LAPACK  3.10.0
LAPACK: Linear Algebra PACKage
zdrvst2stg.f
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1 *> \brief \b ZDRVST2STG
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
7 *
8 * Definition:
9 * ===========
10 *
11 * SUBROUTINE ZDRVST2STG( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
12 * NOUNIT, A, LDA, D1, D2, D3, WA1, WA2, WA3, U,
13 * LDU, V, TAU, Z, WORK, LWORK, RWORK, LRWORK,
14 * IWORK, LIWORK, RESULT, INFO )
15 *
16 * .. Scalar Arguments ..
17 * INTEGER INFO, LDA, LDU, LIWORK, LRWORK, LWORK, NOUNIT,
18 * $ NSIZES, NTYPES
19 * DOUBLE PRECISION THRESH
20 * ..
21 * .. Array Arguments ..
22 * LOGICAL DOTYPE( * )
23 * INTEGER ISEED( 4 ), IWORK( * ), NN( * )
24 * DOUBLE PRECISION D1( * ), D2( * ), D3( * ), RESULT( * ),
25 * $ RWORK( * ), WA1( * ), WA2( * ), WA3( * )
26 * COMPLEX*16 A( LDA, * ), TAU( * ), U( LDU, * ),
27 * $ V( LDU, * ), WORK( * ), Z( LDU, * )
28 * ..
29 *
30 *
31 *> \par Purpose:
32 * =============
33 *>
34 *> \verbatim
35 *>
36 *> ZDRVST2STG checks the Hermitian eigenvalue problem drivers.
37 *>
38 *> ZHEEVD computes all eigenvalues and, optionally,
39 *> eigenvectors of a complex Hermitian matrix,
40 *> using a divide-and-conquer algorithm.
41 *>
42 *> ZHEEVX computes selected eigenvalues and, optionally,
43 *> eigenvectors of a complex Hermitian matrix.
44 *>
45 *> ZHEEVR computes selected eigenvalues and, optionally,
46 *> eigenvectors of a complex Hermitian matrix
47 *> using the Relatively Robust Representation where it can.
48 *>
49 *> ZHPEVD computes all eigenvalues and, optionally,
50 *> eigenvectors of a complex Hermitian matrix in packed
51 *> storage, using a divide-and-conquer algorithm.
52 *>
53 *> ZHPEVX computes selected eigenvalues and, optionally,
54 *> eigenvectors of a complex Hermitian matrix in packed
55 *> storage.
56 *>
57 *> ZHBEVD computes all eigenvalues and, optionally,
58 *> eigenvectors of a complex Hermitian band matrix,
59 *> using a divide-and-conquer algorithm.
60 *>
61 *> ZHBEVX computes selected eigenvalues and, optionally,
62 *> eigenvectors of a complex Hermitian band matrix.
63 *>
64 *> ZHEEV computes all eigenvalues and, optionally,
65 *> eigenvectors of a complex Hermitian matrix.
66 *>
67 *> ZHPEV computes all eigenvalues and, optionally,
68 *> eigenvectors of a complex Hermitian matrix in packed
69 *> storage.
70 *>
71 *> ZHBEV computes all eigenvalues and, optionally,
72 *> eigenvectors of a complex Hermitian band matrix.
73 *>
74 *> When ZDRVST2STG is called, a number of matrix "sizes" ("n's") and a
75 *> number of matrix "types" are specified. For each size ("n")
76 *> and each type of matrix, one matrix will be generated and used
77 *> to test the appropriate drivers. For each matrix and each
78 *> driver routine called, the following tests will be performed:
79 *>
80 *> (1) | A - Z D Z' | / ( |A| n ulp )
81 *>
82 *> (2) | I - Z Z' | / ( n ulp )
83 *>
84 *> (3) | D1 - D2 | / ( |D1| ulp )
85 *>
86 *> where Z is the matrix of eigenvectors returned when the
87 *> eigenvector option is given and D1 and D2 are the eigenvalues
88 *> returned with and without the eigenvector option.
89 *>
90 *> The "sizes" are specified by an array NN(1:NSIZES); the value of
91 *> each element NN(j) specifies one size.
92 *> The "types" are specified by a logical array DOTYPE( 1:NTYPES );
93 *> if DOTYPE(j) is .TRUE., then matrix type "j" will be generated.
94 *> Currently, the list of possible types is:
95 *>
96 *> (1) The zero matrix.
97 *> (2) The identity matrix.
98 *>
99 *> (3) A diagonal matrix with evenly spaced entries
100 *> 1, ..., ULP and random signs.
101 *> (ULP = (first number larger than 1) - 1 )
102 *> (4) A diagonal matrix with geometrically spaced entries
103 *> 1, ..., ULP and random signs.
104 *> (5) A diagonal matrix with "clustered" entries 1, ULP, ..., ULP
105 *> and random signs.
106 *>
107 *> (6) Same as (4), but multiplied by SQRT( overflow threshold )
108 *> (7) Same as (4), but multiplied by SQRT( underflow threshold )
109 *>
110 *> (8) A matrix of the form U* D U, where U is unitary and
111 *> D has evenly spaced entries 1, ..., ULP with random signs
112 *> on the diagonal.
113 *>
114 *> (9) A matrix of the form U* D U, where U is unitary and
115 *> D has geometrically spaced entries 1, ..., ULP with random
116 *> signs on the diagonal.
117 *>
118 *> (10) A matrix of the form U* D U, where U is unitary and
119 *> D has "clustered" entries 1, ULP,..., ULP with random
120 *> signs on the diagonal.
121 *>
122 *> (11) Same as (8), but multiplied by SQRT( overflow threshold )
123 *> (12) Same as (8), but multiplied by SQRT( underflow threshold )
124 *>
125 *> (13) Symmetric matrix with random entries chosen from (-1,1).
126 *> (14) Same as (13), but multiplied by SQRT( overflow threshold )
127 *> (15) Same as (13), but multiplied by SQRT( underflow threshold )
128 *> (16) A band matrix with half bandwidth randomly chosen between
129 *> 0 and N-1, with evenly spaced eigenvalues 1, ..., ULP
130 *> with random signs.
131 *> (17) Same as (16), but multiplied by SQRT( overflow threshold )
132 *> (18) Same as (16), but multiplied by SQRT( underflow threshold )
133 *> \endverbatim
134 *
135 * Arguments:
136 * ==========
137 *
138 *> \verbatim
139 *> NSIZES INTEGER
140 *> The number of sizes of matrices to use. If it is zero,
141 *> ZDRVST2STG does nothing. It must be at least zero.
142 *> Not modified.
143 *>
144 *> NN INTEGER array, dimension (NSIZES)
145 *> An array containing the sizes to be used for the matrices.
146 *> Zero values will be skipped. The values must be at least
147 *> zero.
148 *> Not modified.
149 *>
150 *> NTYPES INTEGER
151 *> The number of elements in DOTYPE. If it is zero, ZDRVST2STG
152 *> does nothing. It must be at least zero. If it is MAXTYP+1
153 *> and NSIZES is 1, then an additional type, MAXTYP+1 is
154 *> defined, which is to use whatever matrix is in A. This
155 *> is only useful if DOTYPE(1:MAXTYP) is .FALSE. and
156 *> DOTYPE(MAXTYP+1) is .TRUE. .
157 *> Not modified.
158 *>
159 *> DOTYPE LOGICAL array, dimension (NTYPES)
160 *> If DOTYPE(j) is .TRUE., then for each size in NN a
161 *> matrix of that size and of type j will be generated.
162 *> If NTYPES is smaller than the maximum number of types
163 *> defined (PARAMETER MAXTYP), then types NTYPES+1 through
164 *> MAXTYP will not be generated. If NTYPES is larger
165 *> than MAXTYP, DOTYPE(MAXTYP+1) through DOTYPE(NTYPES)
166 *> will be ignored.
167 *> Not modified.
168 *>
169 *> ISEED INTEGER array, dimension (4)
170 *> On entry ISEED specifies the seed of the random number
171 *> generator. The array elements should be between 0 and 4095;
172 *> if not they will be reduced mod 4096. Also, ISEED(4) must
173 *> be odd. The random number generator uses a linear
174 *> congruential sequence limited to small integers, and so
175 *> should produce machine independent random numbers. The
176 *> values of ISEED are changed on exit, and can be used in the
177 *> next call to ZDRVST2STG to continue the same random number
178 *> sequence.
179 *> Modified.
180 *>
181 *> THRESH DOUBLE PRECISION
182 *> A test will count as "failed" if the "error", computed as
183 *> described above, exceeds THRESH. Note that the error
184 *> is scaled to be O(1), so THRESH should be a reasonably
185 *> small multiple of 1, e.g., 10 or 100. In particular,
186 *> it should not depend on the precision (single vs. double)
187 *> or the size of the matrix. It must be at least zero.
188 *> Not modified.
189 *>
190 *> NOUNIT INTEGER
191 *> The FORTRAN unit number for printing out error messages
192 *> (e.g., if a routine returns IINFO not equal to 0.)
193 *> Not modified.
194 *>
195 *> A COMPLEX*16 array, dimension (LDA , max(NN))
196 *> Used to hold the matrix whose eigenvalues are to be
197 *> computed. On exit, A contains the last matrix actually
198 *> used.
199 *> Modified.
200 *>
201 *> LDA INTEGER
202 *> The leading dimension of A. It must be at
203 *> least 1 and at least max( NN ).
204 *> Not modified.
205 *>
206 *> D1 DOUBLE PRECISION array, dimension (max(NN))
207 *> The eigenvalues of A, as computed by ZSTEQR simlutaneously
208 *> with Z. On exit, the eigenvalues in D1 correspond with the
209 *> matrix in A.
210 *> Modified.
211 *>
212 *> D2 DOUBLE PRECISION array, dimension (max(NN))
213 *> The eigenvalues of A, as computed by ZSTEQR if Z is not
214 *> computed. On exit, the eigenvalues in D2 correspond with
215 *> the matrix in A.
216 *> Modified.
217 *>
218 *> D3 DOUBLE PRECISION array, dimension (max(NN))
219 *> The eigenvalues of A, as computed by DSTERF. On exit, the
220 *> eigenvalues in D3 correspond with the matrix in A.
221 *> Modified.
222 *>
223 *> WA1 DOUBLE PRECISION array, dimension
224 *>
225 *> WA2 DOUBLE PRECISION array, dimension
226 *>
227 *> WA3 DOUBLE PRECISION array, dimension
228 *>
229 *> U COMPLEX*16 array, dimension (LDU, max(NN))
230 *> The unitary matrix computed by ZHETRD + ZUNGC3.
231 *> Modified.
232 *>
233 *> LDU INTEGER
234 *> The leading dimension of U, Z, and V. It must be at
235 *> least 1 and at least max( NN ).
236 *> Not modified.
237 *>
238 *> V COMPLEX*16 array, dimension (LDU, max(NN))
239 *> The Housholder vectors computed by ZHETRD in reducing A to
240 *> tridiagonal form.
241 *> Modified.
242 *>
243 *> TAU COMPLEX*16 array, dimension (max(NN))
244 *> The Householder factors computed by ZHETRD in reducing A
245 *> to tridiagonal form.
246 *> Modified.
247 *>
248 *> Z COMPLEX*16 array, dimension (LDU, max(NN))
249 *> The unitary matrix of eigenvectors computed by ZHEEVD,
250 *> ZHEEVX, ZHPEVD, CHPEVX, ZHBEVD, and CHBEVX.
251 *> Modified.
252 *>
253 *> WORK - COMPLEX*16 array of dimension ( LWORK )
254 *> Workspace.
255 *> Modified.
256 *>
257 *> LWORK - INTEGER
258 *> The number of entries in WORK. This must be at least
259 *> 2*max( NN(j), 2 )**2.
260 *> Not modified.
