LAPACK  3.10.0
LAPACK: Linear Algebra PACKage
dchkge.f
Go to the documentation of this file.
1 *> \brief \b DCHKGE
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 DCHKGE( DOTYPE, NM, MVAL, NN, NVAL, NNB, NBVAL, NNS,
12 * NSVAL, THRESH, TSTERR, NMAX, A, AFAC, AINV, B,
13 * X, XACT, WORK, RWORK, IWORK, NOUT )
14 *
15 * .. Scalar Arguments ..
16 * LOGICAL TSTERR
17 * INTEGER NM, NMAX, NN, NNB, NNS, NOUT
18 * DOUBLE PRECISION THRESH
19 * ..
20 * .. Array Arguments ..
21 * LOGICAL DOTYPE( * )
22 * INTEGER IWORK( * ), MVAL( * ), NBVAL( * ), NSVAL( * ),
23 * $ NVAL( * )
24 * DOUBLE PRECISION A( * ), AFAC( * ), AINV( * ), B( * ),
25 * $ RWORK( * ), WORK( * ), X( * ), XACT( * )
26 * ..
27 *
28 *
29 *> \par Purpose:
30 * =============
31 *>
32 *> \verbatim
33 *>
34 *> DCHKGE tests DGETRF, -TRI, -TRS, -RFS, and -CON.
35 *> \endverbatim
36 *
37 * Arguments:
38 * ==========
39 *
40 *> \param[in] DOTYPE
41 *> \verbatim
42 *> DOTYPE is LOGICAL array, dimension (NTYPES)
43 *> The matrix types to be used for testing. Matrices of type j
44 *> (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
45 *> .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
46 *> \endverbatim
47 *>
48 *> \param[in] NM
49 *> \verbatim
50 *> NM is INTEGER
51 *> The number of values of M contained in the vector MVAL.
52 *> \endverbatim
53 *>
54 *> \param[in] MVAL
55 *> \verbatim
56 *> MVAL is INTEGER array, dimension (NM)
57 *> The values of the matrix row dimension M.
58 *> \endverbatim
59 *>
60 *> \param[in] NN
61 *> \verbatim
62 *> NN is INTEGER
63 *> The number of values of N contained in the vector NVAL.
64 *> \endverbatim
65 *>
66 *> \param[in] NVAL
67 *> \verbatim
68 *> NVAL is INTEGER array, dimension (NN)
69 *> The values of the matrix column dimension N.
70 *> \endverbatim
71 *>
72 *> \param[in] NNB
73 *> \verbatim
74 *> NNB is INTEGER
75 *> The number of values of NB contained in the vector NBVAL.
76 *> \endverbatim
77 *>
78 *> \param[in] NBVAL
79 *> \verbatim
80 *> NBVAL is INTEGER array, dimension (NNB)
81 *> The values of the blocksize NB.
82 *> \endverbatim
83 *>
84 *> \param[in] NNS
85 *> \verbatim
86 *> NNS is INTEGER
87 *> The number of values of NRHS contained in the vector NSVAL.
88 *> \endverbatim
89 *>
90 *> \param[in] NSVAL
91 *> \verbatim
92 *> NSVAL is INTEGER array, dimension (NNS)
93 *> The values of the number of right hand sides NRHS.
94 *> \endverbatim
95 *>
96 *> \param[in] THRESH
97 *> \verbatim
98 *> THRESH is DOUBLE PRECISION
99 *> The threshold value for the test ratios. A result is
100 *> included in the output file if RESULT >= THRESH. To have
101 *> every test ratio printed, use THRESH = 0.
102 *> \endverbatim
103 *>
104 *> \param[in] TSTERR
105 *> \verbatim
106 *> TSTERR is LOGICAL
107 *> Flag that indicates whether error exits are to be tested.
108 *> \endverbatim
109 *>
110 *> \param[in] NMAX
111 *> \verbatim
112 *> NMAX is INTEGER
113 *> The maximum value permitted for M or N, used in dimensioning
114 *> the work arrays.
