LAPACK  3.10.1
LAPACK: Linear Algebra PACKage
zchkbb.f
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1 *> \brief \b ZCHKBB
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 ZCHKBB( NSIZES, MVAL, NVAL, NWDTHS, KK, NTYPES, DOTYPE,
12 * NRHS, ISEED, THRESH, NOUNIT, A, LDA, AB, LDAB,
13 * BD, BE, Q, LDQ, P, LDP, C, LDC, CC, WORK,
14 * LWORK, RWORK, RESULT, INFO )
15 *
16 * .. Scalar Arguments ..
17 * INTEGER INFO, LDA, LDAB, LDC, LDP, LDQ, LWORK, NOUNIT,
18 * $ NRHS, NSIZES, NTYPES, NWDTHS
19 * DOUBLE PRECISION THRESH
20 * ..
21 * .. Array Arguments ..
22 * LOGICAL DOTYPE( * )
23 * INTEGER ISEED( 4 ), KK( * ), MVAL( * ), NVAL( * )
24 * DOUBLE PRECISION BD( * ), BE( * ), RESULT( * ), RWORK( * )
25 * COMPLEX*16 A( LDA, * ), AB( LDAB, * ), C( LDC, * ),
26 * $ CC( LDC, * ), P( LDP, * ), Q( LDQ, * ),
27 * $ WORK( * )
28 * ..
29 *
30 *
31 *> \par Purpose:
32 * =============
33 *>
34 *> \verbatim
35 *>
36 *> ZCHKBB tests the reduction of a general complex rectangular band
37 *> matrix to real bidiagonal form.
38 *>
39 *> ZGBBRD factors a general band matrix A as Q B P* , where * means
40 *> conjugate transpose, B is upper bidiagonal, and Q and P are unitary;
41 *> ZGBBRD can also overwrite a given matrix C with Q* C .
42 *>
43 *> For each pair of matrix dimensions (M,N) and each selected matrix
44 *> type, an M by N matrix A and an M by NRHS matrix C are generated.
45 *> The problem dimensions are as follows
46 *> A: M x N
47 *> Q: M x M
48 *> P: N x N
49 *> B: min(M,N) x min(M,N)
50 *> C: M x NRHS
51 *>
52 *> For each generated matrix, 4 tests are performed:
53 *>
54 *> (1) | A - Q B PT | / ( |A| max(M,N) ulp ), PT = P'
55 *>
56 *> (2) | I - Q' Q | / ( M ulp )
57 *>
58 *> (3) | I - PT PT' | / ( N ulp )
59 *>
60 *> (4) | Y - Q' C | / ( |Y| max(M,NRHS) ulp ), where Y = Q' C.
61 *>
62 *> The "types" are specified by a logical array DOTYPE( 1:NTYPES );
63 *> if DOTYPE(j) is .TRUE., then matrix type "j" will be generated.
64 *> Currently, the list of possible types is:
65 *>
66 *> The possible matrix types are
67 *>
68 *> (1) The zero matrix.
69 *> (2) The identity matrix.
70 *>
71 *> (3) A diagonal matrix with evenly spaced entries
72 *> 1, ..., ULP and random signs.
73 *> (ULP = (first number larger than 1) - 1 )
74 *> (4) A diagonal matrix with geometrically spaced entries
75 *> 1, ..., ULP and random signs.
76 *> (5) A diagonal matrix with "clustered" entries 1, ULP, ..., ULP
77 *> and random signs.
78 *>
79 *> (6) Same as (3), but multiplied by SQRT( overflow threshold )
80 *> (7) Same as (3), but multiplied by SQRT( underflow threshold )
81 *>
82 *> (8) A matrix of the form U D V, where U and V are orthogonal and
83 *> D has evenly spaced entries 1, ..., ULP with random signs
84 *> on the diagonal.
85 *>
86 *> (9) A matrix of the form U D V, where U and V are orthogonal and
87 *> D has geometrically spaced entries 1, ..., ULP with random
88 *> signs on the diagonal.
89 *>
90 *> (10) A matrix of the form U D V, where U and V are orthogonal and
91 *> D has "clustered" entries 1, ULP,..., ULP with random
92 *> signs on the diagonal.
93 *>
94 *> (11) Same as (8), but multiplied by SQRT( overflow threshold )
95 *> (12) Same as (8), but multiplied by SQRT( underflow threshold )
96 *>
97 *> (13) Rectangular matrix with random entries chosen from (-1,1).
