c (OR)s -2(T)m -1(RAN)m 11(X3.9-1977)m cmr10.329 @sf 44 c 14(Amer-)m 318 802 p (ican)s 15(National)m 14(Standards)m 15(Institute,)m 14(New)m 16 r 89 c -3(ork,)m 13(NY.)m 248 896 p ([2])s 21(Bates,)m 24(D.)m 22(M.,)m 24(and)m 22(D.)m 22(G.)m 22 r 87 c -3(atts)m 21(\(1988\),)m cmti10.329 @sf 22(Nonline)m -2(ar)m 22 r 82 c -1 r 101 c -2(gr)m -2(es)m -1(sion)m 21 r 65 c (nalysis)s 20(and)m 23(its)m 318 952 p (Applic)s -1(ations)m cmr10.329 @sf 44 c 13(John)m 16(Wiley)m 14(and)m 16(Sons,)m 15(New)m 15 r 89 c -3(ork,)m 13(NY.)m 248 1046 p ([3])s 21(Belsley)m -3 r 44 c 21(D.)m 21(A.,)m 21(E.)m 21(Kuh,)m 23(and)m 21(R.)m 21(E.)m 20 r 87 c -3(elsc)m 104 c 19(\(1980\),)m cmti10.329 @sf 20 r 82 c -1 r 101 c -1(gr)m -3(ession)m 19(diagnostics,)m cmr10.329 @sf 21(John)m 318 1102 p (Wiley)s 15(and)m 15(Sons,)m 15(New)m 15 r 89 c -3(ork,)m 14(NY.)m 248 1196 p ([4])s 21(Bemen)m (t,)s 13(T.)m 12(R.,)m 13(and)m 13(J.)m 13(S.)m 13(Williams)m 10(\(1969\),)m 12(\\V)m -3(aria)m -1(nce)m 12(of)m 13 r 119 c (eigh)s -1(t)m -1(ed)m 12(regression)m 12(estima-)m 318 1253 p (tors)s 12(when)m 13(sampling)m 12(errors)m 12(are)m 12(indep)m 1(enden)m 116 c 13(and)m 13(heteroscedastic,")m cmti10.329 @sf 12(J.)m 14 r 65 c (mer.)s 13(Statists.)m 318 1309 p (Asso)s -1(c.)m cmr10.329 @sf 44 c 13(64:1369-138)m -1(2.)m 248 1403 p ([5])s 21(Bisc)m (hof,)s 17(C.,)m 17(A.)m 17(Carle,)m 17(G.)m 16(Corliss,)m 16(A.)m 18(Griew)m -1(ank,)m 16 r 80 c -3 r 46 c 16(Ho)m (vland)s 16(\(1991\),)m 16(\\ADIF)m (OR)s 17 r 124 c 318 1459 p (generating)s 15(deriv)m -2(ativ)m 101 c 14(co)m 1(des)m 16(from)m 15 r 70 c -3(ortran)m 14(programs,")m 14(ADIF)m (OR)s 15 r 87 c -3(orking)m 14(Note)m 16(#1,)m 318 1516 p (MCS-P263-0991,)s 14(Mathematics)m 15(and)m 16(Computer)m 15(Science)m 17(Division,)m 15(Argonne)m 16(National)m 318 1572 p (Lab)s 1(oratory)m -3 r 44 c 18(Argonne,)m 19(IL;)m 20(also)m 17 r 97 c 118 c -2(ail)m -1(able)m 17(as)m 18(CRPC-TR91185,)m 19(Cen)m (ter)s 17(for)m 18(Researc)m 104 c 318 1629 p (on)s 16 r 80 c (ara)s -1(llel)m 13(Computation,)m 13(Rice)m 16(Univ)m (ersit)s -2 r 121 c -3 r 44 c 12(Houston,)m 15(TX.)m 248 1723 p ([6])s 21(Boggs,)m 14 r 80 c -3 r 46 c 14(T.,)m 14(R.)m 15(H.)m 14(Byrd,)m 15(and)m 15(R.)m 