LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
 subroutine zdrvhe ( logical, dimension( * ) DOTYPE, integer NN, integer, dimension( * ) NVAL, integer NRHS, double precision THRESH, logical TSTERR, integer NMAX, complex*16, dimension( * ) A, complex*16, dimension( * ) AFAC, complex*16, dimension( * ) AINV, complex*16, dimension( * ) B, complex*16, dimension( * ) X, complex*16, dimension( * ) XACT, complex*16, dimension( * ) WORK, double precision, dimension( * ) RWORK, integer, dimension( * ) IWORK, integer NOUT )

ZDRVHE

ZDRVHEX

Purpose:
` ZDRVHE tests the driver routines ZHESV 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 COMPLEX*16 array, dimension (NMAX*NMAX)` [out] AFAC ` AFAC is COMPLEX*16 array, dimension (NMAX*NMAX)` [out] AINV ` AINV is COMPLEX*16 array, dimension (NMAX*NMAX)` [out] B ` B is COMPLEX*16 array, dimension (NMAX*NRHS)` [out] X ` X is COMPLEX*16 array, dimension (NMAX*NRHS)` [out] XACT ` XACT is COMPLEX*16 array, dimension (NMAX*NRHS)` [out] WORK ` WORK is COMPLEX*16 array, dimension (NMAX*max(2,NRHS))` [out] RWORK ` RWORK is DOUBLE PRECISION array, dimension (NMAX+2*NRHS)` [out] IWORK ` IWORK is INTEGER array, dimension (NMAX)` [in] NOUT ``` NOUT is INTEGER The unit number for output.```
Date
November 2013
Purpose:
``` ZDRVHE tests the driver routines ZHESV, -SVX, and -SVXX.

Note that this file is used only when the XBLAS are available,
otherwise zdrvhe.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 COMPLEX*16 array, dimension (NMAX*NMAX)` [out] AFAC ` AFAC is COMPLEX*16 array, dimension (NMAX*NMAX)` [out] AINV ` AINV is COMPLEX*16 array, dimension (NMAX*NMAX)` [out] B ` B is COMPLEX*16 array, dimension (NMAX*NRHS)` [out] X ` X is COMPLEX*16 array, dimension (NMAX*NRHS)` [out] XACT ` XACT is COMPLEX*16 array, dimension (NMAX*NRHS)` [out] WORK ``` WORK is COMPLEX*16 array, dimension (NMAX*max(2,NRHS))``` [out] RWORK ` RWORK is DOUBLE PRECISION array, dimension (2*NMAX+2*NRHS)` [out] IWORK ` IWORK is INTEGER array, dimension (NMAX)` [in] NOUT ``` NOUT is INTEGER The unit number for output.```
Date
April 2012

Definition at line 155 of file zdrvhe.f.

155 *
156 * -- LAPACK test routine (version 3.5.0) --
157 * -- LAPACK is a software package provided by Univ. of Tennessee, --
158 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
159 * November 2013
160 *
161 * .. Scalar Arguments ..
162  LOGICAL tsterr
163  INTEGER nmax, nn, nout, nrhs
164  DOUBLE PRECISION thresh
165 * ..
166 * .. Array Arguments ..
167  LOGICAL dotype( * )
168  INTEGER iwork( * ), nval( * )
169  DOUBLE PRECISION rwork( * )
170  COMPLEX*16 a( * ), afac( * ), ainv( * ), b( * ),
171  \$ work( * ), x( * ), xact( * )
172 * ..
173 *
174 * =====================================================================
175 *
176 * .. Parameters ..
177  DOUBLE PRECISION one, zero
178  parameter ( one = 1.0d+0, zero = 0.0d+0 )
179  INTEGER ntypes, ntests
180  parameter ( ntypes = 10, ntests = 6 )
181  INTEGER nfact
182  parameter ( nfact = 2 )
183 * ..
184 * .. Local Scalars ..
185  LOGICAL zerot
186  CHARACTER dist, fact, TYPE, uplo, xtype
187  CHARACTER*3 path
188  INTEGER i, i1, i2, ifact, imat, in, info, ioff, iuplo,
189  \$ izero, j, k, k1, kl, ku, lda, lwork, mode, n,
190  \$ nb, nbmin, nerrs, nfail, nimat, nrun, nt
191  DOUBLE PRECISION ainvnm, anorm, cndnum, rcond, rcondc
192 * ..
193 * .. Local Arrays ..
