LAPACK  3.8.0 LAPACK: Linear Algebra PACKage

## ◆ zdrvsp()

 subroutine zdrvsp ( 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 )

ZDRVSP

Purpose:
` ZDRVSP tests the driver routines ZSPSV 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+1)/2)``` [out] AFAC ``` AFAC is COMPLEX*16 array, dimension (NMAX*(NMAX+1)/2)``` [out] AINV ``` AINV is COMPLEX*16 array, dimension (NMAX*(NMAX+1)/2)``` [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
December 2016

Definition at line 159 of file zdrvsp.f.

159 *
160 * -- LAPACK test routine (version 3.7.0) --
161 * -- LAPACK is a software package provided by Univ. of Tennessee, --
162 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
163 * December 2016
164 *
165 * .. Scalar Arguments ..
166  LOGICAL tsterr
167  INTEGER nmax, nn, nout, nrhs
168  DOUBLE PRECISION thresh
169 * ..
170 * .. Array Arguments ..
171  LOGICAL dotype( * )
172  INTEGER iwork( * ), nval( * )
173  DOUBLE PRECISION rwork( * )
174  COMPLEX*16 a( * ), afac( * ), ainv( * ), b( * ),
175  \$ work( * ), x( * ), xact( * )
176 * ..
177 *
178 * =====================================================================
179 *
180 * .. Parameters ..
181  DOUBLE PRECISION one, zero
182  parameter( one = 1.0d+0, zero = 0.0d+0 )
183  INTEGER ntypes, ntests
184  parameter( ntypes = 11, ntests = 6 )
185  INTEGER nfact
186  parameter( nfact = 2 )
187 * ..
188 * .. Local Scalars ..
189  LOGICAL zerot
190  CHARACTER dist, fact, packit, TYPE, uplo, xtype
191  CHARACTER*3 path
192  INTEGER i, i1, i2, ifact, imat, in, info, ioff, iuplo,
193  \$ izero, j, k, k1, kl, ku, lda, mode, n, nb,
194  \$ nbmin, nerrs, nfail, nimat, npp, nrun, nt
195  DOUBLE PRECISION ainvnm, anorm, cndnum, rcond, rcondc
196 * ..
197 * .. Local Arrays ..
198  CHARACTER facts( nfact )
199  INTEGER iseed( 4 ), iseedy( 4 )
200  DOUBLE PRECISION result( ntests )
201 * ..
202 * .. External Functions ..
203  DOUBLE PRECISION dget06, zlansp
204  EXTERNAL dget06, zlansp
205 * ..
206 * .. External Subroutines ..
207  EXTERNAL aladhd, alaerh, alasvm, xlaenv, zcopy, zerrvx,
210  \$ zsptrf, zsptri
211 * ..
212 * .. Scalars in Common ..
213  LOGICAL lerr, ok
214  CHARACTER*32 srnamt
215  INTEGER infot, nunit
216 * ..
217 * .. Common blocks ..
218  COMMON / infoc / infot, nunit, ok, lerr
219  COMMON / srnamc / srnamt
220 * ..
221 * .. Intrinsic Functions ..
222  INTRINSIC dcmplx, max, min
223 * ..
224 * .. Data statements ..
225  DATA iseedy / 1988, 1989, 1990, 1991 /
226  DATA facts / 'F', 'N' /
227 * ..
228 * .. Executable Statements ..
229 *
230 * Initialize constants and the random number seed.
231 *
232  path( 1: 1 ) = 'Zomplex precision'
233  path( 2: 3 ) = 'SP'
234  nrun = 0
235  nfail = 0
236  nerrs = 0
237  DO 10 i = 1, 4
238  iseed( i ) = iseedy( i )
239  10 CONTINUE
240 *
241 * Test the error exits
242 *
243  IF( tsterr )
244  \$ CALL zerrvx( path, nout )
245  infot = 0
246 *
247 * Set the block size and minimum block size for testing.
