LAPACK: TESTING/LIN/alahd.f Source File

00001       SUBROUTINE ALAHD( IOUNIT, PATH )
00002 *
00003 *  -- LAPACK test routine (version 3.1) --
00004 *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
00005 *     November 2006
00006 *
00007 *     .. Scalar Arguments ..
00008       CHARACTER*3        PATH
00009       INTEGER            IOUNIT
00010 *     ..
00011 *
00012 *  Purpose
00013 *  =======
00014 *
00015 *  ALAHD prints header information for the different test paths.
00016 *
00017 *  Arguments
00018 *  =========
00019 *
00020 *  IOUNIT  (input) INTEGER
00021 *          The unit number to which the header information should be
00022 *          printed.
00023 *
00024 *  PATH    (input) CHARACTER*3
00025 *          The name of the path for which the header information is to
00026 *          be printed.  Current paths are
00027 *             _GE:  General matrices
00028 *             _GB:  General band
00029 *             _GT:  General Tridiagonal
00030 *             _PO:  Symmetric or Hermitian positive definite
00031 *             _PS:  Symmetric or Hermitian positive semi-definite
00032 *             _PP:  Symmetric or Hermitian positive definite packed
00033 *             _PB:  Symmetric or Hermitian positive definite band
00034 *             _PT:  Symmetric or Hermitian positive definite tridiagonal
00035 *             _SY:  Symmetric indefinite
00036 *             _SP:  Symmetric indefinite packed
00037 *             _HE:  (complex) Hermitian indefinite
00038 *             _HP:  (complex) Hermitian indefinite packed
00039 *             _TR:  Triangular
00040 *             _TP:  Triangular packed
00041 *             _TB:  Triangular band
00042 *             _QR:  QR (general matrices)
00043 *             _LQ:  LQ (general matrices)
00044 *             _QL:  QL (general matrices)
00045 *             _RQ:  RQ (general matrices)
00046 *             _QP:  QR with column pivoting
00047 *             _TZ:  Trapezoidal
00048 *             _LS:  Least Squares driver routines
00049 *             _LU:  LU variants
00050 *             _CH:  Cholesky variants
00051 *             _QS:  QR variants
00052 *          The first character must be one of S, D, C, or Z (C or Z only
00053 *          if complex).
00054 *
00055 *  =====================================================================
00056 *
00057 *     .. Local Scalars ..
00058       LOGICAL            CORZ, SORD
00059       CHARACTER          C1, C3
00060       CHARACTER*2        P2
00061       CHARACTER*4        EIGCNM
00062       CHARACTER*32       SUBNAM
00063       CHARACTER*9        SYM
00064 *     ..
00065 *     .. External Functions ..
00066       LOGICAL            LSAME, LSAMEN
00067       EXTERNAL           LSAME, LSAMEN
00068 *     ..
00069 *     .. Intrinsic Functions ..
00070       INTRINSIC          LEN_TRIM
00071 *     ..
00072 *     .. Executable Statements ..
00073 *
00074       IF( IOUNIT.LE.0 )
00075      $   RETURN
00076       C1 = PATH( 1: 1 )
00077       C3 = PATH( 3: 3 )
00078       P2 = PATH( 2: 3 )
00079       SORD = LSAME( C1, 'S' ) .OR. LSAME( C1, 'D' )
00080       CORZ = LSAME( C1, 'C' ) .OR. LSAME( C1, 'Z' )
00081       IF( .NOT.( SORD .OR. CORZ ) )
00082      $   RETURN
00083 *
00084       IF( LSAMEN( 2, P2, 'GE' ) ) THEN
00085 *
00086 *        GE: General dense
00087 *
00088          WRITE( IOUNIT, FMT = 9999 )PATH
00089          WRITE( IOUNIT, FMT = '( '' Matrix types:'' )' )
00090          WRITE( IOUNIT, FMT = 9979 )
00091          WRITE( IOUNIT, FMT = '( '' Test ratios:'' )' )
00092          WRITE( IOUNIT, FMT = 9962 )1
00093          WRITE( IOUNIT, FMT = 9961 )2
00094          WRITE( IOUNIT, FMT = 9960 )3
00095          WRITE( IOUNIT, FMT = 9959 )4
00096          WRITE( IOUNIT, FMT = 9958 )5
00097          WRITE( IOUNIT, FMT = 9957 )6
00098          WRITE( IOUNIT, FMT = 9956 )7
00099          WRITE( IOUNIT, FMT = 9955 )8
00100          WRITE( IOUNIT, FMT = '( '' Messages:'' )' )
00101 *
00102       ELSE IF( LSAMEN( 2, P2, 'GB' ) ) THEN
00103 *
00104 *        GB: General band
00105 *
00106          WRITE( IOUNIT, FMT = 9998 )PATH
00107          WRITE( IOUNIT, FMT = '( '' Matrix types:'' )' )
00108          WRITE( IOUNIT, FMT = 9978 )
00109          WRITE( IOUNIT, FMT = '( '' Test ratios:'' )' )