115 *> \endverbatim
116 *>
117 *> \param[out] A
118 *> \verbatim
119 *> A is DOUBLE PRECISION array, dimension (NMAX*NMAX)
120 *> \endverbatim
121 *>
122 *> \param[out] AFAC
123 *> \verbatim
124 *> AFAC is DOUBLE PRECISION array, dimension (NMAX*NMAX)
125 *> \endverbatim
126 *>
127 *> \param[out] AINV
128 *> \verbatim
129 *> AINV is DOUBLE PRECISION array, dimension (NMAX*NMAX)
130 *> \endverbatim
131 *>
132 *> \param[out] B
133 *> \verbatim
134 *> B is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
135 *> where NSMAX is the largest entry in NSVAL.
136 *> \endverbatim
137 *>
138 *> \param[out] X
139 *> \verbatim
140 *> X is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
141 *> \endverbatim
142 *>
143 *> \param[out] XACT
144 *> \verbatim
145 *> XACT is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
146 *> \endverbatim
147 *>
148 *> \param[out] WORK
149 *> \verbatim
150 *> WORK is DOUBLE PRECISION array, dimension
151 *> (NMAX*max(3,NSMAX))
152 *> \endverbatim
153 *>
154 *> \param[out] RWORK
155 *> \verbatim
156 *> RWORK is DOUBLE PRECISION array, dimension
157 *> (max(2*NMAX,2*NSMAX+NWORK))
158 *> \endverbatim
159 *>
160 *> \param[out] IWORK
161 *> \verbatim
162 *> IWORK is INTEGER array, dimension (2*NMAX)
163 *> \endverbatim
164 *>
165 *> \param[in] NOUT
166 *> \verbatim
167 *> NOUT is INTEGER
168 *> The unit number for output.
169 *> \endverbatim
170 *
171 * Authors:
172 * ========
173 *
174 *> \author Univ. of Tennessee
175 *> \author Univ. of California Berkeley
176 *> \author Univ. of Colorado Denver
177 *> \author NAG Ltd.
178 *
179 *> \ingroup double_lin
180 *
181 * =====================================================================
182  SUBROUTINE dchkge( DOTYPE, NM, MVAL, NN, NVAL, NNB, NBVAL, NNS,
183  $ NSVAL, THRESH, TSTERR, NMAX, A, AFAC, AINV, B,
184  $ X, XACT, WORK, RWORK, IWORK, NOUT )
185 *
186 * -- LAPACK test routine --
187 * -- LAPACK is a software package provided by Univ. of Tennessee, --
188 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
189 *
190 * .. Scalar Arguments ..
191  LOGICAL TSTERR
192  INTEGER NM, NMAX, NN, NNB, NNS, NOUT
193  DOUBLE PRECISION THRESH
194 * ..
195 * .. Array Arguments ..
196  LOGICAL DOTYPE( * )
197  INTEGER IWORK( * ), MVAL( * ), NBVAL( * ), NSVAL( * ),
198  $ nval( * )
199  DOUBLE PRECISION A( * ), AFAC( * ), AINV( * ), B( * ),
200  $ RWORK( * ), WORK( * ), X( * ), XACT( * )
201 * ..
202 *
203 * =====================================================================
204 *
205 * .. Parameters ..
206  DOUBLE PRECISION ONE, ZERO
207  PARAMETER ( ONE = 1.0d+0, zero = 0.0d+0 )
208  INTEGER NTYPES
209  parameter( ntypes = 11 )
210  INTEGER NTESTS
211  parameter( ntests = 8 )
212  INTEGER NTRAN
213  parameter( ntran = 3 )
214 * ..
215 * .. Local Scalars ..
216  LOGICAL TRFCON, ZEROT
217  CHARACTER DIST, NORM, TRANS, TYPE, XTYPE
218  CHARACTER*3 PATH
219  INTEGER I, IM, IMAT, IN, INB, INFO, IOFF, IRHS, ITRAN,
220  $ izero, k, kl, ku, lda, lwork, m, mode, n, nb,
221  $ nerrs, nfail, nimat, nrhs, nrun, nt
222  DOUBLE PRECISION AINVNM, ANORM, ANORMI, ANORMO, CNDNUM, DUMMY,
223  $ RCOND, RCONDC, RCONDI, RCONDO
224 * ..
225 * .. Local Arrays ..
226  CHARACTER TRANSS( NTRAN )
227  INTEGER ISEED( 4 ), ISEEDY( 4 )
228  DOUBLE PRECISION RESULT( NTESTS )
229 * ..