194  CHARACTER facts( nfact ), uplos( 2 )
195  INTEGER iseed( 4 ), iseedy( 4 )
196  DOUBLE PRECISION result( ntests )
197 * ..
198 * .. External Functions ..
199  DOUBLE PRECISION dget06, zlanhe
200  EXTERNAL dget06, zlanhe
201 * ..
202 * .. External Subroutines ..
203  EXTERNAL aladhd, alaerh, alasvm, xlaenv, zerrvx, zget04,
206  \$ zpot05
207 * ..
208 * .. Scalars in Common ..
209  LOGICAL lerr, ok
210  CHARACTER*32 srnamt
211  INTEGER infot, nunit
212 * ..
213 * .. Common blocks ..
214  COMMON / infoc / infot, nunit, ok, lerr
215  COMMON / srnamc / srnamt
216 * ..
217 * .. Intrinsic Functions ..
218  INTRINSIC dcmplx, max, min
219 * ..
220 * .. Data statements ..
221  DATA iseedy / 1988, 1989, 1990, 1991 /
222  DATA uplos / 'U', 'L' / , facts / 'F', 'N' /
223 * ..
224 * .. Executable Statements ..
225 *
226 * Initialize constants and the random number seed.
227 *
228  path( 1: 1 ) = 'Zomplex precision'
229  path( 2: 3 ) = 'HE'
230  nrun = 0
231  nfail = 0
232  nerrs = 0
233  DO 10 i = 1, 4
234  iseed( i ) = iseedy( i )
235  10 CONTINUE
236  lwork = max( 2*nmax, nmax*nrhs )
237 *
238 * Test the error exits
239 *
240  IF( tsterr )
241  \$ CALL zerrvx( path, nout )
242  infot = 0
243 *
244 * Set the block size and minimum block size for testing.
245 *
246  nb = 1
247  nbmin = 2
248  CALL xlaenv( 1, nb )
249  CALL xlaenv( 2, nbmin )
250 *
251 * Do for each value of N in NVAL
252 *
253  DO 180 in = 1, nn
254  n = nval( in )
255  lda = max( n, 1 )
256  xtype = 'N'
257  nimat = ntypes
258  IF( n.LE.0 )
259  \$ nimat = 1
260 *
261  DO 170 imat = 1, nimat
262 *
263 * Do the tests only if DOTYPE( IMAT ) is true.
264 *
265  IF( .NOT.dotype( imat ) )
266  \$ GO TO 170
267 *
268 * Skip types 3, 4, 5, or 6 if the matrix size is too small.
269 *
270  zerot = imat.GE.3 .AND. imat.LE.6
271  IF( zerot .AND. n.LT.imat-2 )
272  \$ GO TO 170
273 *
274 * Do first for UPLO = 'U', then for UPLO = 'L'
275 *
276  DO 160 iuplo = 1, 2
277  uplo = uplos( iuplo )
278 *
279 * Set up parameters with ZLATB4 and generate a test matrix
280 * with ZLATMS.
281 *
282  CALL zlatb4( path, imat, n, n, TYPE, kl, ku, anorm, mode,
283  \$ cndnum, dist )
284 *
285  srnamt = 'ZLATMS'
286  CALL zlatms( n, n, dist, iseed, TYPE, rwork, mode,
287  \$ cndnum, anorm, kl, ku, uplo, a, lda, work,
288  \$ info )
289 *
290 * Check error code from ZLATMS.
291 *
292  IF( info.NE.0 ) THEN
293  CALL alaerh( path, 'ZLATMS', info, 0, uplo, n, n, -1,
294  \$ -1, -1, imat, nfail, nerrs, nout )
295  GO TO 160
296  END IF
297 *
298 * For types 3-6, zero one or more rows and columns of the
299 * matrix to test that INFO is returned correctly.
300 *
301  IF( zerot ) THEN
302  IF( imat.EQ.3 ) THEN
303  izero = 1
304  ELSE IF( imat.EQ.4 ) THEN
305  izero = n
306  ELSE
307  izero = n / 2 + 1
308  END IF
309 *
310  IF( imat.LT.6 ) THEN
311 *
312 * Set row and column IZERO to zero.
