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/* lapack/complex16/zgesc2.f -- translated by f2c (version 20090411).
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 doublecomplex c_b13 = {1.,0.};
static integer c_n1 = -1;
/*< SUBROUTINE ZGESC2( N, A, LDA, RHS, IPIV, JPIV, SCALE ) >*/
/* Subroutine */ int zgesc2_(integer *n, doublecomplex *a, integer *lda,
doublecomplex *rhs, integer *ipiv, integer *jpiv, doublereal *scale)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5, i__6;
doublereal d__1;
doublecomplex z__1, z__2, z__3;
/* Builtin functions */
double z_abs(doublecomplex *);
void z_div(doublecomplex *, doublecomplex *, doublecomplex *);
/* Local variables */
integer i__, j;
doublereal eps;
doublecomplex temp;
extern /* Subroutine */ int zscal_(integer *, doublecomplex *,
doublecomplex *, integer *), dlabad_(doublereal *, doublereal *);
extern doublereal dlamch_(char *, ftnlen);
doublereal bignum;
extern integer izamax_(integer *, doublecomplex *, integer *);
doublereal smlnum;
extern /* Subroutine */ int zlaswp_(integer *, doublecomplex *, integer *,
integer *, integer *, integer *, integer *);
/* -- LAPACK auxiliary routine (version 3.2) -- */
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
/* November 2006 */
/* .. Scalar Arguments .. */
/*< INTEGER LDA, N >*/
/*< DOUBLE PRECISION SCALE >*/
/* .. */
/* .. Array Arguments .. */
/*< INTEGER IPIV( * ), JPIV( * ) >*/
/*< COMPLEX*16 A( LDA, * ), RHS( * ) >*/
/* .. */
/* Purpose */
/* ======= */
/* ZGESC2 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 ZGETC2. */
/* Arguments */
/* ========= */
/* N (input) INTEGER */
/* The number of columns of the matrix A. */
/* A (input) COMPLEX*16 array, dimension (LDA, N) */
/* On entry, the LU part of the factorization of the n-by-n */
/* matrix A computed by ZGETC2: A = P * L * U * Q */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= max(1, N). */
/* RHS (input/output) COMPLEX*16 array, dimension N. */
/* On entry, the right hand side vector b. */
/* On exit, the solution vector X. */
/* IPIV (input) INTEGER array, dimension (N). */
/* The pivot indices; for 1 <= i <= N, row i of the */
/* matrix has been interchanged with row IPIV(i). */
/* JPIV (input) 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 ZERO, ONE, TWO >*/
/*< PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0, TWO = 2.0D+0 ) >*/
/* .. */
/* .. Local Scalars .. */
/*< INTEGER I, J >*/
/*< DOUBLE PRECISION BIGNUM, EPS, SMLNUM >*/
/*< COMPLEX*16 TEMP >*/
/* .. */
/* .. External Subroutines .. */
/*< EXTERNAL ZLASWP, ZSCAL >*/
/* .. */
/* .. External Functions .. */
/*< INTEGER IZAMAX >*/
/*< DOUBLE PRECISION DLAMCH >*/
/*< EXTERNAL IZAMAX, DLAMCH >*/
/* .. */
/* .. Intrinsic Functions .. */
/*< INTRINSIC ABS, DBLE, DCMPLX >*/
/* .. */
/* .. Executable Statements .. */
/* Set constant to control overflow */
/*< 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 ZLASWP( 1, RHS, LDA, 1, N-1, IPIV, 1 ) >*/
i__1 = *n - 1;
zlaswp_(&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 ) >*/
i__3 = j;
i__4 = j;
i__5 = j + i__ * a_dim1;
i__6 = i__;
z__2.r = a[i__5].r * rhs[i__6].r - a[i__5].i * rhs[i__6].i,
z__2.i = a[i__5].r * rhs[i__6].i + a[i__5].i * rhs[i__6]
.r;
z__1.r = rhs[i__4].r - z__2.r, z__1.i = rhs[i__4].i - z__2.i;
rhs[i__3].r = z__1.r, rhs[i__3].i = z__1.i;
/*< 10 CONTINUE >*/
/* L10: */
}
/*< 20 CONTINUE >*/
/* L20: */
}
/* Solve for U part */
/*< SCALE = ONE >*/
*scale = 1.;
/* Check for scaling */
/*< I = IZAMAX( N, RHS, 1 ) >*/
i__ = izamax_(n, &rhs[1], &c__1);
/*< IF( TWO*SMLNUM*ABS( RHS( I ) ).GT.ABS( A( N, N ) ) ) THEN >*/
if (smlnum * 2. * z_abs(&rhs[i__]) > z_abs(&a[*n + *n * a_dim1])) {
/*< TEMP = DCMPLX( ONE / TWO, ZERO ) / ABS( RHS( I ) ) >*/
d__1 = z_abs(&rhs[i__]);
z__1.r = .5 / d__1, z__1.i = 0. / d__1;
temp.r = z__1.r, temp.i = z__1.i;
/*< CALL ZSCAL( N, TEMP, RHS( 1 ), 1 ) >*/
zscal_(n, &temp, &rhs[1], &c__1);
/*< SCALE = SCALE*DBLE( TEMP ) >*/
*scale *= temp.r;
/*< END IF >*/
}
/*< DO 40 I = N, 1, -1 >*/
for (i__ = *n; i__ >= 1; --i__) {
/*< TEMP = DCMPLX( ONE, ZERO ) / A( I, I ) >*/
z_div(&z__1, &c_b13, &a[i__ + i__ * a_dim1]);
temp.r = z__1.r, temp.i = z__1.i;
/*< RHS( I ) = RHS( I )*TEMP >*/
i__1 = i__;
i__2 = i__;
z__1.r = rhs[i__2].r * temp.r - rhs[i__2].i * temp.i, z__1.i = rhs[
i__2].r * temp.i + rhs[i__2].i * temp.r;
rhs[i__1].r = z__1.r, rhs[i__1].i = z__1.i;
/*< 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 ) >*/
i__2 = i__;
i__3 = i__;
i__4 = j;
i__5 = i__ + j * a_dim1;
z__3.r = a[i__5].r * temp.r - a[i__5].i * temp.i, z__3.i = a[i__5]
.r * temp.i + a[i__5].i * temp.r;
z__2.r = rhs[i__4].r * z__3.r - rhs[i__4].i * z__3.i, z__2.i =
rhs[i__4].r * z__3.i + rhs[i__4].i * z__3.r;
z__1.r = rhs[i__3].r - z__2.r, z__1.i = rhs[i__3].i - z__2.i;
rhs[i__2].r = z__1.r, rhs[i__2].i = z__1.i;
/*< 30 CONTINUE >*/
/* L30: */
}
/*< 40 CONTINUE >*/
/* L40: */
}
/* Apply permutations JPIV to the solution (RHS) */
/*< CALL ZLASWP( 1, RHS, LDA, 1, N-1, JPIV, -1 ) >*/
i__1 = *n - 1;
zlaswp_(&c__1, &rhs[1], lda, &c__1, &i__1, &jpiv[1], &c_n1);
/*< RETURN >*/
return 0;
/* End of ZGESC2 */
/*< END >*/
} /* zgesc2_ */
#ifdef __cplusplus
}
#endif
|