00110          WRITE( IOUNIT, FMT = 9962 )1
00111          WRITE( IOUNIT, FMT = 9960 )2
00112          WRITE( IOUNIT, FMT = 9959 )3
00113          WRITE( IOUNIT, FMT = 9958 )4
00114          WRITE( IOUNIT, FMT = 9957 )5
00115          WRITE( IOUNIT, FMT = 9956 )6
00116          WRITE( IOUNIT, FMT = 9955 )7
00117          WRITE( IOUNIT, FMT = '( '' Messages:'' )' )
00118 *
00119       ELSE IF( LSAMEN( 2, P2, 'GT' ) ) THEN
00120 *
00121 *        GT: General tridiagonal
00122 *
00123          WRITE( IOUNIT, FMT = 9997 )PATH
00124          WRITE( IOUNIT, FMT = 9977 )
00125          WRITE( IOUNIT, FMT = '( '' Test ratios:'' )' )
00126          WRITE( IOUNIT, FMT = 9962 )1
00127          WRITE( IOUNIT, FMT = 9960 )2
00128          WRITE( IOUNIT, FMT = 9959 )3
00129          WRITE( IOUNIT, FMT = 9958 )4
00130          WRITE( IOUNIT, FMT = 9957 )5
00131          WRITE( IOUNIT, FMT = 9956 )6
00132          WRITE( IOUNIT, FMT = 9955 )7
00133          WRITE( IOUNIT, FMT = '( '' Messages:'' )' )
00134 *
00135       ELSE IF( LSAMEN( 2, P2, 'PO' ) .OR. LSAMEN( 2, P2, 'PP' ) ) THEN
00136 *
00137 *        PO: Positive definite full
00138 *        PP: Positive definite packed
00139 *
00140          IF( SORD ) THEN
00141             SYM = 'Symmetric'
00142          ELSE
00143             SYM = 'Hermitian'
00144          END IF
00145          IF( LSAME( C3, 'O' ) ) THEN
00146             WRITE( IOUNIT, FMT = 9996 )PATH, SYM
00147          ELSE
00148             WRITE( IOUNIT, FMT = 9995 )PATH, SYM
00149          END IF
00150          WRITE( IOUNIT, FMT = '( '' Matrix types:'' )' )
00151          WRITE( IOUNIT, FMT = 9975 )PATH
00152          WRITE( IOUNIT, FMT = '( '' Test ratios:'' )' )
00153          WRITE( IOUNIT, FMT = 9954 )1
00154          WRITE( IOUNIT, FMT = 9961 )2
00155          WRITE( IOUNIT, FMT = 9960 )3
00156          WRITE( IOUNIT, FMT = 9959 )4
00157          WRITE( IOUNIT, FMT = 9958 )5
00158          WRITE( IOUNIT, FMT = 9957 )6
00159          WRITE( IOUNIT, FMT = 9956 )7
00160          WRITE( IOUNIT, FMT = 9955 )8
00161          WRITE( IOUNIT, FMT = '( '' Messages:'' )' )
00162 *
00163       ELSE IF( LSAMEN( 2, P2, 'PS' ) ) THEN
00164 *
00165 *        PS: Positive semi-definite full
00166 *
00167          IF( SORD ) THEN
00168             SYM = 'Symmetric'
00169          ELSE
00170             SYM = 'Hermitian'
00171          END IF
00172          IF( LSAME( C1, 'S' ) .OR. LSAME( C1, 'C' ) ) THEN
00173             EIGCNM = '1E04'
00174          ELSE
00175             EIGCNM = '1D12'
00176          END IF
00177          WRITE( IOUNIT, FMT = 9995 )PATH, SYM
00178          WRITE( IOUNIT, FMT = '( '' Matrix types:'' )' )
00179          WRITE( IOUNIT, FMT = 8973 )EIGCNM, EIGCNM, EIGCNM
00180          WRITE( IOUNIT, FMT = '( '' Difference:'' )' )
00181          WRITE( IOUNIT, FMT = 8972 )C1
00182          WRITE( IOUNIT, FMT = '( '' Test ratio:'' )' )
00183          WRITE( IOUNIT, FMT = 8950 )
00184          WRITE( IOUNIT, FMT = '( '' Messages:'' )' )
00185       ELSE IF( LSAMEN( 2, P2, 'PB' ) ) THEN
00186 *
00187 *        PB: Positive definite band
00188 *
00189          IF( SORD ) THEN
00190             WRITE( IOUNIT, FMT = 9994 )PATH, 'Symmetric'
00191          ELSE
00192             WRITE( IOUNIT, FMT = 9994 )PATH, 'Hermitian'
00193          END IF
00194          WRITE( IOUNIT, FMT = '( '' Matrix types:'' )' )
00195          WRITE( IOUNIT, FMT = 9973 )PATH
00196          WRITE( IOUNIT, FMT = '( '' Test ratios:'' )' )
00197          WRITE( IOUNIT, FMT = 9954 )1
00198          WRITE( IOUNIT, FMT = 9960 )2
00199          WRITE( IOUNIT, FMT = 9959 )3
00200          WRITE( IOUNIT, FMT = 9958 )4
00201          WRITE( IOUNIT, FMT = 9957 )5
00202          WRITE( IOUNIT, FMT = 9956 )6
00203          WRITE( IOUNIT, FMT = 9955 )7
00204          WRITE( IOUNIT, FMT = '( '' Messages:'' )' )
00205 *
00206       ELSE IF( LSAMEN( 2, P2, 'PT' ) ) THEN
00207 *
00208 *        PT: Positive definite tridiagonal
00209 *
00210          IF( SORD ) THEN
00211             WRITE( IOUNIT, FMT = 9993 )PATH, 'Symmetric'
00212          ELSE
00213             WRITE( IOUNIT, FMT = 9993 )PATH, 'Hermitian'
00214          END IF
00215          WRITE( IOUNIT, FMT = 9976 )
00216          WRITE( IOUNIT, FMT = '( '' Test ratios:'' )' )
