00001 /* cgesvx.f -- translated by f2c (version 20061008). 00002 You must link the resulting object file with libf2c: 00003 on Microsoft Windows system, link with libf2c.lib; 00004 on Linux or Unix systems, link with .../path/to/libf2c.a -lm 00005 or, if you install libf2c.a in a standard place, with -lf2c -lm 00006 -- in that order, at the end of the command line, as in 00007 cc *.o -lf2c -lm 00008 Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., 00009 00010 http://www.netlib.org/f2c/libf2c.zip 00011 */ 00012 00013 #include "f2c.h" 00014 #include "blaswrap.h" 00015 00016 /* Subroutine */ int cgesvx_(char *fact, char *trans, integer *n, integer * 00017 nrhs, complex *a, integer *lda, complex *af, integer *ldaf, integer * 00018 ipiv, char *equed, real *r__, real *c__, complex *b, integer *ldb, 00019 complex *x, integer *ldx, real *rcond, real *ferr, real *berr, 00020 complex *work, real *rwork, integer *info) 00021 { 00022 /* System generated locals */ 00023 integer a_dim1, a_offset, af_dim1, af_offset, b_dim1, b_offset, x_dim1, 00024 x_offset, i__1, i__2, i__3, i__4, i__5; 00025 real r__1, r__2; 00026 complex q__1; 00027 00028 /* Local variables */ 00029 integer i__, j; 00030 real amax; 00031 char norm[1]; 00032 extern logical lsame_(char *, char *); 00033 real rcmin, rcmax, anorm; 00034 logical equil; 00035 extern doublereal clange_(char *, integer *, integer *, complex *, 00036 integer *, real *); 00037 extern /* Subroutine */ int claqge_(integer *, integer *, complex *, 00038 integer *, real *, real *, real *, real *, real *, char *) 00039 , cgecon_(char *, integer *, complex *, integer *, real *, real *, 00040 complex *, real *, integer *); 00041 real colcnd; 00042 extern doublereal slamch_(char *); 00043 extern /* Subroutine */ int cgeequ_(integer *, integer *, complex *, 00044 integer *, real *, real *, real *, real *, real *, integer *); 00045 logical nofact; 00046 extern /* Subroutine */ int cgerfs_(char *, integer *, integer *, complex 00047 *, integer *, complex *, integer *, integer *, complex *, integer 00048 *, complex *, integer *, real *, real *, complex *, real *, 00049 integer *), cgetrf_(integer *, integer *, complex *, 00050 integer *, integer *, integer *), clacpy_(char *, integer *, 00051 integer *, complex *, integer *, complex *, integer *), 00052 xerbla_(char *, integer *); 00053 real bignum; 00054 extern doublereal clantr_(char *, char *, char *, integer *, integer *, 00055 complex *, integer *, real *); 00056 integer infequ; 00057 logical colequ; 00058 extern /* Subroutine */ int cgetrs_(char *, integer *, integer *, complex 00059 *, integer *, integer *, complex *, integer *, integer *); 00060 real rowcnd; 00061 logical notran; 00062 real smlnum; 00063 logical rowequ; 00064 real rpvgrw; 00065 00066 00067 /* -- LAPACK driver routine (version 3.2) -- */ 00068 /* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ 00069 /* November 2006 */ 00070 00071 /* .. Scalar Arguments .. */ 00072 /* .. */ 00073 /* .. Array Arguments .. */ 00074 /* .. */ 00075 00076 /* Purpose */ 00077 /* ======= */ 00078 00079 /* CGESVX uses the LU factorization to compute the solution