15(B.)m 15(Sc)m (hnab)s 1(el)m 15(\(1987\),)m 12(\\A)m 15(stable)m 14(and)m 15(e\016cien)m 116 c 14(algo-)m 318 1779 p (rithm)s 16(for)m 17(nonlinear)m 16(orthogonal)m 15(distance)m 16(regression,")m cmti10.329 @sf 16(SIAM)m 16(J.)m 18(Sci.)m 17(Stat.)m 18(Comput.)m cmr10.329 @sf 44 c 318 1836 p (8\(6\):1052-10)s -1(78.)m 248 1929 p ([7])s 21(Boggs,)m 13 r 80 c -3 r 46 c 12(T.,)m 13(R.)m 13(H.)m 13(Byrd,)m 14(J.)m 13(R.)m 14(Donaldson,)m 12(and)m 14(R.)m 13(B.)m 13(Sc)m (hnab)s 1(el)m 13(\(1989\),)m 12(\\Algorithm)m 318 1986 p (676)s 12 r 124 c 13(ODRP)m -3 r 65 c (CK:)s 11(Soft)m 119 c -1(are)m 11(for)m 12 r 87 c -3(eigh)m -1(ted)m 11(Orthogonal)m 12(Distance)m 12(Regression,")m cmti10.329 @sf 12 r 65 c (CM)s 318 2042 p 84 c -2 r 114 c -2(ans.)m 14(Math.)m 16(Softwar)m -1 r 101 c cmr10.329 @sf 44 c 14(15\(4\):348-3)m -1(64.)m 248 2136 p ([8])s 21(Boggs,)m 16 r 80 c -3 r 46 c 15(T.,)m 16(J.)m 17(R.)m 16(Donaldson,)m 16(R.)m 17(B.)m 16(Sc)m (hnab)s 1(el,)m 16(and)m 17(C.)m 16(H.)m 16(Spiegelman)m 16(\(1988\),)m 15(\\A)m 318 2193 p (computational)s 19(examination)m 19(of)m 20(orthogonal)m 18(distance)m 20(regression,")m cmti10.329 @sf 20(J.)m 21(Ec)m -1(onometrics)m cmr10.329 @sf 44 c 318 2249 p (38\(1/2\):16)s -1(9-201.)m 248 2343 p ([9])s 21(Boggs,)m 17 r 80 c -3 r 46 c 16(T.,)m 17(and)m 17(J.)m 17(E.)m 17(Rogers)m 17(\(1990a\),)m 15(\\Orthogonal)m 16(Distance)m 17(Regression,")m cmti10.329 @sf 16(Con-)m 318 2399 p (temp)s -1(or)m -1(ary)m 15(Mathematics)m cmr10.329 @sf 44 c 15(112:183-194.)m 1065 2581 p (97)s @eop %%Page: 98 112 98 @bop0 cmti10.329 @sf [ 24 20 -2 0 18.585] 122 @dc [ 8 20 -5 0 13.939] 58 @dc 98 @bop1 cmr10.329 @sf 0 114 p (98)s 1424(Bibliograph)m 121 c 0 134 p 1725 2 ru 0 259 p ([10])s 21(Boggs,)m 13 r 80 c -3 r 46 c 12(T.,)m 13(and)m 14(J.)m 13(E.)m 13(Rogers)m 13(\(1990b\),)m 12(\\The)m 13(Computation)m 12(and)m 14(Use)m 13(of)m 13(the)m 14(Asymp-)m 93 315 p (totic)s 13(Co)m 118 c -2(ar)m -1(iance)m 12(Matrix)m 12(for)m 13(Measuremen)m 116 c 13(Error)m 12(Mo)m 1(dels,")m 13(In)m (ternal)s 13(Rep)m 1(ort)m 14(89-4102,)m 93 372 p (Applied)s 13(and)m 12(Computational)m 10(Mathematics)m 10(Division,)m 11(National)m 10(Institute)m 12(of)m 11(Standards)m 93 