98 *> (14) Same as (13), but multiplied by SQRT( overflow threshold )
99 *> (15) Same as (13), but multiplied by SQRT( underflow threshold )
100 *> \endverbatim
101 *
102 * Arguments:
103 * ==========
104 *
105 *> \param[in] NSIZES
106 *> \verbatim
107 *> NSIZES is INTEGER
108 *> The number of values of M and N contained in the vectors
109 *> MVAL and NVAL. The matrix sizes are used in pairs (M,N).
110 *> If NSIZES is zero, ZCHKBB does nothing. NSIZES must be at
111 *> least zero.
112 *> \endverbatim
113 *>
114 *> \param[in] MVAL
115 *> \verbatim
116 *> MVAL is INTEGER array, dimension (NSIZES)
117 *> The values of the matrix row dimension M.
118 *> \endverbatim
119 *>
120 *> \param[in] NVAL
121 *> \verbatim
122 *> NVAL is INTEGER array, dimension (NSIZES)
123 *> The values of the matrix column dimension N.
124 *> \endverbatim
125 *>
126 *> \param[in] NWDTHS
127 *> \verbatim
128 *> NWDTHS is INTEGER
129 *> The number of bandwidths to use. If it is zero,
130 *> ZCHKBB does nothing. It must be at least zero.
131 *> \endverbatim
132 *>
133 *> \param[in] KK
134 *> \verbatim
135 *> KK is INTEGER array, dimension (NWDTHS)
136 *> An array containing the bandwidths to be used for the band
137 *> matrices. The values must be at least zero.
138 *> \endverbatim
139 *>
140 *> \param[in] NTYPES
141 *> \verbatim
142 *> NTYPES is INTEGER
143 *> The number of elements in DOTYPE. If it is zero, ZCHKBB
144 *> does nothing. It must be at least zero. If it is MAXTYP+1
145 *> and NSIZES is 1, then an additional type, MAXTYP+1 is
146 *> defined, which is to use whatever matrix is in A. This
147 *> is only useful if DOTYPE(1:MAXTYP) is .FALSE. and
148 *> DOTYPE(MAXTYP+1) is .TRUE. .
149 *> \endverbatim
150 *>
151 *> \param[in] DOTYPE
152 *> \verbatim
153 *> DOTYPE is LOGICAL array, dimension (NTYPES)
154 *> If DOTYPE(j) is .TRUE., then for each size in NN a
155 *> matrix of that size and of type j will be generated.
156 *> If NTYPES is smaller than the maximum number of types
157 *> defined (PARAMETER MAXTYP), then types NTYPES+1 through
158 *> MAXTYP will not be generated. If NTYPES is larger
159 *> than MAXTYP, DOTYPE(MAXTYP+1) through DOTYPE(NTYPES)
160 *> will be ignored.
161 *> \endverbatim
162 *>
163 *> \param[in] NRHS
164 *> \verbatim
165 *> NRHS is INTEGER
166 *> The number of columns in the "right-hand side" matrix C.
167 *> If NRHS = 0, then the operations on the right-hand side will
168 *> not be tested. NRHS must be at least 0.
169 *> \endverbatim
170 *>
171 *> \param[in,out] ISEED
172 *> \verbatim
173 *> ISEED is INTEGER array, dimension (4)
174 *> On entry ISEED specifies the seed of the random number
175 *> generator. The array elements should be between 0 and 4095;
176 *> if not they will be reduced mod 4096. Also, ISEED(4) must
177 *> be odd. The random number generator uses a linear
178 *> congruential sequence limited to small integers, and so
179 *> should produce machine independent random numbers. The
180 *> values of ISEED are changed on exit, and can be used in the
181 *> next call to ZCHKBB to continue the same random number
182 *> sequence.
183 *> \endverbatim
184 *>
185 *> \param[in] THRESH
186 *> \verbatim
187 *> THRESH is DOUBLE PRECISION
188 *> A test will count as "failed" if the "error", computed as
189 *> described above, exceeds THRESH. Note that the error
190 *> is scaled to be O(1), so THRESH should be a reasonably
191 *> small multiple of 1, e.g., 10 or 100. In particular,
192 *> it should not depend on the precision (single vs. double)
193 *> or the size of the matrix. It must be at least zero.
