LAPACK  3.8.0
LAPACK: Linear Algebra PACKage
cchkbd.f
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1 *> \brief \b CCHKBD
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 CCHKBD( NSIZES, MVAL, NVAL, NTYPES, DOTYPE, NRHS,
12 * ISEED, THRESH, A, LDA, BD, BE, S1, S2, X, LDX,
13 * Y, Z, Q, LDQ, PT, LDPT, U, VT, WORK, LWORK,
14 * RWORK, NOUT, INFO )
15 *
16 * .. Scalar Arguments ..
17 * INTEGER INFO, LDA, LDPT, LDQ, LDX, LWORK, NOUT, NRHS,
18 * $ NSIZES, NTYPES
19 * REAL THRESH
20 * ..
21 * .. Array Arguments ..
22 * LOGICAL DOTYPE( * )
23 * INTEGER ISEED( 4 ), MVAL( * ), NVAL( * )
24 * REAL BD( * ), BE( * ), RWORK( * ), S1( * ), S2( * )
25 * COMPLEX A( LDA, * ), PT( LDPT, * ), Q( LDQ, * ),
26 * $ U( LDPT, * ), VT( LDPT, * ), WORK( * ),
27 * $ X( LDX, * ), Y( LDX, * ), Z( LDX, * )
28 * ..
29 *
30 *
31 *> \par Purpose:
32 * =============
33 *>
34 *> \verbatim
35 *>
36 *> CCHKBD checks the singular value decomposition (SVD) routines.
37 *>
38 *> CGEBRD reduces a complex general m by n matrix A to real upper or
39 *> lower bidiagonal form by an orthogonal transformation: Q' * A * P = B
40 *> (or A = Q * B * P'). The matrix B is upper bidiagonal if m >= n
41 *> and lower bidiagonal if m < n.
42 *>
43 *> CUNGBR generates the orthogonal matrices Q and P' from CGEBRD.
44 *> Note that Q and P are not necessarily square.
45 *>
46 *> CBDSQR computes the singular value decomposition of the bidiagonal
47 *> matrix B as B = U S V'. It is called three times to compute
48 *> 1) B = U S1 V', where S1 is the diagonal matrix of singular
49 *> values and the columns of the matrices U and V are the left
50 *> and right singular vectors, respectively, of B.
51 *> 2) Same as 1), but the singular values are stored in S2 and the
52 *> singular vectors are not computed.
53 *> 3) A = (UQ) S (P'V'), the SVD of the original matrix A.
54 *> In addition, CBDSQR has an option to apply the left orthogonal matrix
55 *> U to a matrix X, useful in least squares applications.
56 *>
57 *> For each pair of matrix dimensions (M,N) and each selected matrix
58 *> type, an M by N matrix A and an M by NRHS matrix X are generated.
59 *> The problem dimensions are as follows
60 *> A: M x N
61 *> Q: M x min(M,N) (but M x M if NRHS > 0)
62 *> P: min(M,N) x N
63 *> B: min(M,N) x min(M,N)
64 *> U, V: min(M,N) x min(M,N)
65 *> S1, S2 diagonal, order min(M,N)
66 *> X: M x NRHS
67 *>
68 *> For each generated matrix, 14 tests are performed:
69 *>
70 *> Test CGEBRD and CUNGBR
71 *>
72 *> (1) | A - Q B PT | / ( |A| max(M,N) ulp ), PT = P'
73 *>
74 *> (2) | I - Q' Q | / ( M ulp )
75 *>
76 *> (3) | I - PT PT' | / ( N ulp )
77 *>
78 *> Test CBDSQR on bidiagonal matrix B
79 *>
80 *> (4) | B - U S1 VT | / ( |B| min(M,N) ulp ), VT = V'
81 *>
82 *> (5) | Y - U Z | / ( |Y| max(min(M,N),k) ulp ), where Y = Q' X
83 *> and Z = U' Y.
84 *> (6) | I - U' U | / ( min(M,N) ulp )
85 *>
86 *> (7) | I - VT VT' | / ( min(M,N) ulp )
87 *>
88 *> (8) S1 contains min(M,N) nonnegative values in decreasing order.
89 *> (Return 0 if true, 1/ULP if false.)
90 *>
91 *> (9) 0 if the true singular values of B are within THRESH of
92 *> those in S1. 2*THRESH if they are not. (Tested using
93 *> SSVDCH)
94 *>
95 *> (10) | S1 - S2 | / ( |S1| ulp ), where S2 is computed without
96 *> computing U and V.
97 *>
98 *> Test CBDSQR on matrix A
99 *>
100 *> (11) | A - (QU) S (VT PT) | / ( |A| max(M,N) ulp )
101 *>
102 *> (12) | X - (QU) Z | / ( |X| max(M,k) ulp )
103 *>
104 *> (13) | I - (QU)'(QU) | / ( M ulp )
105 *>
106 *> (14) | I - (VT PT) (PT'VT') | / ( N ulp )
107 *>
108 *> The possible matrix types are
109 *>
110 *> (1) The zero matrix.
111 *> (2) The identity matrix.
112 *>
113 *> (3) A diagonal matrix with evenly spaced entries
114 *> 1, ..., ULP and random signs.
115 *> (ULP = (first number larger than 1) - 1 )
116 *> (4) A diagonal matrix with geometrically spaced entries
117 *> 1, ..., ULP and random signs.
118 *> (5) A diagonal matrix with "clustered" entries 1, ULP, ..., ULP
119 *> and random signs.
