180 lines
4.6 KiB
C
180 lines
4.6 KiB
C
|
#include "clapack.h"
|
||
|
|
|
||
|
|
/* Table of constant values */
|
||
|
|
|
||
|
|
static integer c__1 = 1;
|
||
|
|
static real c_b8 = -1.f;
|
||
|
|
|
||
|
|
/* Subroutine */ int sgetf2_(integer *m, integer *n, real *a, integer *lda,
|
||
|
|
integer *ipiv, integer *info)
|
||
|
|
{
|
||
|
|
/* System generated locals */
|
||
|
|
integer a_dim1, a_offset, i__1, i__2, i__3;
|
||
|
|
real r__1;
|
||
|
|
|
||
|
|
/* Local variables */
|
||
|
|
integer i__, j, jp;
|
||
|
|
extern /* Subroutine */ int sger_(integer *, integer *, real *, real *,
|
||
|
|
integer *, real *, integer *, real *, integer *), sscal_(integer *
|
||
|
|
, real *, real *, integer *);
|
||
|
|
real sfmin;
|
||
|
|
extern /* Subroutine */ int sswap_(integer *, real *, integer *, real *,
|
||
|
|
integer *);
|
||
|
|
extern doublereal slamch_(char *);
|
||
|
|
extern /* Subroutine */ int xerbla_(char *, integer *);
|
||
|
|
extern integer isamax_(integer *, real *, integer *);
|
||
|
|
|
||
|
|
|
||
|
|
/* -- LAPACK routine (version 3.1) -- */
|
||
|
|
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
|
||
|
|
/* November 2006 */
|
||
|
|
|
||
|
|
/* .. Scalar Arguments .. */
|
||
|
|
/* .. */
|
||
|
|
/* .. Array Arguments .. */
|
||
|
|
/* .. */
|
||
|
|
|
||
|
|
/* Purpose */
|
||
|
|
/* ======= */
|
||
|
|
|
||
|
|
/* SGETF2 computes an LU factorization of a general m-by-n matrix A */
|
||
|
|
/* using partial pivoting with row interchanges. */
|
||
|
|
|
||
|
|
/* The factorization has the form */
|
||
|
|
/* A = P * L * U */
|
||
|
|
/* where P is a permutation matrix, L is lower triangular with unit */
|
||
|
|
/* diagonal elements (lower trapezoidal if m > n), and U is upper */
|
||
|
|
/* triangular (upper trapezoidal if m < n). */
|
||
|
|
|
||
|
|
/* This is the right-looking Level 2 BLAS version of the algorithm. */
|
||
|
|
|
||
|
|
/* Arguments */
|
||
|
|
/* ========= */
|
||
|
|
|
||
|
|
/* M (input) INTEGER */
|
||
|
|
/* The number of rows of the matrix A. M >= 0. */
|
||
|
|
|
||
|
|
/* N (input) INTEGER */
|
||
|
|
/* The number of columns of the matrix A. N >= 0. */
|
||
|
|
|
||
|
|
/* A (input/output) REAL array, dimension (LDA,N) */
|
||
|
|
/* On entry, the m by n matrix to be factored. */
|
||
|
|
/* On exit, the factors L and U from the factorization */
|
||
|
|
/* A = P*L*U; the unit diagonal elements of L are not stored. */
|
||
|
|
|
||
|
|
/* LDA (input) INTEGER */
|
||
|
|
/* The leading dimension of the array A. LDA >= max(1,M). */
|
||
|
|
|
||
|
|
/* IPIV (output) INTEGER array, dimension (min(M,N)) */
|
||
|
|
/* The pivot indices; for 1 <= i <= min(M,N), row i of the */
|
||
|
|
/* matrix was interchanged with row IPIV(i). */
|
||
|
|
|
||
|
|
/* INFO (output) INTEGER */
|
||
|
|
/* = 0: successful exit */
|
||
|
|
/* < 0: if INFO = -k, the k-th argument had an illegal value */
|
||
|
|