230 * .. External Functions ..
231  DOUBLE PRECISION DGET06, DLANGE
232  EXTERNAL DGET06, DLANGE
233 * ..
234 * .. External Subroutines ..
235  EXTERNAL alaerh, alahd, alasum, derrge, dgecon, dgerfs,
238  $ dlatms, xlaenv
239 * ..
240 * .. Intrinsic Functions ..
241  INTRINSIC max, min
242 * ..
243 * .. Scalars in Common ..
244  LOGICAL LERR, OK
245  CHARACTER*32 SRNAMT
246  INTEGER INFOT, NUNIT
247 * ..
248 * .. Common blocks ..
249  COMMON / infoc / infot, nunit, ok, lerr
250  COMMON / srnamc / srnamt
251 * ..
252 * .. Data statements ..
253  DATA iseedy / 1988, 1989, 1990, 1991 / ,
254  $ transs / 'N', 'T', 'C' /
255 * ..
256 * .. Executable Statements ..
257 *
258 * Initialize constants and the random number seed.
259 *
260  path( 1: 1 ) = 'Double precision'
261  path( 2: 3 ) = 'GE'
262  nrun = 0
263  nfail = 0
264  nerrs = 0
265  DO 10 i = 1, 4
266  iseed( i ) = iseedy( i )
267  10 CONTINUE
268 *
269 * Test the error exits
270 *
271  CALL xlaenv( 1, 1 )
272  IF( tsterr )
273  $ CALL derrge( path, nout )
274  infot = 0
275  CALL xlaenv( 2, 2 )
276 *
277 * Do for each value of M in MVAL
278 *
279  DO 120 im = 1, nm
280  m = mval( im )
281  lda = max( 1, m )
282 *
283 * Do for each value of N in NVAL
284 *
285  DO 110 in = 1, nn
286  n = nval( in )
287  xtype = 'N'
288  nimat = ntypes
289  IF( m.LE.0 .OR. n.LE.0 )
290  $ nimat = 1
291 *
292  DO 100 imat = 1, nimat
293 *
294 * Do the tests only if DOTYPE( IMAT ) is true.
295 *
296  IF( .NOT.dotype( imat ) )
297  $ GO TO 100
298 *
299 * Skip types 5, 6, or 7 if the matrix size is too small.
300 *
301  zerot = imat.GE.5 .AND. imat.LE.7
302  IF( zerot .AND. n.LT.imat-4 )
303  $ GO TO 100
304 *
305 * Set up parameters with DLATB4 and generate a test matrix
306 * with DLATMS.
307 *
308  CALL dlatb4( path, imat, m, n, TYPE, kl, ku, anorm, mode,
309  $ cndnum, dist )
310 *
311  srnamt = 'DLATMS'
312  CALL dlatms( m, n, dist, iseed, TYPE, rwork, mode,
313  $ cndnum, anorm, kl, ku, 'No packing', a, lda,
314  $ work, info )
315 *
316 * Check error code from DLATMS.
317 *
318  IF( info.NE.0 ) THEN
319  CALL alaerh( path, 'DLATMS', info, 0, ' ', m, n, -1,
320  $ -1, -1, imat, nfail, nerrs, nout )
321  GO TO 100
322  END IF
323 *
324 * For types 5-7, zero one or more columns of the matrix to
325 * test that INFO is returned correctly.
326 *
327  IF( zerot ) THEN
328  IF( imat.EQ.5 ) THEN
329  izero = 1
330  ELSE IF( imat.EQ.6 ) THEN
331  izero = min( m, n )
332  ELSE
333  izero = min( m, n ) / 2 + 1
334  END IF
335  ioff = ( izero-1 )*lda
336  IF( imat.LT.7 ) THEN
337  DO 20 i = 1, m
338  a( ioff+i ) = zero
339  20 CONTINUE
340  ELSE
341  CALL dlaset( 'Full', m, n-izero+1, zero, zero,
342  $ a( ioff+1 ), lda )
343  END IF
344  ELSE
345  izero = 0
346  END IF
347 *
348 * These lines, if used in place of the calls in the DO 60
349 * loop, cause the code to bomb on a Sun SPARCstation.