120 *>
121 *> (6) Same as (3), but multiplied by SQRT( overflow threshold )
122 *> (7) Same as (3), but multiplied by SQRT( underflow threshold )
123 *>
124 *> (8) A matrix of the form U D V, where U and V are orthogonal and
125 *> D has evenly spaced entries 1, ..., ULP with random signs
126 *> on the diagonal.
127 *>
128 *> (9) A matrix of the form U D V, where U and V are orthogonal and
129 *> D has geometrically spaced entries 1, ..., ULP with random
130 *> signs on the diagonal.
131 *>
132 *> (10) A matrix of the form U D V, where U and V are orthogonal and
133 *> D has "clustered" entries 1, ULP,..., ULP with random
134 *> signs on the diagonal.
135 *>
136 *> (11) Same as (8), but multiplied by SQRT( overflow threshold )
137 *> (12) Same as (8), but multiplied by SQRT( underflow threshold )
138 *>
139 *> (13) Rectangular matrix with random entries chosen from (-1,1).
140 *> (14) Same as (13), but multiplied by SQRT( overflow threshold )
141 *> (15) Same as (13), but multiplied by SQRT( underflow threshold )
142 *>
143 *> Special case:
144 *> (16) A bidiagonal matrix with random entries chosen from a
145 *> logarithmic distribution on [ulp^2,ulp^(-2)] (I.e., each
146 *> entry is e^x, where x is chosen uniformly on
147 *> [ 2 log(ulp), -2 log(ulp) ] .) For *this* type:
148 *> (a) CGEBRD is not called to reduce it to bidiagonal form.
149 *> (b) the bidiagonal is min(M,N) x min(M,N); if M<N, the
150 *> matrix will be lower bidiagonal, otherwise upper.
151 *> (c) only tests 5--8 and 14 are performed.
152 *>
153 *> A subset of the full set of matrix types may be selected through
154 *> the logical array DOTYPE.
155 *> \endverbatim
156 *
157 * Arguments:
158 * ==========
159 *
160 *> \param[in] NSIZES
161 *> \verbatim
162 *> NSIZES is INTEGER
163 *> The number of values of M and N contained in the vectors
164 *> MVAL and NVAL. The matrix sizes are used in pairs (M,N).
165 *> \endverbatim
166 *>
167 *> \param[in] MVAL
168 *> \verbatim
169 *> MVAL is INTEGER array, dimension (NM)
170 *> The values of the matrix row dimension M.
171 *> \endverbatim
172 *>
173 *> \param[in] NVAL
174 *> \verbatim
175 *> NVAL is INTEGER array, dimension (NM)
176 *> The values of the matrix column dimension N.
177 *> \endverbatim
178 *>
179 *> \param[in] NTYPES
180 *> \verbatim
181 *> NTYPES is INTEGER
182 *> The number of elements in DOTYPE. If it is zero, CCHKBD
183 *> does nothing. It must be at least zero. If it is MAXTYP+1
184 *> and NSIZES is 1, then an additional type, MAXTYP+1 is
185 *> defined, which is to use whatever matrices are in A and B.
186 *> This is only useful if DOTYPE(1:MAXTYP) is .FALSE. and
187 *> DOTYPE(MAXTYP+1) is .TRUE. .
188 *> \endverbatim
189 *>
190 *> \param[in] DOTYPE
191 *> \verbatim
192 *> DOTYPE is LOGICAL array, dimension (NTYPES)
193 *> If DOTYPE(j) is .TRUE., then for each size (m,n), a matrix
194 *> of type j will be generated. If NTYPES is smaller than the
195 *> maximum number of types defined (PARAMETER MAXTYP), then
196 *> types NTYPES+1 through MAXTYP will not be generated. If
197 *> NTYPES is larger than MAXTYP, DOTYPE(MAXTYP+1) through
198 *> DOTYPE(NTYPES) will be ignored.
199 *> \endverbatim
200 *>
201 *> \param[in] NRHS
202 *> \verbatim
203 *> NRHS is INTEGER
204 *> The number of columns in the "right-hand side" matrices X, Y,
205 *> and Z, used in testing CBDSQR. If NRHS = 0, then the
206 *> operations on the right-hand side will not be tested.
207 *> NRHS must be at least 0.
208 *> \endverbatim
209 *>
210 *> \param[in,out] ISEED
211 *> \verbatim
212 *> ISEED is INTEGER array, dimension (4)
213 *> On entry ISEED specifies the seed of the random number
214 *> generator. The array elements should be between 0 and 4095;
215 *> if not they will be reduced mod 4096. Also, ISEED(4) must
216 *> be odd. The values of ISEED are changed on exit, and can be
217 *> used in the next call to CCHKBD to continue the same random
218 *> number sequence.
219 *> \endverbatim
220 *>
221 *> \param[in] THRESH
222 *> \verbatim
223 *> THRESH is REAL
224 *> The threshold value for the test ratios. A result is
225 *> included in the output file if RESULT >= THRESH. To have
226 *> every test ratio printed, use THRESH = 0. Note that the
227 *> expected value of the test ratios is O(1), so THRESH should
228 *> be a reasonably small multiple of 1, e.g., 10 or 100.
229 *> \endverbatim
230 *>
231 *> \param[out] A
232 *> \verbatim
233 *> A is COMPLEX array, dimension (LDA,NMAX)
234 *> where NMAX is the maximum value of N in NVAL.
235 *> \endverbatim
236 *>
237 *> \param[in] LDA
238 *> \verbatim
239 *> LDA is INTEGER
240 *> The leading dimension of the array A. LDA >= max(1,MMAX),
241 *> where MMAX is the maximum value of M in MVAL.