to a complex */ 00080 /* system of linear equations */ 00081 /* A * X = B, */ 00082 /* where A is an N-by-N matrix and X and B are N-by-NRHS matrices. */ 00083 00084 /* Error bounds on the solution and a condition estimate are also */ 00085 /* provided. */ 00086 00087 /* Description */ 00088 /* =========== */ 00089 00090 /* The following steps are performed: */ 00091 00092 /* 1. If FACT = 'E', real scaling factors are computed to equilibrate */ 00093 /* the system: */ 00094 /* TRANS = 'N': diag(R)*A*diag(C) *inv(diag(C))*X = diag(R)*B */ 00095 /* TRANS = 'T': (diag(R)*A*diag(C))**T *inv(diag(R))*X = diag(C)*B */ 00096 /* TRANS = 'C': (diag(R)*A*diag(C))**H *inv(diag(R))*X = diag(C)*B */ 00097 /* Whether or not the system will be equilibrated depends on the */ 00098 /* scaling of the matrix A, but if equilibration is used, A is */ 00099 /* overwritten by diag(R)*A*diag(C) and B by diag(R)*B (if TRANS='N') */ 00100 /* or diag(C)*B (if TRANS = 'T' or 'C'). */ 00101 00102 /* 2. If FACT = 'N' or 'E', the LU decomposition is used to factor the */ 00103 /* matrix A (after equilibration if FACT = 'E') as */ 00104 /* A = P * L * U, */ 00105 /* where P is a permutation matrix, L is a unit lower triangular */ 00106 /* matrix, and U is upper triangular. */ 00107 00108 /* 3. If some U(i,i)=0, so that U is exactly singular, then the routine */ 00109 /* returns with INFO = i. Otherwise, the factored form of A is used */ 00110 /* to estimate the condition number of the matrix A. If the */ 00111 /* reciprocal of the condition number is less than machine precision, */ 00112 /* INFO = N+1 is returned as a warning, but the routine still goes on */ 00113 /* to solve for X and compute error bounds as described below. */ 00114 00115 /* 4. The system of equations is solved for X using the factored form */ 00116 /* of A. */ 00117 00118 /* 5. Iterative refinement is applied to improve the computed solution */ 00119 /* matrix and calculate error bounds and backward error estimates */ 00120 /* for it. */ 00121 00122 /* 6. If equilibration was used, the matrix X is premultiplied by */ 00123 /* diag(C) (if TRANS = 'N') or diag(R) (if TRANS = 'T' or 'C') so */ 00124 /* that it solves the original system before equilibration. */ 00125 00126 /* Arguments */ 00127 /* ========= */ 00128 00129 /* FACT (input) CHARACTER*1 */ 00130 /* Specifies whether or not the factored form of the matrix A is */ 00131 /* supplied on entry, and if not, whether the matrix A should be */ 00132 /* equilibrated before it is factored. */ 00133 /* = 'F': On entry, AF and IPIV contain the factored form of A. */ 00134 /* If EQUED is not 'N', the matrix A has been */ 00135 /* equilibrated with scaling factors given by R and C. */ 00136 /* A, AF, and IPIV are not modified. */ 00137 /* = 'N': The matrix A will be copied to AF and factored. */ 00138 /* = 'E': The matrix A will be equilibrated if necessary, then */ 00139 /* copied to AF and factored. */ 00140 00141 /* TRANS (input) CHARACTER*1 */ 00142 /* Specifies the form of the system of equations: */ 00143 /* = 'N': A * X = B (No transpose) */ 00144 /* = 'T': A**T * X = B (Transpose) */ 00145 /* = 