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: *
8: *> \htmlonly
9: *> Download ZGESVX + dependencies
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11: *> [TGZ]</a>
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13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zgesvx.f">
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: *> \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
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