LAPACK  3.6.0
LAPACK: Linear Algebra PACKage
zgesvx.f
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1 *> \brief <b> ZGESVX computes the solution to system of linear equations A * X = B for GE matrices</b>
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
7 *
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15 *> [TXT]</a>
16 *> \endhtmlonly
17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE ZGESVX( FACT, TRANS, N, NRHS, A, LDA, AF, LDAF, IPIV,
22 * EQUED, R, C, B, LDB, X, LDX, RCOND, FERR, BERR,
23 * WORK, RWORK, INFO )
24 *
25 * .. Scalar Arguments ..
26 * CHARACTER EQUED, FACT, TRANS
27 * INTEGER INFO, LDA, LDAF, LDB, LDX, N, NRHS
28 * DOUBLE PRECISION RCOND
29 * ..
30 * .. Array Arguments ..
31 * INTEGER IPIV( * )
32 * DOUBLE PRECISION BERR( * ), C( * ), FERR( * ), R( * ),
33 * $ RWORK( * )
34 * COMPLEX*16 A( LDA, * ), AF( LDAF, * ), B( LDB, * ),
35 * $ WORK( * ), X( LDX, * )
36 * ..
37 *
38 *
39 *> \par Purpose:
40 * =============
41 *>
42 *> \verbatim
43 *>
44 *> ZGESVX uses the LU factorization to compute the solution to a complex
45 *> system of linear equations
46 *> A * X = B,
47 *> where A is an N-by-N matrix and X and B are N-by-NRHS matrices.
48 *>
49 *> Error bounds on the solution and a condition estimate are also
50 *> provided.
51 *> \endverbatim
52 *
53 *> \par Description:
54 * =================
55 *>
56 *> \verbatim
57 *>
58 *> The following steps are performed:
59 *>
60 *> 1. If FACT = 'E', real scaling factors are computed to equilibrate
61 *> the system:
62 *> TRANS = 'N': diag(R)*A*diag(C) *inv(diag(C))*X = diag(R)*B
63 *> TRANS = 'T': (diag(R)*A*diag(C))**T *inv(diag(R))*X = diag(C)*B
64 *> TRANS = 'C': (diag(R)*A*diag(C))**H *inv(diag(R))*X = diag(C)*B
65 *> Whether or not the system will be equilibrated depends on the
66 *> scaling of the matrix A, but if equilibration is used, A is
67 *> overwritten by diag(R)*A*diag(C) and B by diag(R)*B (if TRANS='N')
68 *> or diag(C)*B (if TRANS = 'T' or 'C').
69 *>
70 *> 2. If FACT = 'N' or 'E', the LU decomposition is used to factor the
71 *> matrix A (after equilibration if FACT = 'E') as
72 *> A = P * L * U,
73 *> where P is a permutation matrix, L is a unit lower triangular
74 *> matrix, and U is upper triangular.
75 *>
76 *> 3. If some U(i,i)=0, so that U is exactly singular, then the routine
77 *> returns with INFO = i. Otherwise, the factored form of A is used
78 *> to estimate the condition number of the matrix A. If the
79 *> reciprocal of the condition number is less than machine precision,
80 *> INFO = N+1 is returned as a warning, but the routine still goes on
81 *> to solve for X and compute error bounds as described below.
82 *>
83 *> 4. The system of equations is solved for X using the factored form
84 *> of A.
85 *>
86 *> 5. Iterative refinement is applied to improve the computed solution
87 *> matrix and calculate error bounds and backward error estimates
88 *> for it.
89 *>
90 *> 6. If equilibration was used, the matrix X is premultiplied by
91 *> diag(C) (if TRANS = 'N') or diag(R) (if TRANS = 'T' or 'C') so
92 *> that it solves the original system before equilibration.
93 *> \endverbatim
94 *
95 * Arguments:
96 * ==========
97 *
98 *> \param[in] FACT
99 *> \verbatim
100 *> FACT is CHARACTER*1
101 *> Specifies whether or not the factored form of the matrix A is
102 *> supplied on entry, and if not, whether the matrix A should be
103 *> equilibrated before it is factored.
104 *> = 'F': On entry, AF and IPIV contain the factored form of A.
105 *> If EQUED is not 'N', the matrix A has been
106 *> equilibrated with scaling factors given by R and C.
107 *> A, AF, and IPIV are not modified.
108 *> = 'N': The matrix A will be copied to AF and factored.