261 *>
262 *> RWORK DOUBLE PRECISION array, dimension (3*max(NN))
263 *> Workspace.
264 *> Modified.
265 *>
266 *> LRWORK - INTEGER
267 *> The number of entries in RWORK.
268 *>
269 *> IWORK INTEGER array, dimension (6*max(NN))
270 *> Workspace.
271 *> Modified.
272 *>
273 *> LIWORK - INTEGER
274 *> The number of entries in IWORK.
275 *>
276 *> RESULT DOUBLE PRECISION array, dimension (??)
277 *> The values computed by the tests described above.
278 *> The values are currently limited to 1/ulp, to avoid
279 *> overflow.
280 *> Modified.
281 *>
282 *> INFO INTEGER
283 *> If 0, then everything ran OK.
284 *> -1: NSIZES < 0
285 *> -2: Some NN(j) < 0
286 *> -3: NTYPES < 0
287 *> -5: THRESH < 0
288 *> -9: LDA < 1 or LDA < NMAX, where NMAX is max( NN(j) ).
289 *> -16: LDU < 1 or LDU < NMAX.
290 *> -21: LWORK too small.
291 *> If DLATMR, SLATMS, ZHETRD, DORGC3, ZSTEQR, DSTERF,
292 *> or DORMC2 returns an error code, the
293 *> absolute value of it is returned.
294 *> Modified.
295 *>
296 *>-----------------------------------------------------------------------
297 *>
298 *> Some Local Variables and Parameters:
299 *> ---- ----- --------- --- ----------
300 *> ZERO, ONE Real 0 and 1.
301 *> MAXTYP The number of types defined.
302 *> NTEST The number of tests performed, or which can
303 *> be performed so far, for the current matrix.
304 *> NTESTT The total number of tests performed so far.
305 *> NMAX Largest value in NN.
306 *> NMATS The number of matrices generated so far.
307 *> NERRS The number of tests which have exceeded THRESH
308 *> so far (computed by DLAFTS).
309 *> COND, IMODE Values to be passed to the matrix generators.
310 *> ANORM Norm of A; passed to matrix generators.
311 *>
312 *> OVFL, UNFL Overflow and underflow thresholds.
313 *> ULP, ULPINV Finest relative precision and its inverse.
314 *> RTOVFL, RTUNFL Square roots of the previous 2 values.
315 *> The following four arrays decode JTYPE:
316 *> KTYPE(j) The general type (1-10) for type "j".
317 *> KMODE(j) The MODE value to be passed to the matrix
318 *> generator for type "j".
319 *> KMAGN(j) The order of magnitude ( O(1),
320 *> O(overflow^(1/2) ), O(underflow^(1/2) )
321 *> \endverbatim
322 *
323 * Authors:
324 * ========
325 *
326 *> \author Univ. of Tennessee
327 *> \author Univ. of California Berkeley
328 *> \author Univ. of Colorado Denver
329 *> \author NAG Ltd.
330 *
331 *> \ingroup complex16_eig
332 *
333 * =====================================================================
334  SUBROUTINE zdrvst2stg( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
335  $ NOUNIT, A, LDA, D1, D2, D3, WA1, WA2, WA3, U,
336  $ LDU, V, TAU, Z, WORK, LWORK, RWORK, LRWORK,
337  $ IWORK, LIWORK, RESULT, INFO )
338 *
339 * -- LAPACK test routine --
340 * -- LAPACK is a software package provided by Univ. of Tennessee, --
341 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
342 *
343 * .. Scalar Arguments ..
344  INTEGER INFO, LDA, LDU, LIWORK, LRWORK, LWORK, NOUNIT,
345  $ NSIZES, NTYPES
346  DOUBLE PRECISION THRESH
347 * ..
348 * .. Array Arguments ..
349  LOGICAL DOTYPE( * )
350  INTEGER ISEED( 4 ), IWORK( * ), NN( * )
351  DOUBLE PRECISION D1( * ), D2( * ), D3( * ), RESULT( * ),
352  $ rwork( * ), wa1( * ), wa2( * ), wa3( * )
353  COMPLEX*16 A( LDA, * ), TAU( * ), U( LDU, * ),
354  $ v( ldu, * ), work( * ), z( ldu, * )
355 * ..
356 *
357 * =====================================================================
358 *
359 *
360 * .. Parameters ..
361  DOUBLE PRECISION ZERO, ONE, TWO, TEN
362  PARAMETER ( ZERO = 0.0d+0, one = 1.0d+0, two = 2.0d+0,
363  $ ten = 10.0d+0 )
364  DOUBLE PRECISION HALF
365  parameter( half = one / two )
366  COMPLEX*16 CZERO, CONE
367  parameter( czero = ( 0.0d+0, 0.0d+0 ),
368  $ cone = ( 1.0d+0, 0.0d+0 ) )
369  INTEGER MAXTYP
370  parameter( maxtyp = 18 )
371 * ..
372 * .. Local Scalars ..
373  LOGICAL BADNN
374  CHARACTER UPLO
375  INTEGER I, IDIAG, IHBW, IINFO, IL, IMODE, INDWRK, INDX,
376  $ irow, itemp, itype, iu, iuplo, j, j1, j2, jcol,
377  $ jsize, jtype, kd, lgn, liwedc, lrwedc, lwedc,
378  $ m, m2, m3, mtypes, n, nerrs, nmats, nmax,
379  $ ntest, ntestt
380  DOUBLE PRECISION ABSTOL, ANINV, ANORM, COND, OVFL, RTOVFL,
381  $ RTUNFL, TEMP1, TEMP2, TEMP3, ULP, ULPINV, UNFL,
382  $ VL, VU
383 * ..
384 * .. Local Arrays ..
385  INTEGER IDUMMA( 1 ), IOLDSD( 4 ), ISEED2( 4 ),
386  $ ISEED3( 4 ), KMAGN( MAXTYP ), KMODE( MAXTYP ),
387  $ KTYPE( MAXTYP )
388 * ..
389 * .. External Functions ..
390  DOUBLE PRECISION DLAMCH, DLARND, DSXT1
391  EXTERNAL DLAMCH, DLARND, DSXT1
392 * ..
393 * .. External Subroutines ..
394  EXTERNAL alasvm, dlabad, dlafts, xerbla, zhbev, zhbevd,
395  $ zhbevx, zheev, zheevd, zheevr, zheevx, zhet21,
396  $ zhet22, zhpev, zhpevd, zhpevx, zlacpy, zlaset,
397  $ zheevd_2stage, zheevr_2stage, zheevx_2stage,
398  $ zheev_2stage, zhbev_2stage, zhbevd_2stage,
399  $ zhbevx_2stage, zhetrd_2stage, zlatmr, zlatms
400 * ..
401 * .. Intrinsic Functions ..
402  INTRINSIC abs, dble, int, log, max, min, sqrt
403 * ..
404 * .. Data statements ..
405  DATA ktype / 1, 2, 5*4, 5*5, 3*8, 3*9 /
406  DATA kmagn / 2*1, 1, 1, 1, 2, 3, 1, 1, 1, 2, 3, 1,
407  $ 2, 3, 1, 2, 3 /
408  DATA kmode / 2*0, 4, 3, 1, 4, 4, 4, 3, 1, 4, 4, 0,
409  $ 0, 0, 4, 4, 4 /
410 * ..
411 * .. Executable Statements ..
412 *
413 * 1) Check for errors
414 *
415  ntestt = 0
416  info = 0
417 *
418  badnn = .false.
419  nmax = 1
420  DO 10 j = 1, nsizes
421  nmax = max( nmax, nn( j ) )
422  IF( nn( j ).LT.0 )
423  $ badnn = .true.
424  10 CONTINUE
425 *
426 * Check for errors
427 *
428  IF( nsizes.LT.0 ) THEN
429  info = -1
430  ELSE IF( badnn ) THEN
431  info = -2
432  ELSE IF( ntypes.LT.0 ) THEN
433  info = -3
434  ELSE IF( lda.LT.nmax ) THEN
435  info = -9
436  ELSE IF( ldu.LT.nmax ) THEN
437  info = -16
438  ELSE IF( 2*max( 2, nmax )**2.GT.lwork ) THEN
439  info = -22
440  END IF
441 *
442  IF( info.NE.0 ) THEN
443  CALL xerbla( 'ZDRVST2STG', -info )
444  RETURN
445  END IF
446 *
447 * Quick return if nothing to do
448 *
449  IF( nsizes.EQ.0 .OR. ntypes.EQ.0 )
450  $ RETURN
451 *
452 * More Important constants
453 *
454  unfl = dlamch( 'Safe minimum' )
455  ovfl = dlamch( 'Overflow' )
456  CALL dlabad( unfl, ovfl )
457  ulp = dlamch( 'Epsilon' )*dlamch( 'Base' )
458  ulpinv = one / ulp
459  rtunfl = sqrt( unfl )
460  rtovfl = sqrt( ovfl )
461 *
462 * Loop over sizes, types
463 *
464  DO 20 i = 1, 4
465  iseed2( i ) = iseed( i )
466  iseed3( i ) = iseed( i )
467  20 CONTINUE
468 *
469  nerrs = 0
470  nmats = 0
471 *
472  DO 1220 jsize = 1, nsizes
473  n = nn( jsize )
474  IF( n.GT.0 ) THEN
475  lgn = int( log( dble( n ) ) / log( two ) )
476  IF( 2**lgn.LT.n )
477  $ lgn = lgn + 1
478  IF( 2**lgn.LT.n )
479  $ lgn = lgn + 1
480  lwedc = max( 2*n+n*n, 2*n*n )
481  lrwedc = 1 + 4*n + 2*n*lgn + 3*n**2
482  liwedc = 3 + 5*n
483  ELSE
484  lwedc = 2
485  lrwedc = 8
486  liwedc = 8
487  END IF
488  aninv = one / dble( max( 1, n ) )
489 *
490  IF( nsizes.NE.1 ) THEN
491  mtypes = min( maxtyp, ntypes )
492  ELSE
493  mtypes = min( maxtyp+1, ntypes )
494  END IF
495 *
496  DO 1210 jtype = 1, mtypes
497  IF( .NOT.dotype( jtype ) )
498  $ GO TO 1210
499  nmats = nmats + 1
500  ntest = 0
501 *
502  DO 30 j = 1, 4
503  ioldsd( j ) = iseed( j )
504  30 CONTINUE
505 *
506 * 2) Compute "A"
507 *
508 * Control parameters:
509 *
510 * KMAGN KMODE KTYPE
511 * =1 O(1) clustered 1 zero
512 * =2 large clustered 2 identity
513 * =3 small exponential (none)
514 * =4 arithmetic diagonal, (w/ eigenvalues)
515 * =5 random log Hermitian, w/ eigenvalues
516 * =6 random (none)
517 * =7 random diagonal
518 * =8 random Hermitian
519 * =9 band Hermitian, w/ eigenvalues
520 *
521  IF( mtypes.GT.maxtyp )
522  $ GO TO 110
523 *
524  itype = ktype( jtype )
525  imode = kmode( jtype )
526 *
527 * Compute norm
528 *
529  GO TO ( 40, 50, 60 )kmagn( jtype )
530 *
531  40 CONTINUE
532  anorm = one
533  GO TO 70
534 *
535  50 CONTINUE
536  anorm = ( rtovfl*ulp )*aninv
537  GO TO 70
538 *
539  60 CONTINUE
540  anorm = rtunfl*n*ulpinv
541  GO TO 70
542 *
543  70 CONTINUE
544 *
545  CALL zlaset( 'Full', lda, n, czero, czero, a, lda )
546  iinfo = 0
547  cond = ulpinv
548 *
549 * Special Matrices -- Identity & Jordan block
550 *
551 * Zero
552 *
553  IF( itype.EQ.1 ) THEN
554  iinfo = 0
555 *
556  ELSE IF( itype.EQ.2 ) THEN
557 *
558 * Identity
559 *
560  DO 80 jcol = 1, n
561  a( jcol, jcol ) = anorm
562  80 CONTINUE
563 *
564  ELSE IF( itype.EQ.4 ) THEN
565 *
566 * Diagonal Matrix, [Eigen]values Specified
567 *
568  CALL zlatms( n, n, 'S', iseed, 'H', rwork, imode, cond,
569  $ anorm, 0, 0, 'N', a, lda, work, iinfo )
570 *
571  ELSE IF( itype.EQ.5 ) THEN
572 *
573 * Hermitian, eigenvalues specified
574 *
575  CALL zlatms( n, n, 'S', iseed, 'H', rwork, imode, cond,
576  $ anorm, n, n, 'N', a, lda, work, iinfo )
577 *
578  ELSE IF( itype.EQ.7 ) THEN
579 *
580 * Diagonal, random eigenvalues
581 *
582  CALL zlatmr( n, n, 'S', iseed, 'H', work, 6, one, cone,
583  $ 'T', 'N', work( n+1 ), 1, one,
584  $ work( 2*n+1 ), 1, one, 'N', idumma, 0, 0,
585  $ zero, anorm, 'NO', a, lda, iwork, iinfo )
586 *
587  ELSE IF( itype.EQ.8 ) THEN
588 *
589 * Hermitian, random eigenvalues
590 *
591  CALL zlatmr( n, n, 'S', iseed, 'H', work, 6, one, cone,
592  $ 'T', 'N', work( n+1 ), 1, one,
593  $ work( 2*n+1 ), 1, one, 'N', idumma, n, n,
594  $ zero, anorm, 'NO', a, lda, iwork, iinfo )
595 *
596  ELSE IF( itype.EQ.9 ) THEN
597 *
598 * Hermitian banded, eigenvalues specified
599 *
600  ihbw = int( ( n-1 )*dlarnd( 1, iseed3 ) )
601  CALL zlatms( n, n, 'S', iseed, 'H', rwork, imode, cond,
602  $ anorm, ihbw, ihbw, 'Z', u, ldu, work,
603  $ iinfo )
604 *
605 * Store as dense matrix for most routines.
