LAPACK  3.9.0
LAPACK: Linear Algebra PACKage
schksy_rk.f
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1 *> \brief \b SCHKSY_RK
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 SCHKSY_RK( DOTYPE, NN, NVAL, NNB, NBVAL, NNS, NSVAL,
12 * THRESH, TSTERR, NMAX, A, AFAC, E, AINV, B,
13 * X, XACT, WORK, RWORK, IWORK, NOUT )
14 *
15 * .. Scalar Arguments ..
16 * LOGICAL TSTERR
17 * INTEGER NMAX, NN, NNB, NNS, NOUT
18 * REAL THRESH
19 * ..
20 * .. Array Arguments ..
21 * LOGICAL DOTYPE( * )
22 * INTEGER IWORK( * ), NBVAL( * ), NSVAL( * ), NVAL( * )
23 * REAL A( * ), AFAC( * ), E( * ), AINV( * ), B( * ),
24 * $ RWORK( * ), WORK( * ), X( * ), XACT( * )
25 * ..
26 *
27 *
28 *> \par Purpose:
29 * =============
30 *>
31 *> \verbatim
32 *> SCHKSY_RK tests SSYTRF_RK, -TRI_3, -TRS_3, and -CON_3.
33 *> \endverbatim
34 *
35 * Arguments:
36 * ==========
37 *
38 *> \param[in] DOTYPE
39 *> \verbatim
40 *> DOTYPE is LOGICAL array, dimension (NTYPES)
41 *> The matrix types to be used for testing. Matrices of type j
42 *> (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
43 *> .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
44 *> \endverbatim
45 *>
46 *> \param[in] NN
47 *> \verbatim
48 *> NN is INTEGER
49 *> The number of values of N contained in the vector NVAL.
50 *> \endverbatim
51 *>
52 *> \param[in] NVAL
53 *> \verbatim
54 *> NVAL is INTEGER array, dimension (NN)
55 *> The values of the matrix dimension N.
56 *> \endverbatim
57 *>
58 *> \param[in] NNB
59 *> \verbatim
60 *> NNB is INTEGER
61 *> The number of values of NB contained in the vector NBVAL.
62 *> \endverbatim
63 *>
64 *> \param[in] NBVAL
65 *> \verbatim
66 *> NBVAL is INTEGER array, dimension (NBVAL)
67 *> The values of the blocksize NB.
68 *> \endverbatim
69 *>
70 *> \param[in] NNS
71 *> \verbatim
72 *> NNS is INTEGER
73 *> The number of values of NRHS contained in the vector NSVAL.
74 *> \endverbatim
75 *>
76 *> \param[in] NSVAL
77 *> \verbatim
78 *> NSVAL is INTEGER array, dimension (NNS)
79 *> The values of the number of right hand sides NRHS.
80 *> \endverbatim
81 *>
82 *> \param[in] THRESH
83 *> \verbatim
84 *> THRESH is REAL
85 *> The threshold value for the test ratios. A result is
86 *> included in the output file if RESULT >= THRESH. To have
87 *> every test ratio printed, use THRESH = 0.
88 *> \endverbatim
89 *>
90 *> \param[in] TSTERR
91 *> \verbatim
92 *> TSTERR is LOGICAL
93 *> Flag that indicates whether error exits are to be tested.
94 *> \endverbatim
95 *>
96 *> \param[in] NMAX
97 *> \verbatim
98 *> NMAX is INTEGER
99 *> The maximum value permitted for N, used in dimensioning the
100 *> work arrays.
101 *> \endverbatim
102 *>
103 *> \param[out] A
104 *> \verbatim
105 *> A is REAL array, dimension (NMAX*NMAX)
106 *> \endverbatim
107 *>
108 *> \param[out] AFAC
109 *> \verbatim
110 *> AFAC is REAL array, dimension (NMAX*NMAX)
111 *> \endverbatim
112 *>
113 *> \param[out] E
114 *> \verbatim
115 *> E is REAL array, dimension (NMAX)
116 *> \endverbatim
117 *>
118 *> \param[out] AINV
119 *> \verbatim
120 *> AINV is REAL array, dimension (NMAX*NMAX)
121 *> \endverbatim
122 *>
123 *> \param[out] B
124 *> \verbatim
125 *> B is REAL array, dimension (NMAX*NSMAX),
126 *> where NSMAX is the largest entry in NSVAL.
