#include "blaswrap.h"
#include "f2c.h"
/* Subroutine */ int slaqsy_(char *uplo, integer *n, real *a, integer *lda,
real *s, real *scond, real *amax, char *equed)
{
/* -- LAPACK auxiliary routine (version 3.1) --
Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
November 2006
Purpose
=======
SLAQSY equilibrates a symmetric matrix A using the scaling factors
in the vector S.
Arguments
=========
UPLO (input) CHARACTER*1
Specifies whether the upper or lower triangular part of the
symmetric matrix A is stored.
= 'U': Upper triangular
= 'L': Lower triangular
N (input) INTEGER
The order of the matrix A. N >= 0.
A (input/output) REAL array, dimension (LDA,N)
On entry, the symmetric matrix A. If UPLO = 'U', the leading
n by n upper triangular part of A contains the upper
triangular part of the matrix A, and the strictly lower
triangular part of A is not referenced. If UPLO = 'L', the
leading n by n lower triangular part of A contains the lower
triangular part of the matrix A, and the strictly upper
triangular part of A is not referenced.
On exit, if EQUED = 'Y', the equilibrated matrix:
diag(S) * A * diag(S).
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(N,1).
S (input) REAL array, dimension (N)
The scale factors for A.
SCOND (input) REAL
Ratio of the smallest S(i) to the largest S(i).
AMAX (input) REAL
Absolute value of largest matrix entry.
EQUED (output) CHARACTER*1
Specifies whether or not equilibration was done.
= 'N': No equilibration.
= 'Y': Equilibration was done, i.e., A has been replaced by
diag(S) * A * diag(S).
Internal Parameters
===================
THRESH is a threshold value used to decide if scaling should be done
based on the ratio of the scaling factors. If SCOND < THRESH,
scaling is done.
LARGE and SMALL are threshold values used to decide if scaling should
be done based on the absolute size of the largest matrix element.
If AMAX > LARGE or AMAX < SMALL, scaling is done.
=====================================================================
Quick return if possible
Parameter adjustments */
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2;
/* Local variables */
static integer i__, j;
static real cj, large;
extern logical lsame_(char *, char *);
static real small;
extern doublereal slamch_(char *);
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--s;
/* Function Body */
if (*n <= 0) {
*(unsigned char *)equed = 'N';
return 0;
}
/* Initialize LARGE and SMALL. */
small = slamch_("Safe minimum") / slamch_("Precision");
large = 1.f / small;
if (*scond >= .1f && *amax >= small && *amax <= large) {
/* No equilibration */
*(unsigned char *)equed = 'N';
} else {
/* Replace A by diag(S) * A * diag(S). */
if (lsame_(uplo, "U")) {
/* Upper triangle of A is stored. */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
cj = s[j];
i__2 = j;
for (i__ = 1; i__ <= i__2; ++i__) {
a[i__ + j * a_dim1] = cj * s[i__] * a[i__ + j * a_dim1];
/* L10: */
}
/* L20: */
}
} else {
/* Lower triangle of A is stored. */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
cj = s[j];
i__2 = *n;
for (i__ = j; i__ <= i__2; ++i__) {
a[i__ + j * a_dim1] = cj * s[i__] * a[i__ + j * a_dim1];
/* L30: */
}
/* L40: */
}
}
*(unsigned char *)equed = 'Y';
}
return 0;
/* End of SLAQSY */
} /* slaqsy_ */