194 *> \endverbatim
195 *>
196 *> \param[in] NOUNIT
197 *> \verbatim
198 *> NOUNIT is INTEGER
199 *> The FORTRAN unit number for printing out error messages
200 *> (e.g., if a routine returns IINFO not equal to 0.)
201 *> \endverbatim
202 *>
203 *> \param[in,out] A
204 *> \verbatim
205 *> A is DOUBLE PRECISION array, dimension
206 *> (LDA, max(NN))
207 *> Used to hold the matrix A.
208 *> \endverbatim
209 *>
210 *> \param[in] LDA
211 *> \verbatim
212 *> LDA is INTEGER
213 *> The leading dimension of A. It must be at least 1
214 *> and at least max( NN ).
215 *> \endverbatim
216 *>
217 *> \param[out] AB
218 *> \verbatim
219 *> AB is DOUBLE PRECISION array, dimension (LDAB, max(NN))
220 *> Used to hold A in band storage format.
221 *> \endverbatim
222 *>
223 *> \param[in] LDAB
224 *> \verbatim
225 *> LDAB is INTEGER
226 *> The leading dimension of AB. It must be at least 2 (not 1!)
227 *> and at least max( KK )+1.
228 *> \endverbatim
229 *>
230 *> \param[out] BD
231 *> \verbatim
232 *> BD is DOUBLE PRECISION array, dimension (max(NN))
233 *> Used to hold the diagonal of the bidiagonal matrix computed
234 *> by ZGBBRD.
235 *> \endverbatim
236 *>
237 *> \param[out] BE
238 *> \verbatim
239 *> BE is DOUBLE PRECISION array, dimension (max(NN))
240 *> Used to hold the off-diagonal of the bidiagonal matrix
241 *> computed by ZGBBRD.
242 *> \endverbatim
243 *>
244 *> \param[out] Q
245 *> \verbatim
246 *> Q is COMPLEX*16 array, dimension (LDQ, max(NN))
247 *> Used to hold the unitary matrix Q computed by ZGBBRD.
248 *> \endverbatim
249 *>
250 *> \param[in] LDQ
251 *> \verbatim
252 *> LDQ is INTEGER
253 *> The leading dimension of Q. It must be at least 1
254 *> and at least max( NN ).
255 *> \endverbatim
256 *>
257 *> \param[out] P
258 *> \verbatim
259 *> P is COMPLEX*16 array, dimension (LDP, max(NN))
260 *> Used to hold the unitary matrix P computed by ZGBBRD.
261 *> \endverbatim
262 *>
263 *> \param[in] LDP
264 *> \verbatim
265 *> LDP is INTEGER
266 *> The leading dimension of P. It must be at least 1
267 *> and at least max( NN ).
268 *> \endverbatim
269 *>
270 *> \param[out] C
271 *> \verbatim
272 *> C is COMPLEX*16 array, dimension (LDC, max(NN))
273 *> Used to hold the matrix C updated by ZGBBRD.
274 *> \endverbatim
275 *>
276 *> \param[in] LDC
277 *> \verbatim
278 *> LDC is INTEGER
279 *> The leading dimension of U. It must be at least 1
280 *> and at least max( NN ).
281 *> \endverbatim
282 *>
283 *> \param[out] CC
284 *> \verbatim
285 *> CC is COMPLEX*16 array, dimension (LDC, max(NN))
286 *> Used to hold a copy of the matrix C.
287 *> \endverbatim
288 *>
289 *> \param[out] WORK
290 *> \verbatim
291 *> WORK is COMPLEX*16 array, dimension (LWORK)
292 *> \endverbatim
293 *>
294 *> \param[in] LWORK
295 *> \verbatim
296 *> LWORK is INTEGER
297 *> The number of entries in WORK. This must be at least
298 *> max( LDA+1, max(NN)+1 )*max(NN).
299 *> \endverbatim
300 *>
301 *> \param[out] RWORK
302 *> \verbatim
303 *> RWORK is DOUBLE PRECISION array, dimension (max(NN))
304 *> \endverbatim
305 *>
306 *> \param[out] RESULT
307 *> \verbatim
308 *> RESULT is DOUBLE PRECISION array, dimension (4)
309 *> The values computed by the tests described above.
310 *> The values are currently limited to 1/ulp, to avoid
311 *> overflow.
312 *> \endverbatim
313 *>
314 *> \param[out] INFO
315 *> \verbatim
316 *> INFO is INTEGER
317 *> If 0, then everything ran OK.