127 *> \endverbatim
128 *>
129 *> \param[out] X
130 *> \verbatim
131 *> X is REAL array, dimension (NMAX*NSMAX),
132 *> where NSMAX is the largest entry in NSVAL.
133 *> \endverbatim
134 *>
135 *> \param[out] XACT
136 *> \verbatim
137 *> XACT is REAL array, dimension (NMAX*NSMAX),
138 *> where NSMAX is the largest entry in NSVAL.
139 *> \endverbatim
140 *>
141 *> \param[out] WORK
142 *> \verbatim
143 *> WORK is REAL array, dimension (NMAX*max(3,NSMAX))
144 *> \endverbatim
145 *>
146 *> \param[out] RWORK
147 *> \verbatim
148 *> RWORK is REAL array, dimension (max(NMAX,2*NSMAX))
149 *> \endverbatim
150 *>
151 *> \param[out] IWORK
152 *> \verbatim
153 *> IWORK is INTEGER array, dimension (2*NMAX)
154 *> \endverbatim
155 *>
156 *> \param[in] NOUT
157 *> \verbatim
158 *> NOUT is INTEGER
159 *> The unit number for output.
160 *> \endverbatim
161 *
162 * Authors:
163 * ========
164 *
165 *> \author Univ. of Tennessee
166 *> \author Univ. of California Berkeley
167 *> \author Univ. of Colorado Denver
168 *> \author NAG Ltd.
169 *
170 *> \date November 2017
171 *
172 *> \ingroup double_lin
173 *
174 * =====================================================================
175  SUBROUTINE schksy_rk( DOTYPE, NN, NVAL, NNB, NBVAL, NNS, NSVAL,
176  $ THRESH, TSTERR, NMAX, A, AFAC, E, AINV, B,
177  $ X, XACT, WORK, RWORK, IWORK, NOUT )
178 *
179 * -- LAPACK test routine (version 3.8.0) --
180 * -- LAPACK is a software package provided by Univ. of Tennessee, --
181 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
182 * November 2017
183 *
184 * .. Scalar Arguments ..
185  LOGICAL tsterr
186  INTEGER nmax, nn, nnb, nns, nout
187  REAL thresh
188 * ..
189 * .. Array Arguments ..
190  LOGICAL dotype( * )
191  INTEGER IWORK( * ), NBVAL( * ), NSVAL( * ), NVAL( * )
192  REAL A( * ), AFAC( * ), AINV( * ), B( * ), E( * ),
193  $ rwork( * ), work( * ), x( * ), xact( * )
194 * ..
195 *
196 * =====================================================================
197 *
198 * .. Parameters ..
199  REAL ZERO, ONE
200  PARAMETER ( ZERO = 0.0e+0, one = 1.0e+0 )
201  REAL EIGHT, SEVTEN
202  parameter( eight = 8.0e+0, sevten = 17.0e+0 )
203  INTEGER NTYPES
204  parameter( ntypes = 10 )
205  INTEGER NTESTS
206  parameter( ntests = 7 )
207 * ..
208 * .. Local Scalars ..
209  LOGICAL TRFCON, ZEROT
210  CHARACTER DIST, TYPE, UPLO, XTYPE
211  CHARACTER*3 PATH, MATPATH
212  INTEGER I, I1, I2, IMAT, IN, INB, INFO, IOFF, IRHS,
213  $ iuplo, izero, j, k, kl, ku, lda, lwork,
214  $ mode, n, nb, nerrs, nfail, nimat, nrhs, nrun,
215  $ nt
216  REAL ALPHA, ANORM, CNDNUM, CONST, STEMP, SING_MAX,
217  $ SING_MIN, RCOND, RCONDC
218 * ..
219 * .. Local Arrays ..