248 *
249  nb = 1
250  nbmin = 2
251  CALL xlaenv( 1, nb )
252  CALL xlaenv( 2, nbmin )
253 *
254 * Do for each value of N in NVAL
255 *
256  DO 180 in = 1, nn
257  n = nval( in )
258  lda = max( n, 1 )
259  npp = n*( n+1 ) / 2
260  xtype = 'N'
261  nimat = ntypes
262  IF( n.LE.0 )
263  \$ nimat = 1
264 *
265  DO 170 imat = 1, nimat
266 *
267 * Do the tests only if DOTYPE( IMAT ) is true.
268 *
269  IF( .NOT.dotype( imat ) )
270  \$ GO TO 170
271 *
272 * Skip types 3, 4, 5, or 6 if the matrix size is too small.
273 *
274  zerot = imat.GE.3 .AND. imat.LE.6
275  IF( zerot .AND. n.LT.imat-2 )
276  \$ GO TO 170
277 *
278 * Do first for UPLO = 'U', then for UPLO = 'L'
279 *
280  DO 160 iuplo = 1, 2
281  IF( iuplo.EQ.1 ) THEN
282  uplo = 'U'
283  packit = 'C'
284  ELSE
285  uplo = 'L'
286  packit = 'R'
287  END IF
288 *
289  IF( imat.NE.ntypes ) THEN
290 *
291 * Set up parameters with ZLATB4 and generate a test
292 * matrix with ZLATMS.
293 *
294  CALL zlatb4( path, imat, n, n, TYPE, kl, ku, anorm,
295  \$ mode, cndnum, dist )
296 *
297  srnamt = 'ZLATMS'
298  CALL zlatms( n, n, dist, iseed, TYPE, rwork, mode,
299  \$ cndnum, anorm, kl, ku, packit, a, lda,
300  \$ work, info )
301 *
302 * Check error code from ZLATMS.
303 *
304  IF( info.NE.0 ) THEN
305  CALL alaerh( path, 'ZLATMS', info, 0, uplo, n, n,
306  \$ -1, -1, -1, imat, nfail, nerrs, nout )
307  GO TO 160
308  END IF
309 *
310 * For types 3-6, zero one or more rows and columns of
311 * the matrix to test that INFO is returned correctly.
312 *
313  IF( zerot ) THEN
314  IF( imat.EQ.3 ) THEN
315  izero = 1
316  ELSE IF( imat.EQ.4 ) THEN
317  izero = n
318  ELSE
319  izero = n / 2 + 1
320  END IF
321 *
322  IF( imat.LT.6 ) THEN
323 *
324 * Set row and column IZERO to zero.
325 *
326  IF( iuplo.EQ.1 ) THEN
327  ioff = ( izero-1 )*izero / 2
328  DO 20 i = 1, izero - 1
329  a( ioff+i ) = zero
330  20 CONTINUE
331  ioff = ioff + izero
332  DO 30 i = izero, n
333  a( ioff ) = zero
334  ioff = ioff + i
335  30 CONTINUE
336  ELSE
337  ioff = izero
338  DO 40 i = 1, izero - 1
339  a( ioff ) = zero
340  ioff = ioff + n - i
341  40 CONTINUE
342  ioff = ioff - izero
343  DO 50 i = izero, n
344  a( ioff+i ) = zero
345  50 CONTINUE
346  END IF
347  ELSE
348  IF( iuplo.EQ.1 ) THEN
349 *
350 * Set the first IZERO rows and columns to zero.
351 *
352  ioff = 0
353  DO 70 j = 1, n
354  i2 = min( j, izero )
355  DO 60 i = 1, i2
356  a( ioff+i ) = zero
357  60 CONTINUE
358  ioff = ioff + j
359  70 CONTINUE
360  ELSE
361 *
362 * Set the last IZERO rows and columns to zero.
