LAPACK  3.8.0 LAPACK: Linear Algebra PACKage

◆ ddrvsy()

 subroutine ddrvsy ( logical, dimension( * ) DOTYPE, integer NN, integer, dimension( * ) NVAL, integer NRHS, double precision THRESH, logical TSTERR, integer NMAX, double precision, dimension( * ) A, double precision, dimension( * ) AFAC, double precision, dimension( * ) AINV, double precision, dimension( * ) B, double precision, dimension( * ) X, double precision, dimension( * ) XACT, double precision, dimension( * ) WORK, double precision, dimension( * ) RWORK, integer, dimension( * ) IWORK, integer NOUT )

DDRVSY

DDRVSYX

Purpose:
` DDRVSY tests the driver routines DSYSV and -SVX.`
Parameters
 [in] DOTYPE ``` DOTYPE is LOGICAL array, dimension (NTYPES) The matrix types to be used for testing. Matrices of type j (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) = .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.``` [in] NN ``` NN is INTEGER The number of values of N contained in the vector NVAL.``` [in] NVAL ``` NVAL is INTEGER array, dimension (NN) The values of the matrix dimension N.``` [in] NRHS ``` NRHS is INTEGER The number of right hand side vectors to be generated for each linear system.``` [in] THRESH ``` THRESH is DOUBLE PRECISION The threshold value for the test ratios. A result is included in the output file if RESULT >= THRESH. To have every test ratio printed, use THRESH = 0.``` [in] TSTERR ``` TSTERR is LOGICAL Flag that indicates whether error exits are to be tested.``` [in] NMAX ``` NMAX is INTEGER The maximum value permitted for N, used in dimensioning the work arrays.``` [out] A ` A is DOUBLE PRECISION array, dimension (NMAX*NMAX)` [out] AFAC ` AFAC is DOUBLE PRECISION array, dimension (NMAX*NMAX)` [out] AINV ` AINV is DOUBLE PRECISION array, dimension (NMAX*NMAX)` [out] B ` B is DOUBLE PRECISION array, dimension (NMAX*NRHS)` [out] X ` X is DOUBLE PRECISION array, dimension (NMAX*NRHS)` [out] XACT ` XACT is DOUBLE PRECISION array, dimension (NMAX*NRHS)` [out] WORK ` WORK is DOUBLE PRECISION array, dimension (NMAX*max(2,NRHS))` [out] RWORK ` RWORK is DOUBLE PRECISION array, dimension (NMAX+2*NRHS)` [out] IWORK ` IWORK is INTEGER array, dimension (2*NMAX)` [in] NOUT ``` NOUT is INTEGER The unit number for output.```
Date
November 2013
Purpose:
``` DDRVSY tests the driver routines DSYSV, -SVX, and -SVXX.

Note that this file is used only when the XBLAS are available,
otherwise ddrvsy.f defines this subroutine.```
Parameters
 [in] DOTYPE ``` DOTYPE is LOGICAL array, dimension (NTYPES) The matrix types to be used for testing. Matrices of type j (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) = .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.``` [in] NN ``` NN is INTEGER The number of values of N contained in the vector NVAL.``` [in] NVAL ``` NVAL is INTEGER array, dimension (NN) The values of the matrix dimension N.``` [in] NRHS ``` NRHS is INTEGER The number of right hand side vectors to be generated for each linear system.``` [in] THRESH ``` THRESH is DOUBLE PRECISION The threshold value for the test ratios. A result is included in the output file if RESULT >= THRESH. To have every test ratio printed, use THRESH = 0.``` [in] TSTERR ``` TSTERR is LOGICAL Flag that indicates whether error exits are to be tested.``` [in] NMAX ``` NMAX is INTEGER The maximum value permitted for N, used in dimensioning the work arrays.``` [out] A ` A is DOUBLE PRECISION array, dimension (NMAX*NMAX)` [out] AFAC ` AFAC is DOUBLE PRECISION array, dimension (NMAX*NMAX)` [out] AINV ` AINV is DOUBLE PRECISION array, dimension (NMAX*NMAX)` [out] B ` B is DOUBLE PRECISION array, dimension (NMAX*NRHS)` [out] X ` X is DOUBLE PRECISION array, dimension (NMAX*NRHS)` [out] XACT ` XACT is DOUBLE PRECISION array, dimension (NMAX*NRHS)` [out] WORK ``` WORK is DOUBLE PRECISION array, dimension (NMAX*max(2,NRHS))``` [out] RWORK ` RWORK is DOUBLE PRECISION array, dimension (NMAX+2*NRHS)` [out] IWORK ` IWORK is INTEGER array, dimension (2*NMAX)` [in] NOUT ``` NOUT is INTEGER The unit number for output.```
Date
December 2016

Definition at line 154 of file ddrvsy.f.