220  CHARACTER UPLOS( 2 )
221  INTEGER ISEED( 4 ), ISEEDY( 4 )
222  REAL BLOCK( 2, 2 ), SDUMMY( 1 ), RESULT( NTESTS )
223 * ..
224 * .. External Functions ..
225  REAL SGET06, SLANGE, SLANSY
226  EXTERNAL SGET06, SLANGE, SLANSY
227 * ..
228 * .. External Subroutines ..
229  EXTERNAL alaerh, alahd, alasum, serrsy, sgesvd, sget04,
230  $ slacpy, slarhs, slatb4, slatms, spot02, spot03,
231  $ ssycon_3, ssyt01_3, ssytrf_rk, ssytri_3,
232  $ ssytrs_3, xlaenv
233 * ..
234 * .. Intrinsic Functions ..
235  INTRINSIC max, min, sqrt
236 * ..
237 * .. Scalars in Common ..
238  LOGICAL LERR, OK
239  CHARACTER*32 SRNAMT
240  INTEGER INFOT, NUNIT
241 * ..
242 * .. Common blocks ..
243  COMMON / infoc / infot, nunit, ok, lerr
244  COMMON / srnamc / srnamt
245 * ..
246 * .. Data statements ..
247  DATA iseedy / 1988, 1989, 1990, 1991 /
248  DATA uplos / 'U', 'L' /
249 * ..
250 * .. Executable Statements ..
251 *
252 * Initialize constants and the random number seed.
253 *
254  alpha = ( one+sqrt( sevten ) ) / eight
255 *
256 * Test path
257 *
258  path( 1: 1 ) = 'Single precision'
259  path( 2: 3 ) = 'SK'
260 *
261 * Path to generate matrices
262 *
263  matpath( 1: 1 ) = 'Single precision'
264  matpath( 2: 3 ) = 'SY'
265 *
266  nrun = 0
267  nfail = 0
268  nerrs = 0
269  DO 10 i = 1, 4
270  iseed( i ) = iseedy( i )
271  10 CONTINUE
272 *
273 * Test the error exits
274 *
275  IF( tsterr )
276  $ CALL serrsy( path, nout )
277  infot = 0
278 *
279 * Set the minimum block size for which the block routine should
280 * be used, which will be later returned by ILAENV
281 *
282  CALL xlaenv( 2, 2 )
283 *
284 * Do for each value of N in NVAL
285 *
286  DO 270 in = 1, nn
287  n = nval( in )
288  lda = max( n, 1 )
289  xtype = 'N'
290  nimat = ntypes
291  IF( n.LE.0 )
292  $ nimat = 1
293 *
294  izero = 0
295 *
296 * Do for each value of matrix type IMAT
297 *
298  DO 260 imat = 1, nimat
299 *
300 * Do the tests only if DOTYPE( IMAT ) is true.
301 *
302  IF( .NOT.dotype( imat ) )
303  $ GO TO 260
304 *
305 * Skip types 3, 4, 5, or 6 if the matrix size is too small.
306 *
307  zerot = imat.GE.3 .AND. imat.LE.6
308  IF( zerot .AND. n.LT.imat-2 )
309  $ GO TO 260
310 *
311 * Do first for UPLO = 'U', then for UPLO = 'L'
312 *
313  DO 250 iuplo = 1, 2
314  uplo = uplos( iuplo )
315 *
316 * Begin generate the test matrix A.
317 *
318 * Set up parameters with SLATB4 for the matrix generator
319 * based on the type of matrix to be generated.
320 *
321  CALL slatb4( matpath, imat, n, n, TYPE, kl, ku, anorm,
322  $ mode, cndnum, dist )
323 *
324 * Generate a matrix with SLATMS.
325 *
326  srnamt = 'SLATMS'
327  CALL slatms( n, n, dist, iseed, TYPE, rwork, mode,
328  $ cndnum, anorm, kl, ku, uplo, a, lda, work,
329  $ info )
330 *
331 * Check error code from SLATMS and handle error.