'C': A**H * X = B (Conjugate transpose) */ 00146 00147 /* N (input) INTEGER */ 00148 /* The number of linear equations, i.e., the order of the */ 00149 /* matrix A. N >= 0. */ 00150 00151 /* NRHS (input) INTEGER */ 00152 /* The number of right hand sides, i.e., the number of columns */ 00153 /* of the matrices B and X. NRHS >= 0. */ 00154 00155 /* A (input/output) COMPLEX array, dimension (LDA,N) */ 00156 /* On entry, the N-by-N matrix A. If FACT = 'F' and EQUED is */ 00157 /* not 'N', then A must have been equilibrated by the scaling */ 00158 /* factors in R and/or C. A is not modified if FACT = 'F' or */ 00159 /* 'N', or if FACT = 'E' and EQUED = 'N' on exit. */ 00160 00161 /* On exit, if EQUED .ne. 'N', A is scaled as follows: */ 00162 /* EQUED = 'R': A := diag(R) * A */ 00163 /* EQUED = 'C': A := A * diag(C) */ 00164 /* EQUED = 'B': A := diag(R) * A * diag(C). */ 00165 00166 /* LDA (input) INTEGER */ 00167 /* The leading dimension of the array A. LDA >= max(1,N). */ 00168 00169 /* AF (input or output) COMPLEX array, dimension (LDAF,N) */ 00170 /* If FACT = 'F', then AF is an input argument and on entry */ 00171 /* contains the factors L and U from the factorization */ 00172 /* A = P*L*U as computed by CGETRF. If EQUED .ne. 'N', then */ 00173 /* AF is the factored form of the equilibrated matrix A. */ 00174 00175 /* If FACT = 'N', then AF is an output argument and on exit */ 00176 /* returns the factors L and U from the factorization A = P*L*U */ 00177 /* of the original matrix A. */ 00178 00179 /* If FACT = 'E', then AF is an output argument and on exit */ 00180 /* returns the factors L and U from the factorization A = P*L*U */ 00181 /* of the equilibrated matrix A (see the description of A for */ 00182 /* the form of the equilibrated matrix). */ 00183 00184 /* LDAF (input) INTEGER */ 00185 /* The leading dimension of the array AF. LDAF >= max(1,N). */ 00186 00187 /* IPIV (input or output) INTEGER array, dimension (N) */ 00188 /* If FACT = 'F', then IPIV is an input argument and on entry */ 00189 /* contains the pivot indices from the factorization A = P*L*U */ 00190 /* as computed by CGETRF; row i of the matrix was interchanged */ 00191 /* with row IPIV(i). */ 00192 00193 /* If FACT = 'N', then IPIV is an output argument and on exit */ 00194 /* contains the pivot indices from the factorization A = P*L*U */ 00195 /* of the original matrix A. */ 00196 00197 /* If FACT = 'E', then IPIV is an output argument and on exit */ 00198 /* contains the pivot indices from the factorization A = P*L*U */ 00199 /* of the equilibrated matrix A. */ 00200 00201 /* EQUED (input or output) CHARACTER*1 */ 00202 /* Specifies the form of equilibration that was done. */ 00203 /* = 'N': No equilibration (always true if FACT = 'N'). */ 00204 /* = 'R': Row equilibration, i.e., A has been premultiplied by */ 00205 /* diag(R). */ 00206 /* = 'C': Column equilibration, i.e., A has been postmultiplied */ 00207 /* by diag(C). */ 00208 /* = 'B': Both row and column equilibration, i.e., A has been */ 00209 /* replaced by diag(R) * A * diag(C). */ 00210 /* EQUED is an input argument if FACT = 'F'; otherwise, it is an */ 