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/* dlaqsb.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 dlaqsb_(char *uplo, integer *n, integer *kd, doublereal *
ab, integer *ldab, doublereal *s, doublereal *scond, doublereal *amax,
char *equed)
{
/* System generated locals */
integer ab_dim1, ab_offset, i__1, i__2, i__3, i__4;
/* Local variables */
integer i__, j;
doublereal cj, large;
extern logical lsame_(char *, char *);
doublereal small;
extern doublereal dlamch_(char *);
/* -- LAPACK auxiliary routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* DLAQSB equilibrates a symmetric band 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. */
/* KD (input) INTEGER */
/* The number of super-diagonals of the matrix A if UPLO = 'U', */
/* or the number of sub-diagonals if UPLO = 'L'. KD >= 0. */
/* AB (input/output) DOUBLE PRECISION array, dimension (LDAB,N) */
/* On entry, the upper or lower triangle of the symmetric band */
/* matrix A, stored in the first KD+1 rows of the array. The */
/* j-th column of A is stored in the j-th column of the array AB */
/* as follows: */
/* if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; */
/* if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). */
/* On exit, if INFO = 0, the triangular factor U or L from the */
/* Cholesky factorization A = U'*U or A = L*L' of the band */
/* matrix A, in the same storage format as A. */
/* LDAB (input) INTEGER */
/* The leading dimension of the array AB. LDAB >= KD+1. */
/* S (input) DOUBLE PRECISION array, dimension (N) */
/* The scale factors for A. */
/* SCOND (input) DOUBLE PRECISION */
/* Ratio of the smallest S(i) to the largest S(i). */
/* AMAX (input) DOUBLE PRECISION */
/* 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 .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Quick return if possible */
/* Parameter adjustments */
ab_dim1 = *ldab;
ab_offset = 1 + ab_dim1;
ab -= ab_offset;
--s;
/* Function Body */
if (*n <= 0) {
*(unsigned char *)equed = 'N';
return 0;
}
/* Initialize LARGE and SMALL. */
small = dlamch_("Safe minimum") / dlamch_("Precision");
large = 1. / small;
if (*scond >= .1 && *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 in band format. */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
cj = s[j];
/* Computing MAX */
i__2 = 1, i__3 = j - *kd;
i__4 = j;
for (i__ = max(i__2,i__3); i__ <= i__4; ++i__) {
ab[*kd + 1 + i__ - j + j * ab_dim1] = cj * s[i__] * ab[*
kd + 1 + i__ - j + j * ab_dim1];
/* L10: */
}
/* L20: */
}
} else {
/* Lower triangle of A is stored. */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
cj = s[j];
/* Computing MIN */
i__2 = *n, i__3 = j + *kd;
i__4 = min(i__2,i__3);
for (i__ = j; i__ <= i__4; ++i__) {
ab[i__ + 1 - j + j * ab_dim1] = cj * s[i__] * ab[i__ + 1
- j + j * ab_dim1];
/* L30: */
}
/* L40: */
}
}
*(unsigned char *)equed = 'Y';
}
return 0;
/* End of DLAQSB */
} /* dlaqsb_ */
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