332 *
333  IF( info.NE.0 ) THEN
334  CALL alaerh( path, 'SLATMS', info, 0, uplo, n, n, -1,
335  $ -1, -1, imat, nfail, nerrs, nout )
336 *
337 * Skip all tests for this generated matrix
338 *
339  GO TO 250
340  END IF
341 *
342 * For matrix types 3-6, zero one or more rows and
343 * columns of the matrix to test that INFO is returned
344 * correctly.
345 *
346  IF( zerot ) THEN
347  IF( imat.EQ.3 ) THEN
348  izero = 1
349  ELSE IF( imat.EQ.4 ) THEN
350  izero = n
351  ELSE
352  izero = n / 2 + 1
353  END IF
354 *
355  IF( imat.LT.6 ) THEN
356 *
357 * Set row and column IZERO to zero.
358 *
359  IF( iuplo.EQ.1 ) THEN
360  ioff = ( izero-1 )*lda
361  DO 20 i = 1, izero - 1
362  a( ioff+i ) = zero
363  20 CONTINUE
364  ioff = ioff + izero
365  DO 30 i = izero, n
366  a( ioff ) = zero
367  ioff = ioff + lda
368  30 CONTINUE
369  ELSE
370  ioff = izero
371  DO 40 i = 1, izero - 1
372  a( ioff ) = zero
373  ioff = ioff + lda
374  40 CONTINUE
375  ioff = ioff - izero
376  DO 50 i = izero, n
377  a( ioff+i ) = zero
378  50 CONTINUE
379  END IF
380  ELSE
381  IF( iuplo.EQ.1 ) THEN
382 *
383 * Set the first IZERO rows and columns to zero.
384 *
385  ioff = 0
386  DO 70 j = 1, n
387  i2 = min( j, izero )
388  DO 60 i = 1, i2
389  a( ioff+i ) = zero
390  60 CONTINUE
391  ioff = ioff + lda
392  70 CONTINUE
393  ELSE
394 *
395 * Set the last IZERO rows and columns to zero.
396 *
397  ioff = 0
398  DO 90 j = 1, n
399  i1 = max( j, izero )
400  DO 80 i = i1, n
401  a( ioff+i ) = zero
402  80 CONTINUE
403  ioff = ioff + lda
404  90 CONTINUE
405  END IF
406  END IF
407  ELSE
408  izero = 0
409  END IF
410 *
411 * End generate the test matrix A.
412 *
413 *
414 * Do for each value of NB in NBVAL
415 *
416  DO 240 inb = 1, nnb
417 *
418 * Set the optimal blocksize, which will be later
419 * returned by ILAENV.
420 *
421  nb = nbval( inb )
422  CALL xlaenv( 1, nb )
423 *
424 * Copy the test matrix A into matrix AFAC which
425 * will be factorized in place. This is needed to
426 * preserve the test matrix A for subsequent tests.
427 *
428  CALL slacpy( uplo, n, n, a, lda, afac, lda )
429 *
430 * Compute the L*D*L**T or U*D*U**T factorization of the
431 * matrix. IWORK stores details of the interchanges and
432 * the block structure of D. AINV is a work array for
433 * block factorization, LWORK is the length of AINV.
434 *
435  lwork = max( 2, nb )*lda
436  srnamt = 'SSYTRF_RK'
437  CALL ssytrf_rk( uplo, n, afac, lda, e, iwork, ainv,
438  $ lwork, info )
439 *
440 * Adjust the expected value of INFO to account for
441 * pivoting.
442 *
443  k = izero
444  IF( k.GT.0 ) THEN
445  100 CONTINUE
446  IF( iwork( k ).LT.0 ) THEN
447  IF( iwork( k ).NE.-k ) THEN
448  k = -iwork( k )
449  GO TO 100
450  END IF
451  ELSE IF( iwork( k ).NE.k ) THEN
452  k = iwork( k )
453  GO TO 100
454  END IF
455  END IF
456 *
457 * Check error code from DSYTRF_RK and handle error.
458 *
459  IF( info.NE.k)
460  $ CALL alaerh( path, 'SSYTRF_RK', info, k,
461  $ uplo, n, n, -1, -1, nb, imat,
462  $ nfail, nerrs, nout )
463 *
464 * Set the condition estimate flag if the INFO is not 0.