154 *
155 * -- LAPACK test routine (version 3.5.0) --
156 * -- LAPACK is a software package provided by Univ. of Tennessee, --
157 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
158 * November 2013
159 *
160 * .. Scalar Arguments ..
161  LOGICAL tsterr
162  INTEGER nmax, nn, nout, nrhs
163  DOUBLE PRECISION thresh
164 * ..
165 * .. Array Arguments ..
166  LOGICAL dotype( * )
167  INTEGER iwork( * ), nval( * )
168  DOUBLE PRECISION a( * ), afac( * ), ainv( * ), b( * ),
169  \$ rwork( * ), work( * ), x( * ), xact( * )
170 * ..
171 *
172 * =====================================================================
173 *
174 * .. Parameters ..
175  DOUBLE PRECISION one, zero
176  parameter( one = 1.0d+0, zero = 0.0d+0 )
177  INTEGER ntypes, ntests
178  parameter( ntypes = 10, ntests = 6 )
179  INTEGER nfact
180  parameter( nfact = 2 )
181 * ..
182 * .. Local Scalars ..
183  LOGICAL zerot
184  CHARACTER dist, fact, TYPE, uplo, xtype
185  CHARACTER*3 path
186  INTEGER i, i1, i2, ifact, imat, in, info, ioff, iuplo,
187  \$ izero, j, k, k1, kl, ku, lda, lwork, mode, n,
188  \$ nb, nbmin, nerrs, nfail, nimat, nrun, nt
189  DOUBLE PRECISION ainvnm, anorm, cndnum, rcond, rcondc
190 * ..
191 * .. Local Arrays ..
192  CHARACTER facts( nfact ), uplos( 2 )
193  INTEGER iseed( 4 ), iseedy( 4 )
194  DOUBLE PRECISION result( ntests )
195 * ..
196 * .. External Functions ..
197  DOUBLE PRECISION dget06, dlansy
198  EXTERNAL dget06, dlansy
199 * ..
200 * .. External Subroutines ..
201  EXTERNAL aladhd, alaerh, alasvm, derrvx, dget04, dlacpy,
204 * ..
205 * .. Scalars in Common ..
206  LOGICAL lerr, ok
207  CHARACTER*32 srnamt
208  INTEGER infot, nunit
209 * ..
210 * .. Common blocks ..
211  COMMON / infoc / infot, nunit, ok, lerr
212  COMMON / srnamc / srnamt
213 * ..
214 * .. Intrinsic Functions ..
215  INTRINSIC max, min
216 * ..
217 * .. Data statements ..
218  DATA iseedy / 1988, 1989, 1990, 1991 /
219  DATA uplos / 'U', 'L' / , facts / 'F', 'N' /
220 * ..
221 * .. Executable Statements ..
222 *
223 * Initialize constants and the random number seed.
224 *
225  path( 1: 1 ) = 'Double precision'
226  path( 2: 3 ) = 'SY'
227  nrun = 0
228  nfail = 0
229  nerrs = 0
230  DO 10 i = 1, 4
231  iseed( i ) = iseedy( i )
232  10 CONTINUE
233  lwork = max( 2*nmax, nmax*nrhs )
234 *
235 * Test the error exits
236 *
237  IF( tsterr )
238  \$ CALL derrvx( path, nout )
239  infot = 0
240 *
241 * Set the block size and minimum block size for testing.