242 *> \endverbatim
243 *>
244 *> \param[out] BD
245 *> \verbatim
246 *> BD is REAL array, dimension
247 *> (max(min(MVAL(j),NVAL(j))))
248 *> \endverbatim
249 *>
250 *> \param[out] BE
251 *> \verbatim
252 *> BE is REAL array, dimension
253 *> (max(min(MVAL(j),NVAL(j))))
254 *> \endverbatim
255 *>
256 *> \param[out] S1
257 *> \verbatim
258 *> S1 is REAL array, dimension
259 *> (max(min(MVAL(j),NVAL(j))))
260 *> \endverbatim
261 *>
262 *> \param[out] S2
263 *> \verbatim
264 *> S2 is REAL array, dimension
265 *> (max(min(MVAL(j),NVAL(j))))
266 *> \endverbatim
267 *>
268 *> \param[out] X
269 *> \verbatim
270 *> X is COMPLEX array, dimension (LDX,NRHS)
271 *> \endverbatim
272 *>
273 *> \param[in] LDX
274 *> \verbatim
275 *> LDX is INTEGER
276 *> The leading dimension of the arrays X, Y, and Z.
277 *> LDX >= max(1,MMAX).
278 *> \endverbatim
279 *>
280 *> \param[out] Y
281 *> \verbatim
282 *> Y is COMPLEX array, dimension (LDX,NRHS)
283 *> \endverbatim
284 *>
285 *> \param[out] Z
286 *> \verbatim
287 *> Z is COMPLEX array, dimension (LDX,NRHS)
288 *> \endverbatim
289 *>
290 *> \param[out] Q
291 *> \verbatim
292 *> Q is COMPLEX array, dimension (LDQ,MMAX)
293 *> \endverbatim
294 *>
295 *> \param[in] LDQ
296 *> \verbatim
297 *> LDQ is INTEGER
298 *> The leading dimension of the array Q. LDQ >= max(1,MMAX).
299 *> \endverbatim
300 *>
301 *> \param[out] PT
302 *> \verbatim
303 *> PT is COMPLEX array, dimension (LDPT,NMAX)
304 *> \endverbatim
305 *>
306 *> \param[in] LDPT
307 *> \verbatim
308 *> LDPT is INTEGER
309 *> The leading dimension of the arrays PT, U, and V.
310 *> LDPT >= max(1, max(min(MVAL(j),NVAL(j)))).
311 *> \endverbatim
312 *>
313 *> \param[out] U
314 *> \verbatim
315 *> U is COMPLEX array, dimension
316 *> (LDPT,max(min(MVAL(j),NVAL(j))))
317 *> \endverbatim
318 *>
319 *> \param[out] VT
320 *> \verbatim
321 *> VT is COMPLEX array, dimension
322 *> (LDPT,max(min(MVAL(j),NVAL(j))))
323 *> \endverbatim
324 *>
325 *> \param[out] WORK
326 *> \verbatim
327 *> WORK is COMPLEX array, dimension (LWORK)
328 *> \endverbatim
329 *>
330 *> \param[in] LWORK
331 *> \verbatim
332 *> LWORK is INTEGER
333 *> The number of entries in WORK. This must be at least
334 *> 3(M+N) and M(M + max(M,N,k) + 1) + N*min(M,N) for all
335 *> pairs (M,N)=(MM(j),NN(j))
336 *> \endverbatim
337 *>
338 *> \param[out] RWORK
339 *> \verbatim
340 *> RWORK is REAL array, dimension
341 *> (5*max(min(M,N)))
342 *> \endverbatim
343 *>
344 *> \param[in] NOUT
345 *> \verbatim
346 *> NOUT is INTEGER
347 *> The FORTRAN unit number for printing out error messages
348 *> (e.g., if a routine returns IINFO not equal to 0.)
349 *> \endverbatim
350 *>
351 *> \param[out] INFO
352 *> \verbatim
353 *> INFO is INTEGER
354 *> If 0, then everything ran OK.
355 *> -1: NSIZES < 0
356 *> -2: Some MM(j) < 0
357 *> -3: Some NN(j) < 0
358 *> -4: NTYPES < 0
359 *> -6: NRHS < 0
360 *> -8: THRESH < 0
361 *> -11: LDA < 1 or LDA < MMAX, where MMAX is max( MM(j) ).
362 *> -17: LDB < 1 or LDB < MMAX.
363 *> -21: LDQ < 1 or LDQ < MMAX.
364 *> -23: LDP < 1 or LDP < MNMAX.
365 *> -27: LWORK too small.
366 *> If CLATMR, CLATMS, CGEBRD, CUNGBR, or CBDSQR,
367 *> returns an error code, the
368 *> absolute value of it is returned.
369 *>
370 *>-----------------------------------------------------------------------
371 *>
372 *> Some Local Variables and Parameters:
373 *> ---- ----- --------- --- ----------
374 *>
375 *> ZERO, ONE Real 0 and 1.
376 *> MAXTYP The number of types defined.
377 *> NTEST The number of tests performed, or which can
378 *> be performed so far, for the current matrix.
379 *> MMAX Largest value in NN.
380 *> NMAX Largest value in NN.
381 *> MNMIN min(MM(j), NN(j)) (the dimension of the bidiagonal
382 *> matrix.)
383 *> MNMAX The maximum value of MNMIN for j=1,...,NSIZES.
384 *> NFAIL The number of tests which have exceeded THRESH
385 *> COND, IMODE Values to be passed to the matrix generators.
386 *> ANORM Norm of A; passed to matrix generators.