313 *
314  IF( iuplo.EQ.1 ) THEN
315  ioff = ( izero-1 )*lda
316  DO 20 i = 1, izero - 1
317  a( ioff+i ) = zero
318  20 CONTINUE
319  ioff = ioff + izero
320  DO 30 i = izero, n
321  a( ioff ) = zero
322  ioff = ioff + lda
323  30 CONTINUE
324  ELSE
325  ioff = izero
326  DO 40 i = 1, izero - 1
327  a( ioff ) = zero
328  ioff = ioff + lda
329  40 CONTINUE
330  ioff = ioff - izero
331  DO 50 i = izero, n
332  a( ioff+i ) = zero
333  50 CONTINUE
334  END IF
335  ELSE
336  ioff = 0
337  IF( iuplo.EQ.1 ) THEN
338 *
339 * Set the first IZERO rows and columns to zero.
340 *
341  DO 70 j = 1, n
342  i2 = min( j, izero )
343  DO 60 i = 1, i2
344  a( ioff+i ) = zero
345  60 CONTINUE
346  ioff = ioff + lda
347  70 CONTINUE
348  ELSE
349 *
350 * Set the last IZERO rows and columns to zero.
351 *
352  DO 90 j = 1, n
353  i1 = max( j, izero )
354  DO 80 i = i1, n
355  a( ioff+i ) = zero
356  80 CONTINUE
357  ioff = ioff + lda
358  90 CONTINUE
359  END IF
360  END IF
361  ELSE
362  izero = 0
363  END IF
364 *
365 * Set the imaginary part of the diagonals.
366 *
367  CALL zlaipd( n, a, lda+1, 0 )
368 *
369  DO 150 ifact = 1, nfact
370 *
371 * Do first for FACT = 'F', then for other values.
372 *
373  fact = facts( ifact )
374 *
375 * Compute the condition number for comparison with
376 * the value returned by ZHESVX.
377 *
378  IF( zerot ) THEN
379  IF( ifact.EQ.1 )
380  \$ GO TO 150
381  rcondc = zero
382 *
383  ELSE IF( ifact.EQ.1 ) THEN
384 *
385 * Compute the 1-norm of A.
386 *
387  anorm = zlanhe( '1', uplo, n, a, lda, rwork )
388 *
389 * Factor the matrix A.
390 *
391  CALL zlacpy( uplo, n, n, a, lda, afac, lda )
392  CALL zhetrf( uplo, n, afac, lda, iwork, work,
393  \$ lwork, info )
394 *
395 * Compute inv(A) and take its norm.
396 *
397  CALL zlacpy( uplo, n, n, afac, lda, ainv, lda )
398  lwork = (n+nb+1)*(nb+3)
399  CALL zhetri2( uplo, n, ainv, lda, iwork, work,
400  \$ lwork, info )
401  ainvnm = zlanhe( '1', uplo, n, ainv, lda, rwork )
402 *
403 * Compute the 1-norm condition number of A.
404 *
405  IF( anorm.LE.zero .OR. ainvnm.LE.zero ) THEN
406  rcondc = one
407  ELSE
408  rcondc = ( one / anorm ) / ainvnm
409  END IF
410  END IF
411 *
412 * Form an exact solution and set the right hand side.
413 *
414  srnamt = 'ZLARHS'
415  CALL zlarhs( path, xtype, uplo, ' ', n, n, kl, ku,
416  \$ nrhs, a, lda, xact, lda, b, lda, iseed,
417  \$ info )
418  xtype = 'C'
419 *
420 * --- Test ZHESV ---
421 *
422  IF( ifact.EQ.2 ) THEN
423  CALL zlacpy( uplo, n, n, a, lda, afac, lda )
424  CALL zlacpy( 'Full', n, nrhs, b, lda, x, lda )
425 *
426 * Factor the matrix and solve the system using ZHESV.
427 *
428  srnamt = 'ZHESV '
429  CALL zhesv( uplo, n, nrhs, afac, lda, iwork, x,
430  \$ lda, work, lwork, info )
431 *
432 * Adjust the expected value of INFO to account for
433 * pivoting.
434 *
435  k = izero
436  IF( k.GT.0 ) THEN
437  100 CONTINUE
438  IF( iwork( k ).LT.0 ) THEN
439  IF( iwork( k ).NE.-k ) THEN
440  k = -iwork( k )
441  GO TO 100
442  END IF
443  ELSE IF( iwork( k ).NE.k ) THEN
444  k = iwork( k )
445  GO TO 100
446  END IF
447  END IF
448 *
449 * Check error code from ZHESV .