00217          WRITE( IOUNIT, FMT = 9952 )1
00218          WRITE( IOUNIT, FMT = 9960 )2
00219          WRITE( IOUNIT, FMT = 9959 )3
00220          WRITE( IOUNIT, FMT = 9958 )4
00221          WRITE( IOUNIT, FMT = 9957 )5
00222          WRITE( IOUNIT, FMT = 9956 )6
00223          WRITE( IOUNIT, FMT = 9955 )7
00224          WRITE( IOUNIT, FMT = '( '' Messages:'' )' )
00225 *
00226       ELSE IF( LSAMEN( 2, P2, 'SY' ) .OR. LSAMEN( 2, P2, 'SP' ) ) THEN
00227 *
00228 *        SY: Symmetric indefinite full
00229 *        SP: Symmetric indefinite packed
00230 *
00231          IF( LSAME( C3, 'Y' ) ) THEN
00232             WRITE( IOUNIT, FMT = 9992 )PATH, 'Symmetric'
00233          ELSE
00234             WRITE( IOUNIT, FMT = 9991 )PATH, 'Symmetric'
00235          END IF
00236          WRITE( IOUNIT, FMT = '( '' Matrix types:'' )' )
00237          IF( SORD ) THEN
00238             WRITE( IOUNIT, FMT = 9972 )
00239          ELSE
00240             WRITE( IOUNIT, FMT = 9971 )
00241          END IF
00242          WRITE( IOUNIT, FMT = '( '' Test ratios:'' )' )
00243          WRITE( IOUNIT, FMT = 9953 )1
00244          WRITE( IOUNIT, FMT = 9961 )2
00245          WRITE( IOUNIT, FMT = 9960 )3
00246          WRITE( IOUNIT, FMT = 9959 )4
00247          WRITE( IOUNIT, FMT = 9958 )5
00248          WRITE( IOUNIT, FMT = 9956 )6
00249          WRITE( IOUNIT, FMT = 9957 )7
00250          WRITE( IOUNIT, FMT = 9955 )8
00251          WRITE( IOUNIT, FMT = '( '' Messages:'' )' )
00252 *
00253       ELSE IF( LSAMEN( 2, P2, 'HE' ) .OR. LSAMEN( 2, P2, 'HP' ) ) THEN
00254 *
00255 *        HE: Hermitian indefinite full
00256 *        HP: Hermitian indefinite packed
00257 *
00258          IF( LSAME( C3, 'E' ) ) THEN
00259             WRITE( IOUNIT, FMT = 9992 )PATH, 'Hermitian'
00260          ELSE
00261             WRITE( IOUNIT, FMT = 9991 )PATH, 'Hermitian'
00262          END IF
00263          WRITE( IOUNIT, FMT = '( '' Matrix types:'' )' )
00264          WRITE( IOUNIT, FMT = 9972 )
00265          WRITE( IOUNIT, FMT = '( '' Test ratios:'' )' )
00266          WRITE( IOUNIT, FMT = 9953 )1
00267          WRITE( IOUNIT, FMT = 9961 )2
00268          WRITE( IOUNIT, FMT = 9960 )3
00269          WRITE( IOUNIT, FMT = 9959 )4
00270          WRITE( IOUNIT, FMT = 9958 )5
00271          WRITE( IOUNIT, FMT = 9956 )6
00272          WRITE( IOUNIT, FMT = 9957 )7
00273          WRITE( IOUNIT, FMT = 9955 )8
00274          WRITE( IOUNIT, FMT = '( '' Messages:'' )' )
00275 *
00276       ELSE IF( LSAMEN( 2, P2, 'TR' ) .OR. LSAMEN( 2, P2, 'TP' ) ) THEN
00277 *
00278 *        TR: Triangular full
00279 *        TP: Triangular packed
00280 *
00281          IF( LSAME( C3, 'R' ) ) THEN
00282             WRITE( IOUNIT, FMT = 9990 )PATH
00283             SUBNAM = PATH( 1: 1 ) // 'LATRS'
00284          ELSE
00285             WRITE( IOUNIT, FMT = 9989 )PATH
00286             SUBNAM = PATH( 1: 1 ) // 'LATPS'
00287          END IF
00288          WRITE( IOUNIT, FMT = 9966 )PATH
00289          WRITE( IOUNIT, FMT = 9965 )SUBNAM(1:LEN_TRIM( SUBNAM ))
00290          WRITE( IOUNIT, FMT = '( '' Test ratios:'' )' )
00291          WRITE( IOUNIT, FMT = 9961 )1
00292          WRITE( IOUNIT, FMT = 9960 )2
00293          WRITE( IOUNIT, FMT = 9959 )3
00294          WRITE( IOUNIT, FMT = 9958 )4
00295          WRITE( IOUNIT, FMT = 9957 )5
00296          WRITE( IOUNIT, FMT = 9956 )6
00297          WRITE( IOUNIT, FMT = 9955 )7
00298          WRITE( IOUNIT, FMT = 9951 )SUBNAM(1:LEN_TRIM( SUBNAM )), 8
00299          WRITE( IOUNIT, FMT = '( '' Messages:'' )' )
00300 *
00301       ELSE IF( LSAMEN( 2, P2, 'TB' ) ) THEN
00302 *
00303 *        TB: Triangular band
00304 *
00305          WRITE( IOUNIT, FMT = 9988 )PATH
00306          SUBNAM = PATH( 1: 1 ) // 'LATBS'
00307          WRITE( IOUNIT, FMT = 9964 )PATH
00308          WRITE( IOUNIT, FMT = 9963 )SUBNAM(1:LEN_TRIM( SUBNAM ))
00309          WRITE( IOUNIT, FMT = '( '' Test ratios:'' )' )
00310          WRITE( IOUNIT, FMT = 9960 )1
00311          WRITE( IOUNIT, FMT = 9959 )2
00312          WRITE( IOUNIT, FMT = 9958 )3
00313          WRITE( IOUNIT, FMT = 9957 )4
00314          WRITE( IOUNIT, FMT = 9956 )5
00315          WRITE( IOUNIT, FMT = 9955 )6
00316          WRITE( IOUNIT, FMT = 9951 )SUBNAM(1:LEN_TRIM( SUBNAM )), 7
00317          WRITE( IOUNIT, FMT = '( '' Messages:'' )' )