318 *>
319 *>-----------------------------------------------------------------------
320 *>
321 *> Some Local Variables and Parameters:
322 *> ---- ----- --------- --- ----------
323 *> ZERO, ONE Real 0 and 1.
324 *> MAXTYP The number of types defined.
325 *> NTEST The number of tests performed, or which can
326 *> be performed so far, for the current matrix.
327 *> NTESTT The total number of tests performed so far.
328 *> NMAX Largest value in NN.
329 *> NMATS The number of matrices generated so far.
330 *> NERRS The number of tests which have exceeded THRESH
331 *> so far.
332 *> COND, IMODE Values to be passed to the matrix generators.
333 *> ANORM Norm of A; passed to matrix generators.
334 *>
335 *> OVFL, UNFL Overflow and underflow thresholds.
336 *> ULP, ULPINV Finest relative precision and its inverse.
337 *> RTOVFL, RTUNFL Square roots of the previous 2 values.
338 *> The following four arrays decode JTYPE:
339 *> KTYPE(j) The general type (1-10) for type "j".
340 *> KMODE(j) The MODE value to be passed to the matrix
341 *> generator for type "j".
342 *> KMAGN(j) The order of magnitude ( O(1),
343 *> O(overflow^(1/2) ), O(underflow^(1/2) )
344 *> \endverbatim
345 *
346 * Authors:
347 * ========
348 *
349 *> \author Univ. of Tennessee
350 *> \author Univ. of California Berkeley
351 *> \author Univ. of Colorado Denver
352 *> \author NAG Ltd.
353 *
354 *> \ingroup complex16_eig
355 *
356 * =====================================================================
357  SUBROUTINE zchkbb( NSIZES, MVAL, NVAL, NWDTHS, KK, NTYPES, DOTYPE,
358  $ NRHS, ISEED, THRESH, NOUNIT, A, LDA, AB, LDAB,
359  $ BD, BE, Q, LDQ, P, LDP, C, LDC, CC, WORK,
360  $ LWORK, RWORK, RESULT, INFO )
361 *
362 * -- LAPACK test routine (input) --
363 * -- LAPACK is a software package provided by Univ. of Tennessee, --
364 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
365 *
366 * .. Scalar Arguments ..
367  INTEGER INFO, LDA, LDAB, LDC, LDP, LDQ, LWORK, NOUNIT,
368  $ NRHS, NSIZES, NTYPES, NWDTHS
369  DOUBLE PRECISION THRESH
370 * ..
371 * .. Array Arguments ..
372  LOGICAL DOTYPE( * )
373  INTEGER ISEED( 4 ), KK( * ), MVAL( * ), NVAL( * )
374  DOUBLE PRECISION BD( * ), BE( * ), RESULT( * ), RWORK( * )
375  COMPLEX*16 A( LDA, * ), AB( LDAB, * ), C( LDC, * ),
376  $ cc( ldc, * ), p( ldp, * ), q( ldq, * ),
377  $ work( * )
378 * ..
379 *
380 * =====================================================================
381 *
382 * .. Parameters ..
383  COMPLEX*16 CZERO, CONE
384  PARAMETER ( CZERO = ( 0.0d+0, 0.0d+0 ),
385  $ cone = ( 1.0d+0, 0.0d+0 ) )
386  DOUBLE PRECISION ZERO, ONE
387  parameter( zero = 0.0d+0, one = 1.0d+0 )
388  INTEGER MAXTYP
389  parameter( maxtyp = 15 )
390 * ..
391 * .. Local Scalars ..
392  LOGICAL BADMM, BADNN, BADNNB
393  INTEGER I, IINFO, IMODE, ITYPE, J, JCOL, JR, JSIZE,
394  $ JTYPE, JWIDTH, K, KL, KMAX, KU, M, MMAX, MNMAX,
395  $ mnmin, mtypes, n, nerrs, nmats, nmax, ntest,
396  $ ntestt
397  DOUBLE PRECISION AMNINV, ANORM, COND, OVFL, RTOVFL, RTUNFL, ULP,
398  $ ULPINV, UNFL
399 * ..
400 * .. Local Arrays ..
401  INTEGER IDUMMA( 1 ), IOLDSD( 4 ), KMAGN( MAXTYP ),
402  $ KMODE( MAXTYP ), KTYPE( MAXTYP )
403 * ..
404 * .. External Functions ..