428 p (and)s 16 r 84 c -3(ec)m (hnolog)s -1 r 121 c -3 r 44 c 12(Gaithersburg,)m 14(MD.)m 0 518 p ([11])s 21(Co)m 1(ok,)m 22(D.)m 20(R.)m 21(\(1977\),)m 20(\\Detection)m 19(of)m 21(in\015uen)m (tial)s 19(observ)m -2(ations)m 19(in)m 20(linear)m 20(regression,")m cmti10.329 @sf 93 574 p 84 c -2 r 101 c -2(chnometrics,)m cmr10.329 @sf 13(19:15-18.)m 0 664 p ([12])s 21(Dennis,)m 19(J.)m 19(E.,)m 18(and)m 19(R.)m 18(B.)m 18(Sc)m (hnab)s 1(el)m 18(\(1983\),)m cmti10.329 @sf 18(Numeric)m -1(al)m 18(Metho)m -1(ds)m 18(for)m 19(Unc)m -1(ons)m -1(tr)m -2(aine)m -2 r 100 c 93 721 p (Optimization)s 17(and)m 16(Nonline)m -2(ar)m 15(Equations)m cmr10.329 @sf 44 c 14(Pren)m (tice-Hall,)s 13(Englew)m 111 c 1 r 111 c 1 r 100 c 14(Cli\013s,)m 13(NJ.)m 0 811 p ([13])s 21(Donaldson,)m 19(J.)m 20(R.,)m 19(and)m 20(Sc)m (hnab)s 1(el,)m 19(R.)m 20(B.)m 19(\(1987\),)m 18(\\Computational)m 16(Exp)m 1(erience)m 21(with)m 93 867 p (Con\014dence)s 18(Regions)m 16(and)m 17(Con\014dence)m 17(In)m (terv)s -2(als)m 14(for)m 16(Nonlinear)m 16(Least)m 16(Squares,")m cmti10.329 @sf 16 r 84 c -2 r 101 c -2(c)m -1(h-)m 93 924 p (nometrics)s cmr10.329 @sf 44 c 15(29\(1\):67)m -1(-82.)m 0 1014 p ([14])s 21(Donaldson,)m 12(J.)m 13(R.,)m 13(and)m 13 r 80 c -3 r 46 c 11(V.)m 13 r 84 c -3(ry)m -1(on)m 11(\(1986\),)m 11(\\ST)m -3(ARP)m -3 r 65 c -1 r 67 c 11 r 45 c 13(the)m 12(Standards)m 13(Time)m 12(Series)m 93 1070 p (and)s 14(Regression)m 13 r 80 c (ac)s 107 c -3(age,)m -1 r 34 c 12(In)m (ternal)s 12(Rep)m 1(ort)m 14(86-3448,)m 12(Computing)m 12(and)m 14(Applied)m 13(Math-)m 93 1126 p (ematics)s 13(Lab)m 1(oratory)m -3 r 44 c 11(National)m 11(Institute)m 13(of)m 12(Standards)m 13(and)m 13 r 84 c -3(ec)m (hnology)s -4 r 44 c 11(Boulder,)m 13(CO.)m 0 1216 p ([15])s 21(Dongarra,)m 15(J.)m 16(J.,)m 16(C.)m 16(B.)m 16(Moler,)m 15(J.)m 16(R.)m 17(Bunc)m (h,)s 16(and)m 16(G.)m 16(W.)m 15(Stew)m (art)s 14(\(1979\),)m cmti10.329 @sf 15(LINP)m -3 r 65 c -2(CK)m 93 1273 p (Users')s 16(Guide)m cmr10.329 @sf 44 c 15(SIAM,)m 15(Philadelphia,)m 14 r 80 c -3(A.)m 0 1363 p ([16])s 21(Efron,)m 12(B.)m 11(\(1985\),)m cmti10.329 @sf 10(The)m 12(Jackknife,)m 13(the)m 13(Bo)m -1(otstr)m -2(ap)m 12(and)m 12(Other)m 13 r 82 c -1(esampling)m 