387 *>
388 *> OVFL, UNFL Overflow and underflow thresholds.
389 *> RTOVFL, RTUNFL Square roots of the previous 2 values.
390 *> ULP, ULPINV Finest relative precision and its inverse.
391 *>
392 *> The following four arrays decode JTYPE:
393 *> KTYPE(j) The general type (1-10) for type "j".
394 *> KMODE(j) The MODE value to be passed to the matrix
395 *> generator for type "j".
396 *> KMAGN(j) The order of magnitude ( O(1),
397 *> O(overflow^(1/2) ), O(underflow^(1/2) )
398 *> \endverbatim
399 *
400 * Authors:
401 * ========
402 *
403 *> \author Univ. of Tennessee
404 *> \author Univ. of California Berkeley
405 *> \author Univ. of Colorado Denver
406 *> \author NAG Ltd.
407 *
408 *> \date June 2016
409 *
410 *> \ingroup complex_eig
411 *
412 * =====================================================================
413  SUBROUTINE cchkbd( NSIZES, MVAL, NVAL, NTYPES, DOTYPE, NRHS,
414  $ ISEED, THRESH, A, LDA, BD, BE, S1, S2, X, LDX,
415  $ Y, Z, Q, LDQ, PT, LDPT, U, VT, WORK, LWORK,
416  $ RWORK, NOUT, INFO )
417 *
418 * -- LAPACK test routine (version 3.7.0) --
419 * -- LAPACK is a software package provided by Univ. of Tennessee, --
420 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
421 * June 2016
422 *
423 * .. Scalar Arguments ..
424  INTEGER INFO, LDA, LDPT, LDQ, LDX, LWORK, NOUT, NRHS,
425  $ nsizes, ntypes
426  REAL THRESH
427 * ..
428 * .. Array Arguments ..
429  LOGICAL DOTYPE( * )
430  INTEGER ISEED( 4 ), MVAL( * ), NVAL( * )
431  REAL BD( * ), BE( * ), RWORK( * ), S1( * ), S2( * )
432  COMPLEX A( lda, * ), PT( ldpt, * ), Q( ldq, * ),
433  $ u( ldpt, * ), vt( ldpt, * ), work( * ),
434  $ x( ldx, * ), y( ldx, * ), z( ldx, * )
435 * ..
436 *
437 * ======================================================================
438 *
439 * .. Parameters ..
440  REAL ZERO, ONE, TWO, HALF
441  parameter( zero = 0.0e0, one = 1.0e0, two = 2.0e0,
442  $ half = 0.5e0 )
443  COMPLEX CZERO, CONE
444  parameter( czero = ( 0.0e+0, 0.0e+0 ),
445  $ cone = ( 1.0e+0, 0.0e+0 ) )
446  INTEGER MAXTYP
447  parameter( maxtyp = 16 )
448 * ..
449 * .. Local Scalars ..
450  LOGICAL BADMM, BADNN, BIDIAG
451  CHARACTER UPLO
452  CHARACTER*3 PATH
453  INTEGER I, IINFO, IMODE, ITYPE, J, JCOL, JSIZE, JTYPE,
454  $ log2ui, m, minwrk, mmax, mnmax, mnmin, mq,
455  $ mtypes, n, nfail, nmax, ntest
456  REAL AMNINV, ANORM, COND, OVFL, RTOVFL, RTUNFL,
457  $ temp1, temp2, ulp, ulpinv, unfl
458 * ..
459 * .. Local Arrays ..
460  INTEGER IOLDSD( 4 ), IWORK( 1 ), KMAGN( maxtyp ),
461  $ kmode( maxtyp ), ktype( maxtyp )
462  REAL DUMMA( 1 ), RESULT( 14 )
463 * ..
464 * .. External Functions ..
465  REAL SLAMCH, SLARND
466  EXTERNAL slamch, slarnd
467 * ..
468 * .. External Subroutines ..
469  EXTERNAL alasum, cbdsqr, cbdt01, cbdt02, cbdt03,
472  $ slahd2, ssvdch, xerbla
473 * ..
474 * .. Intrinsic Functions ..
475  INTRINSIC abs, exp, int, log, max, min, sqrt
476 * ..
477 * .. Scalars in Common ..
478  LOGICAL LERR, OK
479  CHARACTER*32 SRNAMT
480  INTEGER INFOT, NUNIT
481 * ..
482 * .. Common blocks ..
483  COMMON / infoc / infot, nunit, ok, lerr
484  COMMON / srnamc / srnamt
485 * ..
486 * .. Data statements ..
487  DATA ktype / 1, 2, 5*4, 5*6, 3*9, 10 /
488  DATA kmagn / 2*1, 3*1, 2, 3, 3*1, 2, 3, 1, 2, 3, 0 /
489  DATA kmode / 2*0, 4, 3, 1, 4, 4, 4, 3, 1, 4, 4, 0,
490  $ 0, 0, 0 /
491 * ..
492 * .. Executable Statements ..
493 *
494 * Check for errors
495 *
496  info = 0
497 *
498  badmm = .false.
499  badnn = .false.
500  mmax = 1
501  nmax = 1
502  mnmax = 1
503  minwrk = 1
504  DO 10 j = 1, nsizes
505  mmax = max( mmax, mval( j ) )
506  IF( mval( j ).LT.0 )
507  $ badmm = .true.
508  nmax = max( nmax, nval( j ) )
509  IF( nval( j ).LT.0 )
510  $ badnn = .true.