465 *
466  IF( info.NE.0 ) THEN
467  trfcon = .true.
468  ELSE
469  trfcon = .false.
470  END IF
471 *
472 *+ TEST 1
473 * Reconstruct matrix from factors and compute residual.
474 *
475  CALL ssyt01_3( uplo, n, a, lda, afac, lda, e, iwork,
476  $ ainv, lda, rwork, result( 1 ) )
477  nt = 1
478 *
479 *+ TEST 2
480 * Form the inverse and compute the residual,
481 * if the factorization was competed without INFO > 0
482 * (i.e. there is no zero rows and columns).
483 * Do it only for the first block size.
484 *
485  IF( inb.EQ.1 .AND. .NOT.trfcon ) THEN
486  CALL slacpy( uplo, n, n, afac, lda, ainv, lda )
487  srnamt = 'SSYTRI_3'
488 *
489 * Another reason that we need to compute the invesrse
490 * is that SPOT03 produces RCONDC which is used later
491 * in TEST6 and TEST7.
492 *
493  lwork = (n+nb+1)*(nb+3)
494  CALL ssytri_3( uplo, n, ainv, lda, e, iwork, work,
495  $ lwork, info )
496 *
497 * Check error code from SSYTRI_3 and handle error.
498 *
499  IF( info.NE.0 )
500  $ CALL alaerh( path, 'SSYTRI_3', info, -1,
501  $ uplo, n, n, -1, -1, -1, imat,
502  $ nfail, nerrs, nout )
503 *
504 * Compute the residual for a symmetric matrix times
505 * its inverse.
506 *
507  CALL spot03( uplo, n, a, lda, ainv, lda, work, lda,
508  $ rwork, rcondc, result( 2 ) )
509  nt = 2
510  END IF
511 *
512 * Print information about the tests that did not pass
513 * the threshold.
514 *
515  DO 110 k = 1, nt
516  IF( result( k ).GE.thresh ) THEN
517  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
518  $ CALL alahd( nout, path )
519  WRITE( nout, fmt = 9999 )uplo, n, nb, imat, k,
520  $ result( k )
521  nfail = nfail + 1
522  END IF
523  110 CONTINUE
524  nrun = nrun + nt
525 *
526 *+ TEST 3
527 * Compute largest element in U or L
528 *
529  result( 3 ) = zero
530  stemp = zero
531 *
532  const = one / ( one-alpha )
533 *
534  IF( iuplo.EQ.1 ) THEN
535 *
536 * Compute largest element in U
537 *
538  k = n
539  120 CONTINUE
540  IF( k.LE.1 )
541  $ GO TO 130
542 *
543  IF( iwork( k ).GT.zero ) THEN
544 *
545 * Get max absolute value from elements
546 * in column k in in U
547 *
548  stemp = slange( 'M', k-1, 1,
549  $ afac( ( k-1 )*lda+1 ), lda, rwork )
550  ELSE
551 *
552 * Get max absolute value from elements
553 * in columns k and k-1 in U
554 *
555  stemp = slange( 'M', k-2, 2,
556  $ afac( ( k-2 )*lda+1 ), lda, rwork )
557  k = k - 1
558 *
559  END IF
560 *
561 * STEMP should be bounded by CONST
562 *
563  stemp = stemp - const + thresh
564  IF( stemp.GT.result( 3 ) )
565  $ result( 3 ) = stemp
566 *
567  k = k - 1
568 *
569  GO TO 120
570  130 CONTINUE
571 *
572  ELSE
573 *
574 * Compute largest element in L
575 *
576  k = 1
577  140 CONTINUE
578  IF( k.GE.n )
579  $ GO TO 150
580 *
581  IF( iwork( k ).GT.zero ) THEN
582 *
583 * Get max absolute value from elements
584 * in column k in in L
585 *
586  stemp = slange( 'M', n-k, 1,
587  $ afac( ( k-1 )*lda+k+1 ), lda, rwork )
588  ELSE
589 *
590 * Get max absolute value from elements