109 *> = 'E': The matrix A will be equilibrated if necessary, then
110 *> copied to AF and factored.
111 *> \endverbatim
112 *>
113 *> \param[in] TRANS
114 *> \verbatim
115 *> TRANS is CHARACTER*1
116 *> Specifies the form of the system of equations:
117 *> = 'N': A * X = B (No transpose)
118 *> = 'T': A**T * X = B (Transpose)
119 *> = 'C': A**H * X = B (Conjugate transpose)
120 *> \endverbatim
121 *>
122 *> \param[in] N
123 *> \verbatim
124 *> N is INTEGER
125 *> The number of linear equations, i.e., the order of the
126 *> matrix A. N >= 0.
127 *> \endverbatim
128 *>
129 *> \param[in] NRHS
130 *> \verbatim
131 *> NRHS is INTEGER
132 *> The number of right hand sides, i.e., the number of columns
133 *> of the matrices B and X. NRHS >= 0.
134 *> \endverbatim
135 *>
136 *> \param[in,out] A
137 *> \verbatim
138 *> A is COMPLEX*16 array, dimension (LDA,N)
139 *> On entry, the N-by-N matrix A. If FACT = 'F' and EQUED is
140 *> not 'N', then A must have been equilibrated by the scaling
141 *> factors in R and/or C. A is not modified if FACT = 'F' or
142 *> 'N', or if FACT = 'E' and EQUED = 'N' on exit.
143 *>
144 *> On exit, if EQUED .ne. 'N', A is scaled as follows:
145 *> EQUED = 'R': A := diag(R) * A
146 *> EQUED = 'C': A := A * diag(C)
147 *> EQUED = 'B': A := diag(R) * A * diag(C).
148 *> \endverbatim
149 *>
150 *> \param[in] LDA
151 *> \verbatim
152 *> LDA is INTEGER
153 *> The leading dimension of the array A. LDA >= max(1,N).
154 *> \endverbatim
155 *>
156 *> \param[in,out] AF
157 *> \verbatim
158 *> AF is COMPLEX*16 array, dimension (LDAF,N)
159 *> If FACT = 'F', then AF is an input argument and on entry
160 *> contains the factors L and U from the factorization
161 *> A = P*L*U as computed by ZGETRF. If EQUED .ne. 'N', then
162 *> AF is the factored form of the equilibrated matrix A.
163 *>
164 *> If FACT = 'N', then AF is an output argument and on exit
165 *> returns the factors L and U from the factorization A = P*L*U
166 *> of the original matrix A.
167 *>
168 *> If FACT = 'E', then AF is an output argument and on exit
169 *> returns the factors L and U from the factorization A = P*L*U
170 *> of the equilibrated matrix A (see the description of A for
171 *> the form of the equilibrated matrix).
172 *> \endverbatim
173 *>
174 *> \param[in] LDAF
175 *> \verbatim
176 *> LDAF is INTEGER
177 *> The leading dimension of the array AF. LDAF >= max(1,N).
178 *> \endverbatim
179 *>
180 *> \param[in,out] IPIV
181 *> \verbatim
182 *> IPIV is INTEGER array, dimension (N)
183 *> If FACT = 'F', then IPIV is an input argument and on entry
184 *> contains the pivot indices from the factorization A = P*L*U
185 *> as computed by ZGETRF; row i of the matrix was interchanged
186 *> with row IPIV(i).
187 *>
188 *> If FACT = 'N', then IPIV is an output argument and on exit
189 *> contains the pivot indices from the factorization A = P*L*U
190 *> of the original matrix A.
191 *>
192 *> If FACT = 'E', then IPIV is an output argument and on exit
193 *> contains the pivot indices from the factorization A = P*L*U
194 *> of the equilibrated matrix A.
195 *> \endverbatim
196 *>
197 *> \param[in,out] EQUED
198 *> \verbatim
199 *> EQUED is CHARACTER*1
200 *> Specifies the form of equilibration that was done.
201 *> = 'N': No equilibration (always true if FACT = 'N').
202 *> = 'R': Row equilibration, i.e., A has been premultiplied by
203 *> diag(R).
204 *> = 'C': Column equilibration, i.e., A has been postmultiplied
205 *> by diag(C).
206 *> = 'B': Both row and column equilibration, i.e., A has been
207 *> replaced by diag(R) * A * diag(C).
208 *> EQUED is an input argument if FACT = 'F'; otherwise, it is an
209 *> output argument.