405  DOUBLE PRECISION DLAMCH
406  EXTERNAL DLAMCH
407 * ..
408 * .. External Subroutines ..
409  EXTERNAL dlahd2, dlasum, xerbla, zbdt01, zbdt02, zgbbrd,
411 * ..
412 * .. Intrinsic Functions ..
413  INTRINSIC abs, dble, max, min, sqrt
414 * ..
415 * .. Data statements ..
416  DATA ktype / 1, 2, 5*4, 5*6, 3*9 /
417  DATA kmagn / 2*1, 3*1, 2, 3, 3*1, 2, 3, 1, 2, 3 /
418  DATA kmode / 2*0, 4, 3, 1, 4, 4, 4, 3, 1, 4, 4, 0,
419  $ 0, 0 /
420 * ..
421 * .. Executable Statements ..
422 *
423 * Check for errors
424 *
425  ntestt = 0
426  info = 0
427 *
428 * Important constants
429 *
430  badmm = .false.
431  badnn = .false.
432  mmax = 1
433  nmax = 1
434  mnmax = 1
435  DO 10 j = 1, nsizes
436  mmax = max( mmax, mval( j ) )
437  IF( mval( j ).LT.0 )
438  $ badmm = .true.
439  nmax = max( nmax, nval( j ) )
440  IF( nval( j ).LT.0 )
441  $ badnn = .true.
442  mnmax = max( mnmax, min( mval( j ), nval( j ) ) )
443  10 CONTINUE
444 *
445  badnnb = .false.
446  kmax = 0
447  DO 20 j = 1, nwdths
448  kmax = max( kmax, kk( j ) )
449  IF( kk( j ).LT.0 )
450  $ badnnb = .true.
451  20 CONTINUE
452 *
453 * Check for errors
454 *
455  IF( nsizes.LT.0 ) THEN
456  info = -1
457  ELSE IF( badmm ) THEN
458  info = -2
459  ELSE IF( badnn ) THEN
460  info = -3
461  ELSE IF( nwdths.LT.0 ) THEN
462  info = -4
463  ELSE IF( badnnb ) THEN
464  info = -5
465  ELSE IF( ntypes.LT.0 ) THEN
466  info = -6
467  ELSE IF( nrhs.LT.0 ) THEN
468  info = -8
469  ELSE IF( lda.LT.nmax ) THEN
470  info = -13
471  ELSE IF( ldab.LT.2*kmax+1 ) THEN
472  info = -15
473  ELSE IF( ldq.LT.nmax ) THEN
474  info = -19
475  ELSE IF( ldp.LT.nmax ) THEN
476  info = -21
477  ELSE IF( ldc.LT.nmax ) THEN
478  info = -23
479  ELSE IF( ( max( lda, nmax )+1 )*nmax.GT.lwork ) THEN
480  info = -26
481  END IF
482 *
483  IF( info.NE.0 ) THEN
484  CALL xerbla( 'ZCHKBB', -info )
485  RETURN
486  END IF
487 *
488 * Quick return if possible
489 *
490  IF( nsizes.EQ.0 .OR. ntypes.EQ.0 .OR. nwdths.EQ.0 )
491  $ RETURN
492 *
493 * More Important constants
494 *
495  unfl = dlamch( 'Safe minimum' )
496  ovfl = one / unfl
497  ulp = dlamch( 'Epsilon' )*dlamch( 'Base' )
498  ulpinv = one / ulp
499  rtunfl = sqrt( unfl )
500  rtovfl = sqrt( ovfl )
501 *
502 * Loop over sizes, widths, types
503 *
504  nerrs = 0
505  nmats = 0
506 *
507  DO 160 jsize = 1, nsizes
508  m = mval( jsize )
509  n = nval( jsize )
510  mnmin = min( m, n )
511  amninv = one / dble( max( 1, m, n ) )
512 *
513  DO 150 jwidth = 1, nwdths
514  k = kk( jwidth )
515  IF( k.GE.m .AND. k.GE.n )
516  $ GO TO 150
517  kl = max( 0, min( m-1, k ) )
518  ku = max( 0, min( n-1, k ) )
519 *
520  IF( nsizes.NE.1 ) THEN
521  mtypes = min( maxtyp, ntypes )
522  ELSE
523  mtypes = min( maxtyp+1, ntypes )
524  END IF
525 *
526  DO 140 jtype = 1, mtypes
527  IF( .NOT.dotype( jtype ) )
528  $ GO TO 140
529  nmats = nmats + 1
530  ntest = 0
531 *
532  DO 30 j = 1, 4
533  ioldsd( j ) = iseed( j )
534  30 CONTINUE
535 *
536 * Compute "A".