591 * in columns k and k+1 in L
592 *
593  stemp = slange( 'M', n-k-1, 2,
594  $ afac( ( k-1 )*lda+k+2 ), lda, rwork )
595  k = k + 1
596 *
597  END IF
598 *
599 * STEMP should be bounded by CONST
600 *
601  stemp = stemp - const + thresh
602  IF( stemp.GT.result( 3 ) )
603  $ result( 3 ) = stemp
604 *
605  k = k + 1
606 *
607  GO TO 140
608  150 CONTINUE
609  END IF
610 *
611 *+ TEST 4
612 * Compute largest 2-Norm (condition number)
613 * of 2-by-2 diag blocks
614 *
615  result( 4 ) = zero
616  stemp = zero
617 *
618  const = ( one+alpha ) / ( one-alpha )
619  CALL slacpy( uplo, n, n, afac, lda, ainv, lda )
620 *
621  IF( iuplo.EQ.1 ) THEN
622 *
623 * Loop backward for UPLO = 'U'
624 *
625  k = n
626  160 CONTINUE
627  IF( k.LE.1 )
628  $ GO TO 170
629 *
630  IF( iwork( k ).LT.zero ) THEN
631 *
632 * Get the two singular values
633 * (real and non-negative) of a 2-by-2 block,
634 * store them in RWORK array
635 *
636  block( 1, 1 ) = afac( ( k-2 )*lda+k-1 )
637  block( 1, 2 ) = e( k )
638  block( 2, 1 ) = block( 1, 2 )
639  block( 2, 2 ) = afac( (k-1)*lda+k )
640 *
641  CALL sgesvd( 'N', 'N', 2, 2, block, 2, rwork,
642  $ sdummy, 1, sdummy, 1,
643  $ work, 10, info )
644 *
645  sing_max = rwork( 1 )
646  sing_min = rwork( 2 )
647 *
648  stemp = sing_max / sing_min
649 *
650 * STEMP should be bounded by CONST
651 *
652  stemp = stemp - const + thresh
653  IF( stemp.GT.result( 4 ) )
654  $ result( 4 ) = stemp
655  k = k - 1
656 *
657  END IF
658 *
659  k = k - 1
660 *
661  GO TO 160
662  170 CONTINUE
663 *
664  ELSE
665 *
666 * Loop forward for UPLO = 'L'
667 *
668  k = 1
669  180 CONTINUE
670  IF( k.GE.n )
671  $ GO TO 190
672 *
673  IF( iwork( k ).LT.zero ) THEN
674 *
675 * Get the two singular values
676 * (real and non-negative) of a 2-by-2 block,
677 * store them in RWORK array
678 *
679  block( 1, 1 ) = afac( ( k-1 )*lda+k )
680  block( 2, 1 ) = e( k )
681  block( 1, 2 ) = block( 2, 1 )
682  block( 2, 2 ) = afac( k*lda+k+1 )
683 *
684  CALL sgesvd( 'N', 'N', 2, 2, block, 2, rwork,
685  $ sdummy, 1, sdummy, 1,
686  $ work, 10, info )
687 *
688 *
689  sing_max = rwork( 1 )
690  sing_min = rwork( 2 )
691 *
692  stemp = sing_max / sing_min
693 *
694 * STEMP should be bounded by CONST
695 *
696  stemp = stemp - const + thresh
697  IF( stemp.GT.result( 4 ) )
698  $ result( 4 ) = stemp
699  k = k + 1
700 *
701  END IF
702 *
703  k = k + 1
704 *
705  GO TO 180
706  190 CONTINUE
707  END IF
708 *
709 * Print information about the tests that did not pass
710 * the threshold.
711 *
712  DO 200 k = 3, 4
713  IF( result( k ).GE.thresh ) THEN
714  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
715  $ CALL alahd( nout, path )
716  WRITE( nout, fmt = 9999 )uplo, n, nb, imat, k,
717  $ result( k )
718  nfail = nfail + 1
719  END IF
720  200 CONTINUE
721  nrun = nrun + 2
722 *
723 * Skip the other tests if this is not the first block
724 * size.
725 *
726  IF( inb.GT.1 )
727  $ GO TO 240
728 *
729 * Do only the condition estimate if INFO is not 0.
