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zchkbd.f
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1*> \brief \b ZCHKBD
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 ZCHKBD( 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* DOUBLE PRECISION THRESH
20* ..
21* .. Array Arguments ..
22* LOGICAL DOTYPE( * )
23* INTEGER ISEED( 4 ), MVAL( * ), NVAL( * )
24* DOUBLE PRECISION BD( * ), BE( * ), RWORK( * ), S1( * ), S2( * )
25* COMPLEX*16 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*> ZCHKBD checks the singular value decomposition (SVD) routines.
37*>
38*> ZGEBRD 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*> ZUNGBR generates the orthogonal matrices Q and P' from ZGEBRD.
44*> Note that Q and P are not necessarily square.
45*>
46*> ZBDSQR 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, ZBDSQR 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 ZGEBRD and ZUNGBR
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 ZBDSQR 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*> DSVDCH)
94*>
95*> (10) | S1 - S2 | / ( |S1| ulp ), where S2 is computed without
96*> computing U and V.
97*>
98*> Test ZBDSQR 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) ZGEBRD 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, ZCHKBD
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 ZBDSQR. 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 ZCHKBD to continue the same random
218*> number sequence.
219*> \endverbatim
220*>
221*> \param[in] THRESH
222*> \verbatim
223*> THRESH is DOUBLE PRECISION
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*16 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 DOUBLE PRECISION array, dimension
247*> (max(min(MVAL(j),NVAL(j))))
248*> \endverbatim
249*>
250*> \param[out] BE
251*> \verbatim
252*> BE is DOUBLE PRECISION array, dimension
253*> (max(min(MVAL(j),NVAL(j))))
254*> \endverbatim
255*>
256*> \param[out] S1
257*> \verbatim
258*> S1 is DOUBLE PRECISION array, dimension
259*> (max(min(MVAL(j),NVAL(j))))
260*> \endverbatim
261*>
262*> \param[out] S2
263*> \verbatim
264*> S2 is DOUBLE PRECISION array, dimension
265*> (max(min(MVAL(j),NVAL(j))))
266*> \endverbatim
267*>
268*> \param[out] X
269*> \verbatim
270*> X is COMPLEX*16 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*16 array, dimension (LDX,NRHS)
283*> \endverbatim
284*>
285*> \param[out] Z
286*> \verbatim
287*> Z is COMPLEX*16 array, dimension (LDX,NRHS)
288*> \endverbatim
289*>
290*> \param[out] Q
291*> \verbatim
292*> Q is COMPLEX*16 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*16 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*16 array, dimension
316*> (LDPT,max(min(MVAL(j),NVAL(j))))
317*> \endverbatim
318*>
319*> \param[out] VT
320*> \verbatim
321*> VT is COMPLEX*16 array, dimension
322*> (LDPT,max(min(MVAL(j),NVAL(j))))
323*> \endverbatim
324*>
325*> \param[out] WORK
326*> \verbatim
327*> WORK is COMPLEX*16 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 DOUBLE PRECISION 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 ZLATMR, CLATMS, ZGEBRD, ZUNGBR, or ZBDSQR,
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*> \ingroup complex16_eig
409*
410* =====================================================================
411 SUBROUTINE zchkbd( NSIZES, MVAL, NVAL, NTYPES, DOTYPE, NRHS,
412 $ ISEED, THRESH, A, LDA, BD, BE, S1, S2, X, LDX,
413 $ Y, Z, Q, LDQ, PT, LDPT, U, VT, WORK, LWORK,
414 $ RWORK, NOUT, INFO )
415*
416* -- LAPACK test routine --
417* -- LAPACK is a software package provided by Univ. of Tennessee, --
418* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
419*
420* .. Scalar Arguments ..
421 INTEGER INFO, LDA, LDPT, LDQ, LDX, LWORK, NOUT, NRHS,
422 $ NSIZES, NTYPES
423 DOUBLE PRECISION THRESH
424* ..
425* .. Array Arguments ..
426 LOGICAL DOTYPE( * )
427 INTEGER ISEED( 4 ), MVAL( * ), NVAL( * )
428 DOUBLE PRECISION BD( * ), BE( * ), RWORK( * ), S1( * ), S2( * )
429 COMPLEX*16 A( LDA, * ), PT( LDPT, * ), Q( LDQ, * ),
430 $ u( ldpt, * ), vt( ldpt, * ), work( * ),
431 $ x( ldx, * ), y( ldx, * ), z( ldx, * )
432* ..