606 *
607  CALL zlaset( 'Full', lda, n, czero, czero, a, lda )
608  DO 100 idiag = -ihbw, ihbw
609  irow = ihbw - idiag + 1
610  j1 = max( 1, idiag+1 )
611  j2 = min( n, n+idiag )
612  DO 90 j = j1, j2
613  i = j - idiag
614  a( i, j ) = u( irow, j )
615  90 CONTINUE
616  100 CONTINUE
617  ELSE
618  iinfo = 1
619  END IF
620 *
621  IF( iinfo.NE.0 ) THEN
622  WRITE( nounit, fmt = 9999 )'Generator', iinfo, n, jtype,
623  $ ioldsd
624  info = abs( iinfo )
625  RETURN
626  END IF
627 *
628  110 CONTINUE
629 *
630  abstol = unfl + unfl
631  IF( n.LE.1 ) THEN
632  il = 1
633  iu = n
634  ELSE
635  il = 1 + int( ( n-1 )*dlarnd( 1, iseed2 ) )
636  iu = 1 + int( ( n-1 )*dlarnd( 1, iseed2 ) )
637  IF( il.GT.iu ) THEN
638  itemp = il
639  il = iu
640  iu = itemp
641  END IF
642  END IF
643 *
644 * Perform tests storing upper or lower triangular
645 * part of matrix.
646 *
647  DO 1200 iuplo = 0, 1
648  IF( iuplo.EQ.0 ) THEN
649  uplo = 'L'
650  ELSE
651  uplo = 'U'
652  END IF
653 *
654 * Call ZHEEVD and CHEEVX.
655 *
656  CALL zlacpy( ' ', n, n, a, lda, v, ldu )
657 *
658  ntest = ntest + 1
659  CALL zheevd( 'V', uplo, n, a, ldu, d1, work, lwedc,
660  $ rwork, lrwedc, iwork, liwedc, iinfo )
661  IF( iinfo.NE.0 ) THEN
662  WRITE( nounit, fmt = 9999 )'ZHEEVD(V,' // uplo //
663  $ ')', iinfo, n, jtype, ioldsd
664  info = abs( iinfo )
665  IF( iinfo.LT.0 ) THEN
666  RETURN
667  ELSE
668  result( ntest ) = ulpinv
669  result( ntest+1 ) = ulpinv
670  result( ntest+2 ) = ulpinv
671  GO TO 130
672  END IF
673  END IF
674 *
675 * Do tests 1 and 2.
676 *
677  CALL zhet21( 1, uplo, n, 0, v, ldu, d1, d2, a, ldu, z,
678  $ ldu, tau, work, rwork, result( ntest ) )
679 *
680  CALL zlacpy( ' ', n, n, v, ldu, a, lda )
681 *
682  ntest = ntest + 2
683  CALL zheevd_2stage( 'N', uplo, n, a, ldu, d3, work,
684  $ lwork, rwork, lrwedc, iwork, liwedc, iinfo )
685  IF( iinfo.NE.0 ) THEN
686  WRITE( nounit, fmt = 9999 )
687  $ 'ZHEEVD_2STAGE(N,' // uplo //
688  $ ')', iinfo, n, jtype, ioldsd
689  info = abs( iinfo )
690  IF( iinfo.LT.0 ) THEN
691  RETURN
692  ELSE
693  result( ntest ) = ulpinv
694  GO TO 130
695  END IF
696  END IF
697 *
698 * Do test 3.
699 *
700  temp1 = zero
701  temp2 = zero
702  DO 120 j = 1, n
703  temp1 = max( temp1, abs( d1( j ) ), abs( d3( j ) ) )
704  temp2 = max( temp2, abs( d1( j )-d3( j ) ) )
705  120 CONTINUE
706  result( ntest ) = temp2 / max( unfl,
707  $ ulp*max( temp1, temp2 ) )
708 *
709  130 CONTINUE
710  CALL zlacpy( ' ', n, n, v, ldu, a, lda )
711 *
712  ntest = ntest + 1
713 *
714  IF( n.GT.0 ) THEN
715  temp3 = max( abs( d1( 1 ) ), abs( d1( n ) ) )
716  IF( il.NE.1 ) THEN
717  vl = d1( il ) - max( half*( d1( il )-d1( il-1 ) ),
718  $ ten*ulp*temp3, ten*rtunfl )
719  ELSE IF( n.GT.0 ) THEN
720  vl = d1( 1 ) - max( half*( d1( n )-d1( 1 ) ),
721  $ ten*ulp*temp3, ten*rtunfl )
722  END IF
723  IF( iu.NE.n ) THEN
724  vu = d1( iu ) + max( half*( d1( iu+1 )-d1( iu ) ),
725  $ ten*ulp*temp3, ten*rtunfl )
726  ELSE IF( n.GT.0 ) THEN
727  vu = d1( n ) + max( half*( d1( n )-d1( 1 ) ),
728  $ ten*ulp*temp3, ten*rtunfl )
729  END IF
730  ELSE
731  temp3 = zero
732  vl = zero
733  vu = one
734  END IF
735 *
736  CALL zheevx( 'V', 'A', uplo, n, a, ldu, vl, vu, il, iu,
737  $ abstol, m, wa1, z, ldu, work, lwork, rwork,
738  $ iwork, iwork( 5*n+1 ), iinfo )
739  IF( iinfo.NE.0 ) THEN
740  WRITE( nounit, fmt = 9999 )'ZHEEVX(V,A,' // uplo //
741  $ ')', iinfo, n, jtype, ioldsd
742  info = abs( iinfo )
743  IF( iinfo.LT.0 ) THEN
744  RETURN
745  ELSE
746  result( ntest ) = ulpinv
747  result( ntest+1 ) = ulpinv
748  result( ntest+2 ) = ulpinv
749  GO TO 150
750  END IF
751  END IF
752 *
753 * Do tests 4 and 5.
754 *
755  CALL zlacpy( ' ', n, n, v, ldu, a, lda )
756 *
757  CALL zhet21( 1, uplo, n, 0, a, ldu, wa1, d2, z, ldu, v,
758  $ ldu, tau, work, rwork, result( ntest ) )
759 *
760  ntest = ntest + 2
761  CALL zheevx_2stage( 'N', 'A', uplo, n, a, ldu, vl, vu,
762  $ il, iu, abstol, m2, wa2, z, ldu,
763  $ work, lwork, rwork, iwork,
764  $ iwork( 5*n+1 ), iinfo )
765  IF( iinfo.NE.0 ) THEN
766  WRITE( nounit, fmt = 9999 )
767  $ 'ZHEEVX_2STAGE(N,A,' // uplo //
768  $ ')', iinfo, n, jtype, ioldsd
769  info = abs( iinfo )
770  IF( iinfo.LT.0 ) THEN
771  RETURN
772  ELSE
773  result( ntest ) = ulpinv
774  GO TO 150
775  END IF
776  END IF
777 *
778 * Do test 6.
779 *
780  temp1 = zero
781  temp2 = zero
782  DO 140 j = 1, n
783  temp1 = max( temp1, abs( wa1( j ) ), abs( wa2( j ) ) )
784  temp2 = max( temp2, abs( wa1( j )-wa2( j ) ) )
785  140 CONTINUE
786  result( ntest ) = temp2 / max( unfl,
787  $ ulp*max( temp1, temp2 ) )
788 *
789  150 CONTINUE
790  CALL zlacpy( ' ', n, n, v, ldu, a, lda )
791 *
792  ntest = ntest + 1
793 *
794  CALL zheevx( 'V', 'I', uplo, n, a, ldu, vl, vu, il, iu,
795  $ abstol, m2, wa2, z, ldu, work, lwork, rwork,
796  $ iwork, iwork( 5*n+1 ), iinfo )
797  IF( iinfo.NE.0 ) THEN
798  WRITE( nounit, fmt = 9999 )'ZHEEVX(V,I,' // uplo //
799  $ ')', iinfo, n, jtype, ioldsd
800  info = abs( iinfo )
801  IF( iinfo.LT.0 ) THEN
802  RETURN
803  ELSE
804  result( ntest ) = ulpinv
805  GO TO 160
806  END IF
807  END IF
808 *
809 * Do tests 7 and 8.
810 *
811  CALL zlacpy( ' ', n, n, v, ldu, a, lda )
812 *
813  CALL zhet22( 1, uplo, n, m2, 0, a, ldu, wa2, d2, z, ldu,
814  $ v, ldu, tau, work, rwork, result( ntest ) )
815 *
816  ntest = ntest + 2
817 *
818  CALL zheevx_2stage( 'N', 'I', uplo, n, a, ldu, vl, vu,
819  $ il, iu, abstol, m3, wa3, z, ldu,
820  $ work, lwork, rwork, iwork,
821  $ iwork( 5*n+1 ), iinfo )
822  IF( iinfo.NE.0 ) THEN
823  WRITE( nounit, fmt = 9999 )
824  $ 'ZHEEVX_2STAGE(N,I,' // uplo //
825  $ ')', iinfo, n, jtype, ioldsd
826  info = abs( iinfo )
827  IF( iinfo.LT.0 ) THEN
828  RETURN
829  ELSE
830  result( ntest ) = ulpinv
831  GO TO 160
832  END IF
833  END IF
834 *
835 * Do test 9.