242 *
243  nb = 1
244  nbmin = 2
245  CALL xlaenv( 1, nb )
246  CALL xlaenv( 2, nbmin )
247 *
248 * Do for each value of N in NVAL
249 *
250  DO 180 in = 1, nn
251  n = nval( in )
252  lda = max( n, 1 )
253  xtype = 'N'
254  nimat = ntypes
255  IF( n.LE.0 )
256  \$ nimat = 1
257 *
258  DO 170 imat = 1, nimat
259 *
260 * Do the tests only if DOTYPE( IMAT ) is true.
261 *
262  IF( .NOT.dotype( imat ) )
263  \$ GO TO 170
264 *
265 * Skip types 3, 4, 5, or 6 if the matrix size is too small.
266 *
267  zerot = imat.GE.3 .AND. imat.LE.6
268  IF( zerot .AND. n.LT.imat-2 )
269  \$ GO TO 170
270 *
271 * Do first for UPLO = 'U', then for UPLO = 'L'
272 *
273  DO 160 iuplo = 1, 2
274  uplo = uplos( iuplo )
275 *
276 * Set up parameters with DLATB4 and generate a test matrix
277 * with DLATMS.
278 *
279  CALL dlatb4( path, imat, n, n, TYPE, kl, ku, anorm, mode,
280  \$ cndnum, dist )
281 *
282  srnamt = 'DLATMS'
283  CALL dlatms( n, n, dist, iseed, TYPE, rwork, mode,
284  \$ cndnum, anorm, kl, ku, uplo, a, lda, work,
285  \$ info )
286 *
287 * Check error code from DLATMS.
288 *
289  IF( info.NE.0 ) THEN
290  CALL alaerh( path, 'DLATMS', info, 0, uplo, n, n, -1,
291  \$ -1, -1, imat, nfail, nerrs, nout )
292  GO TO 160
293  END IF
294 *
295 * For types 3-6, zero one or more rows and columns of the
296 * matrix to test that INFO is returned correctly.
297 *
298  IF( zerot ) THEN
299  IF( imat.EQ.3 ) THEN
300  izero = 1
301  ELSE IF( imat.EQ.4 ) THEN
302  izero = n
303  ELSE
304  izero = n / 2 + 1
305  END IF
306 *
307  IF( imat.LT.6 ) THEN
308 *
309 * Set row and column IZERO to zero.
310 *
311  IF( iuplo.EQ.1 ) THEN
312  ioff = ( izero-1 )*lda
313  DO 20 i = 1, izero - 1
314  a( ioff+i ) = zero
315  20 CONTINUE
316  ioff = ioff + izero
317  DO 30 i = izero, n
318  a( ioff ) = zero
319  ioff = ioff + lda
320  30 CONTINUE
321  ELSE
322  ioff = izero
323  DO 40 i = 1, izero - 1
324  a( ioff ) = zero
325  ioff = ioff + lda
326  40 CONTINUE
327  ioff = ioff - izero
328  DO 50 i = izero, n
329  a( ioff+i ) = zero
330  50 CONTINUE
331  END IF
332  ELSE
333  ioff = 0
334  IF( iuplo.EQ.1 ) THEN
335 *
336 * Set the first IZERO rows and columns to zero.
337 *
338  DO 70 j = 1, n
339  i2 = min( j, izero )
340  DO 60 i = 1, i2
341  a( ioff+i ) = zero
342  60 CONTINUE
343  ioff = ioff + lda
344  70 CONTINUE
345  ELSE
346 *
347 * Set the last IZERO rows and columns to zero.
