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/* sppequ.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 sppequ_(char *uplo, integer *n, real *ap, real *s, real *
scond, real *amax, integer *info)
{
/* System generated locals */
integer i__1;
real r__1, r__2;
/* Builtin functions */
double sqrt(doublereal);
/* Local variables */
integer i__, jj;
real smin;
extern logical lsame_(char *, char *);
logical upper;
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 */
/* ======= */
/* SPPEQU computes row and column scalings intended to equilibrate a */
/* symmetric positive definite matrix A in packed storage 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 */
/* ========= */
/* UPLO (input) CHARACTER*1 */
/* = 'U': Upper triangle of A is stored; */
/* = 'L': Lower triangle of A is stored. */
/* N (input) INTEGER */
/* The order of the matrix A. N >= 0. */
/* AP (input) REAL array, dimension (N*(N+1)/2) */
/* The upper or lower triangle of the symmetric matrix A, packed */
/* columnwise in a linear array. The j-th column of A is stored */
/* in the array AP as follows: */
/* if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; */
/* if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. */
/* S (output) REAL array, dimension (N) */
/* If INFO = 0, S contains the scale factors for A. */
/* SCOND (output) REAL */
/* 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) 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, the i-th diagonal element is nonpositive. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input parameters. */
/* Parameter adjustments */
--s;
--ap;
/* Function Body */
*info = 0;
upper = lsame_(uplo, "U");
if (! upper && ! lsame_(uplo, "L")) {
*info = -1;
} else if (*n < 0) {
*info = -2;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("SPPEQU", &i__1);
return 0;
}
/* Quick return if possible */
if (*n == 0) {
*scond = 1.f;
*amax = 0.f;
return 0;
}
/* Initialize SMIN and AMAX. */
s[1] = ap[1];
smin = s[1];
*amax = s[1];
if (upper) {
/* UPLO = 'U': Upper triangle of A is stored. */
/* Find the minimum and maximum diagonal elements. */
jj = 1;
i__1 = *n;
for (i__ = 2; i__ <= i__1; ++i__) {
jj += i__;
s[i__] = ap[jj];
/* Computing MIN */
r__1 = smin, r__2 = s[i__];
smin = dmin(r__1,r__2);
/* Computing MAX */
r__1 = *amax, r__2 = s[i__];
*amax = dmax(r__1,r__2);
/* L10: */
}
} else {
/* UPLO = 'L': Lower triangle of A is stored. */
/* Find the minimum and maximum diagonal elements. */
jj = 1;
i__1 = *n;
for (i__ = 2; i__ <= i__1; ++i__) {
jj = jj + *n - i__ + 2;
s[i__] = ap[jj];
/* Computing MIN */
r__1 = smin, r__2 = s[i__];
smin = dmin(r__1,r__2);
/* Computing MAX */
r__1 = *amax, r__2 = s[i__];
*amax = dmax(r__1,r__2);
/* L20: */
}
}
if (smin <= 0.f) {
/* Find the first non-positive diagonal element and return. */
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
if (s[i__] <= 0.f) {
*info = i__;
return 0;
}
/* L30: */
}
} 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.f / sqrt(s[i__]);
/* L40: */
}
/* Compute SCOND = min(S(I)) / max(S(I)) */
*scond = sqrt(smin) / sqrt(*amax);
}
return 0;
/* End of SPPEQU */
} /* sppequ_ */
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