00318 *
00319       ELSE IF( LSAMEN( 2, P2, 'QR' ) ) THEN
00320 *
00321 *        QR decomposition of rectangular matrices
00322 *
00323          WRITE( IOUNIT, FMT = 9987 )PATH, 'QR'
00324          WRITE( IOUNIT, FMT = '( '' Matrix types:'' )' )
00325          WRITE( IOUNIT, FMT = 9970 )
00326          WRITE( IOUNIT, FMT = '( '' Test ratios:'' )' )
00327          WRITE( IOUNIT, FMT = 9950 )1
00328          WRITE( IOUNIT, FMT = 9946 )2
00329          WRITE( IOUNIT, FMT = 9944 )3, 'M'
00330          WRITE( IOUNIT, FMT = 9943 )4, 'M'
00331          WRITE( IOUNIT, FMT = 9942 )5, 'M'
00332          WRITE( IOUNIT, FMT = 9941 )6, 'M'
00333          WRITE( IOUNIT, FMT = 9960 )7
00334          WRITE( IOUNIT, FMT = 6660 )8
00335          WRITE( IOUNIT, FMT = '( '' Messages:'' )' )
00336 *
00337       ELSE IF( LSAMEN( 2, P2, 'LQ' ) ) THEN
00338 *
00339 *        LQ decomposition of rectangular matrices
00340 *
00341          WRITE( IOUNIT, FMT = 9987 )PATH, 'LQ'
00342          WRITE( IOUNIT, FMT = '( '' Matrix types:'' )' )
00343          WRITE( IOUNIT, FMT = 9970 )
00344          WRITE( IOUNIT, FMT = '( '' Test ratios:'' )' )
00345          WRITE( IOUNIT, FMT = 9949 )1
00346          WRITE( IOUNIT, FMT = 9945 )2
00347          WRITE( IOUNIT, FMT = 9944 )3, 'N'
00348          WRITE( IOUNIT, FMT = 9943 )4, 'N'
00349          WRITE( IOUNIT, FMT = 9942 )5, 'N'
00350          WRITE( IOUNIT, FMT = 9941 )6, 'N'
00351          WRITE( IOUNIT, FMT = 9960 )7
00352          WRITE( IOUNIT, FMT = '( '' Messages:'' )' )
00353 *
00354       ELSE IF( LSAMEN( 2, P2, 'QL' ) ) THEN
00355 *
00356 *        QL decomposition of rectangular matrices
00357 *
00358          WRITE( IOUNIT, FMT = 9987 )PATH, 'QL'
00359          WRITE( IOUNIT, FMT = '( '' Matrix types:'' )' )
00360          WRITE( IOUNIT, FMT = 9970 )
00361          WRITE( IOUNIT, FMT = '( '' Test ratios:'' )' )
00362          WRITE( IOUNIT, FMT = 9948 )1
00363          WRITE( IOUNIT, FMT = 9946 )2
00364          WRITE( IOUNIT, FMT = 9944 )3, 'M'
00365          WRITE( IOUNIT, FMT = 9943 )4, 'M'
00366          WRITE( IOUNIT, FMT = 9942 )5, 'M'
00367          WRITE( IOUNIT, FMT = 9941 )6, 'M'
00368          WRITE( IOUNIT, FMT = 9960 )7
00369          WRITE( IOUNIT, FMT = '( '' Messages:'' )' )
00370 *
00371       ELSE IF( LSAMEN( 2, P2, 'RQ' ) ) THEN
00372 *
00373 *        RQ decomposition of rectangular matrices
00374 *
00375          WRITE( IOUNIT, FMT = 9987 )PATH, 'RQ'
00376          WRITE( IOUNIT, FMT = '( '' Matrix types:'' )' )
00377          WRITE( IOUNIT, FMT = 9970 )
00378          WRITE( IOUNIT, FMT = '( '' Test ratios:'' )' )
00379          WRITE( IOUNIT, FMT = 9947 )1
00380          WRITE( IOUNIT, FMT = 9945 )2
00381          WRITE( IOUNIT, FMT = 9944 )3, 'N'
00382          WRITE( IOUNIT, FMT = 9943 )4, 'N'
00383          WRITE( IOUNIT, FMT = 9942 )5, 'N'
00384          WRITE( IOUNIT, FMT = 9941 )6, 'N'
00385          WRITE( IOUNIT, FMT = 9960 )7
00386          WRITE( IOUNIT, FMT = '( '' Messages:'' )' )
00387 *
00388       ELSE IF( LSAMEN( 2, P2, 'QP' ) ) THEN
00389 *
00390 *        QR decomposition with column pivoting
00391 *
00392          WRITE( IOUNIT, FMT = 9986 )PATH
00393          WRITE( IOUNIT, FMT = 9969 )
00394          WRITE( IOUNIT, FMT = '( '' Test ratios:'' )' )
00395          WRITE( IOUNIT, FMT = 9940 )1
00396          WRITE( IOUNIT, FMT = 9939 )2
00397          WRITE( IOUNIT, FMT = 9938 )3
00398          WRITE( IOUNIT, FMT = '( '' Messages:'' )' )
00399 *
00400       ELSE IF( LSAMEN( 2, P2, 'TZ' ) ) THEN
00401 *
00402 *        TZ:  Trapezoidal
00403 *
00404          WRITE( IOUNIT, FMT = 9985 )PATH
00405          WRITE( IOUNIT, FMT = 9968 )
00406          WRITE( IOUNIT, FMT = 9929 )C1, C1
00407          WRITE( IOUNIT, FMT = '( '' Test ratios:'' )' )
00408          WRITE( IOUNIT, FMT = 9940 )1
00409          WRITE( IOUNIT, FMT = 9937 )2
00410          WRITE( IOUNIT, FMT = 9938 )3
00411          WRITE( IOUNIT, FMT = 9940 )4
00412          WRITE( IOUNIT, FMT = 9937 )5
00413          WRITE( IOUNIT, FMT = 9938 )6
00414          WRITE( IOUNIT, FMT = '( '' Messages:'' )' )
00415 *
00416       ELSE IF( LSAMEN( 2, P2, 'LS' ) ) THEN
00417 *
00418 *        LS:  Least Squares driver routines for
00419 *             LS, LSD, LSS, LSX and LSY.