350 *
351 * ANORMO = DLANGE( 'O', M, N, A, LDA, RWORK )
352 * ANORMI = DLANGE( 'I', M, N, A, LDA, RWORK )
353 *
354 * Do for each blocksize in NBVAL
355 *
356  DO 90 inb = 1, nnb
357  nb = nbval( inb )
358  CALL xlaenv( 1, nb )
359 *
360 * Compute the LU factorization of the matrix.
361 *
362  CALL dlacpy( 'Full', m, n, a, lda, afac, lda )
363  srnamt = 'DGETRF'
364  CALL dgetrf( m, n, afac, lda, iwork, info )
365 *
366 * Check error code from DGETRF.
367 *
368  IF( info.NE.izero )
369  $ CALL alaerh( path, 'DGETRF', info, izero, ' ', m,
370  $ n, -1, -1, nb, imat, nfail, nerrs,
371  $ nout )
372  trfcon = .false.
373 *
374 *+ TEST 1
375 * Reconstruct matrix from factors and compute residual.
376 *
377  CALL dlacpy( 'Full', m, n, afac, lda, ainv, lda )
378  CALL dget01( m, n, a, lda, ainv, lda, iwork, rwork,
379  $ result( 1 ) )
380  nt = 1
381 *
382 *+ TEST 2
383 * Form the inverse if the factorization was successful
384 * and compute the residual.
385 *
386  IF( m.EQ.n .AND. info.EQ.0 ) THEN
387  CALL dlacpy( 'Full', n, n, afac, lda, ainv, lda )
388  srnamt = 'DGETRI'
389  nrhs = nsval( 1 )
390  lwork = nmax*max( 3, nrhs )
391  CALL dgetri( n, ainv, lda, iwork, work, lwork,
392  $ info )
393 *
394 * Check error code from DGETRI.
395 *
396  IF( info.NE.0 )
397  $ CALL alaerh( path, 'DGETRI', info, 0, ' ', n, n,
398  $ -1, -1, nb, imat, nfail, nerrs,
399  $ nout )
400 *
401 * Compute the residual for the matrix times its
402 * inverse. Also compute the 1-norm condition number
403 * of A.
404 *
405  CALL dget03( n, a, lda, ainv, lda, work, lda,
406  $ rwork, rcondo, result( 2 ) )
407  anormo = dlange( 'O', m, n, a, lda, rwork )
408 *
409 * Compute the infinity-norm condition number of A.
410 *
411  anormi = dlange( 'I', m, n, a, lda, rwork )
412  ainvnm = dlange( 'I', n, n, ainv, lda, rwork )
413  IF( anormi.LE.zero .OR. ainvnm.LE.zero ) THEN
414  rcondi = one
415  ELSE
416  rcondi = ( one / anormi ) / ainvnm
417  END IF
418  nt = 2
419  ELSE
420 *
421 * Do only the condition estimate if INFO > 0.
422 *
423  trfcon = .true.
424  anormo = dlange( 'O', m, n, a, lda, rwork )
425  anormi = dlange( 'I', m, n, a, lda, rwork )
426  rcondo = zero
427  rcondi = zero
428  END IF
429 *
430 * Print information about the tests so far that did not
431 * pass the threshold.
432 *
433  DO 30 k = 1, nt
434  IF( result( k ).GE.thresh ) THEN
435  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
436  $ CALL alahd( nout, path )
437  WRITE( nout, fmt = 9999 )m, n, nb, imat, k,
438  $ result( k )
439  nfail = nfail + 1
440  END IF
441  30 CONTINUE
442  nrun = nrun + nt
443 *
444 * Skip the remaining tests if this is not the first
445 * block size or if M .ne. N. Skip the solve tests if
446 * the matrix is singular.
447 *
448  IF( inb.GT.1 .OR. m.NE.n )
449  $ GO TO 90
450  IF( trfcon )
451  $ GO TO 70
452 *
453  DO 60 irhs = 1, nns
454  nrhs = nsval( irhs )
455  xtype = 'N'
456 *
457  DO 50 itran = 1, ntran
458  trans = transs( itran )
459  IF( itran.EQ.1 ) THEN
460  rcondc = rcondo
461  ELSE
462  rcondc = rcondi
463  END IF
464 *
465 *+ TEST 3
466 * Solve and compute residual for A * X = B.