433*
434* ======================================================================
435*
436* .. Parameters ..
437 DOUBLE PRECISION ZERO, ONE, TWO, HALF
438 PARAMETER ( ZERO = 0.0d0, one = 1.0d0, two = 2.0d0,
439 $ half = 0.5d0 )
440 COMPLEX*16 CZERO, CONE
441 parameter( czero = ( 0.0d+0, 0.0d+0 ),
442 $ cone = ( 1.0d+0, 0.0d+0 ) )
443 INTEGER MAXTYP
444 parameter( maxtyp = 16 )
445* ..
446* .. Local Scalars ..
447 LOGICAL BADMM, BADNN, BIDIAG
448 CHARACTER UPLO
449 CHARACTER*3 PATH
450 INTEGER I, IINFO, IMODE, ITYPE, J, JCOL, JSIZE, JTYPE,
451 $ log2ui, m, minwrk, mmax, mnmax, mnmin, mq,
452 $ mtypes, n, nfail, nmax, ntest
453 DOUBLE PRECISION AMNINV, ANORM, COND, OVFL, RTOVFL, RTUNFL,
454 $ TEMP1, TEMP2, ULP, ULPINV, UNFL
455* ..
456* .. Local Arrays ..
457 INTEGER IOLDSD( 4 ), IWORK( 1 ), KMAGN( MAXTYP ),
458 $ KMODE( MAXTYP ), KTYPE( MAXTYP )
459 DOUBLE PRECISION DUMMA( 1 ), RESULT( 14 )
460* ..
461* .. External Functions ..
462 DOUBLE PRECISION DLAMCH, DLARND
463 EXTERNAL DLAMCH, DLARND
464* ..
465* .. External Subroutines ..
466 EXTERNAL alasum, dcopy, dlabad, dlahd2, dsvdch, xerbla,
467 $ zbdsqr, zbdt01, zbdt02, zbdt03, zgebrd, zgemm,
468 $ zlacpy, zlaset, zlatmr, zlatms, zungbr, zunt01
469* ..
470* .. Intrinsic Functions ..
471 INTRINSIC abs, exp, int, log, max, min, sqrt
472* ..
473* .. Scalars in Common ..
474 LOGICAL LERR, OK
475 CHARACTER*32 SRNAMT
476 INTEGER INFOT, NUNIT
477* ..
478* .. Common blocks ..
479 COMMON / infoc / infot, nunit, ok, lerr
480 COMMON / srnamc / srnamt
481* ..
482* .. Data statements ..
483 DATA ktype / 1, 2, 5*4, 5*6, 3*9, 10 /
484 DATA kmagn / 2*1, 3*1, 2, 3, 3*1, 2, 3, 1, 2, 3, 0 /
485 DATA kmode / 2*0, 4, 3, 1, 4, 4, 4, 3, 1, 4, 4, 0,
486 $ 0, 0, 0 /
487* ..
488* .. Executable Statements ..
489*
490* Check for errors
491*
492 info = 0
493*
494 badmm = .false.
495 badnn = .false.
496 mmax = 1
497 nmax = 1
498 mnmax = 1
499 minwrk = 1
500 DO 10 j = 1, nsizes
501 mmax = max( mmax, mval( j ) )
502 IF( mval( j ).LT.0 )
503 $ badmm = .true.
504 nmax = max( nmax, nval( j ) )
505 IF( nval( j ).LT.0 )
506 $ badnn = .true.