00420 *
00421          WRITE( IOUNIT, FMT = 9984 )PATH
00422          WRITE( IOUNIT, FMT = 9967 )
00423          WRITE( IOUNIT, FMT = 9921 )C1, C1, C1, C1, C1
00424          WRITE( IOUNIT, FMT = 9935 )1
00425          WRITE( IOUNIT, FMT = 9931 )2
00426          WRITE( IOUNIT, FMT = 9933 )3
00427          WRITE( IOUNIT, FMT = 9935 )4
00428          WRITE( IOUNIT, FMT = 9934 )5
00429          WRITE( IOUNIT, FMT = 9932 )6
00430          WRITE( IOUNIT, FMT = 9920 )
00431          WRITE( IOUNIT, FMT = '( '' Messages:'' )' )
00432 *
00433       ELSE IF( LSAMEN( 2, P2, 'LU' ) ) THEN
00434 *
00435 *        LU factorization variants
00436 *
00437          WRITE( IOUNIT, FMT = 9983 )PATH
00438          WRITE( IOUNIT, FMT = '( '' Matrix types:'' )' )
00439          WRITE( IOUNIT, FMT = 9979 )
00440          WRITE( IOUNIT, FMT = '( '' Test ratio:'' )' )
00441          WRITE( IOUNIT, FMT = 9962 )1
00442          WRITE( IOUNIT, FMT = '( '' Messages:'' )' )
00443 *
00444       ELSE IF( LSAMEN( 2, P2, 'CH' ) ) THEN
00445 *
00446 *        Cholesky factorization variants
00447 *
00448          WRITE( IOUNIT, FMT = 9982 )PATH
00449          WRITE( IOUNIT, FMT = '( '' Matrix types:'' )' )
00450          WRITE( IOUNIT, FMT = 9974 )
00451          WRITE( IOUNIT, FMT = '( '' Test ratio:'' )' )
00452          WRITE( IOUNIT, FMT = 9954 )1
00453          WRITE( IOUNIT, FMT = '( '' Messages:'' )' )
00454 *
00455       ELSE IF( LSAMEN( 2, P2, 'QS' ) ) THEN
00456 *
00457 *        QR factorization variants
00458 *
00459          WRITE( IOUNIT, FMT = 9981 )PATH
00460          WRITE( IOUNIT, FMT = '( '' Matrix types:'' )' )
00461          WRITE( IOUNIT, FMT = 9970 )
00462          WRITE( IOUNIT, FMT = '( '' Test ratios:'' )' )
00463 *
00464       ELSE
00465 *
00466 *        Print error message if no header is available.
00467 *
00468          WRITE( IOUNIT, FMT = 9980 )PATH
00469       END IF
00470 *
00471 *     First line of header
00472 *
00473  9999 FORMAT( / 1X, A3, ':  General dense matrices' )
00474  9998 FORMAT( / 1X, A3, ':  General band matrices' )
00475  9997 FORMAT( / 1X, A3, ':  General tridiagonal' )
00476  9996 FORMAT( / 1X, A3, ':  ', A9, ' positive definite matrices' )
00477  9995 FORMAT( / 1X, A3, ':  ', A9, ' positive definite packed matrices'
00478      $       )
00479  9994 FORMAT( / 1X, A3, ':  ', A9, ' positive definite band matrices' )
00480  9993 FORMAT( / 1X, A3, ':  ', A9, ' positive definite tridiagonal' )
00481  9992 FORMAT( / 1X, A3, ':  ', A9, ' indefinite matrices' )
00482  9991 FORMAT( / 1X, A3, ':  ', A9, ' indefinite packed matrices' )
00483  9990 FORMAT( / 1X, A3, ':  Triangular matrices' )
00484  9989 FORMAT( / 1X, A3, ':  Triangular packed matrices' )
00485  9988 FORMAT( / 1X, A3, ':  Triangular band matrices' )
00486  9987 FORMAT( / 1X, A3, ':  ', A2, ' factorization of general matrices'
00487      $       )
00488  9986 FORMAT( / 1X, A3, ':  QR factorization with column pivoting' )
00489  9985 FORMAT( / 1X, A3, ':  RQ factorization of trapezoidal matrix' )
00490  9984 FORMAT( / 1X, A3, ':  Least squares driver routines' )
00491  9983 FORMAT( / 1X, A3, ':  LU factorization variants' )
00492  9982 FORMAT( / 1X, A3, ':  Cholesky factorization variants' )
00493  9981 FORMAT( / 1X, A3, ':  QR factorization variants' )
00494  9980 FORMAT( / 1X, A3, ':  No header available' )
00495 *
00496 *     GE matrix types
00497 *
00498  9979 FORMAT( 4X, '1. Diagonal', 24X, '7. Last n/2 columns zero', / 4X,
00499      $      '2. Upper triangular', 16X,
00500      $      '8. Random, CNDNUM = sqrt(0.1/EPS)', / 4X,
00501      $      '3. Lower triangular', 16X, '9. Random, CNDNUM = 0.1/EPS',
00502      $      / 4X, '4. Random, CNDNUM = 2', 13X,
00503      $      '10. Scaled near underflow', / 4X, '5. First column zero',
00504      $      14X, '11. Scaled near overflow', / 4X,
00505      $      '6. Last column zero' )
00506 *
00507 *     GB matrix types
00508 *
00509  9978 FORMAT( 4X, '1. Random, CNDNUM = 2', 14X,
00510      $      '5. Random, CNDNUM = sqrt(0.1/EPS)', / 4X,
00511      $      '2. First column zero', 15X, '6. Random, CNDNUM = .01/EPS',
00512      $      / 4X, '3. Last column zero', 16X,
00513      $      '7. Scaled near underflow', / 4X,
00514      $      '4. Last n/2 columns zero', 11X, '8. Scaled near overflow' )
00515 *
00516 *     GT matrix types
00517 *
00518  9977 FORMAT( ' Matrix types (1-6 have specified condition numbers):',