730 *
731  IF( trfcon ) THEN
732  rcondc = zero
733  GO TO 230
734  END IF
735 *
736 * Do for each value of NRHS in NSVAL.
737 *
738  DO 220 irhs = 1, nns
739  nrhs = nsval( irhs )
740 *
741 *+ TEST 5 ( Using TRS_3)
742 * Solve and compute residual for A * X = B.
743 *
744 * Choose a set of NRHS random solution vectors
745 * stored in XACT and set up the right hand side B
746 *
747  srnamt = 'SLARHS'
748  CALL slarhs( matpath, xtype, uplo, ' ', n, n,
749  $ kl, ku, nrhs, a, lda, xact, lda,
750  $ b, lda, iseed, info )
751  CALL slacpy( 'Full', n, nrhs, b, lda, x, lda )
752 *
753  srnamt = 'SSYTRS_3'
754  CALL ssytrs_3( uplo, n, nrhs, afac, lda, e, iwork,
755  $ x, lda, info )
756 *
757 * Check error code from SSYTRS_3 and handle error.
758 *
759  IF( info.NE.0 )
760  $ CALL alaerh( path, 'SSYTRS_3', info, 0,
761  $ uplo, n, n, -1, -1, nrhs, imat,
762  $ nfail, nerrs, nout )
763 *
764  CALL slacpy( 'Full', n, nrhs, b, lda, work, lda )
765 *
766 * Compute the residual for the solution
767 *
768  CALL spot02( uplo, n, nrhs, a, lda, x, lda, work,
769  $ lda, rwork, result( 5 ) )
770 *
771 *+ TEST 6
772 * Check solution from generated exact solution.
773 *
774  CALL sget04( n, nrhs, x, lda, xact, lda, rcondc,
775  $ result( 6 ) )
776 *
777 * Print information about the tests that did not pass
778 * the threshold.
779 *
780  DO 210 k = 5, 6
781  IF( result( k ).GE.thresh ) THEN
782  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
783  $ CALL alahd( nout, path )
784  WRITE( nout, fmt = 9998 )uplo, n, nrhs,
785  $ imat, k, result( k )
786  nfail = nfail + 1
787  END IF
788  210 CONTINUE
789  nrun = nrun + 2
790 *
791 * End do for each value of NRHS in NSVAL.
792 *
793  220 CONTINUE
794 *
795 *+ TEST 7
796 * Get an estimate of RCOND = 1/CNDNUM.
797 *
798  230 CONTINUE
799  anorm = slansy( '1', uplo, n, a, lda, rwork )
800  srnamt = 'SSYCON_3'
801  CALL ssycon_3( uplo, n, afac, lda, e, iwork, anorm,
802  $ rcond, work, iwork( n+1 ), info )
803 *
804 * Check error code from DSYCON_3 and handle error.
805 *
806  IF( info.NE.0 )
807  $ CALL alaerh( path, 'SSYCON_3', info, 0,
808  $ uplo, n, n, -1, -1, -1, imat,
809  $ nfail, nerrs, nout )
810 *
811 * Compute the test ratio to compare to values of RCOND
812 *
813  result( 7 ) = sget06( rcond, rcondc )
814 *
815 * Print information about the tests that did not pass
816 * the threshold.
817 *
818  IF( result( 7 ).GE.thresh ) THEN
819  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
820  $ CALL alahd( nout, path )
821  WRITE( nout, fmt = 9997 ) uplo, n, imat, 7,
822  $ result( 7 )
823  nfail = nfail + 1
824  END IF
825  nrun = nrun + 1
826  240 CONTINUE
827 *
828  250 CONTINUE
829  260 CONTINUE
830  270 CONTINUE
831 *
832 * Print a summary of the results.