/* > 0: if INFO = k, U(k,k) is exactly zero. The factorization */
|
||
|
|
/* has been completed, but the factor U is exactly */
|
||
|
|
/* singular, and division by zero will occur if it is used */
|
||
|
|
/* to solve a system of equations. */
|
||
|
|
|
||
|
|
/* ===================================================================== */
|
||
|
|
|
||
|
|
/* .. Parameters .. */
|
||
|
|
/* .. */
|
||
|
|
/* .. Local Scalars .. */
|
||
|
|
/* .. */
|
||
|
|
/* .. External Functions .. */
|
||
|
|
/* .. */
|
||
|
|
/* .. External Subroutines .. */
|
||
|
|
/* .. */
|
||
|
|
/* .. Intrinsic Functions .. */
|
||
|
|
/* .. */
|
||
|
|
/* .. Executable Statements .. */
|
||
|
|
|
||
|
|
/* Test the input parameters. */
|
||
|
|
|
||
|
|
/* Parameter adjustments */
|
||
|
|
a_dim1 = *lda;
|
||
|
|
a_offset = 1 + a_dim1;
|
||
|
|
a -= a_offset;
|
||
|
|
--ipiv;
|
||
|
|
|
||
|
|
/* Function Body */
|
||
|
|
*info = 0;
|
||
|
|
if (*m < 0) {
|
||
|
|
*info = -1;
|
||
|
|
} else if (*n < 0) {
|
||
|
|
*info = -2;
|
||
|
|
} else if (*lda < max(1,*m)) {
|
||
|
|
*info = -4;
|
||
|
|
}
|
||
|
|
if (*info != 0) {
|
||
|
|
i__1 = -(*info);
|
||
|
|
xerbla_("SGETF2", &i__1);
|
||
|
|
return 0;
|
||
|
|
}
|
||
|
|
|
||
|
|
/* Quick return if possible */
|
||
|
|
|
||
|
|
if (*m == 0 || *n == 0) {
|
||
|
|
return 0;
|
||
|
|
}
|
||
|
|
|
||
|
|
/* Compute machine safe minimum */
|
||
|
|
|
||
|
|
sfmin = slamch_("S");
|
||
|
|
|
||
|
|
i__1 = min(*m,*n);
|
||
|
|
for (j = 1; j <= i__1; ++j) {
|
||
|
|
|
||
|
|
/* Find pivot and test for singularity. */
|
||
|
|
|
||
|
|
i__2 = *m - j + 1;
|
||
|
|
jp = j - 1 + isamax_(&i__2, &a[j + j * a_dim1], &c__1);
|
||
|
|
ipiv[j] = jp;
|
||
|
|
if (a[jp + j * a_dim1] != 0.f) {
|
||
|
|
|
||
|
|
/* Apply the interchange to columns 1:N. */
|
||
|
|
|
||
|
|
if (jp != j) {
|
||
|
|
sswap_(n, &a[j + a_dim1], lda, &a[jp + a_dim1], lda);
|
||
|
|
}
|
||
|
|
|
||
|
|
/* Compute elements J+1:M of J-th column. */
|
||
|
|
|
||
|
|
if (j < *m) {
|
||
|
|
if ((r__1 = a[j + j * a_dim1], dabs(r__1)) >= sfmin) {
|
||
|
|
i__2 = *m - j;
|
||
|
|
r__1 = 1.f / a[j + j * a_dim1];
|
||
|
|
sscal_(&i__2, &r__1, &a[j + 1 + j * a_dim1], &c__1);
|
||
|
|
} else {
|
||
|
|
i__2 = *m - j;
|
||
|
|
for (i__ = 1; i__ <= i__2; ++i__) {
|
||
|
|
a[j + i__ + j * a_dim1] /= a[j + j * a_dim1];
|
||
|
|
/* L20: */
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
} else if (*info == 0) {
|
||
|
|
|
||
|
|
*info = j;
|
||
|
|
}
|
||
|
|
|
||
|
|
if (j < min(*m,*n)) {
|
||
|
|
|
||
|
|
/* Update trailing submatrix. */
|
||
|
|
|
||
|
|
i__2 = *m - j;
|
||
|
|
i__3 = *n - j;
|
||
|
|
sger_(&i__2, &i__3, &c_b8, &a[j + 1 + j * a_dim1], &c__1, &a[j + (
|
||
|
|
j + 1) * a_dim1], lda, &a[j + 1 + (j + 1) * a_dim1], lda);
|
||
|
|
}
|
||
|
|
/* L10: */
|
||
|
|
}
|
||
|
|
return 0;
|
||
|
|
|
||
|
|
/* End of SGETF2 */
|
||
|
|
|
||
|
|
} /* sgetf2_ */
|