00211 /* output argument. */ 00212 00213 /* R (input or output) REAL array, dimension (N) */ 00214 /* The row scale factors for A. If EQUED = 'R' or 'B', A is */ 00215 /* multiplied on the left by diag(R); if EQUED = 'N' or 'C', R */ 00216 /* is not accessed. R is an input argument if FACT = 'F'; */ 00217 /* otherwise, R is an output argument. If FACT = 'F' and */ 00218 /* EQUED = 'R' or 'B', each element of R must be positive. */ 00219 00220 /* C (input or output) REAL array, dimension (N) */ 00221 /* The column scale factors for A. If EQUED = 'C' or 'B', A is */ 00222 /* multiplied on the right by diag(C); if EQUED = 'N' or 'R', C */ 00223 /* is not accessed. C is an input argument if FACT = 'F'; */ 00224 /* otherwise, C is an output argument. If FACT = 'F' and */ 00225 /* EQUED = 'C' or 'B', each element of C must be positive. */ 00226 00227 /* B (input/output) COMPLEX array, dimension (LDB,NRHS) */ 00228 /* On entry, the N-by-NRHS right hand side matrix B. */ 00229 /* On exit, */ 00230 /* if EQUED = 'N', B is not modified; */ 00231 /* if TRANS = 'N' and EQUED = 'R' or 'B', B is overwritten by */ 00232 /* diag(R)*B; */ 00233 /* if TRANS = 'T' or 'C' and EQUED = 'C' or 'B', B is */ 00234 /* overwritten by diag(C)*B. */ 00235 00236 /* LDB (input) INTEGER */ 00237 /* The leading dimension of the array B. LDB >= max(1,N). */ 00238 00239 /* X (output) COMPLEX array, dimension (LDX,NRHS) */ 00240 /* If INFO = 0 or INFO = N+1, the N-by-NRHS solution matrix X */ 00241 /* to the original system of equations. Note that A and B are */ 00242 /* modified on exit if EQUED .ne. 'N', and the solution to the */ 00243 /* equilibrated system is inv(diag(C))*X if TRANS = 'N' and */ 00244 /* EQUED = 'C' or 'B', or inv(diag(R))*X if TRANS = 'T' or 'C' */ 00245 /* and EQUED = 'R' or 'B'. */ 00246 00247 /* LDX (input) INTEGER */ 00248 /* The leading dimension of the array X. LDX >= max(1,N). */ 00249 00250 /* RCOND (output) REAL */ 00251 /* The estimate of the reciprocal condition number of the matrix */ 00252 /* A after equilibration (if done). If RCOND is less than the */ 00253 /* machine precision (in particular, if RCOND = 0), the matrix */ 00254 /* is singular to working precision. This condition is */ 00255 /* indicated by a return code of INFO > 0. */ 00256 00257 /* FERR (output) REAL array, dimension (NRHS) */ 00258 /* The estimated forward error bound for each solution vector */ 00259 /* X(j) (the j-th column of the solution matrix X). */ 00260 /* If XTRUE is the true solution corresponding to X(j), FERR(j) */ 00261 /* is an estimated upper bound for the magnitude of the largest */ 00262 /* element in (X(j) - XTRUE) divided by the magnitude of the */ 00263 /* largest element in X(j). The estimate is as reliable as */ 00264 /* the estimate for RCOND, and is almost always a slight */ 00265 /* overestimate of the true error. */ 00266 00267 /* BERR (output) REAL array, dimension (NRHS) */ 00268 /* The componentwise relative backward error of each solution */ 00269 /* vector X(j) (i.e., the smallest relative change in */ 00270 /* any element of A or B that makes X(j) an exact solution). */ 00271 00272 /* WORK (workspace) COMPLEX array, dimension (2*N) */ 00273 00274 /* RWORK (workspace/output) REAL array, dimension (2*N) */ 00275 /* On exit, RWORK(1) contains the reciprocal pivot growth */ 00276 /* factor norm(A)/norm(U). The "max absolute element" norm is */ 00277 /* used. If RWORK(1) is much less than 1, then the stability */ 00278 /* of the LU factorization of the (equilibrated) matrix A */ 00279 /* could be poor. This also means that the solution X, condition */ 00280 /* estimator RCOND, and forward error bound FERR could be */ 00281 /* unreliable. If factorization fails with 0<INFO<=N, then */ 00282 /* RWORK(1) contains the reciprocal pivot growth factor for the */ 00283 /* leading INFO columns of A. */ 00284 00285 /* INFO (output) INTEGER */ 00286 /* = 0: successful exit */ 00287 /* < 0: if INFO = -i, the i-th argument had an illegal value */ 00288 /* > 0: if INFO = i, and i is */ 00289 /* <= N: U(i,i) is exactly zero. The factorization has */ 00290 /* been completed, but the factor U is exactly */ 00291 /* singular, so the solution and error bounds */ 00292 /* could not be computed. RCOND = 0 is returned. */ 00293 /* = N+1: U is nonsingular, but RCOND is less than machine */ 00294 /* precision, meaning that the matrix is singular */ 00295 /* to working precision. Nevertheless, the */ 00296 /* solution and error bounds are computed because */ 00297 /* there are a number of situations where the */ 00298 /* computed solution can be more accurate than the */ 00299 /* value of RCOND would suggest. */ 00300 00301 /* ===================================================================== */ 00302 00303 /* .. Parameters .. */ 00304 /* .. */ 00305 /* .. Local Scalars .. */ 00306 /* .. */ 00307 /* .. External Functions .. */ 00308 /* .. */ 00309 /* .. External Subroutines .. */ 00310 /* .. */ 00311 /* .. Intrinsic Functions .. */ 00312 /* .. */ 00313 /* .. Executable Statements .. */ 00314 00315 /* Parameter adjustments */ 00316 a_dim1 = *lda; 00317 a_offset = 1 + a_dim1; 00318 a -= a_offset; 00319 af_dim1 = *ldaf; 00320 af_offset = 1 + af_dim1; 00321 af -= af_offset; 00322 --ipiv; 00323 --r__; 00324 --c__; 00325 b_dim1 = *ldb; 00326 b_offset = 1 + b_dim1; 00327 b -= b_offset; 00328 x_dim1 = *ldx; 00329 x_offset = 1 + x_dim1; 00330 x -= x_offset; 00331 --ferr; 00332 --berr; 00333 --work; 00334 --rwork; 00335 00336 /* Function Body */ 00337 *info = 0; 00338 nofact = lsame_(fact, "N"); 00339 equil = lsame_(fact, "E"); 00340 notran = lsame_(trans, "N"); 00341 if (nofact || equil) { 00342 *(unsigned char *)equed = 'N'; 00343 rowequ = FALSE_; 00344 colequ = FALSE_; 00345 } else { 00346 rowequ = lsame_(equed, "R") || lsame_(equed, 00347 "B"); 00348 colequ = lsame_(equed, "C") || lsame_(equed, 00349 "B"); 00350 smlnum = slamch_("Safe minimum"); 00351 bignum = 1.f / smlnum; 00352 } 00353 00354 /* Test the input parameters. */ 00355 00356 if (! nofact && ! equil && ! lsame_(fact, "F")) { 00357 *info = -1; 00358 } else if (! notran && ! lsame_(trans, "T") && ! 