11(Plans,)m cmr10.329 @sf 11(SIAM,)m 93 1419 p (Philadelphia,)s 14 r 80 c -3(A.)m 0 1509 p ([17])s 21(Fillib)m 1(en,)m 19(J.)m 19(J.)m 19(\(1977\),)m 18(\\User's)m 19(Guide)m 19(to)m 18(the)m 19 r 68 c 65 c -3 r 84 c -4(AP)m -4 r 65 c -1 r 67 c 17(Data)m 18(Analysis)m 18 r 80 c (ac)s -1 r 107 c -2(ag)m -1(e,")m 93 1566 p (\(unpublished:)s 21 r 97 c 118 c -3(ail)m -1(able)m 12(from)m 14(NIST)m 14(Statistical)m 12(Engineering)m 14(Division,)m 12(Gaithersburg,)m 93 1622 p (MD\).)s 0 1712 p ([18])s 21 r 70 c -3 r 111 c (x,)s 16 r 80 c -3 r 46 c 16(A.,)m 18(A.)m 18(D.)m 17(Hall,)m 17(and)m 18(N.)m 17(L.)m 18(Sc)m (hry)s (er)s 16(\(1978\),)m 16(\\Algorithm)m 16(528)m 17 r 124 c 18 r 70 c -3(ramew)m -1(ork)m 93 1769 p (for)s 15 r 97 c 15 r 80 c (orta)s -1(ble)m 14(Library)m 14([z],")m cmti10.329 @sf 14 r 65 c (CM)s 15 r 84 c -2 r 114 c -3(ans.)m 14(Math.)m 17(Softwar)m -1 r 101 c cmr10.329 @sf 44 c 13(4\(2\):177-188)m -1 r 46 c 0 1858 p ([19])s 21 r 70 c -3(uller,)m 12(W.)m 11(A.)m 13(\(1987\),)m cmti10.329 @sf 11(Me)m -1(asur)m -2(ement)m 12(Err)m -1(or)m 13(Mo)m -1(dels)m cmr10.329 @sf 44 c 10(John)m 13(Wiley)m 12(and)m 13(Sons,)m 13(New)m 13 r 89 c -3(ork,)m 93 1915 p (NY.)s 0 2005 p ([20])s 21(Gill,)m 11 r 80 c -3 r 46 c 10(E.,)m 12(W.)m 11(Murra)m 121 c -4 r 44 c 10(and)m 12(M.)m 11(H.)m 11 r 87 c -3(righ)m -1 r 116 c 9(\(1981\),)m cmti10.329 @sf 11(Pr)m -1(actic)m -2(al)m 11(Optimization)m cmr10.329 @sf 44 c 12(Academic)m 93 2061 p (Press,)s 15(New)m 15 r 89 c -3(ork,)m 14(NY.)m 0 2151 p ([21])s 21(Griew)m (ank,)s 19(A.)m 19(\(1989\),)m 18(\\On)m 20(automatic)m 18(di\013eren)m (tiati)s -1(on,")m 18(in)m cmti10.329 @sf 20(Mathematic)m -1(al)m 19(Pr)m -1 r 111 c -1(g)m -1 r 114 c -2(am-)m 93 2208 p (ming:)s 38 r 82 c -1 r 101 c -2 r 99 c -2(e)m -1(nt)m 23(Developments)m 24(and)m 24(Applic)m -1(ations)m cmr10.329 @sf 44 c 24(M.)m 24(Iri)m 24(and)m 24(K.)m 25 r 84 c -3(anab)m 1(e,)m 25(editors,)m 93 2264 p (Klu)s 119 c (er)s 13(Academic)m 15(Publishers,)m 15(Amsterdam,)m 14(Holland.)m 0 2354 p ([22])s 21(Ha)m (vrilia)s -1(k,)m 22(S.)m 23(Jr.,)m 24(and)m 23(S.)m 22(Negami)m 22(\(1967\),)m 22(\\A)m 23(Complex)m 22(Plane)m 22(Represen)m (tation)s 21(of)m 93 2411 p (Dielectric)s 