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authorshmel1k <shmel1k@ydb.tech>2022-09-02 12:44:59 +0300
committershmel1k <shmel1k@ydb.tech>2022-09-02 12:44:59 +0300
commit90d450f74722da7859d6f510a869f6c6908fd12f (patch)
tree538c718dedc76cdfe37ad6d01ff250dd930d9278 /contrib/libs/clapack/dgesvx.c
parent01f64c1ecd0d4ffa9e3a74478335f1745f26cc75 (diff)
downloadydb-90d450f74722da7859d6f510a869f6c6908fd12f.tar.gz
[] add metering mode to CLI
Diffstat (limited to 'contrib/libs/clapack/dgesvx.c')
-rw-r--r--contrib/libs/clapack/dgesvx.c587
1 files changed, 587 insertions, 0 deletions
diff --git a/contrib/libs/clapack/dgesvx.c b/contrib/libs/clapack/dgesvx.c
new file mode 100644
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+++ b/contrib/libs/clapack/dgesvx.c
@@ -0,0 +1,587 @@
+/* dgesvx.f -- translated by f2c (version 20061008).
+ You must link the resulting object file with libf2c:
+ on Microsoft Windows system, link with libf2c.lib;
+ on Linux or Unix systems, link with .../path/to/libf2c.a -lm
+ or, if you install libf2c.a in a standard place, with -lf2c -lm
+ -- in that order, at the end of the command line, as in
+ cc *.o -lf2c -lm
+ Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
+
+ http://www.netlib.org/f2c/libf2c.zip
+*/
+
+#include "f2c.h"
+#include "blaswrap.h"
+
+/* Subroutine */ int dgesvx_(char *fact, char *trans, integer *n, integer *
+ nrhs, doublereal *a, integer *lda, doublereal *af, integer *ldaf,
+ integer *ipiv, char *equed, doublereal *r__, doublereal *c__,
+ doublereal *b, integer *ldb, doublereal *x, integer *ldx, doublereal *
+ rcond, doublereal *ferr, doublereal *berr, doublereal *work, integer *
+ iwork, integer *info)
+{
+ /* System generated locals */
+ integer a_dim1, a_offset, af_dim1, af_offset, b_dim1, b_offset, x_dim1,
+ x_offset, i__1, i__2;
+ doublereal d__1, d__2;
+
+ /* Local variables */
+ integer i__, j;
+ doublereal amax;
+ char norm[1];
+ extern logical lsame_(char *, char *);
+ doublereal rcmin, rcmax, anorm;
+ logical equil;
+ extern doublereal dlamch_(char *), dlange_(char *, integer *,
+ integer *, doublereal *, integer *, doublereal *);
+ extern /* Subroutine */ int dlaqge_(integer *, integer *, doublereal *,
+ integer *, doublereal *, doublereal *, doublereal *, doublereal *,
+ doublereal *, char *), dgecon_(char *, integer *,
+ doublereal *, integer *, doublereal *, doublereal *, doublereal *,
+ integer *, integer *);
+ doublereal colcnd;
+ logical nofact;
+ extern /* Subroutine */ int dgeequ_(integer *, integer *, doublereal *,
+ integer *, doublereal *, doublereal *, doublereal *, doublereal *,
+ doublereal *, integer *), dgerfs_(char *, integer *, integer *,
+ doublereal *, integer *, doublereal *, integer *, integer *,
+ doublereal *, integer *, doublereal *, integer *, doublereal *,
+ doublereal *, doublereal *, integer *, integer *),
+ dgetrf_(integer *, integer *, doublereal *, integer *, integer *,
+ integer *), dlacpy_(char *, integer *, integer *, doublereal *,
+ integer *, doublereal *, integer *), xerbla_(char *,
+ integer *);
+ doublereal bignum;
+ extern doublereal dlantr_(char *, char *, char *, integer *, integer *,
+ doublereal *, integer *, doublereal *);
+ integer infequ;
+ logical colequ;
+ extern /* Subroutine */ int dgetrs_(char *, integer *, integer *,
+ doublereal *, integer *, integer *, doublereal *, integer *,
+ integer *);
+ doublereal rowcnd;
+ logical notran;
+ doublereal smlnum;
+ logical rowequ;
+ doublereal rpvgrw;
+
+
+/* -- LAPACK driver routine (version 3.2) -- */
+/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
+/* November 2006 */
+
+/* .. Scalar Arguments .. */
+/* .. */
+/* .. Array Arguments .. */
+/* .. */
+
+/* Purpose */
+/* ======= */
+
