/* dpoequ.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 dpoequ_(integer *n, doublereal *a, integer *lda,
doublereal *s, doublereal *scond, doublereal *amax, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, i__1;
doublereal d__1, d__2;
/* Builtin functions */
double sqrt(doublereal);
/* Local variables */
integer i__;
doublereal smin;
extern /* Subroutine */ int xerbla_(char *, integer *);
/* -- LAPACK routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* DPOEQU computes row and column scalings intended to equilibrate a */
/* symmetric positive definite matrix A and reduce its condition number */
/* (with respect to the two-norm). S contains the scale factors, */
/* S(i) = 1/sqrt(A(i,i)), chosen so that the scaled matrix B with */
/* elements B(i,j) = S(i)*A(i,j)*S(j) has ones on the diagonal. This */
/* choice of S puts the condition number of B within a factor N of the */
/* smallest possible condition number over all possible diagonal */
/* scalings. */
/* Arguments */
/* ========= */
/* N (input) INTEGER */
/* The order of the matrix A. N >= 0. */
/* A (input) DOUBLE PRECISION array, dimension (LDA,N) */
/* The N-by-N symmetric positive definite matrix whose scaling */
/* factors are to be computed. Only the diagonal elements of A */
/* are referenced. */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= max(1,N). */
/* S (output) DOUBLE PRECISION array, dimension (N) */
/* If INFO = 0, S contains the scale factors for A. */
/* SCOND (output) DOUBLE PRECISION */
/* If INFO = 0, S contains the ratio of the smallest S(i) to */
/* the largest S(i). If SCOND >= 0.1 and AMAX is neither too */
/* large nor too small, it is not worth scaling by S. */
/* AMAX (output) DOUBLE PRECISION */
/* 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, the i-th diagonal element is nonpositive. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input parameters. */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--s;
/* Function Body */
*info = 0;
if (*n < 0) {
*info = -1;
} else if (*lda < max(1,*n)) {
*info = -3;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("DPOEQU", &i__1);
return 0;
}
/* Quick return if possible */
if (*n == 0) {
*scond = 1.;
*amax = 0.;
return 0;
}
/* Find the minimum and maximum diagonal elements. */
s[1] = a[a_dim1 + 1];
smin = s[1];
*amax = s[1];
i__1 = *n;
for (i__ = 2; i__ <= i__1; ++i__) {
s[i__] = a[i__ + i__ * a_dim1];
/* Computing MIN */
d__1 = smin, d__2 = s[i__];
smin = min(d__1,d__2);
/* Computing MAX */
d__1 = *amax, d__2 = s[i__];
*amax = max(d__1,d__2);
/* L10: */
}
if (smin <= 0.) {
/* Find the first non-positive diagonal element and return. */
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
if (s[i__] <= 0.) {
*info = i__;
return 0;
}
/* L20: */
}
} else {
/* Set the scale factors to the reciprocals */
/* of the diagonal elements. */
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
s[i__] = 1. / sqrt(s[i__]);
/* L30: */
}
/* Compute SCOND = min(S(I)) / max(S(I)) */
*scond = sqrt(smin) / sqrt(*amax);
}
return 0;
/* End of DPOEQU */
} /* dpoequ_ */