00519      $      / 4X, '1. Diagonal', 24X, '7. Random, unspecified CNDNUM',
00520      $      / 4X, '2. Random, CNDNUM = 2', 14X, '8. First column zero',
00521      $      / 4X, '3. Random, CNDNUM = sqrt(0.1/EPS)', 2X,
00522      $      '9. Last column zero', / 4X, '4. Random, CNDNUM = 0.1/EPS',
00523      $      7X, '10. Last n/2 columns zero', / 4X,
00524      $      '5. Scaled near underflow', 10X,
00525      $      '11. Scaled near underflow', / 4X,
00526      $      '6. Scaled near overflow', 11X, '12. Scaled near overflow' )
00527 *
00528 *     PT matrix types
00529 *
00530  9976 FORMAT( ' Matrix types (1-6 have specified condition numbers):',
00531      $      / 4X, '1. Diagonal', 24X, '7. Random, unspecified CNDNUM',
00532      $      / 4X, '2. Random, CNDNUM = 2', 14X,
00533      $      '8. First row and column zero', / 4X,
00534      $      '3. Random, CNDNUM = sqrt(0.1/EPS)', 2X,
00535      $      '9. Last row and column zero', / 4X,
00536      $      '4. Random, CNDNUM = 0.1/EPS', 7X,
00537      $      '10. Middle row and column zero', / 4X,
00538      $      '5. Scaled near underflow', 10X,
00539      $      '11. Scaled near underflow', / 4X,
00540      $      '6. Scaled near overflow', 11X, '12. Scaled near overflow' )
00541 *
00542 *     PO, PP matrix types
00543 *
00544  9975 FORMAT( 4X, '1. Diagonal', 24X,
00545      $      '6. Random, CNDNUM = sqrt(0.1/EPS)', / 4X,
00546      $      '2. Random, CNDNUM = 2', 14X, '7. Random, CNDNUM = 0.1/EPS',
00547      $      / 3X, '*3. First row and column zero', 7X,
00548      $      '8. Scaled near underflow', / 3X,
00549      $      '*4. Last row and column zero', 8X,
00550      $      '9. Scaled near overflow', / 3X,
00551      $      '*5. Middle row and column zero', / 3X,
00552      $      '(* - tests error exits from ', A3,
00553      $      'TRF, no test ratios are computed)' )
00554 *
00555 *     CH matrix types
00556 *
00557  9974 FORMAT( 4X, '1. Diagonal', 24X,
00558      $      '6. Random, CNDNUM = sqrt(0.1/EPS)', / 4X,
00559      $      '2. Random, CNDNUM = 2', 14X, '7. Random, CNDNUM = 0.1/EPS',
00560      $      / 3X, '*3. First row and column zero', 7X,
00561      $      '8. Scaled near underflow', / 3X,
00562      $      '*4. Last row and column zero', 8X,
00563      $      '9. Scaled near overflow', / 3X,
00564      $      '*5. Middle row and column zero', / 3X,
00565      $      '(* - tests error exits, no test ratios are computed)' )
00566 *
00567 *     PS matrix types
00568 *
00569  8973 FORMAT( 4X, '1. Diagonal', / 4X, '2. Random, CNDNUM = 2', 14X,
00570      $      / 3X, '*3. Nonzero eigenvalues of: D(1:RANK-1)=1 and ',
00571      $      'D(RANK) = 1.0/', A4, / 3X,
00572      $      '*4. Nonzero eigenvalues of: D(1)=1 and ',
00573      $      ' D(2:RANK) = 1.0/', A4, / 3X,
00574      $      '*5. Nonzero eigenvalues of: D(I) = ', A4,
00575      $      '**(-(I-1)/(RANK-1)) ', ' I=1:RANK', / 4X,
00576      $      '6. Random, CNDNUM = sqrt(0.1/EPS)', / 4X,
00577      $      '7. Random, CNDNUM = 0.1/EPS', / 4X,
00578      $      '8. Scaled near underflow', / 4X, '9. Scaled near overflow',
00579      $      / 3X, '(* - Semi-definite tests )' )
00580  8972 FORMAT( 3X, 'RANK minus computed rank, returned by ', A, 'PSTRF' )
00581 *
00582 *     PB matrix types
00583 *
00584  9973 FORMAT( 4X, '1. Random, CNDNUM = 2', 14X,
00585      $      '5. Random, CNDNUM = sqrt(0.1/EPS)', / 3X,
00586      $      '*2. First row and column zero', 7X,
00587      $      '6. Random, CNDNUM = 0.1/EPS', / 3X,
00588      $      '*3. Last row and column zero', 8X,
00589      $      '7. Scaled near underflow', / 3X,
00590      $      '*4. Middle row and column zero', 6X,
00591      $      '8. Scaled near overflow', / 3X,
00592      $      '(* - tests error exits from ', A3,
00593      $      'TRF, no test ratios are computed)' )
00594 *
00595 *     SSY, SSP, CHE, CHP matrix types
00596 *
00597  9972 FORMAT( 4X, '1. Diagonal', 24X,
00598      $      '6. Last n/2 rows and columns zero', / 4X,
00599      $      '2. Random, CNDNUM = 2', 14X,
00600      $      '7. Random, CNDNUM = sqrt(0.1/EPS)', / 4X,
00601      $      '3. First row and column zero', 7X,
00602      $      '8. Random, CNDNUM = 0.1/EPS', / 4X,
00603      $      '4. Last row and column zero', 8X,
00604      $      '9. Scaled near underflow', / 4X,
00605      $      '5. Middle row and column zero', 5X,
00606      $      '10. Scaled near overflow' )
00607 *
00608 *     CSY, CSP matrix types