348 *
349  DO 90 j = 1, n
350  i1 = max( j, izero )
351  DO 80 i = i1, n
352  a( ioff+i ) = zero
353  80 CONTINUE
354  ioff = ioff + lda
355  90 CONTINUE
356  END IF
357  END IF
358  ELSE
359  izero = 0
360  END IF
361 *
362  DO 150 ifact = 1, nfact
363 *
364 * Do first for FACT = 'F', then for other values.
365 *
366  fact = facts( ifact )
367 *
368 * Compute the condition number for comparison with
369 * the value returned by DSYSVX.
370 *
371  IF( zerot ) THEN
372  IF( ifact.EQ.1 )
373  \$ GO TO 150
374  rcondc = zero
375 *
376  ELSE IF( ifact.EQ.1 ) THEN
377 *
378 * Compute the 1-norm of A.
379 *
380  anorm = dlansy( '1', uplo, n, a, lda, rwork )
381 *
382 * Factor the matrix A.
383 *
384  CALL dlacpy( uplo, n, n, a, lda, afac, lda )
385  CALL dsytrf( uplo, n, afac, lda, iwork, work,
386  \$ lwork, info )
387 *
388 * Compute inv(A) and take its norm.
389 *
390  CALL dlacpy( uplo, n, n, afac, lda, ainv, lda )
391  lwork = (n+nb+1)*(nb+3)
392  CALL dsytri2( uplo, n, ainv, lda, iwork, work,
393  \$ lwork, info )
394  ainvnm = dlansy( '1', uplo, n, ainv, lda, rwork )
395 *
396 * Compute the 1-norm condition number of A.
397 *
398  IF( anorm.LE.zero .OR. ainvnm.LE.zero ) THEN
399  rcondc = one
400  ELSE
401  rcondc = ( one / anorm ) / ainvnm
402  END IF
403  END IF
404 *
405 * Form an exact solution and set the right hand side.
406 *
407  srnamt = 'DLARHS'
408  CALL dlarhs( path, xtype, uplo, ' ', n, n, kl, ku,
409  \$ nrhs, a, lda, xact, lda, b, lda, iseed,
410  \$ info )
411  xtype = 'C'
412 *
413 * --- Test DSYSV ---
414 *
415  IF( ifact.EQ.2 ) THEN
416  CALL dlacpy( uplo, n, n, a, lda, afac, lda )
417  CALL dlacpy( 'Full', n, nrhs, b, lda, x, lda )
418 *
419 * Factor the matrix and solve the system using DSYSV.
420 *
421  srnamt = 'DSYSV '
422  CALL dsysv( uplo, n, nrhs, afac, lda, iwork, x,
423  \$ lda, work, lwork, info )
424 *
425 * Adjust the expected value of INFO to account for
426 * pivoting.
427 *
428  k = izero
429  IF( k.GT.0 ) THEN
430  100 CONTINUE
431  IF( iwork( k ).LT.0 ) THEN
432  IF( iwork( k ).NE.-k ) THEN
433  k = -iwork( k )
434  GO TO 100
435  END IF
436  ELSE IF( iwork( k ).NE.k ) THEN
437  k = iwork( k )
438  GO TO 100
439  END IF
440  END IF
441 *
442 * Check error code from DSYSV .
443 *
444  IF( info.NE.k ) THEN
445  CALL alaerh( path, 'DSYSV ', info, k, uplo, n,
446  \$ n, -1, -1, nrhs, imat, nfail,
447  \$ nerrs, nout )
448  GO TO 120
449  ELSE IF( info.NE.0 ) THEN
450  GO TO 120
451  END IF
452 *
453 * Reconstruct matrix from factors and compute
454 * residual.
455 *
456  CALL dsyt01( uplo, n, a, lda, afac, lda, iwork,
457  \$ ainv, lda, rwork, result( 1 ) )
458 *
459 * Compute residual of the computed solution.
460 *
461  CALL dlacpy( 'Full', n, nrhs, b, lda, work, lda )
462  CALL dpot02( uplo, n, nrhs, a, lda, x, lda, work,
463  \$ lda, rwork, result( 2 ) )
464 *
465 * Check solution from generated exact solution.