836 *
837  temp1 = dsxt1( 1, wa2, m2, wa3, m3, abstol, ulp, unfl )
838  temp2 = dsxt1( 1, wa3, m3, wa2, m2, abstol, ulp, unfl )
839  IF( n.GT.0 ) THEN
840  temp3 = max( abs( wa1( 1 ) ), abs( wa1( n ) ) )
841  ELSE
842  temp3 = zero
843  END IF
844  result( ntest ) = ( temp1+temp2 ) /
845  $ max( unfl, temp3*ulp )
846 *
847  160 CONTINUE
848  CALL zlacpy( ' ', n, n, v, ldu, a, lda )
849 *
850  ntest = ntest + 1
851 *
852  CALL zheevx( 'V', 'V', uplo, n, a, ldu, vl, vu, il, iu,
853  $ abstol, m2, wa2, z, ldu, work, lwork, rwork,
854  $ iwork, iwork( 5*n+1 ), iinfo )
855  IF( iinfo.NE.0 ) THEN
856  WRITE( nounit, fmt = 9999 )'ZHEEVX(V,V,' // uplo //
857  $ ')', iinfo, n, jtype, ioldsd
858  info = abs( iinfo )
859  IF( iinfo.LT.0 ) THEN
860  RETURN
861  ELSE
862  result( ntest ) = ulpinv
863  GO TO 170
864  END IF
865  END IF
866 *
867 * Do tests 10 and 11.
868 *
869  CALL zlacpy( ' ', n, n, v, ldu, a, lda )
870 *
871  CALL zhet22( 1, uplo, n, m2, 0, a, ldu, wa2, d2, z, ldu,
872  $ v, ldu, tau, work, rwork, result( ntest ) )
873 *
874  ntest = ntest + 2
875 *
876  CALL zheevx_2stage( 'N', 'V', uplo, n, a, ldu, vl, vu,
877  $ il, iu, abstol, m3, wa3, z, ldu,
878  $ work, lwork, rwork, iwork,
879  $ iwork( 5*n+1 ), iinfo )
880  IF( iinfo.NE.0 ) THEN
881  WRITE( nounit, fmt = 9999 )
882  $ 'ZHEEVX_2STAGE(N,V,' // uplo //
883  $ ')', iinfo, n, jtype, ioldsd
884  info = abs( iinfo )
885  IF( iinfo.LT.0 ) THEN
886  RETURN
887  ELSE
888  result( ntest ) = ulpinv
889  GO TO 170
890  END IF
891  END IF
892 *
893  IF( m3.EQ.0 .AND. n.GT.0 ) THEN
894  result( ntest ) = ulpinv
895  GO TO 170
896  END IF
897 *
898 * Do test 12.
899 *
900  temp1 = dsxt1( 1, wa2, m2, wa3, m3, abstol, ulp, unfl )
901  temp2 = dsxt1( 1, wa3, m3, wa2, m2, abstol, ulp, unfl )
902  IF( n.GT.0 ) THEN
903  temp3 = max( abs( wa1( 1 ) ), abs( wa1( n ) ) )
904  ELSE
905  temp3 = zero
906  END IF
907  result( ntest ) = ( temp1+temp2 ) /
908  $ max( unfl, temp3*ulp )
909 *
910  170 CONTINUE
911 *
912 * Call ZHPEVD and CHPEVX.
913 *
914  CALL zlacpy( ' ', n, n, v, ldu, a, lda )
915 *
916 * Load array WORK with the upper or lower triangular
917 * part of the matrix in packed form.
918 *
919  IF( iuplo.EQ.1 ) THEN
920  indx = 1
921  DO 190 j = 1, n
922  DO 180 i = 1, j
923  work( indx ) = a( i, j )
924  indx = indx + 1
925  180 CONTINUE
926  190 CONTINUE
927  ELSE
928  indx = 1
929  DO 210 j = 1, n
930  DO 200 i = j, n
931  work( indx ) = a( i, j )
932  indx = indx + 1
933  200 CONTINUE
934  210 CONTINUE
935  END IF
936 *
937  ntest = ntest + 1
938  indwrk = n*( n+1 ) / 2 + 1
939  CALL zhpevd( 'V', uplo, n, work, d1, z, ldu,
940  $ work( indwrk ), lwedc, rwork, lrwedc, iwork,
941  $ liwedc, iinfo )
942  IF( iinfo.NE.0 ) THEN
943  WRITE( nounit, fmt = 9999 )'ZHPEVD(V,' // uplo //
944  $ ')', iinfo, n, jtype, ioldsd
945  info = abs( iinfo )
946  IF( iinfo.LT.0 ) THEN
947  RETURN
948  ELSE
949  result( ntest ) = ulpinv
950  result( ntest+1 ) = ulpinv
951  result( ntest+2 ) = ulpinv
952  GO TO 270
953  END IF
954  END IF
955 *
956 * Do tests 13 and 14.
957 *
958  CALL zhet21( 1, uplo, n, 0, a, lda, d1, d2, z, ldu, v,
959  $ ldu, tau, work, rwork, result( ntest ) )
960 *
961  IF( iuplo.EQ.1 ) THEN
962  indx = 1
963  DO 230 j = 1, n
964  DO 220 i = 1, j
965  work( indx ) = a( i, j )
966  indx = indx + 1
967  220 CONTINUE
968  230 CONTINUE
969  ELSE
970  indx = 1
971  DO 250 j = 1, n
972  DO 240 i = j, n
973  work( indx ) = a( i, j )
974  indx = indx + 1
975  240 CONTINUE
976  250 CONTINUE
977  END IF
978 *
979  ntest = ntest + 2
980  indwrk = n*( n+1 ) / 2 + 1
981  CALL zhpevd( 'N', uplo, n, work, d3, z, ldu,
982  $ work( indwrk ), lwedc, rwork, lrwedc, iwork,
983  $ liwedc, iinfo )
984  IF( iinfo.NE.0 ) THEN
985  WRITE( nounit, fmt = 9999 )'ZHPEVD(N,' // uplo //
986  $ ')', iinfo, n, jtype, ioldsd
987  info = abs( iinfo )
988  IF( iinfo.LT.0 ) THEN
989  RETURN
990  ELSE
991  result( ntest ) = ulpinv
992  GO TO 270
993  END IF
994  END IF
995 *
996 * Do test 15.
997 *
998  temp1 = zero
999  temp2 = zero
1000  DO 260 j = 1, n
1001  temp1 = max( temp1, abs( d1( j ) ), abs( d3( j ) ) )
1002  temp2 = max( temp2, abs( d1( j )-d3( j ) ) )
1003  260 CONTINUE
1004  result( ntest ) = temp2 / max( unfl,
1005  $ ulp*max( temp1, temp2 ) )
1006 *
1007 * Load array WORK with the upper or lower triangular part
1008 * of the matrix in packed form.
1009 *
1010  270 CONTINUE
1011  IF( iuplo.EQ.1 ) THEN
1012  indx = 1
1013  DO 290 j = 1, n
1014  DO 280 i = 1, j
1015  work( indx ) = a( i, j )
1016  indx = indx + 1
1017  280 CONTINUE
1018  290 CONTINUE
1019  ELSE
1020  indx = 1
1021  DO 310 j = 1, n
1022  DO 300 i = j, n
1023  work( indx ) = a( i, j )
1024  indx = indx + 1
1025  300 CONTINUE
1026  310 CONTINUE
1027  END IF
1028 *
1029  ntest = ntest + 1
1030 *
1031  IF( n.GT.0 ) THEN
1032  temp3 = max( abs( d1( 1 ) ), abs( d1( n ) ) )
1033  IF( il.NE.1 ) THEN
1034  vl = d1( il ) - max( half*( d1( il )-d1( il-1 ) ),
1035  $ ten*ulp*temp3, ten*rtunfl )
1036  ELSE IF( n.GT.0 ) THEN
1037  vl = d1( 1 ) - max( half*( d1( n )-d1( 1 ) ),
1038  $ ten*ulp*temp3, ten*rtunfl )
1039  END IF
1040  IF( iu.NE.n ) THEN
1041  vu = d1( iu ) + max( half*( d1( iu+1 )-d1( iu ) ),
1042  $ ten*ulp*temp3, ten*rtunfl )
1043  ELSE IF( n.GT.0 ) THEN
1044  vu = d1( n ) + max( half*( d1( n )-d1( 1 ) ),
1045  $ ten*ulp*temp3, ten*rtunfl )
1046  END IF
1047  ELSE
1048  temp3 = zero
1049  vl = zero
1050  vu = one
1051  END IF
1052 *
1053  CALL zhpevx( 'V', 'A', uplo, n, work, vl, vu, il, iu,
1054  $ abstol, m, wa1, z, ldu, v, rwork, iwork,
1055  $ iwork( 5*n+1 ), iinfo )
1056  IF( iinfo.NE.0 ) THEN
1057  WRITE( nounit, fmt = 9999 )'ZHPEVX(V,A,' // uplo //
1058  $ ')', iinfo, n, jtype, ioldsd
1059  info = abs( iinfo )
1060  IF( iinfo.LT.0 ) THEN
1061  RETURN
1062  ELSE
1063  result( ntest ) = ulpinv
1064  result( ntest+1 ) = ulpinv
1065  result( ntest+2 ) = ulpinv
1066  GO TO 370
1067  END IF
1068  END IF
1069 *
1070 * Do tests 16 and 17.
1071 *
1072  CALL zhet21( 1, uplo, n, 0, a, ldu, wa1, d2, z, ldu, v,
1073  $ ldu, tau, work, rwork, result( ntest ) )
1074 *
1075  ntest = ntest + 2
1076 *
1077  IF( iuplo.EQ.1 ) THEN
1078  indx = 1
1079  DO 330 j = 1, n
1080  DO 320 i = 1, j
1081  work( indx ) = a( i, j )
1082  indx = indx + 1
1083  320 CONTINUE
1084  330 CONTINUE
1085  ELSE
1086  indx = 1
1087  DO 350 j = 1, n
1088  DO 340 i = j, n
1089  work( indx ) = a( i, j )
1090  indx = indx + 1
1091  340 CONTINUE
1092  350 CONTINUE
1093  END IF
1094 *
1095  CALL zhpevx( 'N', 'A', uplo, n, work, vl, vu, il, iu,
1096  $ abstol, m2, wa2, z, ldu, v, rwork, iwork,
1097  $ iwork( 5*n+1 ), iinfo )
1098  IF( iinfo.NE.0 ) THEN
1099  WRITE( nounit, fmt = 9999 )'ZHPEVX(N,A,' // uplo //
1100  $ ')', iinfo, n, jtype, ioldsd
1101  info = abs( iinfo )
1102  IF( iinfo.LT.0 ) THEN
1103  RETURN
1104  ELSE
1105  result( ntest ) = ulpinv
1106  GO TO 370
1107  END IF
1108  END IF
1109 *
1110 * Do test 18.
1111 *
1112  temp1 = zero
1113  temp2 = zero
1114  DO 360 j = 1, n
1115  temp1 = max( temp1, abs( wa1( j ) ), abs( wa2( j ) ) )
1116  temp2 = max( temp2, abs( wa1( j )-wa2( j ) ) )
1117  360 CONTINUE
1118  result( ntest ) = temp2 / max( unfl,
1119  $ ulp*max( temp1, temp2 ) )
1120 *
1121  370 CONTINUE
1122  ntest = ntest + 1
1123  IF( iuplo.EQ.1 ) THEN
1124  indx = 1
1125  DO 390 j = 1, n
1126  DO 380 i = 1, j
1127  work( indx ) = a( i, j )
1128  indx = indx + 1
1129  380 CONTINUE
1130  390 CONTINUE
1131  ELSE
1132  indx = 1
1133  DO 410 j = 1, n
1134  DO 400 i = j, n
1135  work( indx ) = a( i, j )
1136  indx = indx + 1
1137  400 CONTINUE
1138  410 CONTINUE
1139  END IF
1140 *
1141  CALL zhpevx( 'V', 'I', uplo, n, work, vl, vu, il, iu,
1142  $ abstol, m2, wa2, z, ldu, v, rwork, iwork,
1143  $ iwork( 5*n+1 ), iinfo )
1144  IF( iinfo.NE.0 ) THEN
1145  WRITE( nounit, fmt = 9999 )'ZHPEVX(V,I,' // uplo //
1146  $ ')', iinfo, n, jtype, ioldsd
1147  info = abs( iinfo )
1148  IF( iinfo.LT.0 ) THEN
1149  RETURN
1150  ELSE
1151  result( ntest ) = ulpinv
1152  result( ntest+1 ) = ulpinv
1153  result( ntest+2 ) = ulpinv
1154  GO TO 460
1155  END IF
1156  END IF
1157 *
1158 * Do tests 19 and 20.