18(and)m 19(Mec)m (hanical)s 17(Relaxation)m 18(Pro)m 1(cesses)m 19(in)m 19(Some)m 18 r 80 c (olymers,")s cmti10.329 @sf 17(Polymer)m cmr10.329 @sf 44 c 20(8:)m 93 2467 p (161-205.)s @eop %%Page: 99 113 99 @bop0 cmti10.329 @sf [<0C000C0000000E000C0000000E000E0000000F000E0000000F000F0000000F801F0000000F801F 8000000FC01FC000000FC01EC000000F601EE000000F601E6000000F301E3000000F301E300000 0F181E1800000F181E1800000F0C1E0C00000F0C1E0C00000F061E0600000F061E0600000F031E 0300000F031E0300000F019E0180001F01DE0180001E00DE00C0001E00FE00C0001E007E006000 1E003E0060001E003E0030001E001E0038001F001F007C00FFF0FFE1FF80FFF0FFE1FF80> 48 32 -9 1 45.403] 87 @dc [<7E07C000007F0FF00000FF1F7800007B8F1C0000718E1C000001C00E000001C00E000001C00F00 0000E007000000E007000000E007000000E007800000F003800000700380000070038000007003 8000007003C000007801C000003801C000003801C000003801C000003801E000003C00E000001C 00E000001C00E000001C00E000001C00E00001FFFFFF0001FFFFFF80000E007000000E00700000 0E007000000E007800000F00380000070038000007003800000707BCF00003879CF00003C79EF0 0001FF8FF000007F07E0> 40 41 2 9 27.878] 11 @dc 99 @bop1 cmr10.329 @sf 225 114 p (Bibliograph)s 121 c 1422(99)m 225 134 p 1725 2 ru 225 259 p ([23])s 21(Himmelblau,)m 20(D.)m 19(M.)m 18(\(1970\),)m cmti10.329 @sf 19(Pr)m -1 r 111 c -2 r 99 c -2(es)m -1 r 115 c 18 r 65 c (nalysis)s 18(by)m 20(Statistic)m -1(al)m 18(Metho)m -1(ds)m cmr10.329 @sf 44 c 19(John)m 20(Wiley)m 318 315 p (and)s 16(Sons,)m 15(New)m 15 r 89 c -3(ork,)m 14(NY.)m 225 409 p ([24])s 21(Hoaglin,)m 25(D.)m 23(C.,)m 25(and)m 24(R.)m 24(E.)m 23 r 87 c -3(elsc)m 104 c 22(\(1978\),)m 23(\\The)m 24(hat)m 24(matrix)m 22(in)m 24(regression)m 23(and)m 318 465 p (ANO)s 86 c -4(A,")m cmti10.329 @sf 13 r 65 c (meric)s -1(an)m 14(Statistician,)m cmr10.329 @sf 14(32:17-22.)m 225 559 p ([25])s 21(Jennric)m (h,)s 18(R.)m 18(I.)m 18(\(1969\),)m 16(\\Asymptotic)m 17(Prop)m 1(erties)m 17(of)m 18(Non-linear)m 17(Least)m 18(Squares)m 18(Esti-)m 318 616 p (mators,")s cmti10.329 @sf 14 r 65 c (nn)s -1(als)m 14(of)m 17(Mathematic)m -1(al)m 15(Statistics)m cmr10.329 @sf 44 c 14(40:633-643)m -1 r 46 c 225 709 p ([26])s 21(Juedes,)m 16(D.)m 15(\(1991\))m 13(\\A)m 15(taxonom)m 121 c 13(of)m 15(automatic)m 