210 *> \endverbatim
211 *>
212 *> \param[in,out] R
213 *> \verbatim
214 *> R is DOUBLE PRECISION array, dimension (N)
215 *> The row scale factors for A. If EQUED = 'R' or 'B', A is
216 *> multiplied on the left by diag(R); if EQUED = 'N' or 'C', R
217 *> is not accessed. R is an input argument if FACT = 'F';
218 *> otherwise, R is an output argument. If FACT = 'F' and
219 *> EQUED = 'R' or 'B', each element of R must be positive.
220 *> \endverbatim
221 *>
222 *> \param[in,out] C
223 *> \verbatim
224 *> C is DOUBLE PRECISION array, dimension (N)
225 *> The column scale factors for A. If EQUED = 'C' or 'B', A is
226 *> multiplied on the right by diag(C); if EQUED = 'N' or 'R', C
227 *> is not accessed. C is an input argument if FACT = 'F';
228 *> otherwise, C is an output argument. If FACT = 'F' and
229 *> EQUED = 'C' or 'B', each element of C must be positive.
230 *> \endverbatim
231 *>
232 *> \param[in,out] B
233 *> \verbatim
234 *> B is COMPLEX*16 array, dimension (LDB,NRHS)
235 *> On entry, the N-by-NRHS right hand side matrix B.
236 *> On exit,
237 *> if EQUED = 'N', B is not modified;
238 *> if TRANS = 'N' and EQUED = 'R' or 'B', B is overwritten by
239 *> diag(R)*B;
240 *> if TRANS = 'T' or 'C' and EQUED = 'C' or 'B', B is
241 *> overwritten by diag(C)*B.
242 *> \endverbatim
243 *>
244 *> \param[in] LDB
245 *> \verbatim
246 *> LDB is INTEGER
247 *> The leading dimension of the array B. LDB >= max(1,N).
248 *> \endverbatim
249 *>
250 *> \param[out] X
251 *> \verbatim
252 *> X is COMPLEX*16 array, dimension (LDX,NRHS)
253 *> If INFO = 0 or INFO = N+1, the N-by-NRHS solution matrix X
254 *> to the original system of equations. Note that A and B are
255 *> modified on exit if EQUED .ne. 'N', and the solution to the
256 *> equilibrated system is inv(diag(C))*X if TRANS = 'N' and
257 *> EQUED = 'C' or 'B', or inv(diag(R))*X if TRANS = 'T' or 'C'
258 *> and EQUED = 'R' or 'B'.
259 *> \endverbatim
260 *>
261 *> \param[in] LDX
262 *> \verbatim
263 *> LDX is INTEGER
264 *> The leading dimension of the array X. LDX >= max(1,N).
265 *> \endverbatim
266 *>
267 *> \param[out] RCOND
268 *> \verbatim
269 *> RCOND is DOUBLE PRECISION
270 *> The estimate of the reciprocal condition number of the matrix
271 *> A after equilibration (if done). If RCOND is less than the
272 *> machine precision (in particular, if RCOND = 0), the matrix
273 *> is singular to working precision. This condition is
274 *> indicated by a return code of INFO > 0.
275 *> \endverbatim
276 *>
277 *> \param[out] FERR
278 *> \verbatim
279 *> FERR is DOUBLE PRECISION array, dimension (NRHS)
280 *> The estimated forward error bound for each solution vector
281 *> X(j) (the j-th column of the solution matrix X).
282 *> If XTRUE is the true solution corresponding to X(j), FERR(j)
283 *> is an estimated upper bound for the magnitude of the largest
284 *> element in (X(j) - XTRUE) divided by the magnitude of the
285 *> largest element in X(j). The estimate is as reliable as
286 *> the estimate for RCOND, and is almost always a slight
287 *> overestimate of the true error.
288 *> \endverbatim
289 *>
290 *> \param[out] BERR
291 *> \verbatim
292 *> BERR is DOUBLE PRECISION array, dimension (NRHS)
293 *> The componentwise relative backward error of each solution
294 *> vector X(j) (i.e., the smallest relative change in
295 *> any element of A or B that makes X(j) an exact solution).