+/* DGESVX uses the LU factorization to compute the solution to a real */
+/* system of linear equations */
+/* A * X = B, */
+/* where A is an N-by-N matrix and X and B are N-by-NRHS matrices. */
+
+/* Error bounds on the solution and a condition estimate are also */
+/* provided. */
+
+/* Description */
+/* =========== */
+
+/* The following steps are performed: */
+
+/* 1. If FACT = 'E', real scaling factors are computed to equilibrate */
+/* the system: */
+/* TRANS = 'N': diag(R)*A*diag(C) *inv(diag(C))*X = diag(R)*B */
+/* TRANS = 'T': (diag(R)*A*diag(C))**T *inv(diag(R))*X = diag(C)*B */
+/* TRANS = 'C': (diag(R)*A*diag(C))**H *inv(diag(R))*X = diag(C)*B */
+/* Whether or not the system will be equilibrated depends on the */
+/* scaling of the matrix A, but if equilibration is used, A is */
+/* overwritten by diag(R)*A*diag(C) and B by diag(R)*B (if TRANS='N') */
+/* or diag(C)*B (if TRANS = 'T' or 'C'). */
+
+/* 2. If FACT = 'N' or 'E', the LU decomposition is used to factor the */
+/* matrix A (after equilibration if FACT = 'E') as */
+/* A = P * L * U, */
+/* where P is a permutation matrix, L is a unit lower triangular */
+/* matrix, and U is upper triangular. */
+
+/* 3. If some U(i,i)=0, so that U is exactly singular, then the routine */
+/* returns with INFO = i. Otherwise, the factored form of A is used */
+/* to estimate the condition number of the matrix A. If the */
+/* reciprocal of the condition number is less than machine precision, */
+/* INFO = N+1 is returned as a warning, but the routine still goes on */
+/* to solve for X and compute error bounds as described below. */
+
+/* 4. The system of equations is solved for X using the factored form */
+/* of A. */
+
+/* 5. Iterative refinement is applied to improve the computed solution */
+/* matrix and calculate error bounds and backward error estimates */
+/* for it. */
+
+/* 6. If equilibration was used, the matrix X is premultiplied by */
+/* diag(C) (if TRANS = 'N') or diag(R) (if TRANS = 'T' or 'C') so */
+/* that it solves the original system before equilibration. */
+
+/* Arguments */
+/* ========= */
+
+/* FACT (input) CHARACTER*1 */
+/* Specifies whether or not the factored form of the matrix A is */
+/* supplied on entry, and if not, whether the matrix A should be */
+/* equilibrated before it is factored. */
+/* = 'F': On entry, AF and IPIV contain the factored form of A. */
+/* If EQUED is not 'N', the matrix A has been */
+/* equilibrated with scaling factors given by R and C. */
+/* A, AF, and IPIV are not modified. */
+/* = 'N': The matrix A will be copied to AF and factored. */
+/* = 'E': The matrix A will be equilibrated if necessary, then */
+/* copied to AF and factored. */
+
+/* TRANS (input) CHARACTER*1 */
+/* Specifies the form of the system of equations: */
+/* = 'N': A * X = B (No transpose) */
+/* = 'T': A**T * X = B (Transpose) */
+/* = 'C': A**H * X = B (Transpose) */
+
+/* N (input) INTEGER */
+/* The number of linear equations, i.e., the order of the */
+/* matrix A. N >= 0. */
+
+/* NRHS (input) INTEGER */
+/* The number of right hand sides, i.e., the number of columns */
+/* of the matrices B and X. NRHS >= 0. */
+
+/* A (input/output) DOUBLE PRECISION array, dimension (LDA,N) */
+/* On entry, the N-by-N matrix A. If FACT = 'F' and EQUED is */
+/* not 'N', then A must have been equilibrated by the scaling */
+/* factors in R and/or C. A is not modified if FACT = 'F' or */
+/* 'N', or if FACT = 'E' and EQUED = 'N' on exit. */
+
+/* On exit, if EQUED .ne. 'N', A is scaled as follows: */
+/* EQUED = 'R': A := diag(R) * A */
+/* EQUED = 'C': A := A * diag(C) */
+/* EQUED = 'B': A := diag(R) * A * diag(C). */
+
+/* LDA (input) INTEGER */
+/* The leading dimension of the array A. LDA >= max(1,N). */
+