1159 *
1160  CALL zhet22( 1, uplo, n, m2, 0, a, ldu, wa2, d2, z, ldu,
1161  $ v, ldu, tau, work, rwork, result( ntest ) )
1162 *
1163  ntest = ntest + 2
1164 *
1165  IF( iuplo.EQ.1 ) THEN
1166  indx = 1
1167  DO 430 j = 1, n
1168  DO 420 i = 1, j
1169  work( indx ) = a( i, j )
1170  indx = indx + 1
1171  420 CONTINUE
1172  430 CONTINUE
1173  ELSE
1174  indx = 1
1175  DO 450 j = 1, n
1176  DO 440 i = j, n
1177  work( indx ) = a( i, j )
1178  indx = indx + 1
1179  440 CONTINUE
1180  450 CONTINUE
1181  END IF
1182 *
1183  CALL zhpevx( 'N', 'I', uplo, n, work, vl, vu, il, iu,
1184  $ abstol, m3, wa3, z, ldu, v, rwork, iwork,
1185  $ iwork( 5*n+1 ), iinfo )
1186  IF( iinfo.NE.0 ) THEN
1187  WRITE( nounit, fmt = 9999 )'ZHPEVX(N,I,' // uplo //
1188  $ ')', iinfo, n, jtype, ioldsd
1189  info = abs( iinfo )
1190  IF( iinfo.LT.0 ) THEN
1191  RETURN
1192  ELSE
1193  result( ntest ) = ulpinv
1194  GO TO 460
1195  END IF
1196  END IF
1197 *
1198 * Do test 21.
1199 *
1200  temp1 = dsxt1( 1, wa2, m2, wa3, m3, abstol, ulp, unfl )
1201  temp2 = dsxt1( 1, wa3, m3, wa2, m2, abstol, ulp, unfl )
1202  IF( n.GT.0 ) THEN
1203  temp3 = max( abs( wa1( 1 ) ), abs( wa1( n ) ) )
1204  ELSE
1205  temp3 = zero
1206  END IF
1207  result( ntest ) = ( temp1+temp2 ) /
1208  $ max( unfl, temp3*ulp )
1209 *
1210  460 CONTINUE
1211  ntest = ntest + 1
1212  IF( iuplo.EQ.1 ) THEN
1213  indx = 1
1214  DO 480 j = 1, n
1215  DO 470 i = 1, j
1216  work( indx ) = a( i, j )
1217  indx = indx + 1
1218  470 CONTINUE
1219  480 CONTINUE
1220  ELSE
1221  indx = 1
1222  DO 500 j = 1, n
1223  DO 490 i = j, n
1224  work( indx ) = a( i, j )
1225  indx = indx + 1
1226  490 CONTINUE
1227  500 CONTINUE
1228  END IF
1229 *
1230  CALL zhpevx( 'V', 'V', uplo, n, work, vl, vu, il, iu,
1231  $ abstol, m2, wa2, z, ldu, v, rwork, iwork,
1232  $ iwork( 5*n+1 ), iinfo )
1233  IF( iinfo.NE.0 ) THEN
1234  WRITE( nounit, fmt = 9999 )'ZHPEVX(V,V,' // uplo //
1235  $ ')', iinfo, n, jtype, ioldsd
1236  info = abs( iinfo )
1237  IF( iinfo.LT.0 ) THEN
1238  RETURN
1239  ELSE
1240  result( ntest ) = ulpinv
1241  result( ntest+1 ) = ulpinv
1242  result( ntest+2 ) = ulpinv
1243  GO TO 550
1244  END IF
1245  END IF
1246 *
1247 * Do tests 22 and 23.
1248 *
1249  CALL zhet22( 1, uplo, n, m2, 0, a, ldu, wa2, d2, z, ldu,
1250  $ v, ldu, tau, work, rwork, result( ntest ) )
1251 *
1252  ntest = ntest + 2
1253 *
1254  IF( iuplo.EQ.1 ) THEN
1255  indx = 1
1256  DO 520 j = 1, n
1257  DO 510 i = 1, j
1258  work( indx ) = a( i, j )
1259  indx = indx + 1
1260  510 CONTINUE
1261  520 CONTINUE
1262  ELSE
1263  indx = 1
1264  DO 540 j = 1, n
1265  DO 530 i = j, n
1266  work( indx ) = a( i, j )
1267  indx = indx + 1
1268  530 CONTINUE
1269  540 CONTINUE
1270  END IF
1271 *
1272  CALL zhpevx( 'N', 'V', uplo, n, work, vl, vu, il, iu,
1273  $ abstol, m3, wa3, z, ldu, v, rwork, iwork,
1274  $ iwork( 5*n+1 ), iinfo )
1275  IF( iinfo.NE.0 ) THEN
1276  WRITE( nounit, fmt = 9999 )'ZHPEVX(N,V,' // uplo //
1277  $ ')', iinfo, n, jtype, ioldsd
1278  info = abs( iinfo )
1279  IF( iinfo.LT.0 ) THEN
1280  RETURN
1281  ELSE
1282  result( ntest ) = ulpinv
1283  GO TO 550
1284  END IF
1285  END IF
1286 *
1287  IF( m3.EQ.0 .AND. n.GT.0 ) THEN
1288  result( ntest ) = ulpinv
1289  GO TO 550
1290  END IF
1291 *
1292 * Do test 24.
1293 *
1294  temp1 = dsxt1( 1, wa2, m2, wa3, m3, abstol, ulp, unfl )
1295  temp2 = dsxt1( 1, wa3, m3, wa2, m2, abstol, ulp, unfl )
1296  IF( n.GT.0 ) THEN
1297  temp3 = max( abs( wa1( 1 ) ), abs( wa1( n ) ) )
1298  ELSE
1299  temp3 = zero
1300  END IF
1301  result( ntest ) = ( temp1+temp2 ) /
1302  $ max( unfl, temp3*ulp )
1303 *
1304  550 CONTINUE
1305 *
1306 * Call ZHBEVD and CHBEVX.
1307 *
1308  IF( jtype.LE.7 ) THEN
1309  kd = 0
1310  ELSE IF( jtype.GE.8 .AND. jtype.LE.15 ) THEN
1311  kd = max( n-1, 0 )
1312  ELSE
1313  kd = ihbw
1314  END IF
1315 *
1316 * Load array V with the upper or lower triangular part
1317 * of the matrix in band form.
1318 *
1319  IF( iuplo.EQ.1 ) THEN
1320  DO 570 j = 1, n
1321  DO 560 i = max( 1, j-kd ), j
1322  v( kd+1+i-j, j ) = a( i, j )
1323  560 CONTINUE
1324  570 CONTINUE
1325  ELSE
1326  DO 590 j = 1, n
1327  DO 580 i = j, min( n, j+kd )
1328  v( 1+i-j, j ) = a( i, j )
1329  580 CONTINUE
1330  590 CONTINUE
1331  END IF
1332 *
1333  ntest = ntest + 1
1334  CALL zhbevd( 'V', uplo, n, kd, v, ldu, d1, z, ldu, work,
1335  $ lwedc, rwork, lrwedc, iwork, liwedc, iinfo )
1336  IF( iinfo.NE.0 ) THEN
1337  WRITE( nounit, fmt = 9998 )'ZHBEVD(V,' // uplo //
1338  $ ')', iinfo, n, kd, jtype, ioldsd
1339  info = abs( iinfo )
1340  IF( iinfo.LT.0 ) THEN
1341  RETURN
1342  ELSE
1343  result( ntest ) = ulpinv
1344  result( ntest+1 ) = ulpinv
1345  result( ntest+2 ) = ulpinv
1346  GO TO 650
1347  END IF
1348  END IF
1349 *
1350 * Do tests 25 and 26.
1351 *
1352  CALL zhet21( 1, uplo, n, 0, a, lda, d1, d2, z, ldu, v,
1353  $ ldu, tau, work, rwork, result( ntest ) )
1354 *
1355  IF( iuplo.EQ.1 ) THEN
1356  DO 610 j = 1, n
1357  DO 600 i = max( 1, j-kd ), j
1358  v( kd+1+i-j, j ) = a( i, j )
1359  600 CONTINUE
1360  610 CONTINUE
1361  ELSE
1362  DO 630 j = 1, n
1363  DO 620 i = j, min( n, j+kd )
1364  v( 1+i-j, j ) = a( i, j )
1365  620 CONTINUE
1366  630 CONTINUE
1367  END IF
1368 *
1369  ntest = ntest + 2
1370  CALL zhbevd_2stage( 'N', uplo, n, kd, v, ldu, d3,
1371  $ z, ldu, work, lwork, rwork,
1372  $ lrwedc, iwork, liwedc, iinfo )
1373  IF( iinfo.NE.0 ) THEN
1374  WRITE( nounit, fmt = 9998 )
1375  $ 'ZHBEVD_2STAGE(N,' // uplo //
1376  $ ')', iinfo, n, kd, jtype, ioldsd
1377  info = abs( iinfo )
1378  IF( iinfo.LT.0 ) THEN
1379  RETURN
1380  ELSE
1381  result( ntest ) = ulpinv
1382  GO TO 650
1383  END IF
1384  END IF
1385 *
1386 * Do test 27.
1387 *
1388  temp1 = zero
1389  temp2 = zero
1390  DO 640 j = 1, n
1391  temp1 = max( temp1, abs( d1( j ) ), abs( d3( j ) ) )
1392  temp2 = max( temp2, abs( d1( j )-d3( j ) ) )
1393  640 CONTINUE
1394  result( ntest ) = temp2 / max( unfl,
1395  $ ulp*max( temp1, temp2 ) )
1396 *
1397 * Load array V with the upper or lower triangular part
1398 * of the matrix in band form.
1399 *
1400  650 CONTINUE
1401  IF( iuplo.EQ.1 ) THEN
1402  DO 670 j = 1, n
1403  DO 660 i = max( 1, j-kd ), j
1404  v( kd+1+i-j, j ) = a( i, j )
1405  660 CONTINUE
1406  670 CONTINUE
1407  ELSE
1408  DO 690 j = 1, n
1409  DO 680 i = j, min( n, j+kd )
1410  v( 1+i-j, j ) = a( i, j )
1411  680 CONTINUE
1412  690 CONTINUE
1413  END IF
1414 *
1415  ntest = ntest + 1
1416  CALL zhbevx( 'V', 'A', uplo, n, kd, v, ldu, u, ldu, vl,
1417  $ vu, il, iu, abstol, m, wa1, z, ldu, work,
1418  $ rwork, iwork, iwork( 5*n+1 ), iinfo )
1419  IF( iinfo.NE.0 ) THEN
1420  WRITE( nounit, fmt = 9999 )'ZHBEVX(V,A,' // uplo //
1421  $ ')', iinfo, n, kd, jtype, ioldsd
1422  info = abs( iinfo )
1423  IF( iinfo.LT.0 ) THEN
1424  RETURN
1425  ELSE
1426  result( ntest ) = ulpinv
1427  result( ntest+1 ) = ulpinv
1428  result( ntest+2 ) = ulpinv
1429  GO TO 750
1430  END IF
1431  END IF
1432 *
1433 * Do tests 28 and 29.