296 *> \endverbatim
297 *>
298 *> \param[out] WORK
299 *> \verbatim
300 *> WORK is COMPLEX*16 array, dimension (2*N)
301 *> \endverbatim
302 *>
303 *> \param[out] RWORK
304 *> \verbatim
305 *> RWORK is DOUBLE PRECISION array, dimension (2*N)
306 *> On exit, RWORK(1) contains the reciprocal pivot growth
307 *> factor norm(A)/norm(U). The "max absolute element" norm is
308 *> used. If RWORK(1) is much less than 1, then the stability
309 *> of the LU factorization of the (equilibrated) matrix A
310 *> could be poor. This also means that the solution X, condition
311 *> estimator RCOND, and forward error bound FERR could be
312 *> unreliable. If factorization fails with 0<INFO<=N, then
313 *> RWORK(1) contains the reciprocal pivot growth factor for the
314 *> leading INFO columns of A.
315 *> \endverbatim
316 *>
317 *> \param[out] INFO
318 *> \verbatim
319 *> INFO is INTEGER
320 *> = 0: successful exit
321 *> < 0: if INFO = -i, the i-th argument had an illegal value
322 *> > 0: if INFO = i, and i is
323 *> <= N: U(i,i) is exactly zero. The factorization has
324 *> been completed, but the factor U is exactly
325 *> singular, so the solution and error bounds
326 *> could not be computed. RCOND = 0 is returned.
327 *> = N+1: U is nonsingular, but RCOND is less than machine
328 *> precision, meaning that the matrix is singular
329 *> to working precision. Nevertheless, the
330 *> solution and error bounds are computed because
331 *> there are a number of situations where the
332 *> computed solution can be more accurate than the
333 *> value of RCOND would suggest.
334 *> \endverbatim
335 *
336 * Authors:
337 * ========
338 *
339 *> \author Univ. of Tennessee
340 *> \author Univ. of California Berkeley
341 *> \author Univ. of Colorado Denver
342 *> \author NAG Ltd.
343 *
344 *> \date April 2012
345 *
346 *> \ingroup complex16GEsolve
347 *
348 * =====================================================================
349  SUBROUTINE zgesvx( FACT, TRANS, N, NRHS, A, LDA, AF, LDAF, IPIV,
350  $ equed, r, c, b, ldb, x, ldx, rcond, ferr, berr,
351  $ work, rwork, info )
352 *
353 * -- LAPACK driver routine (version 3.4.1) --
354 * -- LAPACK is a software package provided by Univ. of Tennessee, --
355 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
356 * April 2012
357 *
358 * .. Scalar Arguments ..
359  CHARACTER EQUED, FACT, TRANS
360  INTEGER INFO, LDA, LDAF, LDB, LDX, N, NRHS
361  DOUBLE PRECISION RCOND
362 * ..
363 * .. Array Arguments ..
364  INTEGER IPIV( * )
365  DOUBLE PRECISION BERR( * ), C( * ), FERR( * ), R( * ),
366  $ rwork( * )
367  COMPLEX*16 A( lda, * ), AF( ldaf, * ), B( ldb, * ),
368  $ work( * ), x( ldx, * )
369 * ..
370 *
371 * =====================================================================
372 *
373 * .. Parameters ..
374  DOUBLE PRECISION ZERO, ONE
375  parameter( zero = 0.0d+0, one = 1.0d+0 )
376 * ..
377 * .. Local Scalars ..
378  LOGICAL COLEQU, EQUIL, NOFACT, NOTRAN, ROWEQU
379  CHARACTER NORM
380  INTEGER I, INFEQU, J
381  DOUBLE PRECISION AMAX, ANORM, BIGNUM, COLCND, RCMAX, RCMIN,
382  $ rowcnd, rpvgrw, smlnum
383 * ..
384 * .. External Functions ..
385  LOGICAL LSAME
386  DOUBLE PRECISION DLAMCH, ZLANGE, ZLANTR
387  EXTERNAL lsame, dlamch, zlange, zlantr
388 * ..
389 * .. External Subroutines ..
390  EXTERNAL xerbla, zgecon, zgeequ, zgerfs, zgetrf, zgetrs,
391  $ zlacpy, zlaqge
392 * ..
393 * .. Intrinsic Functions ..
394  INTRINSIC max, min
395 * ..
396 * .. Executable Statements ..
397 *
398  info = 0
399  nofact = lsame( fact, 'N' )
400  equil = lsame( fact, 'E' )
401  notran = lsame( trans, 'N' )
402  IF( nofact .OR. equil ) THEN
403  equed = 'N'
404  rowequ = .false.
405  colequ = .false.
406  ELSE
407  rowequ = lsame( equed, 'R' ) .OR. lsame( equed, 'B' )
408  colequ = lsame( equed, 'C' ) .OR. lsame( equed, 'B' )
409  smlnum = dlamch( 'Safe minimum' )
410  bignum = one / smlnum
411  END IF
412 *
413 * Test the input parameters.
