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cgesc2.c
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/* cgesc2.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"
/* Table of constant values */
static integer c__1 = 1;
static complex c_b13 = {1.f,0.f};
static integer c_n1 = -1;
/* Subroutine */ int cgesc2_(integer *n, complex *a, integer *lda, complex *
rhs, integer *ipiv, integer *jpiv, real *scale)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5, i__6;
real r__1;
complex q__1, q__2, q__3;
/* Builtin functions */
double c_abs(complex *);
void c_div(complex *, complex *, complex *);
/* Local variables */
integer i__, j;
real eps;
complex temp;
extern /* Subroutine */ int cscal_(integer *, complex *, complex *,
integer *), slabad_(real *, real *);
extern integer icamax_(integer *, complex *, integer *);
extern doublereal slamch_(char *);
real bignum;
extern /* Subroutine */ int claswp_(integer *, complex *, integer *,
integer *, integer *, integer *, integer *);
real smlnum;
/* -- LAPACK auxiliary routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* CGESC2 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 CGETC2. */
/* Arguments */
/* ========= */
/* N (input) INTEGER */
/* The number of columns of the matrix A. */
/* A (input) COMPLEX array, dimension (LDA, N) */
/* On entry, the LU part of the factorization of the n-by-n */
/* matrix A computed by CGETC2: A = P * L * U * Q */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= max(1, N). */
/* RHS (input/output) COMPLEX 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) REAL */
/* 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 .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Set constant to control overflow */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--rhs;
--ipiv;
--jpiv;
/* Function Body */
eps = slamch_("P");
smlnum = slamch_("S") / eps;
bignum = 1.f / smlnum;
slabad_(&smlnum, &bignum);
/* Apply permutations IPIV to RHS */
i__1 = *n - 1;
claswp_(&c__1, &rhs[1], lda, &c__1, &i__1, &ipiv[1], &c__1);
/* Solve for L part */
i__1 = *n - 1;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = *n;
for (j = i__ + 1; j <= i__2; ++j) {
i__3 = j;
i__4 = j;
i__5 = j + i__ * a_dim1;
i__6 = i__;
q__2.r = a[i__5].r * rhs[i__6].r - a[i__5].i * rhs[i__6].i,
q__2.i = a[i__5].r * rhs[i__6].i + a[i__5].i * rhs[i__6]
.r;
q__1.r = rhs[i__4].r - q__2.r, q__1.i = rhs[i__4].i - q__2.i;
rhs[i__3].r = q__1.r, rhs[i__3].i = q__1.i;
/* L10: */
}
/* L20: */
}
/* Solve for U part */
*scale = 1.f;
/* Check for scaling */
i__ = icamax_(n, &rhs[1], &c__1);
if (smlnum * 2.f * c_abs(&rhs[i__]) > c_abs(&a[*n + *n * a_dim1])) {
r__1 = c_abs(&rhs[i__]);
q__1.r = .5f / r__1, q__1.i = 0.f / r__1;
temp.r = q__1.r, temp.i = q__1.i;
cscal_(n, &temp, &rhs[1], &c__1);
*scale *= temp.r;
}
for (i__ = *n; i__ >= 1; --i__) {
c_div(&q__1, &c_b13, &a[i__ + i__ * a_dim1]);
temp.r = q__1.r, temp.i = q__1.i;
i__1 = i__;
i__2 = i__;
q__1.r = rhs[i__2].r * temp.r - rhs[i__2].i * temp.i, q__1.i = rhs[
i__2].r * temp.i + rhs[i__2].i * temp.r;
rhs[i__1].r = q__1.r, rhs[i__1].i = q__1.i;
i__1 = *n;
for (j = i__ + 1; j <= i__1; ++j) {
i__2 = i__;
i__3 = i__;
i__4 = j;
i__5 = i__ + j * a_dim1;
q__3.r = a[i__5].r * temp.r - a[i__5].i * temp.i, q__3.i = a[i__5]
.r * temp.i + a[i__5].i * temp.r;
q__2.r = rhs[i__4].r * q__3.r - rhs[i__4].i * q__3.i, q__2.i =
rhs[i__4].r * q__3.i + rhs[i__4].i * q__3.r;
q__1.r = rhs[i__3].r - q__2.r, q__1.i = rhs[i__3].i - q__2.i;
rhs[i__2].r = q__1.r, rhs[i__2].i = q__1.i;
/* L30: */
}
/* L40: */
}
/* Apply permutations JPIV to the solution (RHS) */
i__1 = *n - 1;
claswp_(&c__1, &rhs[1], lda, &c__1, &i__1, &jpiv[1], &c_n1);
return 0;
/* End of CGESC2 */
} /* cgesc2_ */