511  mnmax = max( mnmax, min( mval( j ), nval( j ) ) )
512  minwrk = max( minwrk, 3*( mval( j )+nval( j ) ),
513  $ mval( j )*( mval( j )+max( mval( j ), nval( j ),
514  $ nrhs )+1 )+nval( j )*min( nval( j ), mval( j ) ) )
515  10 CONTINUE
516 *
517 * Check for errors
518 *
519  IF( nsizes.LT.0 ) THEN
520  info = -1
521  ELSE IF( badmm ) THEN
522  info = -2
523  ELSE IF( badnn ) THEN
524  info = -3
525  ELSE IF( ntypes.LT.0 ) THEN
526  info = -4
527  ELSE IF( nrhs.LT.0 ) THEN
528  info = -6
529  ELSE IF( lda.LT.mmax ) THEN
530  info = -11
531  ELSE IF( ldx.LT.mmax ) THEN
532  info = -17
533  ELSE IF( ldq.LT.mmax ) THEN
534  info = -21
535  ELSE IF( ldpt.LT.mnmax ) THEN
536  info = -23
537  ELSE IF( minwrk.GT.lwork ) THEN
538  info = -27
539  END IF
540 *
541  IF( info.NE.0 ) THEN
542  CALL xerbla( 'CCHKBD', -info )
543  RETURN
544  END IF
545 *
546 * Initialize constants
547 *
548  path( 1: 1 ) = 'Complex precision'
549  path( 2: 3 ) = 'BD'
550  nfail = 0
551  ntest = 0
552  unfl = slamch( 'Safe minimum' )
553  ovfl = slamch( 'Overflow' )
554  CALL slabad( unfl, ovfl )
555  ulp = slamch( 'Precision' )
556  ulpinv = one / ulp
557  log2ui = int( log( ulpinv ) / log( two ) )
558  rtunfl = sqrt( unfl )
559  rtovfl = sqrt( ovfl )
560  infot = 0
561 *
562 * Loop over sizes, types
563 *
564  DO 180 jsize = 1, nsizes
565  m = mval( jsize )
566  n = nval( jsize )
567  mnmin = min( m, n )
568  amninv = one / max( m, n, 1 )
569 *
570  IF( nsizes.NE.1 ) THEN
571  mtypes = min( maxtyp, ntypes )
572  ELSE
573  mtypes = min( maxtyp+1, ntypes )
574  END IF
575 *
576  DO 170 jtype = 1, mtypes
577  IF( .NOT.dotype( jtype ) )
578  $ GO TO 170
579 *
580  DO 20 j = 1, 4
581  ioldsd( j ) = iseed( j )
582  20 CONTINUE
583 *
584  DO 30 j = 1, 14
585  result( j ) = -one
586  30 CONTINUE
587 *
588  uplo = ' '
589 *
590 * Compute "A"
591 *
592 * Control parameters:
593 *
594 * KMAGN KMODE KTYPE
595 * =1 O(1) clustered 1 zero
596 * =2 large clustered 2 identity
597 * =3 small exponential (none)
598 * =4 arithmetic diagonal, (w/ eigenvalues)
599 * =5 random symmetric, w/ eigenvalues
600 * =6 nonsymmetric, w/ singular values
601 * =7 random diagonal
602 * =8 random symmetric
603 * =9 random nonsymmetric
604 * =10 random bidiagonal (log. distrib.)
605 *
606  IF( mtypes.GT.maxtyp )
607  $ GO TO 100
608 *
609  itype = ktype( jtype )
610  imode = kmode( jtype )
611 *
612 * Compute norm
613 *
614  GO TO ( 40, 50, 60 )kmagn( jtype )
615 *
616  40 CONTINUE
617  anorm = one
618  GO TO 70
619 *
620  50 CONTINUE
621  anorm = ( rtovfl*ulp )*amninv
622  GO TO 70
623 *
624  60 CONTINUE
625  anorm = rtunfl*max( m, n )*ulpinv
626  GO TO 70
627 *
628  70 CONTINUE
629 *
630  CALL claset( 'Full', lda, n, czero, czero, a, lda )
631  iinfo = 0
632  cond = ulpinv
633 *
634  bidiag = .false.