14(di\013eren)m (tia)s -1(tio)m -1 r 110 c 14(to)m 1(ols,")m 13(in)m cmti10.329 @sf 15(Pr)m -1 r 111 c -1 r 99 c -2 r 101 c -3 r 101 c -2(din)m -1(gs)m 318 766 p (of)s 18(the)m 18(Workshop)m 18(on)m 18 r 65 c (utomatic)s 17(Di\013er)m -1(entiation)m 16(of)m 17 r 65 c (lgorithms:)s 22(The)m -1(ory,)m 17(Implemen-)m 318 822 p (tation,)s 16(and)m 15(Applic)m -1(ation)m cmr10.329 @sf 44 c 12(A.)m 13(Griew)m (ank)s 12(and)m 14 r 80 c -3 r 46 c 12(L.)m 14 r 84 c -3(oin)m -1(t,)m 12(editors,)m 13(SIAM,)m 13(Philidelphia,)m 318 879 p 80 c -3(A.)m 225 973 p ([27])s 21(La)m (wson,)s 18(C.,)m 19(R.)m 19(Hanson,)m 19(D.)m 18(Kincaid,)m 20(and)m 19(F.)m 18(Krogh)m 18(\(1979\),)m 18(\\Basic)m 18(linear)m 18(algebra)m 318 1029 p (subprograms)s 15(for)m 14 r 70 c (OR)s -3(TRAN)m 14(usage",)m cmti10.329 @sf 15 r 65 c (CM)s 14 r 84 c -2 r 114 c -2(ans)m -1 r 46 c 14(Math.)m 17(Softwar)m -1 r 101 c cmr10.329 @sf 44 c 14(5\(3\):308)m -1(-371.)m 225 1123 p ([28])s 21(Sc)m (hnab)s 1(el,)m 16(R.)m 17(B.)m 16(\(1982\),)m 15(\\Finite)m 15(di\013erence)m 16(deriv)m -2(ativ)m -1(es)m 15 r 45 c 16(theory)m 16(and)m 17(practice,")m 16(\(un-)m 318 1179 p (published:)s 21 r 97 c 118 c -2(ai)m -1(labl)m -1 r 101 c 14(from)m 14(author\).)m 225 1273 p ([29])s 21(Seb)m 1(er,)m 22(G.)m 20(A.)m 20(F.,)m 20(and)m 20(C.)m 20(J.)m 20(Wild)m 19(\(1989\),)m cmti10.329 @sf 19(Nonline)m -1(ar)m 19 r 82 c -1 r 101 c -2(gr)m -2(es)m -1(sion)m cmr10.329 @sf 44 c 19(John)m 20(Wiley)m 20(and)m 318 1330 p (Sons,)s 15(New)m 16 r 89 c -3(ork,)m 13(NY.)m 225 1423 p ([30])s 21(Stephens,)m 14(B.)m 12(R.,)m 13(and)m 13(J.)m 12(D.)m 12(Pryce)m 13(\(1991\),)m 11(\\D)m (APRE:)s 10 r 97 c 12(di\013eren)m (tiati)s -1(on)m 11(arithmetic)m 11(sys-)m 318 1480 p (tem)s 16(for)m 16 r 70 c -3(ortra)m -1(n,")m 14 r 84 c -3(ec)m (hnical)s 14(Rep)m 1(ort)m 16 r 65 c (CM-91-3,)s 14(Ro)m 121 c (a)s -1 r 108 c 14(Military)m 14(College)m 15(of)m 15(Science,)m 318 1536 p (Shriv)s (enham,)s 14(UK.)m 225 1630 p ([31])s 21(Stew)m (art,)s 10(G.)m 11(W.)m 10(\(1973\),)m cmti10.329 @sf 10(Intr)m -1 r 111 c -2(duction)m 11(to)m 13(Matrix)m 13(Computations)m cmr10.329 @sf 44 c 12(Academic)m 11(Press,)m 12(New)m 318 1687 p 89 c -3(ork,)m 14(NY.)m @eop @end .