+/* AF (input or output) DOUBLE PRECISION array, dimension (LDAF,N) */
+/* If FACT = 'F', then AF is an input argument and on entry */
+/* contains the factors L and U from the factorization */
+/* A = P*L*U as computed by DGETRF. If EQUED .ne. 'N', then */
+/* AF is the factored form of the equilibrated matrix A. */
+
+/* If FACT = 'N', then AF is an output argument and on exit */
+/* returns the factors L and U from the factorization A = P*L*U */
+/* of the original matrix A. */
+
+/* If FACT = 'E', then AF is an output argument and on exit */
+/* returns the factors L and U from the factorization A = P*L*U */
+/* of the equilibrated matrix A (see the description of A for */
+/* the form of the equilibrated matrix). */
+
+/* LDAF (input) INTEGER */
+/* The leading dimension of the array AF. LDAF >= max(1,N). */
+
+/* IPIV (input or output) INTEGER array, dimension (N) */
+/* If FACT = 'F', then IPIV is an input argument and on entry */
+/* contains the pivot indices from the factorization A = P*L*U */
+/* as computed by DGETRF; row i of the matrix was interchanged */
+/* with row IPIV(i). */
+
+/* If FACT = 'N', then IPIV is an output argument and on exit */
+/* contains the pivot indices from the factorization A = P*L*U */
+/* of the original matrix A. */
+
+/* If FACT = 'E', then IPIV is an output argument and on exit */
+/* contains the pivot indices from the factorization A = P*L*U */
+/* of the equilibrated matrix A. */
+
+/* EQUED (input or output) CHARACTER*1 */
+/* Specifies the form of equilibration that was done. */
+/* = 'N': No equilibration (always true if FACT = 'N'). */
+/* = 'R': Row equilibration, i.e., A has been premultiplied by */
+/* diag(R). */
+/* = 'C': Column equilibration, i.e., A has been postmultiplied */
+/* by diag(C). */
+/* = 'B': Both row and column equilibration, i.e., A has been */
+/* replaced by diag(R) * A * diag(C). */
+/* EQUED is an input argument if FACT = 'F'; otherwise, it is an */
+/* output argument. */
+
+/* R (input or output) DOUBLE PRECISION array, dimension (N) */
+/* The row scale factors for A. If EQUED = 'R' or 'B', A is */
+/* multiplied on the left by diag(R); if EQUED = 'N' or 'C', R */
+/* is not accessed. R is an input argument if FACT = 'F'; */
+/* otherwise, R is an output argument. If FACT = 'F' and */
+/* EQUED = 'R' or 'B', each element of R must be positive. */
+
+/* C (input or output) DOUBLE PRECISION array, dimension (N) */
+/* The column scale factors for A. If EQUED = 'C' or 'B', A is */
+/* multiplied on the right by diag(C); if EQUED = 'N' or 'R', C */
+/* is not accessed. C is an input argument if FACT = 'F'; */
+/* otherwise, C is an output argument. If FACT = 'F' and */
+/* EQUED = 'C' or 'B', each element of C must be positive. */
+
+/* B (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS) */
+/* On entry, the N-by-NRHS right hand side matrix B. */
+/* On exit, */
+/* if EQUED = 'N', B is not modified; */
+/* if TRANS = 'N' and EQUED = 'R' or 'B', B is overwritten by */
+/* diag(R)*B; */
+/* if TRANS = 'T' or 'C' and EQUED = 'C' or 'B', B is */
+/* overwritten by diag(C)*B. */
+
+/* LDB (input) INTEGER */
+/* The leading dimension of the array B. LDB >= max(1,N). */
+
+/* X (output) DOUBLE PRECISION array, dimension (LDX,NRHS) */
+/* If INFO = 0 or INFO = N+1, the N-by-NRHS solution matrix X */
+/* to the original system of equations. Note that A and B are */
+/* modified on exit if EQUED .ne. 'N', and the solution to the */
+/* equilibrated system is inv(diag(C))*X if TRANS = 'N' and */
+/* EQUED = 'C' or 'B', or inv(diag(R))*X if TRANS = 'T' or 'C' */
+/* and EQUED = 'R' or 'B'. */
+
+/* LDX (input) INTEGER */
+/* The leading dimension of the array X. LDX >= max(1,N). */
+
+/* RCOND (output) DOUBLE PRECISION */