507 mnmax = max( mnmax, min( mval( j ), nval( j ) ) )
508 minwrk = max( minwrk, 3*( mval( j )+nval( j ) ),
509 $ mval( j )*( mval( j )+max( mval( j ), nval( j ),
510 $ nrhs )+1 )+nval( j )*min( nval( j ), mval( j ) ) )
511 10 CONTINUE
512*
513* Check for errors
514*
515 IF( nsizes.LT.0 ) THEN
516 info = -1
517 ELSE IF( badmm ) THEN
518 info = -2
519 ELSE IF( badnn ) THEN
520 info = -3
521 ELSE IF( ntypes.LT.0 ) THEN
522 info = -4
523 ELSE IF( nrhs.LT.0 ) THEN
524 info = -6
525 ELSE IF( lda.LT.mmax ) THEN
526 info = -11
527 ELSE IF( ldx.LT.mmax ) THEN
528 info = -17
529 ELSE IF( ldq.LT.mmax ) THEN
530 info = -21
531 ELSE IF( ldpt.LT.mnmax ) THEN
532 info = -23
533 ELSE IF( minwrk.GT.lwork ) THEN
534 info = -27
535 END IF
536*
537 IF( info.NE.0 ) THEN
538 CALL xerbla( 'ZCHKBD', -info )
539 RETURN
540 END IF
541*
542* Initialize constants
543*
544 path( 1: 1 ) = 'Zomplex precision'
545 path( 2: 3 ) = 'BD'
546 nfail = 0
547 ntest = 0
548 unfl = dlamch( 'Safe minimum' )
549 ovfl = dlamch( 'Overflow' )
550 CALL dlabad( unfl, ovfl )
551 ulp = dlamch( 'Precision' )
552 ulpinv = one / ulp
553 log2ui = int( log( ulpinv ) / log( two ) )
554 rtunfl = sqrt( unfl )
555 rtovfl = sqrt( ovfl )
556 infot = 0
557*
558* Loop over sizes, types
559*
560 DO 180 jsize = 1, nsizes
561 m = mval( jsize )
562 n = nval( jsize )
563 mnmin = min( m, n )
564 amninv = one / max( m, n, 1 )
565*
566 IF( nsizes.NE.1 ) THEN
567 mtypes = min( maxtyp, ntypes )
568 ELSE
569 mtypes = min( maxtyp+1, ntypes )
570 END IF
571*
572 DO 170 jtype = 1, mtypes
573 IF( .NOT.dotype( jtype ) )
574 $ GO TO 170
575*
576 DO 20 j = 1, 4
577 ioldsd( j ) = iseed( j )
578 20 CONTINUE
579*
580 DO 30 j = 1, 14
581 result( j ) = -one
582 30 CONTINUE
583*
584 uplo = ' '
585*
586* Compute "A"
587*
588* Control parameters:
589*
590* KMAGN KMODE KTYPE
591* =1 O(1) clustered 1 zero
592* =2 large clustered 2 identity
593* =3 small exponential (none)
594* =4 arithmetic diagonal, (w/ eigenvalues)
595* =5 random symmetric, w/ eigenvalues
596* =6 nonsymmetric, w/ singular values
597* =7 random diagonal
598* =8 random symmetric
599* =9 random nonsymmetric
600* =10 random bidiagonal (log. distrib.)
601*
602 IF( mtypes.GT.maxtyp )
603 $ GO TO 100
604*
605 itype = ktype( jtype )
606 imode = kmode( jtype )
607*
608* Compute norm
609*
610 GO TO ( 40, 50, 60 )kmagn( jtype )
611*
612 40 CONTINUE
613 anorm = one
614 GO TO 70
615*
616 50 CONTINUE
617 anorm = ( rtovfl*ulp )*amninv
618 GO TO 70
619*
620 60 CONTINUE
621 anorm = rtunfl*max( m, n )*ulpinv
622 GO TO 70
623*
624 70 CONTINUE
625*
626 CALL zlaset( 'Full', lda, n, czero, czero, a, lda )
627 iinfo = 0
628 cond = ulpinv
629*
630 bidiag = .false.
