sgeequb.c

Go to the documentation of this file.

/* sgeequb.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 sgeequb_(integer *m, integer *n, real *a, integer *lda, 
        real *r__, real *c__, real *rowcnd, real *colcnd, real *amax, integer 
        *info)
{
    /* System generated locals */
    integer a_dim1, a_offset, i__1, i__2;
    real r__1, r__2, r__3;

    /* Builtin functions */
    double log(doublereal), pow_ri(real *, integer *);

    /* Local variables */
    integer i__, j;
    real radix, rcmin, rcmax;
    extern doublereal slamch_(char *);
    extern /* Subroutine */ int xerbla_(char *, integer *);
    real bignum, logrdx, smlnum;


/*     -- LAPACK routine (version 3.2)                                 -- */
/*     -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and -- */
/*     -- Jason Riedy of Univ. of California Berkeley.                 -- */
/*     -- November 2008                                                -- */

/*     -- LAPACK is a software package provided by Univ. of Tennessee, -- */
/*     -- Univ. of California Berkeley and NAG Ltd.                    -- */

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

/*  Purpose */
/*  ======= */

/*  SGEEQUB computes row and column scalings intended to equilibrate an */
/*  M-by-N matrix A and reduce its condition number.  R returns the row */
/*  scale factors and C the column scale factors, chosen to try to make */
/*  the largest element in each row and column of the matrix B with */
/*  elements B(i,j)=R(i)*A(i,j)*C(j) have an absolute value of at most */
/*  the radix. */

/*  R(i) and C(j) are restricted to be a power of the radix between */
/*  SMLNUM = smallest safe number and BIGNUM = largest safe number.  Use */
/*  of these scaling factors is not guaranteed to reduce the condition */
/*  number of A but works well in practice. */

/*  This routine differs from SGEEQU by restricting the scaling factors */
/*  to a power of the radix.  Baring over- and underflow, scaling by */
/*  these factors introduces no additional rounding errors.  However, the */
/*  scaled entries' magnitured are no longer approximately 1 but lie */
/*  between sqrt(radix) and 1/sqrt(radix). */

/*  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) REAL array, dimension (LDA,N) */
/*          The M-by-N matrix whose equilibration factors are */
/*          to be computed. */

/*  LDA     (input) INTEGER */
/*          The leading dimension of the array A.  LDA >= max(1,M). */

/*  R       (output) REAL array, dimension (M) */
/*          If INFO = 0 or INFO > M, R contains the row scale factors */
/*          for A. */

/*  C       (output) REAL array, dimension (N) */
/*          If INFO = 0,  C contains the column scale factors for A. */

/*  ROWCND  (output) REAL */
/*          If INFO = 0 or INFO > M, ROWCND contains the ratio of the */
/*          smallest R(i) to the largest R(i).  If ROWCND >= 0.1 and */
/*          AMAX is neither too large nor too small, it is not worth */
/*          scaling by R. */

/*  COLCND  (output) REAL */
/*          If INFO = 0, COLCND contains the ratio of the smallest */
/*          C(i) to the largest C(i).  If COLCND >= 0.1, it is not */
/*          worth scaling by C. */

/*  AMAX    (output) REAL */
/*          Absolute value of largest matrix element.  If AMAX is very */
/*          close to overflow or very close to underflow, the matrix */
/*          should be scaled. */

/*  INFO    (output) INTEGER */
/*          = 0:  successful exit */
/*          < 0:  if INFO = -i, the i-th argument had an illegal value */
/*          > 0:  if INFO = i,  and i is */
/*                <= M:  the i-th row of A is exactly zero */
/*                >  M:  the (i-M)-th column of A is exactly zero */

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

/*     .. 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;
    --r__;
    --c__;

    /* 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_("SGEEQUB", &i__1);
        return 0;
    }

/*     Quick return if possible. */

    if (*m == 0 || *n == 0) {
        *rowcnd = 1.f;
        *colcnd = 1.f;
        *amax = 0.f;
        return 0;
    }

/*     Get machine constants.  Assume SMLNUM is a power of the radix. */

    smlnum = slamch_("S");
    bignum = 1.f / smlnum;
    radix = slamch_("B");
    logrdx = log(radix);

/*     Compute row scale factors. */

    i__1 = *m;
    for (i__ = 1; i__ <= i__1; ++i__) {
        r__[i__] = 0.f;
/* L10: */
    }