363 *
364  ioff = 0
365  DO 90 j = 1, n
366  i1 = max( j, izero )
367  DO 80 i = i1, n
368  a( ioff+i ) = zero
369  80 CONTINUE
370  ioff = ioff + n - j
371  90 CONTINUE
372  END IF
373  END IF
374  ELSE
375  izero = 0
376  END IF
377  ELSE
378 *
379 * Use a special block diagonal matrix to test alternate
380 * code for the 2-by-2 blocks.
381 *
382  CALL zlatsp( uplo, n, a, iseed )
383  END IF
384 *
385  DO 150 ifact = 1, nfact
386 *
387 * Do first for FACT = 'F', then for other values.
388 *
389  fact = facts( ifact )
390 *
391 * Compute the condition number for comparison with
392 * the value returned by ZSPSVX.
393 *
394  IF( zerot ) THEN
395  IF( ifact.EQ.1 )
396  \$ GO TO 150
397  rcondc = zero
398 *
399  ELSE IF( ifact.EQ.1 ) THEN
400 *
401 * Compute the 1-norm of A.
402 *
403  anorm = zlansp( '1', uplo, n, a, rwork )
404 *
405 * Factor the matrix A.
406 *
407  CALL zcopy( npp, a, 1, afac, 1 )
408  CALL zsptrf( uplo, n, afac, iwork, info )
409 *
410 * Compute inv(A) and take its norm.
411 *
412  CALL zcopy( npp, afac, 1, ainv, 1 )
413  CALL zsptri( uplo, n, ainv, iwork, work, info )
414  ainvnm = zlansp( '1', uplo, n, ainv, rwork )
415 *
416 * Compute the 1-norm condition number of A.
417 *
418  IF( anorm.LE.zero .OR. ainvnm.LE.zero ) THEN
419  rcondc = one
420  ELSE
421  rcondc = ( one / anorm ) / ainvnm
422  END IF
423  END IF
424 *
425 * Form an exact solution and set the right hand side.
426 *
427  srnamt = 'ZLARHS'
428  CALL zlarhs( path, xtype, uplo, ' ', n, n, kl, ku,
429  \$ nrhs, a, lda, xact, lda, b, lda, iseed,
430  \$ info )
431  xtype = 'C'
432 *
433 * --- Test ZSPSV ---
434 *
435  IF( ifact.EQ.2 ) THEN
436  CALL zcopy( npp, a, 1, afac, 1 )
437  CALL zlacpy( 'Full', n, nrhs, b, lda, x, lda )
438 *
439 * Factor the matrix and solve the system using ZSPSV.
440 *
441  srnamt = 'ZSPSV '
442  CALL zspsv( uplo, n, nrhs, afac, iwork, x, lda,
443  \$ info )
444 *
445 * Adjust the expected value of INFO to account for
446 * pivoting.
447 *
448  k = izero
449  IF( k.GT.0 ) THEN
450  100 CONTINUE
451  IF( iwork( k ).LT.0 ) THEN
452  IF( iwork( k ).NE.-k ) THEN
453  k = -iwork( k )
454  GO TO 100
455  END IF
456  ELSE IF( iwork( k ).NE.k ) THEN
457  k = iwork( k )
458  GO TO 100
459  END IF
460  END IF
461 *
462 * Check error code from ZSPSV .
463 *
464  IF( info.NE.k ) THEN
465  CALL alaerh( path, 'ZSPSV ', info, k, uplo, n,
466  \$ n, -1, -1, nrhs, imat, nfail,
467  \$ nerrs, nout )
468  GO TO 120
469  ELSE IF( info.NE.0 ) THEN
470  GO TO 120
471  END IF
472 *
473 * Reconstruct matrix from factors and compute
474 * residual.
475 *
476  CALL zspt01( uplo, n, a, afac, iwork, ainv, lda,
477  \$ rwork, result( 1 ) )
478 *
479 * Compute residual of the computed solution.
480 *
481  CALL zlacpy( 'Full', n, nrhs, b, lda, work, lda )
482  CALL zspt02( uplo, n, nrhs, a, x, lda, work, lda,
483  \$ rwork, result( 2 ) )
484 *
485 * Check solution from generated exact solution.