1434 *
1435  CALL zhet21( 1, uplo, n, 0, a, ldu, wa1, d2, z, ldu, v,
1436  $ ldu, tau, work, rwork, result( ntest ) )
1437 *
1438  ntest = ntest + 2
1439 *
1440  IF( iuplo.EQ.1 ) THEN
1441  DO 710 j = 1, n
1442  DO 700 i = max( 1, j-kd ), j
1443  v( kd+1+i-j, j ) = a( i, j )
1444  700 CONTINUE
1445  710 CONTINUE
1446  ELSE
1447  DO 730 j = 1, n
1448  DO 720 i = j, min( n, j+kd )
1449  v( 1+i-j, j ) = a( i, j )
1450  720 CONTINUE
1451  730 CONTINUE
1452  END IF
1453 *
1454  CALL zhbevx_2stage( 'N', 'A', uplo, n, kd, v, ldu,
1455  $ u, ldu, vl, vu, il, iu, abstol,
1456  $ m2, wa2, z, ldu, work, lwork,
1457  $ rwork, iwork, iwork( 5*n+1 ), iinfo )
1458  IF( iinfo.NE.0 ) THEN
1459  WRITE( nounit, fmt = 9998 )
1460  $ 'ZHBEVX_2STAGE(N,A,' // uplo //
1461  $ ')', iinfo, n, kd, jtype, ioldsd
1462  info = abs( iinfo )
1463  IF( iinfo.LT.0 ) THEN
1464  RETURN
1465  ELSE
1466  result( ntest ) = ulpinv
1467  GO TO 750
1468  END IF
1469  END IF
1470 *
1471 * Do test 30.
1472 *
1473  temp1 = zero
1474  temp2 = zero
1475  DO 740 j = 1, n
1476  temp1 = max( temp1, abs( wa1( j ) ), abs( wa2( j ) ) )
1477  temp2 = max( temp2, abs( wa1( j )-wa2( j ) ) )
1478  740 CONTINUE
1479  result( ntest ) = temp2 / max( unfl,
1480  $ ulp*max( temp1, temp2 ) )
1481 *
1482 * Load array V with the upper or lower triangular part
1483 * of the matrix in band form.
1484 *
1485  750 CONTINUE
1486  ntest = ntest + 1
1487  IF( iuplo.EQ.1 ) THEN
1488  DO 770 j = 1, n
1489  DO 760 i = max( 1, j-kd ), j
1490  v( kd+1+i-j, j ) = a( i, j )
1491  760 CONTINUE
1492  770 CONTINUE
1493  ELSE
1494  DO 790 j = 1, n
1495  DO 780 i = j, min( n, j+kd )
1496  v( 1+i-j, j ) = a( i, j )
1497  780 CONTINUE
1498  790 CONTINUE
1499  END IF
1500 *
1501  CALL zhbevx( 'V', 'I', uplo, n, kd, v, ldu, u, ldu, vl,
1502  $ vu, il, iu, abstol, m2, wa2, z, ldu, work,
1503  $ rwork, iwork, iwork( 5*n+1 ), iinfo )
1504  IF( iinfo.NE.0 ) THEN
1505  WRITE( nounit, fmt = 9998 )'ZHBEVX(V,I,' // uplo //
1506  $ ')', iinfo, n, kd, jtype, ioldsd
1507  info = abs( iinfo )
1508  IF( iinfo.LT.0 ) THEN
1509  RETURN
1510  ELSE
1511  result( ntest ) = ulpinv
1512  result( ntest+1 ) = ulpinv
1513  result( ntest+2 ) = ulpinv
1514  GO TO 840
1515  END IF
1516  END IF
1517 *
1518 * Do tests 31 and 32.
1519 *
1520  CALL zhet22( 1, uplo, n, m2, 0, a, ldu, wa2, d2, z, ldu,
1521  $ v, ldu, tau, work, rwork, result( ntest ) )
1522 *
1523  ntest = ntest + 2
1524 *
1525  IF( iuplo.EQ.1 ) THEN
1526  DO 810 j = 1, n
1527  DO 800 i = max( 1, j-kd ), j
1528  v( kd+1+i-j, j ) = a( i, j )
1529  800 CONTINUE
1530  810 CONTINUE
1531  ELSE
1532  DO 830 j = 1, n
1533  DO 820 i = j, min( n, j+kd )
1534  v( 1+i-j, j ) = a( i, j )
1535  820 CONTINUE
1536  830 CONTINUE
1537  END IF
1538  CALL zhbevx_2stage( 'N', 'I', uplo, n, kd, v, ldu,
1539  $ u, ldu, vl, vu, il, iu, abstol,
1540  $ m3, wa3, z, ldu, work, lwork,
1541  $ rwork, iwork, iwork( 5*n+1 ), iinfo )
1542  IF( iinfo.NE.0 ) THEN
1543  WRITE( nounit, fmt = 9998 )
1544  $ 'ZHBEVX_2STAGE(N,I,' // uplo //
1545  $ ')', iinfo, n, kd, jtype, ioldsd
1546  info = abs( iinfo )
1547  IF( iinfo.LT.0 ) THEN
1548  RETURN
1549  ELSE
1550  result( ntest ) = ulpinv
1551  GO TO 840
1552  END IF
1553  END IF
1554 *
1555 * Do test 33.
1556 *
1557  temp1 = dsxt1( 1, wa2, m2, wa3, m3, abstol, ulp, unfl )
1558  temp2 = dsxt1( 1, wa3, m3, wa2, m2, abstol, ulp, unfl )
1559  IF( n.GT.0 ) THEN
1560  temp3 = max( abs( wa1( 1 ) ), abs( wa1( n ) ) )
1561  ELSE
1562  temp3 = zero
1563  END IF
1564  result( ntest ) = ( temp1+temp2 ) /
1565  $ max( unfl, temp3*ulp )
1566 *
1567 * Load array V with the upper or lower triangular part
1568 * of the matrix in band form.
1569 *
1570  840 CONTINUE
1571  ntest = ntest + 1
1572  IF( iuplo.EQ.1 ) THEN
1573  DO 860 j = 1, n
1574  DO 850 i = max( 1, j-kd ), j
1575  v( kd+1+i-j, j ) = a( i, j )
1576  850 CONTINUE
1577  860 CONTINUE
1578  ELSE
1579  DO 880 j = 1, n
1580  DO 870 i = j, min( n, j+kd )
1581  v( 1+i-j, j ) = a( i, j )
1582  870 CONTINUE
1583  880 CONTINUE
1584  END IF
1585  CALL zhbevx( 'V', 'V', uplo, n, kd, v, ldu, u, ldu, vl,
1586  $ vu, il, iu, abstol, m2, wa2, z, ldu, work,
1587  $ rwork, iwork, iwork( 5*n+1 ), iinfo )
1588  IF( iinfo.NE.0 ) THEN
1589  WRITE( nounit, fmt = 9998 )'ZHBEVX(V,V,' // uplo //
1590  $ ')', iinfo, n, kd, jtype, ioldsd
1591  info = abs( iinfo )
1592  IF( iinfo.LT.0 ) THEN
1593  RETURN
1594  ELSE
1595  result( ntest ) = ulpinv
1596  result( ntest+1 ) = ulpinv
1597  result( ntest+2 ) = ulpinv
1598  GO TO 930
1599  END IF
1600  END IF
1601 *
1602 * Do tests 34 and 35.
1603 *
1604  CALL zhet22( 1, uplo, n, m2, 0, a, ldu, wa2, d2, z, ldu,
1605  $ v, ldu, tau, work, rwork, result( ntest ) )
1606 *
1607  ntest = ntest + 2
1608 *
1609  IF( iuplo.EQ.1 ) THEN
1610  DO 900 j = 1, n
1611  DO 890 i = max( 1, j-kd ), j
1612  v( kd+1+i-j, j ) = a( i, j )
1613  890 CONTINUE
1614  900 CONTINUE
1615  ELSE
1616  DO 920 j = 1, n
1617  DO 910 i = j, min( n, j+kd )
1618  v( 1+i-j, j ) = a( i, j )
1619  910 CONTINUE
1620  920 CONTINUE
1621  END IF
1622  CALL zhbevx_2stage( 'N', 'V', uplo, n, kd, v, ldu,
1623  $ u, ldu, vl, vu, il, iu, abstol,
1624  $ m3, wa3, z, ldu, work, lwork,
1625  $ rwork, iwork, iwork( 5*n+1 ), iinfo )
1626  IF( iinfo.NE.0 ) THEN
1627  WRITE( nounit, fmt = 9998 )
1628  $ 'ZHBEVX_2STAGE(N,V,' // uplo //
1629  $ ')', iinfo, n, kd, jtype, ioldsd
1630  info = abs( iinfo )
1631  IF( iinfo.LT.0 ) THEN
1632  RETURN
1633  ELSE
1634  result( ntest ) = ulpinv
1635  GO TO 930
1636  END IF
1637  END IF
1638 *
1639  IF( m3.EQ.0 .AND. n.GT.0 ) THEN
1640  result( ntest ) = ulpinv
1641  GO TO 930
1642  END IF
1643 *
1644 * Do test 36.
1645 *
1646  temp1 = dsxt1( 1, wa2, m2, wa3, m3, abstol, ulp, unfl )
1647  temp2 = dsxt1( 1, wa3, m3, wa2, m2, abstol, ulp, unfl )
1648  IF( n.GT.0 ) THEN
1649  temp3 = max( abs( wa1( 1 ) ), abs( wa1( n ) ) )
1650  ELSE
1651  temp3 = zero
1652  END IF
1653  result( ntest ) = ( temp1+temp2 ) /
1654  $ max( unfl, temp3*ulp )
1655 *
1656  930 CONTINUE
1657 *
1658 * Call ZHEEV
1659 *
1660  CALL zlacpy( ' ', n, n, a, lda, v, ldu )
1661 *
1662  ntest = ntest + 1
1663  CALL zheev( 'V', uplo, n, a, ldu, d1, work, lwork, rwork,
1664  $ iinfo )
1665  IF( iinfo.NE.0 ) THEN
1666  WRITE( nounit, fmt = 9999 )'ZHEEV(V,' // uplo // ')',
1667  $ iinfo, n, jtype, ioldsd
1668  info = abs( iinfo )
1669  IF( iinfo.LT.0 ) THEN
1670  RETURN
1671  ELSE
1672  result( ntest ) = ulpinv
1673  result( ntest+1 ) = ulpinv
1674  result( ntest+2 ) = ulpinv
1675  GO TO 950
1676  END IF
1677  END IF
1678 *
1679 * Do tests 37 and 38
1680 *
1681  CALL zhet21( 1, uplo, n, 0, v, ldu, d1, d2, a, ldu, z,
1682  $ ldu, tau, work, rwork, result( ntest ) )
1683 *
1684  CALL zlacpy( ' ', n, n, v, ldu, a, lda )
1685 *
1686  ntest = ntest + 2
1687  CALL zheev_2stage( 'N', uplo, n, a, ldu, d3,
1688  $ work, lwork, rwork, iinfo )
1689  IF( iinfo.NE.0 ) THEN
1690  WRITE( nounit, fmt = 9999 )
1691  $ 'ZHEEV_2STAGE(N,' // uplo // ')',
1692  $ iinfo, n, jtype, ioldsd
1693  info = abs( iinfo )
1694  IF( iinfo.LT.0 ) THEN
1695  RETURN
1696  ELSE
1697  result( ntest ) = ulpinv
1698  GO TO 950
1699  END IF
1700  END IF
1701 *
1702 * Do test 39
1703 *
1704  temp1 = zero
1705  temp2 = zero
1706  DO 940 j = 1, n
1707  temp1 = max( temp1, abs( d1( j ) ), abs( d3( j ) ) )
1708  temp2 = max( temp2, abs( d1( j )-d3( j ) ) )
1709  940 CONTINUE
1710  result( ntest ) = temp2 / max( unfl,
1711  $ ulp*max( temp1, temp2 ) )
1712 *
1713  950 CONTINUE
1714 *
1715  CALL zlacpy( ' ', n, n, v, ldu, a, lda )
1716 *
1717 * Call ZHPEV
1718 *
1719 * Load array WORK with the upper or lower triangular
1720 * part of the matrix in packed form.