466 *
467  CALL dget04( n, nrhs, x, lda, xact, lda, rcondc,
468  \$ result( 3 ) )
469  nt = 3
470 *
471 * Print information about the tests that did not pass
472 * the threshold.
473 *
474  DO 110 k = 1, nt
475  IF( result( k ).GE.thresh ) THEN
476  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
477  \$ CALL aladhd( nout, path )
478  WRITE( nout, fmt = 9999 )'DSYSV ', uplo, n,
479  \$ imat, k, result( k )
480  nfail = nfail + 1
481  END IF
482  110 CONTINUE
483  nrun = nrun + nt
484  120 CONTINUE
485  END IF
486 *
487 * --- Test DSYSVX ---
488 *
489  IF( ifact.EQ.2 )
490  \$ CALL dlaset( uplo, n, n, zero, zero, afac, lda )
491  CALL dlaset( 'Full', n, nrhs, zero, zero, x, lda )
492 *
493 * Solve the system and compute the condition number and
494 * error bounds using DSYSVX.
495 *
496  srnamt = 'DSYSVX'
497  CALL dsysvx( fact, uplo, n, nrhs, a, lda, afac, lda,
498  \$ iwork, b, lda, x, lda, rcond, rwork,
499  \$ rwork( nrhs+1 ), work, lwork,
500  \$ iwork( n+1 ), info )
501 *
502 * Adjust the expected value of INFO to account for
503 * pivoting.
504 *
505  k = izero
506  IF( k.GT.0 ) THEN
507  130 CONTINUE
508  IF( iwork( k ).LT.0 ) THEN
509  IF( iwork( k ).NE.-k ) THEN
510  k = -iwork( k )
511  GO TO 130
512  END IF
513  ELSE IF( iwork( k ).NE.k ) THEN
514  k = iwork( k )
515  GO TO 130
516  END IF
517  END IF
518 *
519 * Check the error code from DSYSVX.
520 *
521  IF( info.NE.k ) THEN
522  CALL alaerh( path, 'DSYSVX', info, k, fact // uplo,
523  \$ n, n, -1, -1, nrhs, imat, nfail,
524  \$ nerrs, nout )
525  GO TO 150
526  END IF
527 *
528  IF( info.EQ.0 ) THEN
529  IF( ifact.GE.2 ) THEN
530 *
531 * Reconstruct matrix from factors and compute
532 * residual.
533 *
534  CALL dsyt01( uplo, n, a, lda, afac, lda, iwork,
535  \$ ainv, lda, rwork( 2*nrhs+1 ),
536  \$ result( 1 ) )
537  k1 = 1
538  ELSE
539  k1 = 2
540  END IF
541 *
542 * Compute residual of the computed solution.
543 *
544  CALL dlacpy( 'Full', n, nrhs, b, lda, work, lda )
545  CALL dpot02( uplo, n, nrhs, a, lda, x, lda, work,
546  \$ lda, rwork( 2*nrhs+1 ), result( 2 ) )
547 *
548 * Check solution from generated exact solution.
549 *
550  CALL dget04( n, nrhs, x, lda, xact, lda, rcondc,
551  \$ result( 3 ) )
552 *
553 * Check the error bounds from iterative refinement.
554 *
555  CALL dpot05( uplo, n, nrhs, a, lda, b, lda, x, lda,
556  \$ xact, lda, rwork, rwork( nrhs+1 ),
557  \$ result( 4 ) )
558  ELSE
559  k1 = 6
560  END IF
561 *
562 * Compare RCOND from DSYSVX with the computed value
563 * in RCONDC.
564 *
565  result( 6 ) = dget06( rcond, rcondc )
566 *
567 * Print information about the tests that did not pass
568 * the threshold.