486 *
487  CALL zget04( n, nrhs, x, lda, xact, lda, rcondc,
488  \$ result( 3 ) )
489  nt = 3
490 *
491 * Print information about the tests that did not pass
492 * the threshold.
493 *
494  DO 110 k = 1, nt
495  IF( result( k ).GE.thresh ) THEN
496  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
497  \$ CALL aladhd( nout, path )
498  WRITE( nout, fmt = 9999 )'ZSPSV ', uplo, n,
499  \$ imat, k, result( k )
500  nfail = nfail + 1
501  END IF
502  110 CONTINUE
503  nrun = nrun + nt
504  120 CONTINUE
505  END IF
506 *
507 * --- Test ZSPSVX ---
508 *
509  IF( ifact.EQ.2 .AND. npp.GT.0 )
510  \$ CALL zlaset( 'Full', npp, 1, dcmplx( zero ),
511  \$ dcmplx( zero ), afac, npp )
512  CALL zlaset( 'Full', n, nrhs, dcmplx( zero ),
513  \$ dcmplx( zero ), x, lda )
514 *
515 * Solve the system and compute the condition number and
516 * error bounds using ZSPSVX.
517 *
518  srnamt = 'ZSPSVX'
519  CALL zspsvx( fact, uplo, n, nrhs, a, afac, iwork, b,
520  \$ lda, x, lda, rcond, rwork,
521  \$ rwork( nrhs+1 ), work, rwork( 2*nrhs+1 ),
522  \$ info )
523 *
524 * Adjust the expected value of INFO to account for
525 * pivoting.
526 *
527  k = izero
528  IF( k.GT.0 ) THEN
529  130 CONTINUE
530  IF( iwork( k ).LT.0 ) THEN
531  IF( iwork( k ).NE.-k ) THEN
532  k = -iwork( k )
533  GO TO 130
534  END IF
535  ELSE IF( iwork( k ).NE.k ) THEN
536  k = iwork( k )
537  GO TO 130
538  END IF
539  END IF
540 *
541 * Check the error code from ZSPSVX.
542 *
543  IF( info.NE.k ) THEN
544  CALL alaerh( path, 'ZSPSVX', info, k, fact // uplo,
545  \$ n, n, -1, -1, nrhs, imat, nfail,
546  \$ nerrs, nout )
547  GO TO 150
548  END IF
549 *
550  IF( info.EQ.0 ) THEN
551  IF( ifact.GE.2 ) THEN
552 *
553 * Reconstruct matrix from factors and compute
554 * residual.
555 *
556  CALL zspt01( uplo, n, a, afac, iwork, ainv, lda,
557  \$ rwork( 2*nrhs+1 ), result( 1 ) )
558  k1 = 1
559  ELSE
560  k1 = 2
561  END IF
562 *
563 * Compute residual of the computed solution.
564 *
565  CALL zlacpy( 'Full', n, nrhs, b, lda, work, lda )
566  CALL zspt02( uplo, n, nrhs, a, x, lda, work, lda,
567  \$ rwork( 2*nrhs+1 ), result( 2 ) )
568 *
569 * Check solution from generated exact solution.
570 *
571  CALL zget04( n, nrhs, x, lda, xact, lda, rcondc,
572  \$ result( 3 ) )
573 *
574 * Check the error bounds from iterative refinement.
575 *
576  CALL zppt05( uplo, n, nrhs, a, b, lda, x, lda,
577  \$ xact, lda, rwork, rwork( nrhs+1 ),
578  \$ result( 4 ) )
579  ELSE
580  k1 = 6
581  END IF
582 *
583 * Compare RCOND from ZSPSVX with the computed value
584 * in RCONDC.
585 *
586  result( 6 ) = dget06( rcond, rcondc )
587 *
588 * Print information about the tests that did not pass
589 * the threshold.