+/* The estimate of the reciprocal condition number of the matrix */
+/* A after equilibration (if done). If RCOND is less than the */
+/* machine precision (in particular, if RCOND = 0), the matrix */
+/* is singular to working precision. This condition is */
+/* indicated by a return code of INFO > 0. */
+
+/* FERR (output) DOUBLE PRECISION array, dimension (NRHS) */
+/* The estimated forward error bound for each solution vector */
+/* X(j) (the j-th column of the solution matrix X). */
+/* If XTRUE is the true solution corresponding to X(j), FERR(j) */
+/* is an estimated upper bound for the magnitude of the largest */
+/* element in (X(j) - XTRUE) divided by the magnitude of the */
+/* largest element in X(j). The estimate is as reliable as */
+/* the estimate for RCOND, and is almost always a slight */
+/* overestimate of the true error. */
+
+/* BERR (output) DOUBLE PRECISION array, dimension (NRHS) */
+/* The componentwise relative backward error of each solution */
+/* vector X(j) (i.e., the smallest relative change in */
+/* any element of A or B that makes X(j) an exact solution). */
+
+/* WORK (workspace/output) DOUBLE PRECISION array, dimension (4*N) */
+/* On exit, WORK(1) contains the reciprocal pivot growth */
+/* factor norm(A)/norm(U). The "max absolute element" norm is */
+/* used. If WORK(1) is much less than 1, then the stability */
+/* of the LU factorization of the (equilibrated) matrix A */
+/* could be poor. This also means that the solution X, condition */
+/* estimator RCOND, and forward error bound FERR could be */
+/* unreliable. If factorization fails with 0<INFO<=N, then */
+/* WORK(1) contains the reciprocal pivot growth factor for the */
+/* leading INFO columns of A. */
+
+/* IWORK (workspace) INTEGER array, dimension (N) */
+
+/* INFO (output) INTEGER */
+/* = 0: successful exit */
+/* < 0: if INFO = -i, the i-th argument had an illegal value */
+/* > 0: if INFO = i, and i is */
+/* <= N: U(i,i) is exactly zero. The factorization has */
+/* been completed, but the factor U is exactly */
+/* singular, so the solution and error bounds */
+/* could not be computed. RCOND = 0 is returned. */
+/* = N+1: U is nonsingular, but RCOND is less than machine */
+/* precision, meaning that the matrix is singular */
+/* to working precision. Nevertheless, the */
+/* solution and error bounds are computed because */
+/* there are a number of situations where the */
+/* computed solution can be more accurate than the */
+/* value of RCOND would suggest. */
+
+/* ===================================================================== */
+
+/* .. Parameters .. */
+/* .. */
+/* .. Local Scalars .. */
+/* .. */
+/* .. External Functions .. */
+/* .. */
+/* .. External Subroutines .. */
+/* .. */
+/* .. Intrinsic Functions .. */
+/* .. */
+/* .. Executable Statements .. */
+
+ /* Parameter adjustments */
+ a_dim1 = *lda;
+ a_offset = 1 + a_dim1;
+ a -= a_offset;
+ af_dim1 = *ldaf;
+ af_offset = 1 + af_dim1;
+ af -= af_offset;
+ --ipiv;
+ --r__;
+ --c__;
+ b_dim1 = *ldb;
+ b_offset = 1 + b_dim1;
+ b -= b_offset;
+ x_dim1 = *ldx;
+ x_offset = 1 + x_dim1;
+ x -= x_offset;
+ --ferr;
+ --berr;
+ --work;
+ --iwork;
+
+ /* Function Body */
+ *info = 0;
+ nofact = lsame_(fact, "N");
+ equil = lsame_(fact, "E");
+ notran = lsame_(trans, "N");
+ if (nofact || equil) {
+ *(unsigned char *)equed = 'N';
+ rowequ = FALSE_;
+ colequ = FALSE_;
+ } else {
+ rowequ = lsame_(equed, "R") || lsame_(equed,
+ "B");
+ colequ = lsame_(equed, "C") || lsame_(equed,
+ "B");
+ smlnum = dlamch_("Safe minimum");
+ bignum = 1. / smlnum;
+ }
+
+/* Test the input parameters. */
+
+ if (! nofact && ! equil && ! lsame_(fact, "F")) {
+ *info = -1;
+ } else if (! notran && ! lsame_(trans, "T") && !
