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/* lapack/double/dgesc2.f -- translated by f2c (version 20050501).
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
*/
#ifdef __cplusplus
extern "C" {
#endif
#include "v3p_netlib.h"
/* Table of constant values */
static integer c__1 = 1;
static integer c_n1 = -1;
/*< SUBROUTINE DGESC2( N, A, LDA, RHS, IPIV, JPIV, SCALE ) >*/
/* Subroutine */ int dgesc2_(integer *n, doublereal *a, integer *lda,
doublereal *rhs, integer *ipiv, integer *jpiv, doublereal *scale)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2;
doublereal d__1, d__2;
/* Local variables */
integer i__, j;
doublereal eps, temp;
extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *,
integer *), dlabad_(doublereal *, doublereal *);
extern doublereal dlamch_(char *, ftnlen);
extern integer idamax_(integer *, doublereal *, integer *);
doublereal bignum;
extern /* Subroutine */ int dlaswp_(integer *, doublereal *, integer *,
integer *, integer *, integer *, integer *);
doublereal smlnum;
/* -- LAPACK auxiliary routine (version 3.0) -- */
/* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., */
/* Courant Institute, Argonne National Lab, and Rice University */
/* June 30, 1999 */
/* .. Scalar Arguments .. */
/*< INTEGER LDA, N >*/
/*< DOUBLE PRECISION SCALE >*/
/* .. */
/* .. Array Arguments .. */
/*< INTEGER IPIV( * ), JPIV( * ) >*/
/*< DOUBLE PRECISION A( LDA, * ), RHS( * ) >*/
/* .. */
/* Purpose */
/* ======= */
/* DGESC2 solves a system of linear equations */
/* A * X = scale* RHS */
/* with a general N-by-N matrix A using the LU factorization with */
/* complete pivoting computed by DGETC2. */
/* Arguments */
/* ========= */
/* N (input) INTEGER */
/* The order of the matrix A. */
/* A (input) DOUBLE PRECISION array, dimension (LDA,N) */
/* On entry, the LU part of the factorization of the n-by-n */
/* matrix A computed by DGETC2: A = P * L * U * Q */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= max(1, N). */
/* RHS (input/output) DOUBLE PRECISION array, dimension (N). */
/* On entry, the right hand side vector b. */
/* On exit, the solution vector X. */
/* IPIV (iput) INTEGER array, dimension (N). */
/* The pivot indices; for 1 <= i <= N, row i of the */
/* matrix has been interchanged with row IPIV(i). */
/* JPIV (iput) INTEGER array, dimension (N). */
/* The pivot indices; for 1 <= j <= N, column j of the */
/* matrix has been interchanged with column JPIV(j). */
/* SCALE (output) DOUBLE PRECISION */
/* On exit, SCALE contains the scale factor. SCALE is chosen */
/* 0 <= SCALE <= 1 to prevent owerflow in the solution. */
/* Further Details */
/* =============== */
/* Based on contributions by */
/* Bo Kagstrom and Peter Poromaa, Department of Computing Science, */
/* Umea University, S-901 87 Umea, Sweden. */
/* ===================================================================== */
/* .. Parameters .. */
/*< DOUBLE PRECISION ONE, TWO >*/
/*< PARAMETER ( ONE = 1.0D+0, TWO = 2.0D+0 ) >*/
/* .. */
/* .. Local Scalars .. */
/*< INTEGER I, J >*/
/*< DOUBLE PRECISION BIGNUM, EPS, SMLNUM, TEMP >*/
/* .. */
/* .. External Subroutines .. */
/*< EXTERNAL DLASWP, DSCAL >*/
/* .. */
/* .. External Functions .. */
/*< INTEGER IDAMAX >*/
/*< DOUBLE PRECISION DLAMCH >*/
/*< EXTERNAL IDAMAX, DLAMCH >*/
/* .. */
/* .. Intrinsic Functions .. */
/*< INTRINSIC ABS >*/
/* .. */
/* .. Executable Statements .. */
/* Set constant to control owerflow */
/*< EPS = DLAMCH( 'P' ) >*/
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--rhs;
--ipiv;
--jpiv;
/* Function Body */
eps = dlamch_("P", (ftnlen)1);
/*< SMLNUM = DLAMCH( 'S' ) / EPS >*/
smlnum = dlamch_("S", (ftnlen)1) / eps;
/*< BIGNUM = ONE / SMLNUM >*/
bignum = 1. / smlnum;
/*< CALL DLABAD( SMLNUM, BIGNUM ) >*/
dlabad_(&smlnum, &bignum);
/* Apply permutations IPIV to RHS */
/*< CALL DLASWP( 1, RHS, LDA, 1, N-1, IPIV, 1 ) >*/
i__1 = *n - 1;
dlaswp_(&c__1, &rhs[1], lda, &c__1, &i__1, &ipiv[1], &c__1);
/* Solve for L part */
/*< DO 20 I = 1, N - 1 >*/
i__1 = *n - 1;
for (i__ = 1; i__ <= i__1; ++i__) {
/*< DO 10 J = I + 1, N >*/
i__2 = *n;
for (j = i__ + 1; j <= i__2; ++j) {
/*< RHS( J ) = RHS( J ) - A( J, I )*RHS( I ) >*/
rhs[j] -= a[j + i__ * a_dim1] * rhs[i__];
/*< 10 CONTINUE >*/
/* L10: */
}
/*< 20 CONTINUE >*/
/* L20: */
}
/* Solve for U part */
/*< SCALE = ONE >*/
*scale = 1.;
/* Check for scaling */
/*< I = IDAMAX( N, RHS, 1 ) >*/
i__ = idamax_(n, &rhs[1], &c__1);
/*< IF( TWO*SMLNUM*ABS( RHS( I ) ).GT.ABS( A( N, N ) ) ) THEN >*/
if (smlnum * 2. * (d__1 = rhs[i__], abs(d__1)) > (d__2 = a[*n + *n *
a_dim1], abs(d__2))) {
/*< TEMP = ( ONE / TWO ) / ABS( RHS( I ) ) >*/
temp = .5 / (d__1 = rhs[i__], abs(d__1));
/*< CALL DSCAL( N, TEMP, RHS( 1 ), 1 ) >*/
dscal_(n, &temp, &rhs[1], &c__1);
/*< SCALE = SCALE*TEMP >*/
*scale *= temp;
/*< END IF >*/
}
/*< DO 40 I = N, 1, -1 >*/
for (i__ = *n; i__ >= 1; --i__) {
/*< TEMP = ONE / A( I, I ) >*/
temp = 1. / a[i__ + i__ * a_dim1];
/*< RHS( I ) = RHS( I )*TEMP >*/
rhs[i__] *= temp;
/*< DO 30 J = I + 1, N >*/
i__1 = *n;
for (j = i__ + 1; j <= i__1; ++j) {
/*< RHS( I ) = RHS( I ) - RHS( J )*( A( I, J )*TEMP ) >*/
rhs[i__] -= rhs[j] * (a[i__ + j * a_dim1] * temp);
/*< 30 CONTINUE >*/
/* L30: */
}
/*< 40 CONTINUE >*/
/* L40: */
}
/* Apply permutations JPIV to the solution (RHS) */
/*< CALL DLASWP( 1, RHS, LDA, 1, N-1, JPIV, -1 ) >*/
i__1 = *n - 1;
dlaswp_(&c__1, &rhs[1], lda, &c__1, &i__1, &jpiv[1], &c_n1);
/*< RETURN >*/
return 0;
/* End of DGESC2 */
/*< END >*/
} /* dgesc2_ */
#ifdef __cplusplus
}
#endif
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