569 *
570  DO 140 k = k1, 6
571  IF( result( k ).GE.thresh ) THEN
572  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
573  \$ CALL aladhd( nout, path )
574  WRITE( nout, fmt = 9998 )'DSYSVX', fact, uplo,
575  \$ n, imat, k, result( k )
576  nfail = nfail + 1
577  END IF
578  140 CONTINUE
579  nrun = nrun + 7 - k1
580 *
581  150 CONTINUE
582 *
583  160 CONTINUE
584  170 CONTINUE
585  180 CONTINUE
586 *
587 * Print a summary of the results.
588 *
589  CALL alasvm( path, nout, nfail, nrun, nerrs )
590 *
591  9999 FORMAT( 1x, a, ', UPLO=''', a1, ''', N =', i5, ', type ', i2,
592  \$ ', test ', i2, ', ratio =', g12.5 )
593  9998 FORMAT( 1x, a, ', FACT=''', a1, ''', UPLO=''', a1, ''', N =', i5,
594  \$ ', type ', i2, ', test ', i2, ', ratio =', g12.5 )
595  RETURN
596 *
597 * End of DDRVSY
598 *
subroutine dlacpy(UPLO, M, N, A, LDA, B, LDB)
DLACPY copies all or part of one two-dimensional array to another.
Definition: dlacpy.f:105
subroutine dlatb4(PATH, IMAT, M, N, TYPE, KL, KU, ANORM, MODE, CNDNUM, DIST)
DLATB4
Definition: dlatb4.f:122
subroutine alasvm(TYPE, NOUT, NFAIL, NRUN, NERRS)
ALASVM
Definition: alasvm.f:75
double precision function dlansy(NORM, UPLO, N, A, LDA, WORK)
DLANSY returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric matrix.
Definition: dlansy.f:124
subroutine alaerh(PATH, SUBNAM, INFO, INFOE, OPTS, M, N, KL, KU, N5, IMAT, NFAIL, NERRS, NOUT)
ALAERH
Definition: alaerh.f:149
subroutine dsytri2(UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO)
DSYTRI2
Definition: dsytri2.f:129
subroutine dsyt01(UPLO, N, A, LDA, AFAC, LDAFAC, IPIV, C, LDC, RWORK, RESID)
DSYT01
Definition: dsyt01.f:126
subroutine dlarhs(PATH, XTYPE, UPLO, TRANS, M, N, KL, KU, NRHS, A, LDA, X, LDX, B, LDB, ISEED, INFO)
DLARHS
Definition: dlarhs.f:206
subroutine dlatms(M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX, KL, KU, PACK, A, LDA, WORK, INFO)
DLATMS
Definition: dlatms.f:323
subroutine dpot05(UPLO, N, NRHS, A, LDA, B, LDB, X, LDX, XACT, LDXACT, FERR, BERR, RESLTS)
DPOT05
Definition: dpot05.f:166
subroutine dsysv(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, LWORK, INFO)
DSYSV computes the solution to system of linear equations A * X = B for SY matrices ...
Definition: dsysv.f:173
subroutine dlaset(UPLO, M, N, ALPHA, BETA, A, LDA)
DLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values...
Definition: dlaset.f:112
subroutine xlaenv(ISPEC, NVALUE)
XLAENV
Definition: xlaenv.f:83
subroutine dget04(N, NRHS, X, LDX, XACT, LDXACT, RCOND, RESID)
DGET04
Definition: dget04.f:104
subroutine derrvx(PATH, NUNIT)
DERRVX
Definition: derrvx.f:57
subroutine dsytrf(UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO)
DSYTRF
Definition: dsytrf.f:184
double precision function dget06(RCOND, RCONDC)
DGET06
Definition: dget06.f:57
subroutine dsysvx(FACT, UPLO, N, NRHS, A, LDA, AF, LDAF, IPIV, B, LDB, X, LDX, RCOND, FERR, BERR, WORK, LWORK, IWORK, INFO)
DSYSVX computes the solution to system of linear equations A * X = B for SY matrices ...
Definition: dsysvx.f:286
subroutine dpot02(UPLO, N, NRHS, A, LDA, X, LDX, B, LDB, RWORK, RESID)
DPOT02
Definition: dpot02.f:129
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