/*     Find the maximum element in each row. */

    i__1 = *n;
    for (j = 1; j <= i__1; ++j) {
        i__2 = *m;
        for (i__ = 1; i__ <= i__2; ++i__) {
/* Computing MAX */
            r__2 = r__[i__], r__3 = (r__1 = a[i__ + j * a_dim1], dabs(r__1));
            r__[i__] = dmax(r__2,r__3);
/* L20: */
        }
/* L30: */
    }
    i__1 = *m;
    for (i__ = 1; i__ <= i__1; ++i__) {
        if (r__[i__] > 0.f) {
            i__2 = (integer) (log(r__[i__]) / logrdx);
            r__[i__] = pow_ri(&radix, &i__2);
        }
    }

/*     Find the maximum and minimum scale factors. */

    rcmin = bignum;
    rcmax = 0.f;
    i__1 = *m;
    for (i__ = 1; i__ <= i__1; ++i__) {
/* Computing MAX */
        r__1 = rcmax, r__2 = r__[i__];
        rcmax = dmax(r__1,r__2);
/* Computing MIN */
        r__1 = rcmin, r__2 = r__[i__];
        rcmin = dmin(r__1,r__2);
/* L40: */
    }
    *amax = rcmax;

    if (rcmin == 0.f) {

/*        Find the first zero scale factor and return an error code. */

        i__1 = *m;
        for (i__ = 1; i__ <= i__1; ++i__) {
            if (r__[i__] == 0.f) {
                *info = i__;
                return 0;
            }
/* L50: */
        }
    } else {

/*        Invert the scale factors. */

        i__1 = *m;
        for (i__ = 1; i__ <= i__1; ++i__) {
/* Computing MIN */
/* Computing MAX */
            r__2 = r__[i__];
            r__1 = dmax(r__2,smlnum);
            r__[i__] = 1.f / dmin(r__1,bignum);
/* L60: */
        }

/*        Compute ROWCND = min(R(I)) / max(R(I)). */

        *rowcnd = dmax(rcmin,smlnum) / dmin(rcmax,bignum);
    }

/*     Compute column scale factors */

    i__1 = *n;
    for (j = 1; j <= i__1; ++j) {
        c__[j] = 0.f;
/* L70: */
    }

/*     Find the maximum element in each column, */
/*     assuming the row scaling computed above. */

    i__1 = *n;
    for (j = 1; j <= i__1; ++j) {
        i__2 = *m;
        for (i__ = 1; i__ <= i__2; ++i__) {
/* Computing MAX */
            r__2 = c__[j], r__3 = (r__1 = a[i__ + j * a_dim1], dabs(r__1)) * 
                    r__[i__];
            c__[j] = dmax(r__2,r__3);
/* L80: */
        }
        if (c__[j] > 0.f) {
            i__2 = (integer) (log(c__[j]) / logrdx);
            c__[j] = pow_ri(&radix, &i__2);
        }
/* L90: */
    }

/*     Find the maximum and minimum scale factors. */

    rcmin = bignum;
    rcmax = 0.f;
    i__1 = *n;
    for (j = 1; j <= i__1; ++j) {
/* Computing MIN */
        r__1 = rcmin, r__2 = c__[j];
        rcmin = dmin(r__1,r__2);
/* Computing MAX */
        r__1 = rcmax, r__2 = c__[j];
        rcmax = dmax(r__1,r__2);
/* L100: */
    }

    if (rcmin == 0.f) {

/*        Find the first zero scale factor and return an error code. */

        i__1 = *n;
        for (j = 1; j <= i__1; ++j) {
            if (c__[j] == 0.f) {
                *info = *m + j;
                return 0;
            }
/* L110: */
        }
    } else {

/*        Invert the scale factors. */

        i__1 = *n;
        for (j = 1; j <= i__1; ++j) {
/* Computing MIN */
/* Computing MAX */
            r__2 = c__[j];
            r__1 = dmax(r__2,smlnum);
            c__[j] = 1.f / dmin(r__1,bignum);
/* L120: */
        }

/*        Compute COLCND = min(C(J)) / max(C(J)). */

        *colcnd = dmax(rcmin,smlnum) / dmin(rcmax,bignum);
    }

    return 0;

/*     End of SGEEQUB */

} /* sgeequb_ */