00359 lsame_(trans, "C")) { 00360 *info = -2; 00361 } else if (*n < 0) { 00362 *info = -3; 00363 } else if (*nrhs < 0) { 00364 *info = -4; 00365 } else if (*lda < max(1,*n)) { 00366 *info = -6; 00367 } else if (*ldaf < max(1,*n)) { 00368 *info = -8; 00369 } else if (lsame_(fact, "F") && ! (rowequ || colequ 00370 || lsame_(equed, "N"))) { 00371 *info = -10; 00372 } else { 00373 if (rowequ) { 00374 rcmin = bignum; 00375 rcmax = 0.f; 00376 i__1 = *n; 00377 for (j = 1; j <= i__1; ++j) { 00378 /* Computing MIN */ 00379 r__1 = rcmin, r__2 = r__[j]; 00380 rcmin = dmin(r__1,r__2); 00381 /* Computing MAX */ 00382 r__1 = rcmax, r__2 = r__[j]; 00383 rcmax = dmax(r__1,r__2); 00384 /* L10: */ 00385 } 00386 if (rcmin <= 0.f) { 00387 *info = -11; 00388 } else if (*n > 0) { 00389 rowcnd = dmax(rcmin,smlnum) / dmin(rcmax,bignum); 00390 } else { 00391 rowcnd = 1.f; 00392 } 00393 } 00394 if (colequ && *info == 0) { 00395 rcmin = bignum; 00396 rcmax = 0.f; 00397 i__1 = *n; 00398 for (j = 1; j <= i__1; ++j) { 00399 /* Computing MIN */ 00400 r__1 = rcmin, r__2 = c__[j]; 00401 rcmin = dmin(r__1,r__2); 00402 /* Computing MAX */ 00403 r__1 = rcmax, r__2 = c__[j]; 00404 rcmax = dmax(r__1,r__2); 00405 /* L20: */ 00406 } 00407 if (rcmin <= 0.f) { 00408 *info = -12; 00409 } else if (*n > 0) { 00410 colcnd = dmax(rcmin,smlnum) / dmin(rcmax,bignum); 00411 } else { 00412 colcnd = 1.f; 00413 } 00414 } 00415 if (*info == 0) { 00416 if (*ldb < max(1,*n)) { 00417 *info = -14; 00418 } else if (*ldx < max(1,*n)) { 00419 *info = -16; 00420 } 00421 } 00422 } 00423 00424 if (*info != 0) { 00425 i__1 = -(*info); 00426 xerbla_("CGESVX", &i__1); 00427 return 0; 00428 } 00429 00430 if (equil) { 00431 00432 /* Compute row and column scalings to equilibrate the matrix A. */ 00433 00434 cgeequ_(n, n, &a[a_offset], lda, &r__[1], &c__[1], &rowcnd, &colcnd, & 00435 amax, &infequ); 00436 if (infequ == 0) { 00437 00438 /* Equilibrate the matrix. */ 00439 00440 claqge_(n, n, &a[a_offset], lda, &r__[1], &c__[1], &rowcnd, & 00441 colcnd, &amax, equed); 00442 rowequ = lsame_(equed, "R") || lsame_(equed, 00443 "B"); 00444 colequ = lsame_(equed, "C") || lsame_(equed, 00445 "B"); 00446 } 00447 } 00448 00449 /* Scale the right hand side. */ 00450 00451 if (notran) { 00452 if (rowequ) { 00453 i__1 = *nrhs; 00454 for (j = 1; j <= i__1; ++j) { 00455 i__2 = *n; 00456 for (i__ = 1; i__ <= i__2; ++i__) { 00457 i__3 = i__ + j * b_dim1; 00458 i__4 = i__; 00459 i__5 = i__ + j * b_dim1; 00460 q__1.r = r__[i__4] * b[i__5].r, q__1.i = r__[i__4] * b[ 00461 i__5].i; 00462 b[i__3].r = q__1.r, b[i__3].i = q__1.i; 00463 /* L30: */ 00464 } 00465 /* L40: */ 00466 } 00467 } 00468 } else if (colequ) { 00469 i__1 = *nrhs; 00470 for (j = 1; j <= i__1; ++j) { 00471 i__2 = *n; 00472 for (i__ = 1; i__ <= i__2; ++i__) { 00473 i__3 = i__ + j * b_dim1; 00474 i__4 = i__; 00475 i__5 = i__ + j * b_dim1; 00476 q__1.r = c__[i__4] * b[i__5].r, q__1.i = c__[i__4] * b[i__5] 00477 .i; 00478 b[i__3].r = q__1.r, b[i__3].i = q__1.i; 00479 /* L50: */ 00480 } 00481 /* L60: */ 00482 } 00483 } 00484 00485 if (nofact || equil) { 00486 00487 /* Compute the LU factorization of A. */ 00488 00489 clacpy_("Full", n, n, &a[a_offset], lda, &af[af_offset], ldaf); 00490 cgetrf_(n, n, &af[af_offset], ldaf, &ipiv[1], info); 00491 00492 /* Return if