635  IF( itype.EQ.1 ) THEN
636 *
637 * Zero matrix
638 *
639  iinfo = 0
640 *
641  ELSE IF( itype.EQ.2 ) THEN
642 *
643 * Identity
644 *
645  DO 80 jcol = 1, mnmin
646  a( jcol, jcol ) = anorm
647  80 CONTINUE
648 *
649  ELSE IF( itype.EQ.4 ) THEN
650 *
651 * Diagonal Matrix, [Eigen]values Specified
652 *
653  CALL clatms( mnmin, mnmin, 'S', iseed, 'N', rwork, imode,
654  $ cond, anorm, 0, 0, 'N', a, lda, work,
655  $ iinfo )
656 *
657  ELSE IF( itype.EQ.5 ) THEN
658 *
659 * Symmetric, eigenvalues specified
660 *
661  CALL clatms( mnmin, mnmin, 'S', iseed, 'S', rwork, imode,
662  $ cond, anorm, m, n, 'N', a, lda, work,
663  $ iinfo )
664 *
665  ELSE IF( itype.EQ.6 ) THEN
666 *
667 * Nonsymmetric, singular values specified
668 *
669  CALL clatms( m, n, 'S', iseed, 'N', rwork, imode, cond,
670  $ anorm, m, n, 'N', a, lda, work, iinfo )
671 *
672  ELSE IF( itype.EQ.7 ) THEN
673 *
674 * Diagonal, random entries
675 *
676  CALL clatmr( mnmin, mnmin, 'S', iseed, 'N', work, 6, one,
677  $ cone, 'T', 'N', work( mnmin+1 ), 1, one,
678  $ work( 2*mnmin+1 ), 1, one, 'N', iwork, 0, 0,
679  $ zero, anorm, 'NO', a, lda, iwork, iinfo )
680 *
681  ELSE IF( itype.EQ.8 ) THEN
682 *
683 * Symmetric, random entries
684 *
685  CALL clatmr( mnmin, mnmin, 'S', iseed, 'S', work, 6, one,
686  $ cone, 'T', 'N', work( mnmin+1 ), 1, one,
687  $ work( m+mnmin+1 ), 1, one, 'N', iwork, m, n,
688  $ zero, anorm, 'NO', a, lda, iwork, iinfo )
689 *
690  ELSE IF( itype.EQ.9 ) THEN
691 *
692 * Nonsymmetric, random entries
693 *
694  CALL clatmr( m, n, 'S', iseed, 'N', work, 6, one, cone,
695  $ 'T', 'N', work( mnmin+1 ), 1, one,
696  $ work( m+mnmin+1 ), 1, one, 'N', iwork, m, n,
697  $ zero, anorm, 'NO', a, lda, iwork, iinfo )
698 *
699  ELSE IF( itype.EQ.10 ) THEN
700 *
701 * Bidiagonal, random entries
702 *
703  temp1 = -two*log( ulp )
704  DO 90 j = 1, mnmin
705  bd( j ) = exp( temp1*slarnd( 2, iseed ) )
706  IF( j.LT.mnmin )
707  $ be( j ) = exp( temp1*slarnd( 2, iseed ) )
708  90 CONTINUE
709 *
710  iinfo = 0
711  bidiag = .true.
712  IF( m.GE.n ) THEN
713  uplo = 'U'
714  ELSE
715  uplo = 'L'
716  END IF
717  ELSE
718  iinfo = 1
719  END IF
720 *
721  IF( iinfo.EQ.0 ) THEN
722 *
723 * Generate Right-Hand Side
724 *
725  IF( bidiag ) THEN
726  CALL clatmr( mnmin, nrhs, 'S', iseed, 'N', work, 6,
727  $ one, cone, 'T', 'N', work( mnmin+1 ), 1,
728  $ one, work( 2*mnmin+1 ), 1, one, 'N',
729  $ iwork, mnmin, nrhs, zero, one, 'NO', y,
730  $ ldx, iwork, iinfo )
731  ELSE
732  CALL clatmr( m, nrhs, 'S', iseed, 'N', work, 6, one,
733  $ cone, 'T', 'N', work( m+1 ), 1, one,
734  $ work( 2*m+1 ), 1, one, 'N', iwork, m,
735  $ nrhs, zero, one, 'NO', x, ldx, iwork,
736  $ iinfo )
737  END IF
738  END IF
739 *
740 * Error Exit
741 *
742  IF( iinfo.NE.0 ) THEN
743  WRITE( nout, fmt = 9998 )'Generator', iinfo, m, n,
744  $ jtype, ioldsd
745  info = abs( iinfo )
746  RETURN
747  END IF
748 *
749  100 CONTINUE
750 *
751 * Call CGEBRD and CUNGBR to compute B, Q, and P, do tests.
752 *
753  IF( .NOT.bidiag ) THEN
754 *
755 * Compute transformations to reduce A to bidiagonal form:
756 * B := Q' * A * P.
757 *
758  CALL clacpy( ' ', m, n, a, lda, q, ldq )
759  CALL cgebrd( m, n, q, ldq, bd, be, work, work( mnmin+1 ),
760  $ work( 2*mnmin+1 ), lwork-2*mnmin, iinfo )
761 *
762 * Check error code from CGEBRD.
763 *
764  IF( iinfo.NE.0 ) THEN
765  WRITE( nout, fmt = 9998 )'CGEBRD', iinfo, m, n,
766  $ jtype, ioldsd
767  info = abs( iinfo )
768  RETURN
769  END IF
770 *
771  CALL clacpy( ' ', m, n, q, ldq, pt, ldpt )
772  IF( m.GE.n ) THEN
773  uplo = 'U'
774  ELSE
775  uplo = 'L'
776  END IF
777 *
778 * Generate Q
779 *
780  mq = m
781  IF( nrhs.LE.0 )
782  $ mq = mnmin
783  CALL cungbr( 'Q', m, mq, n, q, ldq, work,
784  $ work( 2*mnmin+1 ), lwork-2*mnmin, iinfo )
785 *
786 * Check error code from CUNGBR.
787 *
788  IF( iinfo.NE.0 ) THEN
789  WRITE( nout, fmt = 9998 )'CUNGBR(Q)', iinfo, m, n,
790  $ jtype, ioldsd
791  info = abs( iinfo )
792  RETURN
793  END IF
794 *
795 * Generate P'
796 *
797  CALL cungbr( 'P', mnmin, n, m, pt, ldpt, work( mnmin+1 ),
798  $ work( 2*mnmin+1 ), lwork-2*mnmin, iinfo )
799 *
800 * Check error code from CUNGBR.
801 *
802  IF( iinfo.NE.0 ) THEN
803  WRITE( nout, fmt = 9998 )'CUNGBR(P)', iinfo, m, n,
804  $ jtype, ioldsd
805  info = abs( iinfo )
806  RETURN
807  END IF
808 *
809 * Apply Q' to an M by NRHS matrix X: Y := Q' * X.