450 *
451  IF( info.NE.k ) THEN
452  CALL alaerh( path, 'ZHESV ', info, k, uplo, n,
453  \$ n, -1, -1, nrhs, imat, nfail,
454  \$ nerrs, nout )
455  GO TO 120
456  ELSE IF( info.NE.0 ) THEN
457  GO TO 120
458  END IF
459 *
460 * Reconstruct matrix from factors and compute
461 * residual.
462 *
463  CALL zhet01( uplo, n, a, lda, afac, lda, iwork,
464  \$ ainv, lda, rwork, result( 1 ) )
465 *
466 * Compute residual of the computed solution.
467 *
468  CALL zlacpy( 'Full', n, nrhs, b, lda, work, lda )
469  CALL zpot02( uplo, n, nrhs, a, lda, x, lda, work,
470  \$ lda, rwork, result( 2 ) )
471 *
472 * Check solution from generated exact solution.
473 *
474  CALL zget04( n, nrhs, x, lda, xact, lda, rcondc,
475  \$ result( 3 ) )
476  nt = 3
477 *
478 * Print information about the tests that did not pass
479 * the threshold.
480 *
481  DO 110 k = 1, nt
482  IF( result( k ).GE.thresh ) THEN
483  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
484  \$ CALL aladhd( nout, path )
485  WRITE( nout, fmt = 9999 )'ZHESV ', uplo, n,
486  \$ imat, k, result( k )
487  nfail = nfail + 1
488  END IF
489  110 CONTINUE
490  nrun = nrun + nt
491  120 CONTINUE
492  END IF
493 *
494 * --- Test ZHESVX ---
495 *
496  IF( ifact.EQ.2 )
497  \$ CALL zlaset( uplo, n, n, dcmplx( zero ),
498  \$ dcmplx( zero ), afac, lda )
499  CALL zlaset( 'Full', n, nrhs, dcmplx( zero ),
500  \$ dcmplx( zero ), x, lda )
501 *
502 * Solve the system and compute the condition number and
503 * error bounds using ZHESVX.
504 *
505  srnamt = 'ZHESVX'
506  CALL zhesvx( fact, uplo, n, nrhs, a, lda, afac, lda,
507  \$ iwork, b, lda, x, lda, rcond, rwork,
508  \$ rwork( nrhs+1 ), work, lwork,
509  \$ rwork( 2*nrhs+1 ), info )
510 *
511 * Adjust the expected value of INFO to account for
512 * pivoting.
513 *
514  k = izero
515  IF( k.GT.0 ) THEN
516  130 CONTINUE
517  IF( iwork( k ).LT.0 ) THEN
518  IF( iwork( k ).NE.-k ) THEN
519  k = -iwork( k )
520  GO TO 130
521  END IF
522  ELSE IF( iwork( k ).NE.k ) THEN
523  k = iwork( k )
524  GO TO 130
525  END IF
526  END IF
527 *
528 * Check the error code from ZHESVX.
529 *
530  IF( info.NE.k ) THEN
531  CALL alaerh( path, 'ZHESVX', info, k, fact // uplo,
532  \$ n, n, -1, -1, nrhs, imat, nfail,
533  \$ nerrs, nout )
534  GO TO 150
535  END IF
536 *
537  IF( info.EQ.0 ) THEN
538  IF( ifact.GE.2 ) THEN
539 *
540 * Reconstruct matrix from factors and compute
541 * residual.
542 *
543  CALL zhet01( uplo, n, a, lda, afac, lda, iwork,
544  \$ ainv, lda, rwork( 2*nrhs+1 ),
545  \$ result( 1 ) )
546  k1 = 1
547  ELSE
548  k1 = 2
549  END IF
550 *
551 * Compute residual of the computed solution.
552 *
553  CALL zlacpy( 'Full', n, nrhs, b, lda, work, lda )
554  CALL zpot02( uplo, n, nrhs, a, lda, x, lda, work,
555  \$ lda, rwork( 2*nrhs+1 ), result( 2 ) )
556 *
557 * Check solution from generated exact solution.
558 *
559  CALL zget04( n, nrhs, x, lda, xact, lda, rcondc,
560  \$ result( 3 ) )
561 *
562 * Check the error bounds from iterative refinement.
563 *
564  CALL zpot05( uplo, n, nrhs, a, lda, b, lda, x, lda,
565  \$ xact, lda, rwork, rwork( nrhs+1 ),
566  \$ result( 4 ) )
567  ELSE
568  k1 = 6
569  END IF
570 *
571 * Compare RCOND from ZHESVX with the computed value
572 * in RCONDC.