1721 *
1722  IF( iuplo.EQ.1 ) THEN
1723  indx = 1
1724  DO 970 j = 1, n
1725  DO 960 i = 1, j
1726  work( indx ) = a( i, j )
1727  indx = indx + 1
1728  960 CONTINUE
1729  970 CONTINUE
1730  ELSE
1731  indx = 1
1732  DO 990 j = 1, n
1733  DO 980 i = j, n
1734  work( indx ) = a( i, j )
1735  indx = indx + 1
1736  980 CONTINUE
1737  990 CONTINUE
1738  END IF
1739 *
1740  ntest = ntest + 1
1741  indwrk = n*( n+1 ) / 2 + 1
1742  CALL zhpev( 'V', uplo, n, work, d1, z, ldu,
1743  $ work( indwrk ), rwork, iinfo )
1744  IF( iinfo.NE.0 ) THEN
1745  WRITE( nounit, fmt = 9999 )'ZHPEV(V,' // uplo // ')',
1746  $ iinfo, n, jtype, ioldsd
1747  info = abs( iinfo )
1748  IF( iinfo.LT.0 ) THEN
1749  RETURN
1750  ELSE
1751  result( ntest ) = ulpinv
1752  result( ntest+1 ) = ulpinv
1753  result( ntest+2 ) = ulpinv
1754  GO TO 1050
1755  END IF
1756  END IF
1757 *
1758 * Do tests 40 and 41.
1759 *
1760  CALL zhet21( 1, uplo, n, 0, a, lda, d1, d2, z, ldu, v,
1761  $ ldu, tau, work, rwork, result( ntest ) )
1762 *
1763  IF( iuplo.EQ.1 ) THEN
1764  indx = 1
1765  DO 1010 j = 1, n
1766  DO 1000 i = 1, j
1767  work( indx ) = a( i, j )
1768  indx = indx + 1
1769  1000 CONTINUE
1770  1010 CONTINUE
1771  ELSE
1772  indx = 1
1773  DO 1030 j = 1, n
1774  DO 1020 i = j, n
1775  work( indx ) = a( i, j )
1776  indx = indx + 1
1777  1020 CONTINUE
1778  1030 CONTINUE
1779  END IF
1780 *
1781  ntest = ntest + 2
1782  indwrk = n*( n+1 ) / 2 + 1
1783  CALL zhpev( 'N', uplo, n, work, d3, z, ldu,
1784  $ work( indwrk ), rwork, iinfo )
1785  IF( iinfo.NE.0 ) THEN
1786  WRITE( nounit, fmt = 9999 )'ZHPEV(N,' // uplo // ')',
1787  $ iinfo, n, jtype, ioldsd
1788  info = abs( iinfo )
1789  IF( iinfo.LT.0 ) THEN
1790  RETURN
1791  ELSE
1792  result( ntest ) = ulpinv
1793  GO TO 1050
1794  END IF
1795  END IF
1796 *
1797 * Do test 42
1798 *
1799  temp1 = zero
1800  temp2 = zero
1801  DO 1040 j = 1, n
1802  temp1 = max( temp1, abs( d1( j ) ), abs( d3( j ) ) )
1803  temp2 = max( temp2, abs( d1( j )-d3( j ) ) )
1804  1040 CONTINUE
1805  result( ntest ) = temp2 / max( unfl,
1806  $ ulp*max( temp1, temp2 ) )
1807 *
1808  1050 CONTINUE
1809 *
1810 * Call ZHBEV
1811 *
1812  IF( jtype.LE.7 ) THEN
1813  kd = 0
1814  ELSE IF( jtype.GE.8 .AND. jtype.LE.15 ) THEN
1815  kd = max( n-1, 0 )
1816  ELSE
1817  kd = ihbw
1818  END IF
1819 *
1820 * Load array V with the upper or lower triangular part
1821 * of the matrix in band form.
1822 *
1823  IF( iuplo.EQ.1 ) THEN
1824  DO 1070 j = 1, n
1825  DO 1060 i = max( 1, j-kd ), j
1826  v( kd+1+i-j, j ) = a( i, j )
1827  1060 CONTINUE
1828  1070 CONTINUE
1829  ELSE
1830  DO 1090 j = 1, n
1831  DO 1080 i = j, min( n, j+kd )
1832  v( 1+i-j, j ) = a( i, j )
1833  1080 CONTINUE
1834  1090 CONTINUE
1835  END IF
1836 *
1837  ntest = ntest + 1
1838  CALL zhbev( 'V', uplo, n, kd, v, ldu, d1, z, ldu, work,
1839  $ rwork, iinfo )
1840  IF( iinfo.NE.0 ) THEN
1841  WRITE( nounit, fmt = 9998 )'ZHBEV(V,' // uplo // ')',
1842  $ iinfo, n, kd, jtype, ioldsd
1843  info = abs( iinfo )
1844  IF( iinfo.LT.0 ) THEN
1845  RETURN
1846  ELSE
1847  result( ntest ) = ulpinv
1848  result( ntest+1 ) = ulpinv
1849  result( ntest+2 ) = ulpinv
1850  GO TO 1140
1851  END IF
1852  END IF
1853 *
1854 * Do tests 43 and 44.
1855 *
1856  CALL zhet21( 1, uplo, n, 0, a, lda, d1, d2, z, ldu, v,
1857  $ ldu, tau, work, rwork, result( ntest ) )
1858 *
1859  IF( iuplo.EQ.1 ) THEN
1860  DO 1110 j = 1, n
1861  DO 1100 i = max( 1, j-kd ), j
1862  v( kd+1+i-j, j ) = a( i, j )
1863  1100 CONTINUE
1864  1110 CONTINUE
1865  ELSE
1866  DO 1130 j = 1, n
1867  DO 1120 i = j, min( n, j+kd )
1868  v( 1+i-j, j ) = a( i, j )
1869  1120 CONTINUE
1870  1130 CONTINUE
1871  END IF
1872 *
1873  ntest = ntest + 2
1874  CALL zhbev_2stage( 'N', uplo, n, kd, v, ldu, d3, z, ldu,
1875  $ work, lwork, rwork, iinfo )
1876  IF( iinfo.NE.0 ) THEN
1877  WRITE( nounit, fmt = 9998 )
1878  $ 'ZHBEV_2STAGE(N,' // uplo // ')',
1879  $ iinfo, n, kd, jtype, ioldsd
1880  info = abs( iinfo )
1881  IF( iinfo.LT.0 ) THEN
1882  RETURN
1883  ELSE
1884  result( ntest ) = ulpinv
1885  GO TO 1140
1886  END IF
1887  END IF
1888 *
1889  1140 CONTINUE
1890 *
1891 * Do test 45.
1892 *
1893  temp1 = zero
1894  temp2 = zero
1895  DO 1150 j = 1, n
1896  temp1 = max( temp1, abs( d1( j ) ), abs( d3( j ) ) )
1897  temp2 = max( temp2, abs( d1( j )-d3( j ) ) )
1898  1150 CONTINUE
1899  result( ntest ) = temp2 / max( unfl,
1900  $ ulp*max( temp1, temp2 ) )
1901 *
1902  CALL zlacpy( ' ', n, n, a, lda, v, ldu )
1903  ntest = ntest + 1
1904  CALL zheevr( 'V', 'A', uplo, n, a, ldu, vl, vu, il, iu,
1905  $ abstol, m, wa1, z, ldu, iwork, work, lwork,
1906  $ rwork, lrwork, iwork( 2*n+1 ), liwork-2*n,
1907  $ iinfo )
1908  IF( iinfo.NE.0 ) THEN
1909  WRITE( nounit, fmt = 9999 )'ZHEEVR(V,A,' // uplo //
1910  $ ')', iinfo, n, jtype, ioldsd
1911  info = abs( iinfo )
1912  IF( iinfo.LT.0 ) THEN
1913  RETURN
1914  ELSE
1915  result( ntest ) = ulpinv
1916  result( ntest+1 ) = ulpinv
1917  result( ntest+2 ) = ulpinv
1918  GO TO 1170
1919  END IF
1920  END IF
1921 *
1922 * Do tests 45 and 46 (or ... )
1923 *
1924  CALL zlacpy( ' ', n, n, v, ldu, a, lda )
1925 *
1926  CALL zhet21( 1, uplo, n, 0, a, ldu, wa1, d2, z, ldu, v,
1927  $ ldu, tau, work, rwork, result( ntest ) )
1928 *
1929  ntest = ntest + 2
1930  CALL zheevr_2stage( 'N', 'A', uplo, n, a, ldu, vl, vu,
1931  $ il, iu, abstol, m2, wa2, z, ldu,
1932  $ iwork, work, lwork, rwork, lrwork,
1933  $ iwork( 2*n+1 ), liwork-2*n, iinfo )
1934  IF( iinfo.NE.0 ) THEN
1935  WRITE( nounit, fmt = 9999 )
1936  $ 'ZHEEVR_2STAGE(N,A,' // uplo //
1937  $ ')', iinfo, n, jtype, ioldsd
1938  info = abs( iinfo )
1939  IF( iinfo.LT.0 ) THEN
1940  RETURN
1941  ELSE
1942  result( ntest ) = ulpinv
1943  GO TO 1170
1944  END IF
1945  END IF
1946 *
1947 * Do test 47 (or ... )
1948 *
1949  temp1 = zero
1950  temp2 = zero
1951  DO 1160 j = 1, n
1952  temp1 = max( temp1, abs( wa1( j ) ), abs( wa2( j ) ) )
1953  temp2 = max( temp2, abs( wa1( j )-wa2( j ) ) )
1954  1160 CONTINUE
1955  result( ntest ) = temp2 / max( unfl,
1956  $ ulp*max( temp1, temp2 ) )
1957 *
1958  1170 CONTINUE
1959 *
1960  ntest = ntest + 1
1961  CALL zlacpy( ' ', n, n, v, ldu, a, lda )
1962  CALL zheevr( 'V', 'I', uplo, n, a, ldu, vl, vu, il, iu,
1963  $ abstol, m2, wa2, z, ldu, iwork, work, lwork,
1964  $ rwork, lrwork, iwork( 2*n+1 ), liwork-2*n,
1965  $ iinfo )
1966  IF( iinfo.NE.0 ) THEN
1967  WRITE( nounit, fmt = 9999 )'ZHEEVR(V,I,' // uplo //
1968  $ ')', iinfo, n, jtype, ioldsd
1969  info = abs( iinfo )
1970  IF( iinfo.LT.0 ) THEN
1971  RETURN
1972  ELSE
1973  result( ntest ) = ulpinv
1974  result( ntest+1 ) = ulpinv
1975  result( ntest+2 ) = ulpinv
1976  GO TO 1180
1977  END IF
1978  END IF
1979 *
1980 * Do tests 48 and 49 (or +??)
1981 *
1982  CALL zlacpy( ' ', n, n, v, ldu, a, lda )
1983 *
1984  CALL zhet22( 1, uplo, n, m2, 0, a, ldu, wa2, d2, z, ldu,
1985  $ v, ldu, tau, work, rwork, result( ntest ) )
1986 *
1987  ntest = ntest + 2
1988  CALL zlacpy( ' ', n, n, v, ldu, a, lda )
1989  CALL zheevr_2stage( 'N', 'I', uplo, n, a, ldu, vl, vu,
1990  $ il, iu, abstol, m3, wa3, z, ldu,
1991  $ iwork, work, lwork, rwork, lrwork,
1992  $ iwork( 2*n+1 ), liwork-2*n, iinfo )
1993  IF( iinfo.NE.0 ) THEN
1994  WRITE( nounit, fmt = 9999 )
1995  $ 'ZHEEVR_2STAGE(N,I,' // uplo //
1996  $ ')', iinfo, n, jtype, ioldsd
1997  info = abs( iinfo )
1998  IF( iinfo.LT.0 ) THEN
1999  RETURN
2000  ELSE
2001  result( ntest ) = ulpinv
2002  GO TO 1180
2003  END IF
2004  END IF
2005 *
2006 * Do test 50 (or +??)
