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/* lapack/double/dgetc2.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 doublereal c_b10 = -1.;
/*< SUBROUTINE DGETC2( N, A, LDA, IPIV, JPIV, INFO ) >*/
/* Subroutine */ int dgetc2_(integer *n, doublereal *a, integer *lda, integer
*ipiv, integer *jpiv, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3;
doublereal d__1;
/* Local variables */
integer i__, j, ip, jp;
doublereal eps;
integer ipv=0, jpv=0;
extern /* Subroutine */ int dger_(integer *, integer *, doublereal *,
doublereal *, integer *, doublereal *, integer *, doublereal *,
integer *);
doublereal smin=0, xmax;
extern /* Subroutine */ int dswap_(integer *, doublereal *, integer *,
doublereal *, integer *), dlabad_(doublereal *, doublereal *);
extern doublereal dlamch_(char *, ftnlen);
doublereal bignum, 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 INFO, LDA, N >*/
/* .. */
/* .. Array Arguments .. */
/*< INTEGER IPIV( * ), JPIV( * ) >*/
/*< DOUBLE PRECISION A( LDA, * ) >*/
/* .. */
/* Purpose */
/* ======= */
/* DGETC2 computes an LU factorization with complete pivoting of the */
/* n-by-n matrix A. The factorization has the form A = P * L * U * Q, */
/* where P and Q are permutation matrices, L is lower triangular with */
/* unit diagonal elements and U is upper triangular. */
/* This is the Level 2 BLAS algorithm. */
/* Arguments */
/* ========= */
/* N (input) INTEGER */
/* The order of the matrix A. N >= 0. */
/* A (input/output) DOUBLE PRECISION array, dimension (LDA, N) */
/* On entry, the n-by-n matrix A to be factored. */
/* On exit, the factors L and U from the factorization */
/* A = P*L*U*Q; the unit diagonal elements of L are not stored. */
/* If U(k, k) appears to be less than SMIN, U(k, k) is given the */
/* value of SMIN, i.e., giving a nonsingular perturbed system. */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= max(1,N). */
/* IPIV (output) INTEGER array, dimension(N). */
/* The pivot indices; for 1 <= i <= N, row i of the */
/* matrix has been interchanged with row IPIV(i). */
/* JPIV (output) INTEGER array, dimension(N). */
/* The pivot indices; for 1 <= j <= N, column j of the */
/* matrix has been interchanged with column JPIV(j). */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* > 0: if INFO = k, U(k, k) is likely to produce owerflow if */
/* we try to solve for x in Ax = b. So U is perturbed to */
/* avoid the overflow. */
/* 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 >*/
/*< PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) >*/
/* .. */
/* .. Local Scalars .. */
/*< INTEGER I, IP, IPV, J, JP, JPV >*/
/*< DOUBLE PRECISION BIGNUM, EPS, SMIN, SMLNUM, XMAX >*/
/* .. */
/* .. External Subroutines .. */
/*< EXTERNAL DGER, DSWAP >*/
/* .. */
/* .. External Functions .. */
/*< DOUBLE PRECISION DLAMCH >*/
/*< EXTERNAL DLAMCH >*/
/* .. */
/* .. Intrinsic Functions .. */
/*< INTRINSIC ABS, MAX >*/
/* .. */
/* .. Executable Statements .. */
/* Set constants to control overflow */
/*< INFO = 0 >*/
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--ipiv;
--jpiv;
/* Function Body */
*info = 0;
/*< EPS = DLAMCH( 'P' ) >*/
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);
/* Factorize A using complete pivoting. */
/* Set pivots less than SMIN to SMIN. */
/*< DO 40 I = 1, N - 1 >*/
i__1 = *n - 1;
for (i__ = 1; i__ <= i__1; ++i__) {
/* Find max element in matrix A */
/*< XMAX = ZERO >*/
xmax = 0.;
/*< DO 20 IP = I, N >*/
i__2 = *n;
for (ip = i__; ip <= i__2; ++ip) {
/*< DO 10 JP = I, N >*/
i__3 = *n;
for (jp = i__; jp <= i__3; ++jp) {
/*< IF( ABS( A( IP, JP ) ).GE.XMAX ) THEN >*/
if ((d__1 = a[ip + jp * a_dim1], abs(d__1)) >= xmax) {
/*< XMAX = ABS( A( IP, JP ) ) >*/
xmax = (d__1 = a[ip + jp * a_dim1], abs(d__1));
/*< IPV = IP >*/
ipv = ip;
/*< JPV = JP >*/
jpv = jp;
/*< END IF >*/
}
/*< 10 CONTINUE >*/
/* L10: */
}
/*< 20 CONTINUE >*/
/* L20: */
}
/*< >*/
if (i__ == 1) {
/* Computing MAX */
d__1 = eps * xmax;
smin = max(d__1,smlnum);
}
/* Swap rows */
/*< >*/
if (ipv != i__) {
dswap_(n, &a[ipv + a_dim1], lda, &a[i__ + a_dim1], lda);
}
/*< IPIV( I ) = IPV >*/
ipiv[i__] = ipv;
/* Swap columns */
/*< >*/
if (jpv != i__) {
dswap_(n, &a[jpv * a_dim1 + 1], &c__1, &a[i__ * a_dim1 + 1], &
c__1);
}
/*< JPIV( I ) = JPV >*/
jpiv[i__] = jpv;
/* Check for singularity */
/*< IF( ABS( A( I, I ) ).LT.SMIN ) THEN >*/
if ((d__1 = a[i__ + i__ * a_dim1], abs(d__1)) < smin) {
/*< INFO = I >*/
*info = i__;
/*< A( I, I ) = SMIN >*/
a[i__ + i__ * a_dim1] = smin;
/*< END IF >*/
}
/*< DO 30 J = I + 1, N >*/
i__2 = *n;
for (j = i__ + 1; j <= i__2; ++j) {
/*< A( J, I ) = A( J, I ) / A( I, I ) >*/
a[j + i__ * a_dim1] /= a[i__ + i__ * a_dim1];
/*< 30 CONTINUE >*/
/* L30: */
}
/*< >*/
i__2 = *n - i__;
i__3 = *n - i__;
dger_(&i__2, &i__3, &c_b10, &a[i__ + 1 + i__ * a_dim1], &c__1, &a[i__
+ (i__ + 1) * a_dim1], lda, &a[i__ + 1 + (i__ + 1) * a_dim1],
lda);
/*< 40 CONTINUE >*/
/* L40: */
}
/*< IF( ABS( A( N, N ) ).LT.SMIN ) THEN >*/
if ((d__1 = a[*n + *n * a_dim1], abs(d__1)) < smin) {
/*< INFO = N >*/
*info = *n;
/*< A( N, N ) = SMIN >*/
a[*n + *n * a_dim1] = smin;
/*< END IF >*/
}
/*< RETURN >*/
return 0;
/* End of DGETC2 */
/*< END >*/
} /* dgetc2_ */
#ifdef __cplusplus
}
#endif
|