+ lsame_(trans, "C")) {
+ *info = -2;
+ } else if (*n < 0) {
+ *info = -3;
+ } else if (*nrhs < 0) {
+ *info = -4;
+ } else if (*lda < max(1,*n)) {
+ *info = -6;
+ } else if (*ldaf < max(1,*n)) {
+ *info = -8;
+ } else if (lsame_(fact, "F") && ! (rowequ || colequ
+ || lsame_(equed, "N"))) {
+ *info = -10;
+ } else {
+ if (rowequ) {
+ rcmin = bignum;
+ rcmax = 0.;
+ i__1 = *n;
+ for (j = 1; j <= i__1; ++j) {
+/* Computing MIN */
+ d__1 = rcmin, d__2 = r__[j];
+ rcmin = min(d__1,d__2);
+/* Computing MAX */
+ d__1 = rcmax, d__2 = r__[j];
+ rcmax = max(d__1,d__2);
+/* L10: */
+ }
+ if (rcmin <= 0.) {
+ *info = -11;
+ } else if (*n > 0) {
+ rowcnd = max(rcmin,smlnum) / min(rcmax,bignum);
+ } else {
+ rowcnd = 1.;
+ }
+ }
+ if (colequ && *info == 0) {
+ rcmin = bignum;
+ rcmax = 0.;
+ i__1 = *n;
+ for (j = 1; j <= i__1; ++j) {
+/* Computing MIN */
+ d__1 = rcmin, d__2 = c__[j];
+ rcmin = min(d__1,d__2);
+/* Computing MAX */
+ d__1 = rcmax, d__2 = c__[j];
+ rcmax = max(d__1,d__2);
+/* L20: */
+ }
+ if (rcmin <= 0.) {
+ *info = -12;
+ } else if (*n > 0) {
+ colcnd = max(rcmin,smlnum) / min(rcmax,bignum);
+ } else {
+ colcnd = 1.;
+ }
+ }
+ if (*info == 0) {
+ if (*ldb < max(1,*n)) {
+ *info = -14;
+ } else if (*ldx < max(1,*n)) {
+ *info = -16;
+ }
+ }
+ }
+
+ if (*info != 0) {
+ i__1 = -(*info);
+ xerbla_("DGESVX", &i__1);
+ return 0;
+ }
+
+ if (equil) {
+
+/* Compute row and column scalings to equilibrate the matrix A. */
+
+ dgeequ_(n, n, &a[a_offset], lda, &r__[1], &c__[1], &rowcnd, &colcnd, &
+ amax, &infequ);
+ if (infequ == 0) {
+
+/* Equilibrate the matrix. */
+
+ dlaqge_(n, n, &a[a_offset], lda, &r__[1], &c__[1], &rowcnd, &
+ colcnd, &amax, equed);
+ rowequ = lsame_(equed, "R") || lsame_(equed,
+ "B");
+ colequ = lsame_(equed, "C") || lsame_(equed,
+ "B");
+ }
+ }
+
+/* Scale the right hand side. */
+
+ if (notran) {
+ if (rowequ) {
+ i__1 = *nrhs;
+ for (j = 1; j <= i__1; ++j) {
+ i__2 = *n;
+ for (i__ = 1; i__ <= i__2; ++i__) {
+ b[i__ + j * b_dim1] = r__[i__] * b[i__ + j * b_dim1];
+/* L30: */
+ }
+/* L40: */
+ }
+ }
+ } else if (colequ) {
+ i__1 = *nrhs;
+ for (j = 1; j <= i__1; ++j) {
+ i__2 = *n;
+ for (i__ = 1; i__ <= i__2; ++i__) {
+ b[i__ + j * b_dim1] = c__[i__] * b[i__ + j * b_dim1];
+/* L50: */
+ }
+/* L60: */
+ }
+ }
+
+ if (nofact || equil) {
+
+/* Compute the LU factorization of A. */
+
+ dlacpy_("Full", n, n, &a[a_offset], lda, &af[af_offset], ldaf);
+ dgetrf_(n, n, &af[af_offset], ldaf, &ipiv[1], info);