590 *
591  DO 140 k = k1, 6
592  IF( result( k ).GE.thresh ) THEN
593  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
594  \$ CALL aladhd( nout, path )
595  WRITE( nout, fmt = 9998 )'ZSPSVX', fact, uplo,
596  \$ n, imat, k, result( k )
597  nfail = nfail + 1
598  END IF
599  140 CONTINUE
600  nrun = nrun + 7 - k1
601 *
602  150 CONTINUE
603 *
604  160 CONTINUE
605  170 CONTINUE
606  180 CONTINUE
607 *
608 * Print a summary of the results.
609 *
610  CALL alasvm( path, nout, nfail, nrun, nerrs )
611 *
612  9999 FORMAT( 1x, a, ', UPLO=''', a1, ''', N =', i5, ', type ', i2,
613  \$ ', test ', i2, ', ratio =', g12.5 )
614  9998 FORMAT( 1x, a, ', FACT=''', a1, ''', UPLO=''', a1, ''', N =', i5,
615  \$ ', type ', i2, ', test ', i2, ', ratio =', g12.5 )
616  RETURN
617 *
618 * End of ZDRVSP
619 *
subroutine xlaenv(ISPEC, NVALUE)
XLAENV
Definition: xlaenv.f:83
double precision function dget06(RCOND, RCONDC)
DGET06
Definition: dget06.f:57
double precision function zlansp(NORM, UPLO, N, AP, WORK)
ZLANSP returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a symmetric matrix supplied in packed form.
Definition: zlansp.f:117
subroutine zspsv(UPLO, N, NRHS, AP, IPIV, B, LDB, INFO)
ZSPSV computes the solution to system of linear equations A * X = B for OTHER matrices ...
Definition: zspsv.f:164
subroutine zspsvx(FACT, UPLO, N, NRHS, AP, AFP, IPIV, B, LDB, X, LDX, RCOND, FERR, BERR, WORK, RWORK, INFO)
ZSPSVX computes the solution to system of linear equations A * X = B for OTHER matrices ...
Definition: zspsvx.f:279
subroutine zlatms(M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX, KL, KU, PACK, A, LDA, WORK, INFO)
ZLATMS
Definition: zlatms.f:334
subroutine alasvm(TYPE, NOUT, NFAIL, NRUN, NERRS)
ALASVM
Definition: alasvm.f:75
subroutine zcopy(N, ZX, INCX, ZY, INCY)
ZCOPY
Definition: zcopy.f:83
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 zspt01(UPLO, N, A, AFAC, IPIV, C, LDC, RWORK, RESID)
ZSPT01
Definition: zspt01.f:114
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 zlatsp(UPLO, N, X, ISEED)
ZLATSP
Definition: zlatsp.f:86
subroutine zspt02(UPLO, N, NRHS, A, X, LDX, B, LDB, RWORK, RESID)
ZSPT02
Definition: zspt02.f:125
subroutine alaerh(PATH, SUBNAM, INFO, INFOE, OPTS, M, N, KL, KU, N5, IMAT, NFAIL, NERRS, NOUT)
ALAERH
Definition: alaerh.f:149
subroutine zlatb4(PATH, IMAT, M, N, TYPE, KL, KU, ANORM, MODE, CNDNUM, DIST)
ZLATB4
Definition: zlatb4.f:123
subroutine zget04(N, NRHS, X, LDX, XACT, LDXACT, RCOND, RESID)
ZGET04
Definition: zget04.f:104
subroutine zsptri(UPLO, N, AP, IPIV, WORK, INFO)
ZSPTRI
Definition: zsptri.f:111
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 zerrvx(PATH, NUNIT)
ZERRVX
Definition: zerrvx.f:57
subroutine zsptrf(UPLO, N, AP, IPIV, INFO)
ZSPTRF
Definition: zsptrf.f:160
subroutine zppt05(UPLO, N, NRHS, AP, B, LDB, X, LDX, XACT, LDXACT, FERR, BERR, RESLTS)
ZPPT05
Definition: zppt05.f:159
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