631 IF( itype.EQ.1 ) THEN
632*
633* Zero matrix
634*
635 iinfo = 0
636*
637 ELSE IF( itype.EQ.2 ) THEN
638*
639* Identity
640*
641 DO 80 jcol = 1, mnmin
642 a( jcol, jcol ) = anorm
643 80 CONTINUE
644*
645 ELSE IF( itype.EQ.4 ) THEN
646*
647* Diagonal Matrix, [Eigen]values Specified
648*
649 CALL zlatms( mnmin, mnmin, 's', ISEED, 'n', RWORK, IMODE,
650 $ COND, ANORM, 0, 0, 'n', A, LDA, WORK,
651 $ IINFO )
652*
653.EQ. ELSE IF( ITYPE5 ) THEN
654*
655* Symmetric, eigenvalues specified
656*
657 CALL ZLATMS( MNMIN, MNMIN, 's', ISEED, 's', RWORK, IMODE,
658 $ COND, ANORM, M, N, 'n', A, LDA, WORK,
659 $ IINFO )
660*
661.EQ. ELSE IF( ITYPE6 ) THEN
662*
663* Nonsymmetric, singular values specified
664*
665 CALL ZLATMS( M, N, 's', ISEED, 'n', RWORK, IMODE, COND,
666 $ ANORM, M, N, 'n', A, LDA, WORK, IINFO )
667*
668.EQ. ELSE IF( ITYPE7 ) THEN
669*
670* Diagonal, random entries
671*
672 CALL ZLATMR( MNMIN, MNMIN, 's', ISEED, 'n', WORK, 6, ONE,
673 $ CONE, 't', 'n', WORK( MNMIN+1 ), 1, ONE,
674 $ WORK( 2*MNMIN+1 ), 1, ONE, 'n', IWORK, 0, 0,
675 $ ZERO, ANORM, 'no', A, LDA, IWORK, IINFO )
676*
677.EQ. ELSE IF( ITYPE8 ) THEN
678*
679* Symmetric, random entries
680*
681 CALL ZLATMR( MNMIN, MNMIN, 's', ISEED, 's', WORK, 6, ONE,
682 $ CONE, 't', 'n', WORK( MNMIN+1 ), 1, ONE,
683 $ WORK( M+MNMIN+1 ), 1, ONE, 'n', IWORK, M, N,
684 $ ZERO, ANORM, 'no', a, lda, iwork, iinfo )
685*
686 ELSE IF( itype.EQ.9 ) THEN
687*
688* Nonsymmetric, random entries
689*
690 CALL zlatmr( m, n, 'S', iseed, 'N', work, 6, one, cone,
691 $ 'T', 'n', WORK( MNMIN+1 ), 1, ONE,
692 $ WORK( M+MNMIN+1 ), 1, ONE, 'n', IWORK, M, N,
693 $ ZERO, ANORM, 'no', a, lda, iwork, iinfo )
694*
695 ELSE IF( itype.EQ.10 ) THEN
696*
697* Bidiagonal, random entries
698*
699 temp1 = -two*log( ulp )
700 DO 90 j = 1, mnmin
701 bd( j ) = exp( temp1*dlarnd( 2, iseed ) )
702 IF( j.LT.mnmin )
703 $ be( j ) = exp( temp1*dlarnd( 2, iseed ) )
704 90 CONTINUE
705*
706 iinfo = 0
707 bidiag = .true.
708 IF( m.GE.n ) THEN
709 uplo = 'U'
710 ELSE
711 uplo = 'L'
712 END IF
713 ELSE
714 iinfo = 1
715 END IF
716*
717 IF( iinfo.EQ.0 ) THEN
718*
719* Generate Right-Hand Side
720*
721 IF( bidiag ) THEN
722 CALL zlatmr( mnmin, nrhs, 'S', iseed, 'N', work, 6,
723 $ one, cone, 'T', 'N', work( mnmin+1 ), 1,
724 $ one, work( 2*mnmin+1 ), 1, one, 'N',
725 $ iwork, mnmin, nrhs, zero, one, 'NO', y,
726 $ ldx, iwork, iinfo )
727 ELSE
728 CALL zlatmr( m, nrhs, 'S', iseed, 'N', work, 6, one,
729 $ cone, 'T', 'N', work( m+1 ), 1, one,
730 $ work( 2*m+1 ), 1, one, 'N', iwork, m,
731 $ nrhs, zero, one, 'NO', x, ldx, iwork,
732 $ iinfo )
733 END IF
734 END IF
735*
736* Error Exit
737*
738 IF( iinfo.NE.0 ) THEN
739 WRITE( nout, fmt = 9998 )'Generator', iinfo, m, n,
740 $ jtype, ioldsd
741 info = abs( iinfo )
742 RETURN
743 END IF
744*
745 100 CONTINUE
746*
747* Call ZGEBRD and ZUNGBR to compute B, Q, and P, do tests.
748*
749 IF( .NOT.bidiag ) THEN
750*
751* Compute transformations to reduce A to bidiagonal form:
752* B := Q' * A * P.
