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/* dlaqgb.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 dlaqgb_(integer *m, integer *n, integer *kl, integer *ku,
doublereal *ab, integer *ldab, doublereal *r__, doublereal *c__,
doublereal *rowcnd, doublereal *colcnd, doublereal *amax, char *equed)
{
/* System generated locals */
integer ab_dim1, ab_offset, i__1, i__2, i__3, i__4, i__5, i__6;
/* Local variables */
integer i__, j;
doublereal cj, large, 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 */
/* ======= */
/* DLAQGB equilibrates a general M by N band matrix A with KL */
/* subdiagonals and KU superdiagonals using the row and scaling factors */
/* in the vectors R and C. */
/* 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. */
/* KL (input) INTEGER */
/* The number of subdiagonals within the band of A. KL >= 0. */
/* KU (input) INTEGER */
/* The number of superdiagonals within the band of A. KU >= 0. */
/* AB (input/output) DOUBLE PRECISION array, dimension (LDAB,N) */
/* On entry, the matrix A in band storage, in rows 1 to KL+KU+1. */
/* The j-th column of A is stored in the j-th column of the */
/* array AB as follows: */
/* AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(m,j+kl) */
/* On exit, the equilibrated matrix, in the same storage format */
/* as A. See EQUED for the form of the equilibrated matrix. */
/* LDAB (input) INTEGER */
/* The leading dimension of the array AB. LDA >= KL+KU+1. */
/* R (input) DOUBLE PRECISION array, dimension (M) */
/* The row scale factors for A. */
/* C (input) DOUBLE PRECISION array, dimension (N) */
/* The column scale factors for A. */
/* ROWCND (input) DOUBLE PRECISION */
/* Ratio of the smallest R(i) to the largest R(i). */
/* COLCND (input) DOUBLE PRECISION */
/* Ratio of the smallest C(i) to the largest C(i). */
/* AMAX (input) DOUBLE PRECISION */
/* Absolute value of largest matrix entry. */
/* EQUED (output) CHARACTER*1 */
/* Specifies the form of equilibration that was done. */
/* = 'N': No equilibration */
/* = 'R': Row equilibration, i.e., A has been premultiplied by */
/* diag(R). */
/* = 'C': Column equilibration, i.e., A has been postmultiplied */
/* by diag(C). */
/* = 'B': Both row and column equilibration, i.e., A has been */
/* replaced by diag(R) * A * diag(C). */
/* Internal Parameters */
/* =================== */
/* THRESH is a threshold value used to decide if row or column scaling */
/* should be done based on the ratio of the row or column scaling */
/* factors. If ROWCND < THRESH, row scaling is done, and if */
/* COLCND < THRESH, column scaling is done. */
/* LARGE and SMALL are threshold values used to decide if row scaling */
/* should be done based on the absolute size of the largest matrix */
/* element. If AMAX > LARGE or AMAX < SMALL, row 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;
--r__;
--c__;
/* Function Body */
if (*m <= 0 || *n <= 0) {
*(unsigned char *)equed = 'N';
return 0;
}
/* Initialize LARGE and SMALL. */
small = dlamch_("Safe minimum") / dlamch_("Precision");
large = 1. / small;
if (*rowcnd >= .1 && *amax >= small && *amax <= large) {
/* No row scaling */
if (*colcnd >= .1) {
/* No column scaling */
*(unsigned char *)equed = 'N';
} else {
/* Column scaling */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
cj = c__[j];
/* Computing MAX */
i__2 = 1, i__3 = j - *ku;
/* Computing MIN */
i__5 = *m, i__6 = j + *kl;
i__4 = min(i__5,i__6);
for (i__ = max(i__2,i__3); i__ <= i__4; ++i__) {
ab[*ku + 1 + i__ - j + j * ab_dim1] = cj * ab[*ku + 1 +
i__ - j + j * ab_dim1];
/* L10: */
}
/* L20: */
}
*(unsigned char *)equed = 'C';
}
} else if (*colcnd >= .1) {
/* Row scaling, no column scaling */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
/* Computing MAX */
i__4 = 1, i__2 = j - *ku;
/* Computing MIN */
i__5 = *m, i__6 = j + *kl;
i__3 = min(i__5,i__6);
for (i__ = max(i__4,i__2); i__ <= i__3; ++i__) {
ab[*ku + 1 + i__ - j + j * ab_dim1] = r__[i__] * ab[*ku + 1 +
i__ - j + j * ab_dim1];
/* L30: */
}
/* L40: */
}
*(unsigned char *)equed = 'R';
} else {
/* Row and column scaling */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
cj = c__[j];
/* Computing MAX */
i__3 = 1, i__4 = j - *ku;
/* Computing MIN */
i__5 = *m, i__6 = j + *kl;
i__2 = min(i__5,i__6);
for (i__ = max(i__3,i__4); i__ <= i__2; ++i__) {
ab[*ku + 1 + i__ - j + j * ab_dim1] = cj * r__[i__] * ab[*ku
+ 1 + i__ - j + j * ab_dim1];
/* L50: */
}
/* L60: */
}
*(unsigned char *)equed = 'B';
}
return 0;
/* End of DLAQGB */
} /* dlaqgb_ */
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