810 *
811  CALL cgemm( 'Conjugate transpose', 'No transpose', m,
812  $ nrhs, m, cone, q, ldq, x, ldx, czero, y,
813  $ ldx )
814 *
815 * Test 1: Check the decomposition A := Q * B * PT
816 * 2: Check the orthogonality of Q
817 * 3: Check the orthogonality of PT
818 *
819  CALL cbdt01( m, n, 1, a, lda, q, ldq, bd, be, pt, ldpt,
820  $ work, rwork, result( 1 ) )
821  CALL cunt01( 'Columns', m, mq, q, ldq, work, lwork,
822  $ rwork, result( 2 ) )
823  CALL cunt01( 'Rows', mnmin, n, pt, ldpt, work, lwork,
824  $ rwork, result( 3 ) )
825  END IF
826 *
827 * Use CBDSQR to form the SVD of the bidiagonal matrix B:
828 * B := U * S1 * VT, and compute Z = U' * Y.
829 *
830  CALL scopy( mnmin, bd, 1, s1, 1 )
831  IF( mnmin.GT.0 )
832  $ CALL scopy( mnmin-1, be, 1, rwork, 1 )
833  CALL clacpy( ' ', m, nrhs, y, ldx, z, ldx )
834  CALL claset( 'Full', mnmin, mnmin, czero, cone, u, ldpt )
835  CALL claset( 'Full', mnmin, mnmin, czero, cone, vt, ldpt )
836 *
837  CALL cbdsqr( uplo, mnmin, mnmin, mnmin, nrhs, s1, rwork, vt,
838  $ ldpt, u, ldpt, z, ldx, rwork( mnmin+1 ),
839  $ iinfo )
840 *
841 * Check error code from CBDSQR.
842 *
843  IF( iinfo.NE.0 ) THEN
844  WRITE( nout, fmt = 9998 )'CBDSQR(vects)', iinfo, m, n,
845  $ jtype, ioldsd
846  info = abs( iinfo )
847  IF( iinfo.LT.0 ) THEN
848  RETURN
849  ELSE
850  result( 4 ) = ulpinv
851  GO TO 150
852  END IF
853  END IF
854 *
855 * Use CBDSQR to compute only the singular values of the
856 * bidiagonal matrix B; U, VT, and Z should not be modified.
857 *
858  CALL scopy( mnmin, bd, 1, s2, 1 )
859  IF( mnmin.GT.0 )
860  $ CALL scopy( mnmin-1, be, 1, rwork, 1 )
861 *
862  CALL cbdsqr( uplo, mnmin, 0, 0, 0, s2, rwork, vt, ldpt, u,
863  $ ldpt, z, ldx, rwork( mnmin+1 ), iinfo )
864 *
865 * Check error code from CBDSQR.
866 *
867  IF( iinfo.NE.0 ) THEN
868  WRITE( nout, fmt = 9998 )'CBDSQR(values)', iinfo, m, n,
869  $ jtype, ioldsd
870  info = abs( iinfo )
871  IF( iinfo.LT.0 ) THEN
872  RETURN
873  ELSE
874  result( 9 ) = ulpinv
875  GO TO 150
876  END IF
877  END IF
878 *
879 * Test 4: Check the decomposition B := U * S1 * VT
880 * 5: Check the computation Z := U' * Y
881 * 6: Check the orthogonality of U
882 * 7: Check the orthogonality of VT
883 *
884  CALL cbdt03( uplo, mnmin, 1, bd, be, u, ldpt, s1, vt, ldpt,
885  $ work, result( 4 ) )
886  CALL cbdt02( mnmin, nrhs, y, ldx, z, ldx, u, ldpt, work,
887  $ rwork, result( 5 ) )
888  CALL cunt01( 'Columns', mnmin, mnmin, u, ldpt, work, lwork,
889  $ rwork, result( 6 ) )
890  CALL cunt01( 'Rows', mnmin, mnmin, vt, ldpt, work, lwork,
891  $ rwork, result( 7 ) )
892 *
893 * Test 8: Check that the singular values are sorted in
894 * non-increasing order and are non-negative
895 *
896  result( 8 ) = zero
897  DO 110 i = 1, mnmin - 1
898  IF( s1( i ).LT.s1( i+1 ) )
899  $ result( 8 ) = ulpinv
900  IF( s1( i ).LT.zero )
901  $ result( 8 ) = ulpinv
902  110 CONTINUE
903  IF( mnmin.GE.1 ) THEN
904  IF( s1( mnmin ).LT.zero )
905  $ result( 8 ) = ulpinv
906  END IF
907 *
908 * Test 9: Compare CBDSQR with and without singular vectors
909 *
910  temp2 = zero
911 *
912  DO 120 j = 1, mnmin
913  temp1 = abs( s1( j )-s2( j ) ) /
914  $ max( sqrt( unfl )*max( s1( 1 ), one ),
915  $ ulp*max( abs( s1( j ) ), abs( s2( j ) ) ) )
916  temp2 = max( temp1, temp2 )
917  120 CONTINUE
918 *
919  result( 9 ) = temp2
920 *
921 * Test 10: Sturm sequence test of singular values
922 * Go up by factors of two until it succeeds
923 *
924  temp1 = thresh*( half-ulp )
925 *
926  DO 130 j = 0, log2ui
927  CALL ssvdch( mnmin, bd, be, s1, temp1, iinfo )
928  IF( iinfo.EQ.0 )
929  $ GO TO 140
930  temp1 = temp1*two
931  130 CONTINUE
932 *
933  140 CONTINUE
934  result( 10 ) = temp1
935 *
936 * Use CBDSQR to form the decomposition A := (QU) S (VT PT)
937 * from the bidiagonal form A := Q B PT.
