slaqsy.c

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/* slaqsy.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"

/* Subroutine */ int slaqsy_(char *uplo, integer *n, real *a, integer *lda, 
        real *s, real *scond, real *amax, char *equed)
{
    /* System generated locals */
    integer a_dim1, a_offset, i__1, i__2;

    /* Local variables */
    integer i__, j;
    real cj, large;
    extern logical lsame_(char *, char *);
    real small;
    extern doublereal slamch_(char *);


/*  -- LAPACK auxiliary routine (version 3.2) -- */
/*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/*     November 2006 */

/*     .. Scalar Arguments .. */
/*     .. */
/*     .. Array Arguments .. */
/*     .. */

/*  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. */

/*  ===================================================================== */

/*     .. Parameters .. */
/*     .. */
/*     .. Local Scalars .. */
/*     .. */
/*     .. External Functions .. */
/*     .. */
/*     .. Executable Statements .. */

/*     Quick return if possible */

    /* Parameter adjustments */
    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_ */