833 *
834  CALL alasum( path, nout, nfail, nrun, nerrs )
835 *
836  9999 FORMAT( ' UPLO = ''', a1, ''', N =', i5, ', NB =', i4, ', type ',
837  $ i2, ', test ', i2, ', ratio =', g12.5 )
838  9998 FORMAT( ' UPLO = ''', a1, ''', N =', i5, ', NRHS=', i3, ', type ',
839  $ i2, ', test(', i2, ') =', g12.5 )
840  9997 FORMAT( ' UPLO = ''', a1, ''', N =', i5, ',', 10x, ' type ', i2,
841  $ ', test(', i2, ') =', g12.5 )
842  RETURN
843 *
844 * End of SCHKSY_RK
845 *
846  END
slarhs
subroutine slarhs(PATH, XTYPE, UPLO, TRANS, M, N, KL, KU, NRHS, A, LDA, X, LDX, B, LDB, ISEED, INFO)
SLARHS
Definition: slarhs.f:206
spot02
subroutine spot02(UPLO, N, NRHS, A, LDA, X, LDX, B, LDB, RWORK, RESID)
SPOT02
Definition: spot02.f:129
ssytrf_rk
subroutine ssytrf_rk(UPLO, N, A, LDA, E, IPIV, WORK, LWORK, INFO)
SSYTRF_RK computes the factorization of a real symmetric indefinite matrix using the bounded Bunch-Ka...
Definition: ssytrf_rk.f:261
alahd
subroutine alahd(IOUNIT, PATH)
ALAHD
Definition: alahd.f:109
schksy_rk
subroutine schksy_rk(DOTYPE, NN, NVAL, NNB, NBVAL, NNS, NSVAL, THRESH, TSTERR, NMAX, A, AFAC, E, AINV, B, X, XACT, WORK, RWORK, IWORK, NOUT)
SCHKSY_RK
Definition: schksy_rk.f:178
slacpy
subroutine slacpy(UPLO, M, N, A, LDA, B, LDB)
SLACPY copies all or part of one two-dimensional array to another.
Definition: slacpy.f:105
sgesvd
subroutine sgesvd(JOBU, JOBVT, M, N, A, LDA, S, U, LDU, VT, LDVT, WORK, LWORK, INFO)
SGESVD computes the singular value decomposition (SVD) for GE matrices
Definition: sgesvd.f:213
ssytrs_3
subroutine ssytrs_3(UPLO, N, NRHS, A, LDA, E, IPIV, B, LDB, INFO)
SSYTRS_3
Definition: ssytrs_3.f:167
serrsy
subroutine serrsy(PATH, NUNIT)
SERRSY
Definition: serrsy.f:57
ssycon_3
subroutine ssycon_3(UPLO, N, A, LDA, E, IPIV, ANORM, RCOND, WORK, IWORK, INFO)
SSYCON_3
Definition: ssycon_3.f:173
sget04
subroutine sget04(N, NRHS, X, LDX, XACT, LDXACT, RCOND, RESID)
SGET04
Definition: sget04.f:104
alaerh
subroutine alaerh(PATH, SUBNAM, INFO, INFOE, OPTS, M, N, KL, KU, N5, IMAT, NFAIL, NERRS, NOUT)
ALAERH
Definition: alaerh.f:149
ssytri_3
subroutine ssytri_3(UPLO, N, A, LDA, E, IPIV, WORK, LWORK, INFO)
SSYTRI_3
Definition: ssytri_3.f:172
slatms
subroutine slatms(M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX, KL, KU, PACK, A, LDA, WORK, INFO)
SLATMS
Definition: slatms.f:323
ssyt01_3
subroutine ssyt01_3(UPLO, N, A, LDA, AFAC, LDAFAC, E, IPIV, C, LDC, RWORK, RESID)
SSYT01_3
Definition: ssyt01_3.f:142
slatb4
subroutine slatb4(PATH, IMAT, M, N, TYPE, KL, KU, ANORM, MODE, CNDNUM, DIST)
SLATB4
Definition: slatb4.f:122
spot03
subroutine spot03(UPLO, N, A, LDA, AINV, LDAINV, WORK, LDWORK, RWORK, RCOND, RESID)
SPOT03
Definition: spot03.f:127
alasum
subroutine alasum(TYPE, NOUT, NFAIL, NRUN, NERRS)
ALASUM
Definition: alasum.f:75
xlaenv
subroutine xlaenv(ISPEC, NVALUE)
XLAENV
Definition: xlaenv.f:83