2007 *
2008  temp1 = dsxt1( 1, wa2, m2, wa3, m3, abstol, ulp, unfl )
2009  temp2 = dsxt1( 1, wa3, m3, wa2, m2, abstol, ulp, unfl )
2010  result( ntest ) = ( temp1+temp2 ) /
2011  $ max( unfl, ulp*temp3 )
2012  1180 CONTINUE
2013 *
2014  ntest = ntest + 1
2015  CALL zlacpy( ' ', n, n, v, ldu, a, lda )
2016  CALL zheevr( 'V', 'V', uplo, n, a, ldu, vl, vu, il, iu,
2017  $ abstol, m2, wa2, z, ldu, iwork, work, lwork,
2018  $ rwork, lrwork, iwork( 2*n+1 ), liwork-2*n,
2019  $ iinfo )
2020  IF( iinfo.NE.0 ) THEN
2021  WRITE( nounit, fmt = 9999 )'ZHEEVR(V,V,' // uplo //
2022  $ ')', iinfo, n, jtype, ioldsd
2023  info = abs( iinfo )
2024  IF( iinfo.LT.0 ) THEN
2025  RETURN
2026  ELSE
2027  result( ntest ) = ulpinv
2028  result( ntest+1 ) = ulpinv
2029  result( ntest+2 ) = ulpinv
2030  GO TO 1190
2031  END IF
2032  END IF
2033 *
2034 * Do tests 51 and 52 (or +??)
2035 *
2036  CALL zlacpy( ' ', n, n, v, ldu, a, lda )
2037 *
2038  CALL zhet22( 1, uplo, n, m2, 0, a, ldu, wa2, d2, z, ldu,
2039  $ v, ldu, tau, work, rwork, result( ntest ) )
2040 *
2041  ntest = ntest + 2
2042  CALL zlacpy( ' ', n, n, v, ldu, a, lda )
2043  CALL zheevr_2stage( 'N', 'V', uplo, n, a, ldu, vl, vu,
2044  $ il, iu, abstol, m3, wa3, z, ldu,
2045  $ iwork, work, lwork, rwork, lrwork,
2046  $ iwork( 2*n+1 ), liwork-2*n, iinfo )
2047  IF( iinfo.NE.0 ) THEN
2048  WRITE( nounit, fmt = 9999 )
2049  $ 'ZHEEVR_2STAGE(N,V,' // uplo //
2050  $ ')', iinfo, n, jtype, ioldsd
2051  info = abs( iinfo )
2052  IF( iinfo.LT.0 ) THEN
2053  RETURN
2054  ELSE
2055  result( ntest ) = ulpinv
2056  GO TO 1190
2057  END IF
2058  END IF
2059 *
2060  IF( m3.EQ.0 .AND. n.GT.0 ) THEN
2061  result( ntest ) = ulpinv
2062  GO TO 1190
2063  END IF
2064 *
2065 * Do test 52 (or +??)
2066 *
2067  temp1 = dsxt1( 1, wa2, m2, wa3, m3, abstol, ulp, unfl )
2068  temp2 = dsxt1( 1, wa3, m3, wa2, m2, abstol, ulp, unfl )
2069  IF( n.GT.0 ) THEN
2070  temp3 = max( abs( wa1( 1 ) ), abs( wa1( n ) ) )
2071  ELSE
2072  temp3 = zero
2073  END IF
2074  result( ntest ) = ( temp1+temp2 ) /
2075  $ max( unfl, temp3*ulp )
2076 *
2077  CALL zlacpy( ' ', n, n, v, ldu, a, lda )
2078 *
2079 *
2080 *
2081 *
2082 * Load array V with the upper or lower triangular part
2083 * of the matrix in band form.
2084 *
2085  1190 CONTINUE
2086 *
2087  1200 CONTINUE
2088 *
2089 * End of Loop -- Check for RESULT(j) > THRESH
2090 *
2091  ntestt = ntestt + ntest
2092  CALL dlafts( 'ZST', n, n, jtype, ntest, result, ioldsd,
2093  $ thresh, nounit, nerrs )
2094 *
2095  1210 CONTINUE
2096  1220 CONTINUE
2097 *
2098 * Summary
2099 *
2100  CALL alasvm( 'ZST', nounit, nerrs, ntestt, 0 )
2101 *
2102  9999 FORMAT( ' ZDRVST2STG: ', a, ' returned INFO=', i6, / 9x, 'N=', i6,
2103  $ ', JTYPE=', i6, ', ISEED=(', 3( i5, ',' ), i5, ')' )
2104  9998 FORMAT( ' ZDRVST2STG: ', a, ' returned INFO=', i6, / 9x, 'N=', i6,
2105  $ ', KD=', i6, ', JTYPE=', i6, ', ISEED=(', 3( i5, ',' ), i5,
2106  $ ')' )
2107 *
2108  RETURN
2109 *
2110 * End of ZDRVST2STG
2111 *
2112  END
dlabad
subroutine dlabad(SMALL, LARGE)
DLABAD
Definition: dlabad.f:74
xerbla
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
alasvm
subroutine alasvm(TYPE, NOUT, NFAIL, NRUN, NERRS)
ALASVM
Definition: alasvm.f:73
zhet21
subroutine zhet21(ITYPE, UPLO, N, KBAND, A, LDA, D, E, U, LDU, V, LDV, TAU, WORK, RWORK, RESULT)
ZHET21
Definition: zhet21.f:214
zdrvst2stg
subroutine zdrvst2stg(NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH, NOUNIT, A, LDA, D1, D2, D3, WA1, WA2, WA3, U, LDU, V, TAU, Z, WORK, LWORK, RWORK, LRWORK, IWORK, LIWORK, RESULT, INFO)
ZDRVST2STG
Definition: zdrvst2stg.f:338
zhet22
subroutine zhet22(ITYPE, UPLO, N, M, KBAND, A, LDA, D, E, U, LDU, V, LDV, TAU, WORK, RWORK, RESULT)
ZHET22
Definition: zhet22.f:161
zlatms
subroutine zlatms(M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX, KL, KU, PACK, A, LDA, WORK, INFO)
ZLATMS
Definition: zlatms.f:332
zlatmr
subroutine zlatmr(M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX, RSIGN, GRADE, DL, MODEL, CONDL, DR, MODER, CONDR, PIVTNG, IPIVOT, KL, KU, SPARSE, ANORM, PACK, A, LDA, IWORK, INFO)
ZLATMR
Definition: zlatmr.f:490
zhetrd_2stage
subroutine zhetrd_2stage(VECT, UPLO, N, A, LDA, D, E, TAU, HOUS2, LHOUS2, WORK, LWORK, INFO)
ZHETRD_2STAGE
Definition: zhetrd_2stage.f:224
zheevd_2stage
subroutine zheevd_2stage(JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO)
ZHEEVD_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for HE mat...
Definition: zheevd_2stage.f:253
zheevr
subroutine zheevr(JOBZ, RANGE, UPLO, N, A, LDA, VL, VU, IL, IU, ABSTOL, M, W, Z, LDZ, ISUPPZ, WORK, LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO)
ZHEEVR computes the eigenvalues and, optionally, the left and/or right eigenvectors for HE matrices
Definition: zheevr.f:357
zheevd
subroutine zheevd(JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO)
ZHEEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for HE matrices
Definition: zheevd.f:205
zheevx
subroutine zheevx(JOBZ, RANGE, UPLO, N, A, LDA, VL, VU, IL, IU, ABSTOL, M, W, Z, LDZ, WORK, LWORK, RWORK, IWORK, IFAIL, INFO)
ZHEEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for HE matrices
Definition: zheevx.f:259
zheevx_2stage
subroutine zheevx_2stage(JOBZ, RANGE, UPLO, N, A, LDA, VL, VU, IL, IU, ABSTOL, M, W, Z, LDZ, WORK, LWORK, RWORK, IWORK, IFAIL, INFO)
ZHEEVX_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for HE mat...
Definition: zheevx_2stage.f:306
zheev_2stage
subroutine zheev_2stage(JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, RWORK, INFO)
ZHEEV_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for HE matr...
Definition: zheev_2stage.f:189
zheevr_2stage
subroutine zheevr_2stage(JOBZ, RANGE, UPLO, N, A, LDA, VL, VU, IL, IU, ABSTOL, M, W, Z, LDZ, ISUPPZ, WORK, LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO)
ZHEEVR_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for HE mat...
Definition: zheevr_2stage.f:406
zheev
subroutine zheev(JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, RWORK, INFO)
ZHEEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for HE matrices
Definition: zheev.f:140
zlacpy
subroutine zlacpy(UPLO, M, N, A, LDA, B, LDB)
ZLACPY copies all or part of one two-dimensional array to another.
Definition: zlacpy.f:103
zlaset
subroutine zlaset(UPLO, M, N, ALPHA, BETA, A, LDA)
ZLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values.
Definition: zlaset.f:106
zhpev
subroutine zhpev(JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, RWORK, INFO)
ZHPEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices
Definition: zhpev.f:138
zhbevd_2stage
subroutine zhbevd_2stage(JOBZ, UPLO, N, KD, AB, LDAB, W, Z, LDZ, WORK, LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO)
ZHBEVD_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER ...
Definition: zhbevd_2stage.f:260
zhpevd
subroutine zhpevd(JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO)
ZHPEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrice...
Definition: zhpevd.f:200
zhbevd
subroutine zhbevd(JOBZ, UPLO, N, KD, AB, LDAB, W, Z, LDZ, WORK, LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO)
ZHBEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrice...
Definition: zhbevd.f:215
zhbevx_2stage
subroutine zhbevx_2stage(JOBZ, RANGE, UPLO, N, KD, AB, LDAB, Q, LDQ, VL, VU, IL, IU, ABSTOL, M, W, Z, LDZ, WORK, LWORK, RWORK, IWORK, IFAIL, INFO)
ZHBEVX_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER ...
Definition: zhbevx_2stage.f:327
zhpevx
subroutine zhpevx(JOBZ, RANGE, UPLO, N, AP, VL, VU, IL, IU, ABSTOL, M, W, Z, LDZ, WORK, RWORK, IWORK, IFAIL, INFO)
ZHPEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrice...
Definition: zhpevx.f:240
zhbev
subroutine zhbev(JOBZ, UPLO, N, KD, AB, LDAB, W, Z, LDZ, WORK, RWORK, INFO)
ZHBEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices
Definition: zhbev.f:152
zhbevx
subroutine zhbevx(JOBZ, RANGE, UPLO, N, KD, AB, LDAB, Q, LDQ, VL, VU, IL, IU, ABSTOL, M, W, Z, LDZ, WORK, RWORK, IWORK, IFAIL, INFO)
ZHBEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrice...
Definition: zhbevx.f:267
zhbev_2stage
subroutine zhbev_2stage(JOBZ, UPLO, N, KD, AB, LDAB, W, Z, LDZ, WORK, LWORK, RWORK, INFO)
ZHBEV_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER m...
Definition: zhbev_2stage.f:211
dlafts
subroutine dlafts(TYPE, M, N, IMAT, NTESTS, RESULT, ISEED, THRESH, IOUNIT, IE)
DLAFTS
Definition: dlafts.f:99