+
+/* Return if INFO is non-zero. */
+
+ if (*info > 0) {
+
+/* Compute the reciprocal pivot growth factor of the */
+/* leading rank-deficient INFO columns of A. */
+
+ rpvgrw = dlantr_("M", "U", "N", info, info, &af[af_offset], ldaf,
+ &work[1]);
+ if (rpvgrw == 0.) {
+ rpvgrw = 1.;
+ } else {
+ rpvgrw = dlange_("M", n, info, &a[a_offset], lda, &work[1]) / rpvgrw;
+ }
+ work[1] = rpvgrw;
+ *rcond = 0.;
+ return 0;
+ }
+ }
+
+/* Compute the norm of the matrix A and the */
+/* reciprocal pivot growth factor RPVGRW. */
+
+ if (notran) {
+ *(unsigned char *)norm = '1';
+ } else {
+ *(unsigned char *)norm = 'I';
+ }
+ anorm = dlange_(norm, n, n, &a[a_offset], lda, &work[1]);
+ rpvgrw = dlantr_("M", "U", "N", n, n, &af[af_offset], ldaf, &work[1]);
+ if (rpvgrw == 0.) {
+ rpvgrw = 1.;
+ } else {
+ rpvgrw = dlange_("M", n, n, &a[a_offset], lda, &work[1]) /
+ rpvgrw;
+ }
+
+/* Compute the reciprocal of the condition number of A. */
+
+ dgecon_(norm, n, &af[af_offset], ldaf, &anorm, rcond, &work[1], &iwork[1],
+ info);
+
+/* Compute the solution matrix X. */
+
+ dlacpy_("Full", n, nrhs, &b[b_offset], ldb, &x[x_offset], ldx);
+ dgetrs_(trans, n, nrhs, &af[af_offset], ldaf, &ipiv[1], &x[x_offset], ldx,
+ info);
+
+/* Use iterative refinement to improve the computed solution and */
+/* compute error bounds and backward error estimates for it. */
+
+ dgerfs_(trans, n, nrhs, &a[a_offset], lda, &af[af_offset], ldaf, &ipiv[1],
+ &b[b_offset], ldb, &x[x_offset], ldx, &ferr[1], &berr[1], &work[
+ 1], &iwork[1], info);
+
+/* Transform the solution matrix X to a solution of the original */
+/* system. */
+
+ if (notran) {
+ if (colequ) {
+ i__1 = *nrhs;
+ for (j = 1; j <= i__1; ++j) {
+ i__2 = *n;
+ for (i__ = 1; i__ <= i__2; ++i__) {
+ x[i__ + j * x_dim1] = c__[i__] * x[i__ + j * x_dim1];
+/* L70: */
+ }
+/* L80: */
+ }
+ i__1 = *nrhs;
+ for (j = 1; j <= i__1; ++j) {
+ ferr[j] /= colcnd;
+/* L90: */
+ }
+ }
+ } else if (rowequ) {
+ i__1 = *nrhs;
+ for (j = 1; j <= i__1; ++j) {
+ i__2 = *n;
+ for (i__ = 1; i__ <= i__2; ++i__) {
+ x[i__ + j * x_dim1] = r__[i__] * x[i__ + j * x_dim1];
+/* L100: */
+ }
+/* L110: */
+ }
+ i__1 = *nrhs;
+ for (j = 1; j <= i__1; ++j) {
+ ferr[j] /= rowcnd;
+/* L120: */
+ }
+ }
+
+ work[1] = rpvgrw;
+
+/* Set INFO = N+1 if the matrix is singular to working precision. */
+
+ if (*rcond < dlamch_("Epsilon")) {
+ *info = *n + 1;
+ }
+ return 0;
+
+/* End of DGESVX */
+
+} /* dgesvx_ */