INFO is non-zero. */ 00493 00494 if (*info > 0) { 00495 00496 /* Compute the reciprocal pivot growth factor of the */ 00497 /* leading rank-deficient INFO columns of A. */ 00498 00499 rpvgrw = clantr_("M", "U", "N", info, info, &af[af_offset], ldaf, 00500 &rwork[1]); 00501 if (rpvgrw == 0.f) { 00502 rpvgrw = 1.f; 00503 } else { 00504 rpvgrw = clange_("M", n, info, &a[a_offset], lda, &rwork[1]) / rpvgrw; 00505 } 00506 rwork[1] = rpvgrw; 00507 *rcond = 0.f; 00508 return 0; 00509 } 00510 } 00511 00512 /* Compute the norm of the matrix A and the */ 00513 /* reciprocal pivot growth factor RPVGRW. */ 00514 00515 if (notran) { 00516 *(unsigned char *)norm = '1'; 00517 } else { 00518 *(unsigned char *)norm = 'I'; 00519 } 00520 anorm = clange_(norm, n, n, &a[a_offset], lda, &rwork[1]); 00521 rpvgrw = clantr_("M", "U", "N", n, n, &af[af_offset], ldaf, &rwork[1]); 00522 if (rpvgrw == 0.f) { 00523 rpvgrw = 1.f; 00524 } else { 00525 rpvgrw = clange_("M", n, n, &a[a_offset], lda, &rwork[1]) / 00526 rpvgrw; 00527 } 00528 00529 /* Compute the reciprocal of the condition number of A. */ 00530 00531 cgecon_(norm, n, &af[af_offset], ldaf, &anorm, rcond, &work[1], &rwork[1], 00532 info); 00533 00534 /* Compute the solution matrix X. */ 00535 00536 clacpy_("Full", n, nrhs, &b[b_offset], ldb, &x[x_offset], ldx); 00537 cgetrs_(trans, n, nrhs, &af[af_offset], ldaf, &ipiv[1], &x[x_offset], ldx, 00538 info); 00539 00540 /* Use iterative refinement to improve the computed solution and */ 00541 /* compute error bounds and backward error estimates for it. */ 00542 00543 cgerfs_(trans, n, nrhs, &a[a_offset], lda, &af[af_offset], ldaf, &ipiv[1], 00544 &b[b_offset], ldb, &x[x_offset], ldx, &ferr[1], &berr[1], &work[ 00545 1], &rwork[1], info); 00546 00547 /* Transform the solution matrix X to a solution of the original */ 00548 /* system. */ 00549 00550 if (notran) { 00551 if (colequ) { 00552 i__1 = *nrhs; 00553 for (j = 1; j <= i__1; ++j) { 00554 i__2 = *n; 00555 for (i__ = 1; i__ <= i__2; ++i__) { 00556 i__3 = i__ + j * x_dim1; 00557 i__4 = i__; 00558 i__5 = i__ + j * x_dim1; 00559 q__1.r = c__[i__4] * x[i__5].r, q__1.i = c__[i__4] * x[ 00560 i__5].i; 00561 x[i__3].r = q__1.r, x[i__3].i = q__1.i; 00562 /* L70: */ 00563 } 00564 /* L80: */ 00565 } 00566 i__1 = *nrhs; 00567 for (j = 1; j <= i__1; ++j) { 00568 ferr[j] /= colcnd; 00569 /* L90: */ 00570 } 00571 } 00572 } else if (rowequ) { 00573 i__1 = *nrhs; 00574 for (j = 1; j <= i__1; ++j) { 00575 i__2 = *n; 00576 for (i__ = 1; i__ <= i__2; ++i__) { 00577 i__3 = i__ + j * x_dim1; 00578 i__4 = i__; 00579 i__5 = i__ + j * x_dim1; 00580 q__1.r = r__[i__4] * x[i__5].r, q__1.i = r__[i__4] * x[i__5] 00581 .i; 00582 x[i__3].r = q__1.r, x[i__3].i = q__1.i; 00583 /* L100: */ 00584 } 00585 /* L110: */ 00586 } 00587 i__1 = *nrhs; 00588 for (j = 1; j <= i__1; ++j) { 00589 ferr[j] /= rowcnd; 00590 /* L120: */ 00591 } 00592 } 00593 00594 /* Set INFO = N+1 if the matrix is singular to working precision. */ 00595 00596 if (*rcond < slamch_("Epsilon")) { 00597 *info = *n + 1; 00598 } 00599 00600 rwork[1] = rpvgrw; 00601 return 0; 00602 00603 /* End of CGESVX */ 00604 00605 } /* cgesvx_ */