938 *
939  IF( .NOT.bidiag ) THEN
940  CALL scopy( mnmin, bd, 1, s2, 1 )
941  IF( mnmin.GT.0 )
942  $ CALL scopy( mnmin-1, be, 1, rwork, 1 )
943 *
944  CALL cbdsqr( uplo, mnmin, n, m, nrhs, s2, rwork, pt,
945  $ ldpt, q, ldq, y, ldx, rwork( mnmin+1 ),
946  $ iinfo )
947 *
948 * Test 11: Check the decomposition A := Q*U * S2 * VT*PT
949 * 12: Check the computation Z := U' * Q' * X
950 * 13: Check the orthogonality of Q*U
951 * 14: Check the orthogonality of VT*PT
952 *
953  CALL cbdt01( m, n, 0, a, lda, q, ldq, s2, dumma, pt,
954  $ ldpt, work, rwork, result( 11 ) )
955  CALL cbdt02( m, nrhs, x, ldx, y, ldx, q, ldq, work,
956  $ rwork, result( 12 ) )
957  CALL cunt01( 'Columns', m, mq, q, ldq, work, lwork,
958  $ rwork, result( 13 ) )
959  CALL cunt01( 'Rows', mnmin, n, pt, ldpt, work, lwork,
960  $ rwork, result( 14 ) )
961  END IF
962 *
963 * End of Loop -- Check for RESULT(j) > THRESH
964 *
965  150 CONTINUE
966  DO 160 j = 1, 14
967  IF( result( j ).GE.thresh ) THEN
968  IF( nfail.EQ.0 )
969  $ CALL slahd2( nout, path )
970  WRITE( nout, fmt = 9999 )m, n, jtype, ioldsd, j,
971  $ result( j )
972  nfail = nfail + 1
973  END IF
974  160 CONTINUE
975  IF( .NOT.bidiag ) THEN
976  ntest = ntest + 14
977  ELSE
978  ntest = ntest + 5
979  END IF
980 *
981  170 CONTINUE
982  180 CONTINUE
983 *
984 * Summary
985 *
986  CALL alasum( path, nout, nfail, ntest, 0 )
987 *
988  RETURN
989 *
990 * End of CCHKBD
991 *
992  9999 FORMAT( ' M=', i5, ', N=', i5, ', type ', i2, ', seed=',
993  $ 4( i4, ',' ), ' test(', i2, ')=', g11.4 )
994  9998 FORMAT( ' CCHKBD: ', a, ' returned INFO=', i6, '.', / 9x, 'M=',
995  $ i6, ', N=', i6, ', JTYPE=', i6, ', ISEED=(', 3( i5, ',' ),
996  $ i5, ')' )
997 *
998  END
subroutine cungbr(VECT, M, N, K, A, LDA, TAU, WORK, LWORK, INFO)
CUNGBR
Definition: cungbr.f:159
subroutine cbdt03(UPLO, N, KD, D, E, U, LDU, S, VT, LDVT, WORK, RESID)
CBDT03
Definition: cbdt03.f:137
subroutine cbdsqr(UPLO, N, NCVT, NRU, NCC, D, E, VT, LDVT, U, LDU, C, LDC, RWORK, INFO)
CBDSQR
Definition: cbdsqr.f:224
subroutine clatmr(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)
CLATMR
Definition: clatmr.f:492
subroutine claset(UPLO, M, N, ALPHA, BETA, A, LDA)
CLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values...
Definition: claset.f:108
subroutine cbdt01(M, N, KD, A, LDA, Q, LDQ, D, E, PT, LDPT, WORK, RWORK, RESID)
CBDT01
Definition: cbdt01.f:148
subroutine slahd2(IOUNIT, PATH)
SLAHD2
Definition: slahd2.f:67
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
subroutine cbdt02(M, N, B, LDB, C, LDC, U, LDU, WORK, RWORK, RESID)
CBDT02
Definition: cbdt02.f:121
subroutine cgebrd(M, N, A, LDA, D, E, TAUQ, TAUP, WORK, LWORK, INFO)
CGEBRD
Definition: cgebrd.f:208
subroutine clacpy(UPLO, M, N, A, LDA, B, LDB)
CLACPY copies all or part of one two-dimensional array to another.
Definition: clacpy.f:105
subroutine slabad(SMALL, LARGE)
SLABAD
Definition: slabad.f:76
subroutine clatms(M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX, KL, KU, PACK, A, LDA, WORK, INFO)
CLATMS
Definition: clatms.f:334
subroutine cunt01(ROWCOL, M, N, U, LDU, WORK, LWORK, RWORK, RESID)
CUNT01
Definition: cunt01.f:128
subroutine ssvdch(N, S, E, SVD, TOL, INFO)
SSVDCH
Definition: ssvdch.f:99
subroutine cchkbd(NSIZES, MVAL, NVAL, NTYPES, DOTYPE, NRHS, ISEED, THRESH, A, LDA, BD, BE, S1, S2, X, LDX, Y, Z, Q, LDQ, PT, LDPT, U, VT, WORK, LWORK, RWORK, NOUT, INFO)
CCHKBD
Definition: cchkbd.f:417
subroutine cgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
CGEMM
Definition: cgemm.f:189
subroutine scopy(N, SX, INCX, SY, INCY)
SCOPY
Definition: scopy.f:84
subroutine alasum(TYPE, NOUT, NFAIL, NRUN, NERRS)
ALASUM
Definition: alasum.f:75