414 *
415  IF( .NOT.nofact .AND. .NOT.equil .AND. .NOT.lsame( fact, 'F' ) )
416  $ THEN
417  info = -1
418  ELSE IF( .NOT.notran .AND. .NOT.lsame( trans, 'T' ) .AND. .NOT.
419  $ lsame( trans, 'C' ) ) THEN
420  info = -2
421  ELSE IF( n.LT.0 ) THEN
422  info = -3
423  ELSE IF( nrhs.LT.0 ) THEN
424  info = -4
425  ELSE IF( lda.LT.max( 1, n ) ) THEN
426  info = -6
427  ELSE IF( ldaf.LT.max( 1, n ) ) THEN
428  info = -8
429  ELSE IF( lsame( fact, 'F' ) .AND. .NOT.
430  $ ( rowequ .OR. colequ .OR. lsame( equed, 'N' ) ) ) THEN
431  info = -10
432  ELSE
433  IF( rowequ ) THEN
434  rcmin = bignum
435  rcmax = zero
436  DO 10 j = 1, n
437  rcmin = min( rcmin, r( j ) )
438  rcmax = max( rcmax, r( j ) )
439  10 CONTINUE
440  IF( rcmin.LE.zero ) THEN
441  info = -11
442  ELSE IF( n.GT.0 ) THEN
443  rowcnd = max( rcmin, smlnum ) / min( rcmax, bignum )
444  ELSE
445  rowcnd = one
446  END IF
447  END IF
448  IF( colequ .AND. info.EQ.0 ) THEN
449  rcmin = bignum
450  rcmax = zero
451  DO 20 j = 1, n
452  rcmin = min( rcmin, c( j ) )
453  rcmax = max( rcmax, c( j ) )
454  20 CONTINUE
455  IF( rcmin.LE.zero ) THEN
456  info = -12
457  ELSE IF( n.GT.0 ) THEN
458  colcnd = max( rcmin, smlnum ) / min( rcmax, bignum )
459  ELSE
460  colcnd = one
461  END IF
462  END IF
463  IF( info.EQ.0 ) THEN
464  IF( ldb.LT.max( 1, n ) ) THEN
465  info = -14
466  ELSE IF( ldx.LT.max( 1, n ) ) THEN
467  info = -16
468  END IF
469  END IF
470  END IF
471 *
472  IF( info.NE.0 ) THEN
473  CALL xerbla( 'ZGESVX', -info )
474  RETURN
475  END IF
476 *
477  IF( equil ) THEN
478 *
479 * Compute row and column scalings to equilibrate the matrix A.
480 *
481  CALL zgeequ( n, n, a, lda, r, c, rowcnd, colcnd, amax, infequ )
482  IF( infequ.EQ.0 ) THEN
483 *
484 * Equilibrate the matrix.
485 *
486  CALL zlaqge( n, n, a, lda, r, c, rowcnd, colcnd, amax,
487  $ equed )
488  rowequ = lsame( equed, 'R' ) .OR. lsame( equed, 'B' )
489  colequ = lsame( equed, 'C' ) .OR. lsame( equed, 'B' )
490  END IF
491  END IF
492 *
493 * Scale the right hand side.
494 *
495  IF( notran ) THEN
496  IF( rowequ ) THEN
497  DO 40 j = 1, nrhs
498  DO 30 i = 1, n
499  b( i, j ) = r( i )*b( i, j )
500  30 CONTINUE
501  40 CONTINUE
502  END IF
503  ELSE IF( colequ ) THEN
504  DO 60 j = 1, nrhs
505  DO 50 i = 1, n
506  b( i, j ) = c( i )*b( i, j )
507  50 CONTINUE
508  60 CONTINUE
509  END IF
510 *
511  IF( nofact .OR. equil ) THEN
512 *
513 * Compute the LU factorization of A.
514 *
515  CALL zlacpy( 'Full', n, n, a, lda, af, ldaf )
516  CALL zgetrf( n, n, af, ldaf, ipiv, info )
517 *
518 * Return if INFO is non-zero.
519 *
520  IF( info.GT.0 ) THEN
521 *
522 * Compute the reciprocal pivot growth factor of the
523 * leading rank-deficient INFO columns of A.