753*
754 CALL zlacpy( ' ', m, n, a, lda, q, ldq )
755 CALL zgebrd( m, n, q, ldq, bd, be, work, work( mnmin+1 ),
756 $ work( 2*mnmin+1 ), lwork-2*mnmin, iinfo )
757*
758* Check error code from ZGEBRD.
759*
760 IF( iinfo.NE.0 ) THEN
761 WRITE( nout, fmt = 9998 )'ZGEBRD', iinfo, m, n,
762 $ jtype, ioldsd
763 info = abs( iinfo )
764 RETURN
765 END IF
766*
767 CALL zlacpy( ' ', m, n, q, ldq, pt, ldpt )
768 IF( m.GE.n ) THEN
769 uplo = 'U'
770 ELSE
771 uplo = 'L'
772 END IF
773*
774* Generate Q
775*
776 mq = m
777 IF( nrhs.LE.0 )
778 $ mq = mnmin
779 CALL zungbr( 'Q', m, mq, n, q, ldq, work,
780 $ work( 2*mnmin+1 ), lwork-2*mnmin, iinfo )
781*
782* Check error code from ZUNGBR.
783*
784 IF( iinfo.NE.0 ) THEN
785 WRITE( nout, fmt = 9998 )'ZUNGBR(Q)', iinfo, m, n,
786 $ jtype, ioldsd
787 info = abs( iinfo )
788 RETURN
789 END IF
790*
791* Generate P'
792*
793 CALL zungbr( 'P', mnmin, n, m, pt, ldpt, work( mnmin+1 ),
794 $ work( 2*mnmin+1 ), lwork-2*mnmin, iinfo )
795*
796* Check error code from ZUNGBR.
797*
798 IF( iinfo.NE.0 ) THEN
799 WRITE( nout, fmt = 9998 )'ZUNGBR(P)', iinfo, m, n,
800 $ jtype, ioldsd
801 info = abs( iinfo )
802 RETURN
803 END IF
804*
805* Apply Q' to an M by NRHS matrix X: Y := Q' * X.
806*
807 CALL zgemm( 'Conjugate transpose', 'No transpose', m,
808 $ nrhs, m, cone, q, ldq, x, ldx, czero, y,
809 $ ldx )
810*
811* Test 1: Check the decomposition A := Q * B * PT
812* 2: Check the orthogonality of Q
813* 3: Check the orthogonality of PT
814*
815 CALL zbdt01( m, n, 1, a, lda, q, ldq, bd, be, pt, ldpt,
816 $ work, rwork, result( 1 ) )
817 CALL zunt01( 'Columns', m, mq, q, ldq, work, lwork,
818 $ rwork, result( 2 ) )
819 CALL zunt01( 'Rows', mnmin, n, pt, ldpt, work, lwork,
820 $ rwork, result( 3 ) )
821 END IF
822*
823* Use ZBDSQR to form the SVD of the bidiagonal matrix B:
824* B := U * S1 * VT, and compute Z = U' * Y.
825*
826 CALL dcopy( mnmin, bd, 1, s1, 1 )
827 IF( mnmin.GT.0 )
828 $ CALL dcopy( mnmin-1, be, 1, rwork, 1 )
829 CALL zlacpy( ' ', m, nrhs, y, ldx, z, ldx )
830 CALL zlaset( 'Full', mnmin, mnmin, czero, cone, u, ldpt )
831 CALL zlaset( 'Full', mnmin, mnmin, czero, cone, vt, ldpt )
832*
833 CALL zbdsqr( uplo, mnmin, mnmin, mnmin, nrhs, s1, rwork, vt,
834 $ ldpt, u, ldpt, z, ldx, rwork( mnmin+1 ),
835 $ iinfo )
836*
837* Check error code from ZBDSQR.
838*
839 IF( iinfo.NE.0 ) THEN
840 WRITE( nout, fmt = 9998 )'ZBDSQR(vects)', iinfo, m, n,
841 $ jtype, ioldsd
842 info = abs( iinfo )
843 IF( iinfo.LT.0 ) THEN
844 RETURN
845 ELSE
846 result( 4 ) = ulpinv
847 GO TO 150
848 END IF
849 END IF
850*
851* Use ZBDSQR to compute only the singular values of the
852* bidiagonal matrix B; U, VT, and Z should not be modified.