573 *
574  result( 6 ) = dget06( rcond, rcondc )
575 *
576 * Print information about the tests that did not pass
577 * the threshold.
578 *
579  DO 140 k = k1, 6
580  IF( result( k ).GE.thresh ) THEN
581  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
582  \$ CALL aladhd( nout, path )
583  WRITE( nout, fmt = 9998 )'ZHESVX', fact, uplo,
584  \$ n, imat, k, result( k )
585  nfail = nfail + 1
586  END IF
587  140 CONTINUE
588  nrun = nrun + 7 - k1
589 *
590  150 CONTINUE
591 *
592  160 CONTINUE
593  170 CONTINUE
594  180 CONTINUE
595 *
596 * Print a summary of the results.
597 *
598  CALL alasvm( path, nout, nfail, nrun, nerrs )
599 *
600  9999 FORMAT( 1x, a, ', UPLO=''', a1, ''', N =', i5, ', type ', i2,
601  \$ ', test ', i2, ', ratio =', g12.5 )
602  9998 FORMAT( 1x, a, ', FACT=''', a1, ''', UPLO=''', a1, ''', N =', i5,
603  \$ ', type ', i2, ', test ', i2, ', ratio =', g12.5 )
604  RETURN
605 *
606 * End of ZDRVHE
607 *
subroutine alasvm(TYPE, NOUT, NFAIL, NRUN, NERRS)
ALASVM
Definition: alasvm.f:75
subroutine alaerh(PATH, SUBNAM, INFO, INFOE, OPTS, M, N, KL, KU, N5, IMAT, NFAIL, NERRS, NOUT)
ALAERH
Definition: alaerh.f:149
subroutine zhetri2(UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO)
ZHETRI2
Definition: zhetri2.f:129
subroutine zlacpy(UPLO, M, N, A, LDA, B, LDB)
ZLACPY copies all or part of one two-dimensional array to another.
Definition: zlacpy.f:105
subroutine zget04(N, NRHS, X, LDX, XACT, LDXACT, RCOND, RESID)
ZGET04
Definition: zget04.f:104
subroutine zpot02(UPLO, N, NRHS, A, LDA, X, LDX, B, LDB, RWORK, RESID)
ZPOT02
Definition: zpot02.f:129
double precision function zlanhe(NORM, UPLO, N, A, LDA, WORK)
ZLANHE returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex Hermitian matrix.
Definition: zlanhe.f:126
subroutine zlarhs(PATH, XTYPE, UPLO, TRANS, M, N, KL, KU, NRHS, A, LDA, X, LDX, B, LDB, ISEED, INFO)
ZLARHS
Definition: zlarhs.f:211
subroutine zhet01(UPLO, N, A, LDA, AFAC, LDAFAC, IPIV, C, LDC, RWORK, RESID)
ZHET01
Definition: zhet01.f:128
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:108
subroutine xlaenv(ISPEC, NVALUE)
XLAENV
Definition: xlaenv.f:83
subroutine zlatb4(PATH, IMAT, M, N, TYPE, KL, KU, ANORM, MODE, CNDNUM, DIST)
ZLATB4
Definition: zlatb4.f:123
subroutine zhesv(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, LWORK, INFO)
ZHESV computes the solution to system of linear equations A * X = B for HE matrices ...
Definition: zhesv.f:173
subroutine zlaipd(N, A, INDA, VINDA)
ZLAIPD
Definition: zlaipd.f:85
subroutine zhetrf(UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO)
ZHETRF
Definition: zhetrf.f:179
double precision function dget06(RCOND, RCONDC)
DGET06
Definition: dget06.f:57
subroutine zerrvx(PATH, NUNIT)
ZERRVX
Definition: zerrvx.f:57
subroutine zhesvx(FACT, UPLO, N, NRHS, A, LDA, AF, LDAF, IPIV, B, LDB, X, LDX, RCOND, FERR, BERR, WORK, LWORK, RWORK, INFO)
ZHESVX computes the solution to system of linear equations A * X = B for HE matrices ...
Definition: zhesvx.f:287
subroutine zlatms(M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX, KL, KU, PACK, A, LDA, WORK, INFO)
ZLATMS
Definition: zlatms.f:334
subroutine zpot05(UPLO, N, NRHS, A, LDA, B, LDB, X, LDX, XACT, LDXACT, FERR, BERR, RESLTS)
ZPOT05
Definition: zpot05.f:167

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