537 *
538 * Control parameters:
539 *
540 * KMAGN KMODE KTYPE
541 * =1 O(1) clustered 1 zero
542 * =2 large clustered 2 identity
543 * =3 small exponential (none)
544 * =4 arithmetic diagonal, (w/ singular values)
545 * =5 random log (none)
546 * =6 random nonhermitian, w/ singular values
547 * =7 (none)
548 * =8 (none)
549 * =9 random nonhermitian
550 *
551  IF( mtypes.GT.maxtyp )
552  $ GO TO 90
553 *
554  itype = ktype( jtype )
555  imode = kmode( jtype )
556 *
557 * Compute norm
558 *
559  GO TO ( 40, 50, 60 )kmagn( jtype )
560 *
561  40 CONTINUE
562  anorm = one
563  GO TO 70
564 *
565  50 CONTINUE
566  anorm = ( rtovfl*ulp )*amninv
567  GO TO 70
568 *
569  60 CONTINUE
570  anorm = rtunfl*max( m, n )*ulpinv
571  GO TO 70
572 *
573  70 CONTINUE
574 *
575  CALL zlaset( 'Full', lda, n, czero, czero, a, lda )
576  CALL zlaset( 'Full', ldab, n, czero, czero, ab, ldab )
577  iinfo = 0
578  cond = ulpinv
579 *
580 * Special Matrices -- Identity & Jordan block
581 *
582 * Zero
583 *
584  IF( itype.EQ.1 ) THEN
585  iinfo = 0
586 *
587  ELSE IF( itype.EQ.2 ) THEN
588 *
589 * Identity
590 *
591  DO 80 jcol = 1, n
592  a( jcol, jcol ) = anorm
593  80 CONTINUE
594 *
595  ELSE IF( itype.EQ.4 ) THEN
596 *
597 * Diagonal Matrix, singular values specified
598 *
599  CALL zlatms( m, n, 'S', iseed, 'N', rwork, imode,
600  $ cond, anorm, 0, 0, 'N', a, lda, work,
601  $ iinfo )
602 *
603  ELSE IF( itype.EQ.6 ) THEN
604 *
605 * Nonhermitian, singular values specified
606 *
607  CALL zlatms( m, n, 'S', iseed, 'N', rwork, imode,
608  $ cond, anorm, kl, ku, 'N', a, lda, work,
609  $ iinfo )
610 *
611  ELSE IF( itype.EQ.9 ) THEN
612 *
613 * Nonhermitian, random entries
614 *
615  CALL zlatmr( m, n, 'S', iseed, 'N', work, 6, one,
616  $ cone, 'T', 'N', work( n+1 ), 1, one,
617  $ work( 2*n+1 ), 1, one, 'N', idumma, kl,
618  $ ku, zero, anorm, 'N', a, lda, idumma,
619  $ iinfo )
620 *
621  ELSE
622 *
623  iinfo = 1
624  END IF
625 *
626 * Generate Right-Hand Side
627 *
628  CALL zlatmr( m, nrhs, 'S', iseed, 'N', work, 6, one,
629  $ cone, 'T', 'N', work( m+1 ), 1, one,
630  $ work( 2*m+1 ), 1, one, 'N', idumma, m, nrhs,
631  $ zero, one, 'NO', c, ldc, idumma, iinfo )
632 *
633  IF( iinfo.NE.0 ) THEN
634  WRITE( nounit, fmt = 9999 )'Generator', iinfo, n,
635  $ jtype, ioldsd
636  info = abs( iinfo )
637  RETURN
638  END IF
639 *
640  90 CONTINUE
641 *
642 * Copy A to band storage.
643 *
644  DO 110 j = 1, n
645  DO 100 i = max( 1, j-ku ), min( m, j+kl )
646  ab( ku+1+i-j, j ) = a( i, j )
647  100 CONTINUE
648  110 CONTINUE
649 *
650 * Copy C
651 *
652  CALL zlacpy( 'Full', m, nrhs, c, ldc, cc, ldc )
653 *
654 * Call ZGBBRD to compute B, Q and P, and to update C.
