LAPACK  3.10.0 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 *
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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 *> \ingroup complex16GEsolve
345 *
346 * =====================================================================
347  SUBROUTINE zgesvx( FACT, TRANS, N, NRHS, A, LDA, AF, LDAF, IPIV,
348  \$ EQUED, R, C, B, LDB, X, LDX, RCOND, FERR, BERR,
349  \$ WORK, RWORK, INFO )
350 *
351 * -- LAPACK driver routine --
352 * -- LAPACK is a software package provided by Univ. of Tennessee, --
353 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
354 *
355 * .. Scalar Arguments ..
356  CHARACTER EQUED, FACT, TRANS
357  INTEGER INFO, LDA, LDAF, LDB, LDX, N, NRHS
358  DOUBLE PRECISION RCOND
359 * ..
360 * .. Array Arguments ..
361  INTEGER IPIV( * )
362  DOUBLE PRECISION BERR( * ), C( * ), FERR( * ), R( * ),
363  \$ rwork( * )
364  COMPLEX*16 A( LDA, * ), AF( LDAF, * ), B( LDB, * ),
365  \$ WORK( * ), X( LDX, * )
366 * ..
367 *
368 * =====================================================================
369 *
370 * .. Parameters ..
371  DOUBLE PRECISION ZERO, ONE
372  PARAMETER ( ZERO = 0.0d+0, one = 1.0d+0 )
373 * ..
374 * .. Local Scalars ..
375  LOGICAL COLEQU, EQUIL, NOFACT, NOTRAN, ROWEQU
376  CHARACTER NORM
377  INTEGER I, INFEQU, J
378  DOUBLE PRECISION AMAX, ANORM, BIGNUM, COLCND, RCMAX, RCMIN,
379  \$ rowcnd, rpvgrw, smlnum
380 * ..
381 * .. External Functions ..
382  LOGICAL LSAME
383  DOUBLE PRECISION DLAMCH, ZLANGE, ZLANTR
384  EXTERNAL lsame, dlamch, zlange, zlantr
385 * ..
386 * .. External Subroutines ..
387  EXTERNAL xerbla, zgecon, zgeequ, zgerfs, zgetrf, zgetrs,
388  \$ zlacpy, zlaqge
389 * ..
390 * .. Intrinsic Functions ..
391  INTRINSIC max, min
392 * ..
393 * .. Executable Statements ..
394 *
395  info = 0
396  nofact = lsame( fact, 'N' )
397  equil = lsame( fact, 'E' )
398  notran = lsame( trans, 'N' )
399  IF( nofact .OR. equil ) THEN
400  equed = 'N'
401  rowequ = .false.
402  colequ = .false.
403  ELSE
404  rowequ = lsame( equed, 'R' ) .OR. lsame( equed, 'B' )
405  colequ = lsame( equed, 'C' ) .OR. lsame( equed, 'B' )
406  smlnum = dlamch( 'Safe minimum' )
407  bignum = one / smlnum
408  END IF
409 *
410 * Test the input parameters.
411 *
412  IF( .NOT.nofact .AND. .NOT.equil .AND. .NOT.lsame( fact, 'F' ) )
413  \$ THEN
414  info = -1
415  ELSE IF( .NOT.notran .AND. .NOT.lsame( trans, 'T' ) .AND. .NOT.
416  \$ lsame( trans, 'C' ) ) THEN
417  info = -2
418  ELSE IF( n.LT.0 ) THEN
419  info = -3
420  ELSE IF( nrhs.LT.0 ) THEN
421  info = -4
422  ELSE IF( lda.LT.max( 1, n ) ) THEN
423  info = -6
424  ELSE IF( ldaf.LT.max( 1, n ) ) THEN
425  info = -8
426  ELSE IF( lsame( fact, 'F' ) .AND. .NOT.
427  \$ ( rowequ .OR. colequ .OR. lsame( equed, 'N' ) ) ) THEN
428  info = -10
429  ELSE
430  IF( rowequ ) THEN
431  rcmin = bignum
432  rcmax = zero
433  DO 10 j = 1, n
434  rcmin = min( rcmin, r( j ) )
435  rcmax = max( rcmax, r( j ) )
436  10 CONTINUE
437  IF( rcmin.LE.zero ) THEN
438  info = -11
439  ELSE IF( n.GT.0 ) THEN
440  rowcnd = max( rcmin, smlnum ) / min( rcmax, bignum )
441  ELSE
442  rowcnd = one
443  END IF
444  END IF
445  IF( colequ .AND. info.EQ.0 ) THEN
446  rcmin = bignum
447  rcmax = zero
448  DO 20 j = 1, n
449  rcmin = min( rcmin, c( j ) )
450  rcmax = max( rcmax, c( j ) )
451  20 CONTINUE
452  IF( rcmin.LE.zero ) THEN
453  info = -12
454  ELSE IF( n.GT.0 ) THEN
455  colcnd = max( rcmin, smlnum ) / min( rcmax, bignum )
456  ELSE
457  colcnd = one
458  END IF
459  END IF
460  IF( info.EQ.0 ) THEN
461  IF( ldb.LT.max( 1, n ) ) THEN
462  info = -14
463  ELSE IF( ldx.LT.max( 1, n ) ) THEN
464  info = -16
465  END IF
466  END IF
467  END IF
468 *
469  IF( info.NE.0 ) THEN
470  CALL xerbla( 'ZGESVX', -info )
471  RETURN
472  END IF
473 *
474  IF( equil ) THEN
475 *
476 * Compute row and column scalings to equilibrate the matrix A.
477 *
478  CALL zgeequ( n, n, a, lda, r, c, rowcnd, colcnd, amax, infequ )
479  IF( infequ.EQ.0 ) THEN
480 *
481 * Equilibrate the matrix.