00609 *
00610  9971 FORMAT( 4X, '1. Diagonal', 24X,
00611      $      '7. Random, CNDNUM = sqrt(0.1/EPS)', / 4X,
00612      $      '2. Random, CNDNUM = 2', 14X, '8. Random, CNDNUM = 0.1/EPS',
00613      $      / 4X, '3. First row and column zero', 7X,
00614      $      '9. Scaled near underflow', / 4X,
00615      $      '4. Last row and column zero', 7X,
00616      $      '10. Scaled near overflow', / 4X,
00617      $      '5. Middle row and column zero', 5X,
00618      $      '11. Block diagonal matrix', / 4X,
00619      $      '6. Last n/2 rows and columns zero' )
00620 *
00621 *     QR matrix types
00622 *
00623  9970 FORMAT( 4X, '1. Diagonal', 24X,
00624      $      '5. Random, CNDNUM = sqrt(0.1/EPS)', / 4X,
00625      $      '2. Upper triangular', 16X, '6. Random, CNDNUM = 0.1/EPS',
00626      $      / 4X, '3. Lower triangular', 16X,
00627      $      '7. Scaled near underflow', / 4X, '4. Random, CNDNUM = 2',
00628      $      14X, '8. Scaled near overflow' )
00629 *
00630 *     QP matrix types
00631 *
00632  9969 FORMAT( ' Matrix types (2-6 have condition 1/EPS):', / 4X,
00633      $      '1. Zero matrix', 21X, '4. First n/2 columns fixed', / 4X,
00634      $      '2. One small eigenvalue', 12X, '5. Last n/2 columns fixed',
00635      $      / 4X, '3. Geometric distribution', 10X,
00636      $      '6. Every second column fixed' )
00637 *
00638 *     TZ matrix types
00639 *
00640  9968 FORMAT( ' Matrix types (2-3 have condition 1/EPS):', / 4X,
00641      $      '1. Zero matrix', / 4X, '2. One small eigenvalue', / 4X,
00642      $      '3. Geometric distribution' )
00643 *
00644 *     LS matrix types
00645 *
00646  9967 FORMAT( ' Matrix types (1-3: full rank, 4-6: rank deficient):',
00647      $      / 4X, '1 and 4. Normal scaling', / 4X,
00648      $      '2 and 5. Scaled near overflow', / 4X,
00649      $      '3 and 6. Scaled near underflow' )
00650 *
00651 *     TR, TP matrix types
00652 *
00653  9966 FORMAT( ' Matrix types for ', A3, ' routines:', / 4X,
00654      $      '1. Diagonal', 24X, '6. Scaled near overflow', / 4X,
00655      $      '2. Random, CNDNUM = 2', 14X, '7. Identity', / 4X,
00656      $      '3. Random, CNDNUM = sqrt(0.1/EPS)  ',
00657      $      '8. Unit triangular, CNDNUM = 2', / 4X,
00658      $      '4. Random, CNDNUM = 0.1/EPS', 8X,
00659      $      '9. Unit, CNDNUM = sqrt(0.1/EPS)', / 4X,
00660      $      '5. Scaled near underflow', 10X,
00661      $      '10. Unit, CNDNUM = 0.1/EPS' )
00662  9965 FORMAT( ' Special types for testing ', A, ':', / 3X,
00663      $      '11. Matrix elements are O(1), large right hand side', / 3X,
00664      $      '12. First diagonal causes overflow,',
00665      $      ' offdiagonal column norms < 1', / 3X,
00666      $      '13. First diagonal causes overflow,',
00667      $      ' offdiagonal column norms > 1', / 3X,
00668      $      '14. Growth factor underflows, solution does not overflow',
00669      $      / 3X, '15. Small diagonal causes gradual overflow', / 3X,
00670      $      '16. One zero diagonal element', / 3X,
00671      $      '17. Large offdiagonals cause overflow when adding a column'
00672      $      , / 3X, '18. Unit triangular with large right hand side' )
00673 *
00674 *     TB matrix types
00675 *
00676  9964 FORMAT( ' Matrix types for ', A3, ' routines:', / 4X,
00677      $      '1. Random, CNDNUM = 2', 14X, '6. Identity', / 4X,
00678      $      '2. Random, CNDNUM = sqrt(0.1/EPS)  ',
00679      $      '7. Unit triangular, CNDNUM = 2', / 4X,
00680      $      '3. Random, CNDNUM = 0.1/EPS', 8X,
00681      $      '8. Unit, CNDNUM = sqrt(0.1/EPS)', / 4X,
00682      $      '4. Scaled near underflow', 11X,
00683      $      '9. Unit, CNDNUM = 0.1/EPS', / 4X,
00684      $      '5. Scaled near overflow' )
00685  9963 FORMAT( ' Special types for testing ', A, ':', / 3X,
00686      $      '10. Matrix elements are O(1), large right hand side', / 3X,
00687      $      '11. First diagonal causes overflow,',
00688      $      ' offdiagonal column norms < 1', / 3X,
00689      $      '12. First diagonal causes overflow,',
00690      $      ' offdiagonal column norms > 1', / 3X,
00691      $      '13. Growth factor underflows, solution does not overflow',
00692      $      / 3X, '14. Small diagonal causes gradual overflow', / 3X,
00693      $      '15. One zero diagonal element', / 3X,
00694      $      '16. Large offdiagonals cause overflow when adding a column'