524 *
525  rpvgrw = zlantr( 'M', 'U', 'N', info, info, af, ldaf,
526  $ rwork )
527  IF( rpvgrw.EQ.zero ) THEN
528  rpvgrw = one
529  ELSE
530  rpvgrw = zlange( 'M', n, info, a, lda, rwork ) /
531  $ rpvgrw
532  END IF
533  rwork( 1 ) = rpvgrw
534  rcond = zero
535  RETURN
536  END IF
537  END IF
538 *
539 * Compute the norm of the matrix A and the
540 * reciprocal pivot growth factor RPVGRW.
541 *
542  IF( notran ) THEN
543  norm = '1'
544  ELSE
545  norm = 'I'
546  END IF
547  anorm = zlange( norm, n, n, a, lda, rwork )
548  rpvgrw = zlantr( 'M', 'U', 'N', n, n, af, ldaf, rwork )
549  IF( rpvgrw.EQ.zero ) THEN
550  rpvgrw = one
551  ELSE
552  rpvgrw = zlange( 'M', n, n, a, lda, rwork ) / rpvgrw
553  END IF
554 *
555 * Compute the reciprocal of the condition number of A.
556 *
557  CALL zgecon( norm, n, af, ldaf, anorm, rcond, work, rwork, info )
558 *
559 * Compute the solution matrix X.
560 *
561  CALL zlacpy( 'Full', n, nrhs, b, ldb, x, ldx )
562  CALL zgetrs( trans, n, nrhs, af, ldaf, ipiv, x, ldx, info )
563 *
564 * Use iterative refinement to improve the computed solution and
565 * compute error bounds and backward error estimates for it.
566 *
567  CALL zgerfs( trans, n, nrhs, a, lda, af, ldaf, ipiv, b, ldb, x,
568  $ ldx, ferr, berr, work, rwork, info )
569 *
570 * Transform the solution matrix X to a solution of the original
571 * system.
572 *
573  IF( notran ) THEN
574  IF( colequ ) THEN
575  DO 80 j = 1, nrhs
576  DO 70 i = 1, n
577  x( i, j ) = c( i )*x( i, j )
578  70 CONTINUE
579  80 CONTINUE
580  DO 90 j = 1, nrhs
581  ferr( j ) = ferr( j ) / colcnd
582  90 CONTINUE
583  END IF
584  ELSE IF( rowequ ) THEN
585  DO 110 j = 1, nrhs
586  DO 100 i = 1, n
587  x( i, j ) = r( i )*x( i, j )
588  100 CONTINUE
589  110 CONTINUE
590  DO 120 j = 1, nrhs
591  ferr( j ) = ferr( j ) / rowcnd
592  120 CONTINUE
593  END IF
594 *
595 * Set INFO = N+1 if the matrix is singular to working precision.
596 *
597  IF( rcond.LT.dlamch( 'Epsilon' ) )
598  $ info = n + 1
599 *
600  rwork( 1 ) = rpvgrw
601  RETURN
602 *
603 * End of ZGESVX
604 *
605  END
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 zgesvx(FACT, TRANS, N, NRHS, A, LDA, AF, LDAF, IPIV, EQUED, R, C, B, LDB, X, LDX, RCOND, FERR, BERR, WORK, RWORK, INFO)
ZGESVX computes the solution to system of linear equations A * X = B for GE matrices ...
Definition: zgesvx.f:352
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
subroutine zgecon(NORM, N, A, LDA, ANORM, RCOND, WORK, RWORK, INFO)
ZGECON
Definition: zgecon.f:126
subroutine zlaqge(M, N, A, LDA, R, C, ROWCND, COLCND, AMAX, EQUED)
ZLAQGE scales a general rectangular matrix, using row and column scaling factors computed by sgeequ...
Definition: zlaqge.f:145
subroutine zgeequ(M, N, A, LDA, R, C, ROWCND, COLCND, AMAX, INFO)
ZGEEQU
Definition: zgeequ.f:142
subroutine zgetrf(M, N, A, LDA, IPIV, INFO)
ZGETRF VARIANT: Crout Level 3 BLAS version of the algorithm.
Definition: zgetrf.f:102
subroutine zgerfs(TRANS, N, NRHS, A, LDA, AF, LDAF, IPIV, B, LDB, X, LDX, FERR, BERR, WORK, RWORK, INFO)
ZGERFS
Definition: zgerfs.f:188
subroutine zgetrs(TRANS, N, NRHS, A, LDA, IPIV, B, LDB, INFO)
ZGETRS
Definition: zgetrs.f:123