482 *
483  CALL zlaqge( n, n, a, lda, r, c, rowcnd, colcnd, amax,
484  \$ equed )
485  rowequ = lsame( equed, 'R' ) .OR. lsame( equed, 'B' )
486  colequ = lsame( equed, 'C' ) .OR. lsame( equed, 'B' )
487  END IF
488  END IF
489 *
490 * Scale the right hand side.
491 *
492  IF( notran ) THEN
493  IF( rowequ ) THEN
494  DO 40 j = 1, nrhs
495  DO 30 i = 1, n
496  b( i, j ) = r( i )*b( i, j )
497  30 CONTINUE
498  40 CONTINUE
499  END IF
500  ELSE IF( colequ ) THEN
501  DO 60 j = 1, nrhs
502  DO 50 i = 1, n
503  b( i, j ) = c( i )*b( i, j )
504  50 CONTINUE
505  60 CONTINUE
506  END IF
507 *
508  IF( nofact .OR. equil ) THEN
509 *
510 * Compute the LU factorization of A.
511 *
512  CALL zlacpy( 'Full', n, n, a, lda, af, ldaf )
513  CALL zgetrf( n, n, af, ldaf, ipiv, info )
514 *
515 * Return if INFO is non-zero.
516 *
517  IF( info.GT.0 ) THEN
518 *
519 * Compute the reciprocal pivot growth factor of the
520 * leading rank-deficient INFO columns of A.
521 *
522  rpvgrw = zlantr( 'M', 'U', 'N', info, info, af, ldaf,
523  \$ rwork )
524  IF( rpvgrw.EQ.zero ) THEN
525  rpvgrw = one
526  ELSE
527  rpvgrw = zlange( 'M', n, info, a, lda, rwork ) /
528  \$ rpvgrw
529  END IF
530  rwork( 1 ) = rpvgrw
531  rcond = zero
532  RETURN
533  END IF
534  END IF
535 *
536 * Compute the norm of the matrix A and the
537 * reciprocal pivot growth factor RPVGRW.
538 *
539  IF( notran ) THEN
540  norm = '1'
541  ELSE
542  norm = 'I'
543  END IF
544  anorm = zlange( norm, n, n, a, lda, rwork )
545  rpvgrw = zlantr( 'M', 'U', 'N', n, n, af, ldaf, rwork )
546  IF( rpvgrw.EQ.zero ) THEN
547  rpvgrw = one
548  ELSE
549  rpvgrw = zlange( 'M', n, n, a, lda, rwork ) / rpvgrw
550  END IF
551 *
552 * Compute the reciprocal of the condition number of A.
553 *
554  CALL zgecon( norm, n, af, ldaf, anorm, rcond, work, rwork, info )
555 *
556 * Compute the solution matrix X.
557 *
558  CALL zlacpy( 'Full', n, nrhs, b, ldb, x, ldx )
559  CALL zgetrs( trans, n, nrhs, af, ldaf, ipiv, x, ldx, info )
560 *
561 * Use iterative refinement to improve the computed solution and
562 * compute error bounds and backward error estimates for it.
563 *
564  CALL zgerfs( trans, n, nrhs, a, lda, af, ldaf, ipiv, b, ldb, x,
565  \$ ldx, ferr, berr, work, rwork, info )
566 *
567 * Transform the solution matrix X to a solution of the original
568 * system.
569 *
570  IF( notran ) THEN
571  IF( colequ ) THEN
572  DO 80 j = 1, nrhs
573  DO 70 i = 1, n
574  x( i, j ) = c( i )*x( i, j )
575  70 CONTINUE
576  80 CONTINUE
577  DO 90 j = 1, nrhs
578  ferr( j ) = ferr( j ) / colcnd
579  90 CONTINUE
580  END IF
581  ELSE IF( rowequ ) THEN
582  DO 110 j = 1, nrhs
583  DO 100 i = 1, n
584  x( i, j ) = r( i )*x( i, j )
585  100 CONTINUE
586  110 CONTINUE
587  DO 120 j = 1, nrhs
588  ferr( j ) = ferr( j ) / rowcnd
589  120 CONTINUE
590  END IF
591 *
592 * Set INFO = N+1 if the matrix is singular to working precision.
593 *
594  IF( rcond.LT.dlamch( 'Epsilon' ) )
595  \$ info = n + 1
596 *
597  rwork( 1 ) = rpvgrw
598  RETURN
599 *
600 * End of ZGESVX
601 *
602  END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
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:143
subroutine zgetrs(TRANS, N, NRHS, A, LDA, IPIV, B, LDB, INFO)
ZGETRS
Definition: zgetrs.f:121
subroutine zgerfs(TRANS, N, NRHS, A, LDA, AF, LDAF, IPIV, B, LDB, X, LDX, FERR, BERR, WORK, RWORK, INFO)
ZGERFS
Definition: zgerfs.f:186
subroutine zgeequ(M, N, A, LDA, R, C, ROWCND, COLCND, AMAX, INFO)
ZGEEQU
Definition: zgeequ.f:140
subroutine zgecon(NORM, N, A, LDA, ANORM, RCOND, WORK, RWORK, INFO)
ZGECON
Definition: zgecon.f:124
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:350
subroutine zlacpy(UPLO, M, N, A, LDA, B, LDB)
ZLACPY copies all or part of one two-dimensional array to another.
Definition: zlacpy.f:103
subroutine zgetrf(M, N, A, LDA, IPIV, INFO)
ZGETRF VARIANT: Crout Level 3 BLAS version of the algorithm.
Definition: zgetrf.f:102