00695      $      , / 3X, '17. Unit triangular with large right hand side' )
00696 *
00697 *     Test ratios
00698 *
00699  9962 FORMAT( 3X, I2, ': norm( L * U - A )  / ( N * norm(A) * EPS )' )
00700  9961 FORMAT( 3X, I2, ': norm( I - A*AINV ) / ',
00701      $      '( N * norm(A) * norm(AINV) * EPS )' )
00702  9960 FORMAT( 3X, I2, ': norm( B - A * X )  / ',
00703      $      '( norm(A) * norm(X) * EPS )' )
00704  6660 FORMAT( 3X, I2, ': diagonal is not non-negative')
00705  9959 FORMAT( 3X, I2, ': norm( X - XACT )   / ',
00706      $      '( norm(XACT) * CNDNUM * EPS )' )
00707  9958 FORMAT( 3X, I2, ': norm( X - XACT )   / ',
00708      $      '( norm(XACT) * CNDNUM * EPS ), refined' )
00709  9957 FORMAT( 3X, I2, ': norm( X - XACT )   / ',
00710      $      '( norm(XACT) * (error bound) )' )
00711  9956 FORMAT( 3X, I2, ': (backward error)   / EPS' )
00712  9955 FORMAT( 3X, I2, ': RCOND * CNDNUM - 1.0' )
00713  9954 FORMAT( 3X, I2, ': norm( U'' * U - A ) / ( N * norm(A) * EPS )',
00714      $      ', or', / 7X, 'norm( L * L'' - A ) / ( N * norm(A) * EPS )'
00715      $       )
00716  8950 FORMAT( 3X,
00717      $      'norm( P * U'' * U * P'' - A ) / ( N * norm(A) * EPS )',
00718      $      ', or', / 3X,
00719      $      'norm( P * L * L'' * P'' - A ) / ( N * norm(A) * EPS )' )
00720  9953 FORMAT( 3X, I2, ': norm( U*D*U'' - A ) / ( N * norm(A) * EPS )',
00721      $      ', or', / 7X, 'norm( L*D*L'' - A ) / ( N * norm(A) * EPS )'
00722      $       )
00723  9952 FORMAT( 3X, I2, ': norm( U''*D*U - A ) / ( N * norm(A) * EPS )',
00724      $      ', or', / 7X, 'norm( L*D*L'' - A ) / ( N * norm(A) * EPS )'
00725      $       )
00726  9951 FORMAT( ' Test ratio for ', A, ':', / 3X, I2,
00727      $      ': norm( s*b - A*x )  / ( norm(A) * norm(x) * EPS )' )
00728  9950 FORMAT( 3X, I2, ': norm( R - Q'' * A ) / ( M * norm(A) * EPS )' )
00729  9949 FORMAT( 3X, I2, ': norm( L - A * Q'' ) / ( N * norm(A) * EPS )' )
00730  9948 FORMAT( 3X, I2, ': norm( L - Q'' * A ) / ( M * norm(A) * EPS )' )
00731  9947 FORMAT( 3X, I2, ': norm( R - A * Q'' ) / ( N * norm(A) * EPS )' )
00732  9946 FORMAT( 3X, I2, ': norm( I - Q''*Q )   / ( M * EPS )' )
00733  9945 FORMAT( 3X, I2, ': norm( I - Q*Q'' )   / ( N * EPS )' )
00734  9944 FORMAT( 3X, I2, ': norm( Q*C - Q*C )  / ', '( ', A1,
00735      $      ' * norm(C) * EPS )' )
00736  9943 FORMAT( 3X, I2, ': norm( C*Q - C*Q )  / ', '( ', A1,
00737      $      ' * norm(C) * EPS )' )
00738  9942 FORMAT( 3X, I2, ': norm( Q''*C - Q''*C )/ ', '( ', A1,
00739      $      ' * norm(C) * EPS )' )
00740  9941 FORMAT( 3X, I2, ': norm( C*Q'' - C*Q'' )/ ', '( ', A1,
00741      $      ' * norm(C) * EPS )' )
00742  9940 FORMAT( 3X, I2, ': norm(svd(A) - svd(R)) / ',
00743      $      '( M * norm(svd(R)) * EPS )' )
00744  9939 FORMAT( 3X, I2, ': norm( A*P - Q*R )     / ( M * norm(A) * EPS )'
00745      $       )
00746  9938 FORMAT( 3X, I2, ': norm( I - Q''*Q )      / ( M * EPS )' )
00747  9937 FORMAT( 3X, I2, ': norm( A - R*Q )       / ( M * norm(A) * EPS )'
00748      $       )
00749  9936 FORMAT( ' Test ratios (1-2: ', A1, 'GELS, 3-6: ', A1,
00750      $      'GELSS, 7-10: ', A1, 'GELSX):' )
00751  9935 FORMAT( 3X, I2, ': norm( B - A * X )   / ',
00752      $      '( max(M,N) * norm(A) * norm(X) * EPS )' )
00753  9934 FORMAT( 3X, I2, ': norm( (A*X-B)'' *A ) / ',
00754      $      '( max(M,N,NRHS) * norm(A) * norm(B) * EPS )' )
00755  9933 FORMAT( 3X, I2, ': norm(svd(A)-svd(R)) / ',
00756      $      '( min(M,N) * norm(svd(R)) * EPS )' )
00757  9932 FORMAT( 3X, I2, ': Check if X is in the row space of A or A''' )
00758  9931 FORMAT( 3X, I2, ': norm( (A*X-B)'' *A ) / ',
00759      $      '( max(M,N,NRHS) * norm(A) * norm(B) * EPS )', / 7X,
00760      $      'if TRANS=''N'' and M.GE.N or TRANS=''T'' and M.LT.N, ',
00761      $      'otherwise', / 7X,
00762      $      'check if X is in the row space of A or A'' ',
00763      $      '(overdetermined case)' )
00764  9930 FORMAT( 3X, ' 7-10: same as 3-6' )
00765  9929 FORMAT( ' Test ratios (1-3: ', A1, 'TZRQF, 4-6: ', A1,
00766      $      'TZRZF):' )
00767  9920 FORMAT( 3X, ' 7-10: same as 3-6', 3X, ' 11-14: same as 3-6',
00768      $      3X, ' 15-18: same as 3-6' )
00769  9921 FORMAT( ' Test ratios:', / '    (1-2: ', A1, 'GELS, 3-6: ', A1,
00770      $      'GELSX, 7-10: ', A1, 'GELSY, 11-14: ', A1, 'GELSS, 15-18: ',
00771      $      A1, 'GELSD)' )
00772 *
00773       RETURN
00774 *
00775 *     End of ALAHD
00776 *
00777       END