655 *
656  CALL zgbbrd( 'B', m, n, nrhs, kl, ku, ab, ldab, bd, be,
657  $ q, ldq, p, ldp, cc, ldc, work, rwork,
658  $ iinfo )
659 *
660  IF( iinfo.NE.0 ) THEN
661  WRITE( nounit, fmt = 9999 )'ZGBBRD', iinfo, n, jtype,
662  $ ioldsd
663  info = abs( iinfo )
664  IF( iinfo.LT.0 ) THEN
665  RETURN
666  ELSE
667  result( 1 ) = ulpinv
668  GO TO 120
669  END IF
670  END IF
671 *
672 * Test 1: Check the decomposition A := Q * B * P'
673 * 2: Check the orthogonality of Q
674 * 3: Check the orthogonality of P
675 * 4: Check the computation of Q' * C
676 *
677  CALL zbdt01( m, n, -1, a, lda, q, ldq, bd, be, p, ldp,
678  $ work, rwork, result( 1 ) )
679  CALL zunt01( 'Columns', m, m, q, ldq, work, lwork, rwork,
680  $ result( 2 ) )
681  CALL zunt01( 'Rows', n, n, p, ldp, work, lwork, rwork,
682  $ result( 3 ) )
683  CALL zbdt02( m, nrhs, c, ldc, cc, ldc, q, ldq, work,
684  $ rwork, result( 4 ) )
685 *
686 * End of Loop -- Check for RESULT(j) > THRESH
687 *
688  ntest = 4
689  120 CONTINUE
690  ntestt = ntestt + ntest
691 *
692 * Print out tests which fail.
693 *
694  DO 130 jr = 1, ntest
695  IF( result( jr ).GE.thresh ) THEN
696  IF( nerrs.EQ.0 )
697  $ CALL dlahd2( nounit, 'ZBB' )
698  nerrs = nerrs + 1
699  WRITE( nounit, fmt = 9998 )m, n, k, ioldsd, jtype,
700  $ jr, result( jr )
701  END IF
702  130 CONTINUE
703 *
704  140 CONTINUE
705  150 CONTINUE
706  160 CONTINUE
707 *
708 * Summary
709 *
710  CALL dlasum( 'ZBB', nounit, nerrs, ntestt )
711  RETURN
712 *
713  9999 FORMAT( ' ZCHKBB: ', a, ' returned INFO=', i5, '.', / 9x, 'M=',
714  $ i5, ' N=', i5, ' K=', i5, ', JTYPE=', i5, ', ISEED=(',
715  $ 3( i5, ',' ), i5, ')' )
716  9998 FORMAT( ' M =', i4, ' N=', i4, ', K=', i3, ', seed=',
717  $ 4( i4, ',' ), ' type ', i2, ', test(', i2, ')=', g10.3 )
718 *
719 * End of ZCHKBB
720 *
721  END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine zbdt01(M, N, KD, A, LDA, Q, LDQ, D, E, PT, LDPT, WORK, RWORK, RESID)
ZBDT01
Definition: zbdt01.f:147
subroutine zunt01(ROWCOL, M, N, U, LDU, WORK, LWORK, RWORK, RESID)
ZUNT01
Definition: zunt01.f:126
subroutine zbdt02(M, N, B, LDB, C, LDC, U, LDU, WORK, RWORK, RESID)
ZBDT02
Definition: zbdt02.f:120
subroutine zchkbb(NSIZES, MVAL, NVAL, NWDTHS, KK, NTYPES, DOTYPE, NRHS, ISEED, THRESH, NOUNIT, A, LDA, AB, LDAB, BD, BE, Q, LDQ, P, LDP, C, LDC, CC, WORK, LWORK, RWORK, RESULT, INFO)
ZCHKBB
Definition: zchkbb.f:361
subroutine zlatms(M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX, KL, KU, PACK, A, LDA, WORK, INFO)
ZLATMS
Definition: zlatms.f:332
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
subroutine zgbbrd(VECT, M, N, NCC, KL, KU, AB, LDAB, D, E, Q, LDQ, PT, LDPT, C, LDC, WORK, RWORK, INFO)
ZGBBRD
Definition: zgbbrd.f:193
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
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
subroutine dlasum(TYPE, IOUNIT, IE, NRUN)
DLASUM
Definition: dlasum.f:43
subroutine dlahd2(IOUNIT, PATH)
DLAHD2
Definition: dlahd2.f:65