853*
854 CALL dcopy( mnmin, bd, 1, s2, 1 )
855 IF( mnmin.GT.0 )
856 $ CALL dcopy( mnmin-1, be, 1, rwork, 1 )
857*
858 CALL zbdsqr( uplo, mnmin, 0, 0, 0, s2, rwork, vt, ldpt, u,
859 $ ldpt, z, ldx, rwork( mnmin+1 ), iinfo )
860*
861* Check error code from ZBDSQR.
862*
863 IF( iinfo.NE.0 ) THEN
864 WRITE( nout, fmt = 9998 )'ZBDSQR(values)', iinfo, m, n,
865 $ jtype, ioldsd
866 info = abs( iinfo )
867 IF( iinfo.LT.0 ) THEN
868 RETURN
869 ELSE
870 result( 9 ) = ulpinv
871 GO TO 150
872 END IF
873 END IF
874*
875* Test 4: Check the decomposition B := U * S1 * VT
876* 5: Check the computation Z := U' * Y
877* 6: Check the orthogonality of U
878* 7: Check the orthogonality of VT
879*
880 CALL zbdt03( uplo, mnmin, 1, bd, be, u, ldpt, s1, vt, ldpt,
881 $ work, result( 4 ) )
882 CALL zbdt02( mnmin, nrhs, y, ldx, z, ldx, u, ldpt, work,
883 $ rwork, result( 5 ) )
884 CALL zunt01( 'Columns', mnmin, mnmin, u, ldpt, work, lwork,
885 $ rwork, result( 6 ) )
886 CALL zunt01( 'Rows', mnmin, mnmin, vt, ldpt, work, lwork,
887 $ rwork, result( 7 ) )
888*
889* Test 8: Check that the singular values are sorted in
890* non-increasing order and are non-negative
891*
892 result( 8 ) = zero
893 DO 110 i = 1, mnmin - 1
894 IF( s1( i ).LT.s1( i+1 ) )
895 $ result( 8 ) = ulpinv
896 IF( s1( i ).LT.zero )
897 $ result( 8 ) = ulpinv
898 110 CONTINUE
899 IF( mnmin.GE.1 ) THEN
900 IF( s1( mnmin ).LT.zero )
901 $ result( 8 ) = ulpinv
902 END IF
903*
904* Test 9: Compare ZBDSQR with and without singular vectors
905*
906 temp2 = zero
907*
908 DO 120 j = 1, mnmin
909 temp1 = abs( s1( j )-s2( j ) ) /
910 $ max( sqrt( unfl )*max( s1( 1 ), one ),
911 $ ulp*max( abs( s1( j ) ), abs( s2( j ) ) ) )
912 temp2 = max( temp1, temp2 )
913 120 CONTINUE
914*
915 result( 9 ) = temp2
916*
917* Test 10: Sturm sequence test of singular values
918* Go up by factors of two until it succeeds
919*
920 temp1 = thresh*( half-ulp )
921*
922 DO 130 j = 0, log2ui
923 CALL dsvdch( mnmin, bd, be, s1, temp1, iinfo )
924 IF( iinfo.EQ.0 )
925 $ GO TO 140
926 temp1 = temp1*two
927 130 CONTINUE
928*
929 140 CONTINUE
930 result( 10 ) = temp1
931*
932* Use ZBDSQR to form the decomposition A := (QU) S (VT PT)
933* from the bidiagonal form A := Q B PT.