467 *
468  srnamt = 'DLARHS'
469  CALL dlarhs( path, xtype, ' ', trans, n, n, kl,
470  $ ku, nrhs, a, lda, xact, lda, b,
471  $ lda, iseed, info )
472  xtype = 'C'
473 *
474  CALL dlacpy( 'Full', n, nrhs, b, lda, x, lda )
475  srnamt = 'DGETRS'
476  CALL dgetrs( trans, n, nrhs, afac, lda, iwork,
477  $ x, lda, info )
478 *
479 * Check error code from DGETRS.
480 *
481  IF( info.NE.0 )
482  $ CALL alaerh( path, 'DGETRS', info, 0, trans,
483  $ n, n, -1, -1, nrhs, imat, nfail,
484  $ nerrs, nout )
485 *
486  CALL dlacpy( 'Full', n, nrhs, b, lda, work,
487  $ lda )
488  CALL dget02( trans, n, n, nrhs, a, lda, x, lda,
489  $ work, lda, rwork, result( 3 ) )
490 *
491 *+ TEST 4
492 * Check solution from generated exact solution.
493 *
494  CALL dget04( n, nrhs, x, lda, xact, lda, rcondc,
495  $ result( 4 ) )
496 *
497 *+ TESTS 5, 6, and 7
498 * Use iterative refinement to improve the
499 * solution.
500 *
501  srnamt = 'DGERFS'
502  CALL dgerfs( trans, n, nrhs, a, lda, afac, lda,
503  $ iwork, b, lda, x, lda, rwork,
504  $ rwork( nrhs+1 ), work,
505  $ iwork( n+1 ), info )
506 *
507 * Check error code from DGERFS.
508 *
509  IF( info.NE.0 )
510  $ CALL alaerh( path, 'DGERFS', info, 0, trans,
511  $ n, n, -1, -1, nrhs, imat, nfail,
512  $ nerrs, nout )
513 *
514  CALL dget04( n, nrhs, x, lda, xact, lda, rcondc,
515  $ result( 5 ) )
516  CALL dget07( trans, n, nrhs, a, lda, b, lda, x,
517  $ lda, xact, lda, rwork, .true.,
518  $ rwork( nrhs+1 ), result( 6 ) )
519 *
520 * Print information about the tests that did not
521 * pass the threshold.
522 *
523  DO 40 k = 3, 7
524  IF( result( k ).GE.thresh ) THEN
525  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
526  $ CALL alahd( nout, path )
527  WRITE( nout, fmt = 9998 )trans, n, nrhs,
528  $ imat, k, result( k )
529  nfail = nfail + 1
530  END IF
531  40 CONTINUE
532  nrun = nrun + 5
533  50 CONTINUE
534  60 CONTINUE
535 *
536 *+ TEST 8
537 * Get an estimate of RCOND = 1/CNDNUM.
538 *
539  70 CONTINUE
540  DO 80 itran = 1, 2
541  IF( itran.EQ.1 ) THEN
542  anorm = anormo
543  rcondc = rcondo
544  norm = 'O'
545  ELSE
546  anorm = anormi
547  rcondc = rcondi
548  norm = 'I'
549  END IF
550  srnamt = 'DGECON'
551  CALL dgecon( norm, n, afac, lda, anorm, rcond,
552  $ work, iwork( n+1 ), info )
553 *
554 * Check error code from DGECON.
555 *
556  IF( info.NE.0 )
557  $ CALL alaerh( path, 'DGECON', info, 0, norm, n,
558  $ n, -1, -1, -1, imat, nfail, nerrs,
559  $ nout )
560 *
561 * This line is needed on a Sun SPARCstation.
562 *
563  dummy = rcond
564 *
565  result( 8 ) = dget06( rcond, rcondc )
566 *
567 * Print information about the tests that did not pass
568 * the threshold.
569 *
570  IF( result( 8 ).GE.thresh ) THEN
571  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
572  $ CALL alahd( nout, path )
573  WRITE( nout, fmt = 9997 )norm, n, imat, 8,
574  $ result( 8 )
575  nfail = nfail + 1
576  END IF
577  nrun = nrun + 1
578  80 CONTINUE
579  90 CONTINUE
580  100 CONTINUE
581  110 CONTINUE
582  120 CONTINUE
583 *
584 * Print a summary of the results.