934*
935 IF( .NOT.bidiag ) THEN
936 CALL dcopy( mnmin, bd, 1, s2, 1 )
937 IF( mnmin.GT.0 )
938 $ CALL dcopy( mnmin-1, be, 1, rwork, 1 )
939*
940 CALL zbdsqr( uplo, mnmin, n, m, nrhs, s2, rwork, pt,
941 $ ldpt, q, ldq, y, ldx, rwork( mnmin+1 ),
942 $ iinfo )
943*
944* Test 11: Check the decomposition A := Q*U * S2 * VT*PT
945* 12: Check the computation Z := U' * Q' * X
946* 13: Check the orthogonality of Q*U
947* 14: Check the orthogonality of VT*PT
948*
949 CALL zbdt01( m, n, 0, a, lda, q, ldq, s2, dumma, pt,
950 $ ldpt, work, rwork, result( 11 ) )
951 CALL zbdt02( m, nrhs, x, ldx, y, ldx, q, ldq, work,
952 $ rwork, result( 12 ) )
953 CALL zunt01( 'Columns', m, mq, q, ldq, work, lwork,
954 $ rwork, result( 13 ) )
955 CALL zunt01( 'Rows', mnmin, n, pt, ldpt, work, lwork,
956 $ rwork, result( 14 ) )
957 END IF
958*
959* End of Loop -- Check for RESULT(j) > THRESH
960*
961 150 CONTINUE
962 DO 160 j = 1, 14
963 IF( result( j ).GE.thresh ) THEN
964 IF( nfail.EQ.0 )
965 $ CALL dlahd2( nout, path )
966 WRITE( nout, fmt = 9999 )m, n, jtype, ioldsd, j,
967 $ result( j )
968 nfail = nfail + 1
969 END IF
970 160 CONTINUE
971 IF( .NOT.bidiag ) THEN
972 ntest = ntest + 14
973 ELSE
974 ntest = ntest + 5
975 END IF
976*
977 170 CONTINUE
978 180 CONTINUE
979*
980* Summary
981*
982 CALL alasum( path, nout, nfail, ntest, 0 )
983*
984 RETURN
985*
986* End of ZCHKBD
987*
988 9999 FORMAT( ' M=', i5, ', N=', i5, ', type ', i2, ', seed=',
989 $ 4( i4, ',' ), ' test(', i2, ')=', g11.4 )
990 9998 FORMAT( ' ZCHKBD: ', a, ' returned INFO=', i6, '.', / 9x, 'M=',
991 $ i6, ', N=', i6, ', JTYPE=', i6, ', ISEED=(', 3( i5, ',' ),
992 $ i5, ')' )
993*
994 END
dlabad
subroutine dlabad(small, large)
DLABAD
Definition dlabad.f:74
xerbla
subroutine xerbla(srname, info)
XERBLA
Definition xerbla.f:60
alasum
subroutine alasum(type, nout, nfail, nrun, nerrs)
ALASUM
Definition alasum.f:73
zungbr
subroutine zungbr(vect, m, n, k, a, lda, tau, work, lwork, info)
ZUNGBR
Definition zungbr.f:157
zgebrd
subroutine zgebrd(m, n, a, lda, d, e, tauq, taup, work, lwork, info)
ZGEBRD
Definition zgebrd.f:205
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
zbdsqr
subroutine zbdsqr(uplo, n, ncvt, nru, ncc, d, e, vt, ldvt, u, ldu, c, ldc, rwork, info)
ZBDSQR
Definition zbdsqr.f:222
zgemm
subroutine zgemm(transa, transb, m, n, k, alpha, a, lda, b, ldb, beta, c, ldc)
ZGEMM
Definition zgemm.f:187
zbdt01
subroutine zbdt01(m, n, kd, a, lda, q, ldq, d, e, pt, ldpt, work, rwork, resid)
ZBDT01
Definition zbdt01.f:147
zchkbd
subroutine zchkbd(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)
ZCHKBD
Definition zchkbd.f:415
zbdt02
subroutine zbdt02(m, n, b, ldb, c, ldc, u, ldu, work, rwork, resid)
ZBDT02
Definition zbdt02.f:120
zbdt03
subroutine zbdt03(uplo, n, kd, d, e, u, ldu, s, vt, ldvt, work, resid)
ZBDT03
Definition zbdt03.f:135
zunt01
subroutine zunt01(rowcol, m, n, u, ldu, work, lwork, rwork, resid)
ZUNT01
Definition zunt01.f:126
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
zlatms
subroutine zlatms(m, n, dist, iseed, sym, d, mode, cond, dmax, kl, ku, pack, a, lda, work, info)
ZLATMS
Definition zlatms.f:332
dcopy
subroutine dcopy(n, dx, incx, dy, incy)
DCOPY
Definition dcopy.f:82
dsvdch
subroutine dsvdch(n, s, e, svd, tol, info)
DSVDCH
Definition dsvdch.f:97
dlahd2
subroutine dlahd2(iounit, path)
DLAHD2
Definition dlahd2.f:65
min
#define min(a, b)
Definition macros.h:20
max
#define max(a, b)
Definition macros.h:21