585 *
586  CALL alasum( path, nout, nfail, nrun, nerrs )
587 *
588  9999 FORMAT( ' M = ', i5, ', N =', i5, ', NB =', i4, ', type ', i2,
589  $ ', test(', i2, ') =', g12.5 )
590  9998 FORMAT( ' TRANS=''', a1, ''', N =', i5, ', NRHS=', i3, ', type ',
591  $ i2, ', test(', i2, ') =', g12.5 )
592  9997 FORMAT( ' NORM =''', a1, ''', N =', i5, ',', 10x, ' type ', i2,
593  $ ', test(', i2, ') =', g12.5 )
594  RETURN
595 *
596 * End of DCHKGE
597 *
598  END
subroutine dlacpy(UPLO, M, N, A, LDA, B, LDB)
DLACPY copies all or part of one two-dimensional array to another.
Definition: dlacpy.f:103
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:110
subroutine alasum(TYPE, NOUT, NFAIL, NRUN, NERRS)
ALASUM
Definition: alasum.f:73
subroutine xlaenv(ISPEC, NVALUE)
XLAENV
Definition: xlaenv.f:81
subroutine alahd(IOUNIT, PATH)
ALAHD
Definition: alahd.f:107
subroutine alaerh(PATH, SUBNAM, INFO, INFOE, OPTS, M, N, KL, KU, N5, IMAT, NFAIL, NERRS, NOUT)
ALAERH
Definition: alaerh.f:147
subroutine dlarhs(PATH, XTYPE, UPLO, TRANS, M, N, KL, KU, NRHS, A, LDA, X, LDX, B, LDB, ISEED, INFO)
DLARHS
Definition: dlarhs.f:205
subroutine dget02(TRANS, M, N, NRHS, A, LDA, X, LDX, B, LDB, RWORK, RESID)
DGET02
Definition: dget02.f:135
subroutine dget07(TRANS, N, NRHS, A, LDA, B, LDB, X, LDX, XACT, LDXACT, FERR, CHKFERR, BERR, RESLTS)
DGET07
Definition: dget07.f:165
subroutine dget04(N, NRHS, X, LDX, XACT, LDXACT, RCOND, RESID)
DGET04
Definition: dget04.f:102
subroutine dget01(M, N, A, LDA, AFAC, LDAFAC, IPIV, RWORK, RESID)
DGET01
Definition: dget01.f:107
subroutine dchkge(DOTYPE, NM, MVAL, NN, NVAL, NNB, NBVAL, NNS, NSVAL, THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK, NOUT)
DCHKGE
Definition: dchkge.f:185
subroutine dget03(N, A, LDA, AINV, LDAINV, WORK, LDWORK, RWORK, RCOND, RESID)
DGET03
Definition: dget03.f:109
subroutine dlatb4(PATH, IMAT, M, N, TYPE, KL, KU, ANORM, MODE, CNDNUM, DIST)
DLATB4
Definition: dlatb4.f:120
subroutine derrge(PATH, NUNIT)
DERRGE
Definition: derrge.f:55
subroutine dlatms(M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX, KL, KU, PACK, A, LDA, WORK, INFO)
DLATMS
Definition: dlatms.f:321
subroutine dgetrf(M, N, A, LDA, IPIV, INFO)
DGETRF
Definition: dgetrf.f:108
subroutine dgecon(NORM, N, A, LDA, ANORM, RCOND, WORK, IWORK, INFO)
DGECON
Definition: dgecon.f:124
subroutine dgetri(N, A, LDA, IPIV, WORK, LWORK, INFO)
DGETRI
Definition: dgetri.f:114
subroutine dgetrs(TRANS, N, NRHS, A, LDA, IPIV, B, LDB, INFO)
DGETRS
Definition: dgetrs.f:121
subroutine dgerfs(TRANS, N, NRHS, A, LDA, AF, LDAF, IPIV, B, LDB, X, LDX, FERR, BERR, WORK, IWORK, INFO)
DGERFS
Definition: dgerfs.f:185