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/* stbcon.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"
/* Table of constant values */
static integer c__1 = 1;
/* Subroutine */ int stbcon_(char *norm, char *uplo, char *diag, integer *n,
integer *kd, real *ab, integer *ldab, real *rcond, real *work,
integer *iwork, integer *info)
{
/* System generated locals */
integer ab_dim1, ab_offset, i__1;
real r__1;
/* Local variables */
integer ix, kase, kase1;
real scale;
extern logical lsame_(char *, char *);
integer isave[3];
real anorm;
extern /* Subroutine */ int srscl_(integer *, real *, real *, integer *);
logical upper;
real xnorm;
extern /* Subroutine */ int slacn2_(integer *, real *, real *, integer *,
real *, integer *, integer *);
extern doublereal slamch_(char *);
extern /* Subroutine */ int xerbla_(char *, integer *);
extern integer isamax_(integer *, real *, integer *);
extern doublereal slantb_(char *, char *, char *, integer *, integer *,
real *, integer *, real *);
real ainvnm;
extern /* Subroutine */ int slatbs_(char *, char *, char *, char *,
integer *, integer *, real *, integer *, real *, real *, real *,
integer *);
logical onenrm;
char normin[1];
real smlnum;
logical nounit;
/* -- LAPACK routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* Modified to call SLACN2 in place of SLACON, 7 Feb 03, SJH. */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* STBCON estimates the reciprocal of the condition number of a */
/* triangular band matrix A, in either the 1-norm or the infinity-norm. */
/* The norm of A is computed and an estimate is obtained for */
/* norm(inv(A)), then the reciprocal of the condition number is */
/* computed as */
/* RCOND = 1 / ( norm(A) * norm(inv(A)) ). */
/* Arguments */
/* ========= */
/* NORM (input) CHARACTER*1 */
/* Specifies whether the 1-norm condition number or the */
/* infinity-norm condition number is required: */
/* = '1' or 'O': 1-norm; */
/* = 'I': Infinity-norm. */
/* UPLO (input) CHARACTER*1 */
/* = 'U': A is upper triangular; */
/* = 'L': A is lower triangular. */
/* DIAG (input) CHARACTER*1 */
/* = 'N': A is non-unit triangular; */
/* = 'U': A is unit triangular. */
/* N (input) INTEGER */
/* The order of the matrix A. N >= 0. */
/* KD (input) INTEGER */
/* The number of superdiagonals or subdiagonals of the */
/* triangular band matrix A. KD >= 0. */
/* AB (input) REAL array, dimension (LDAB,N) */
/* The upper or lower triangular 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). */
/* If DIAG = 'U', the diagonal elements of A are not referenced */
/* and are assumed to be 1. */
/* LDAB (input) INTEGER */
/* The leading dimension of the array AB. LDAB >= KD+1. */
/* RCOND (output) REAL */
/* The reciprocal of the condition number of the matrix A, */
/* computed as RCOND = 1/(norm(A) * norm(inv(A))). */
/* WORK (workspace) REAL array, dimension (3*N) */
/* IWORK (workspace) INTEGER array, dimension (N) */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input parameters. */
/* Parameter adjustments */
ab_dim1 = *ldab;
ab_offset = 1 + ab_dim1;
ab -= ab_offset;
--work;
--iwork;
/* Function Body */
*info = 0;
upper = lsame_(uplo, "U");
onenrm = *(unsigned char *)norm == '1' || lsame_(norm, "O");
nounit = lsame_(diag, "N");
if (! onenrm && ! lsame_(norm, "I")) {
*info = -1;
} else if (! upper && ! lsame_(uplo, "L")) {
*info = -2;
} else if (! nounit && ! lsame_(diag, "U")) {
*info = -3;
} else if (*n < 0) {
*info = -4;
} else if (*kd < 0) {
*info = -5;
} else if (*ldab < *kd + 1) {
*info = -7;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("STBCON", &i__1);
return 0;
}
/* Quick return if possible */
if (*n == 0) {
*rcond = 1.f;
return 0;
}
*rcond = 0.f;
smlnum = slamch_("Safe minimum") * (real) max(1,*n);
/* Compute the norm of the triangular matrix A. */
anorm = slantb_(norm, uplo, diag, n, kd, &ab[ab_offset], ldab, &work[1]);
/* Continue only if ANORM > 0. */
if (anorm > 0.f) {
/* Estimate the norm of the inverse of A. */
ainvnm = 0.f;
*(unsigned char *)normin = 'N';
if (onenrm) {
kase1 = 1;
} else {
kase1 = 2;
}
kase = 0;
L10:
slacn2_(n, &work[*n + 1], &work[1], &iwork[1], &ainvnm, &kase, isave);
if (kase != 0) {
if (kase == kase1) {
/* Multiply by inv(A). */
slatbs_(uplo, "No transpose", diag, normin, n, kd, &ab[
ab_offset], ldab, &work[1], &scale, &work[(*n << 1) +
1], info)
;
} else {
/* Multiply by inv(A'). */
slatbs_(uplo, "Transpose", diag, normin, n, kd, &ab[ab_offset]
, ldab, &work[1], &scale, &work[(*n << 1) + 1], info);
}
*(unsigned char *)normin = 'Y';
/* Multiply by 1/SCALE if doing so will not cause overflow. */
if (scale != 1.f) {
ix = isamax_(n, &work[1], &c__1);
xnorm = (r__1 = work[ix], dabs(r__1));
if (scale < xnorm * smlnum || scale == 0.f) {
goto L20;
}
srscl_(n, &scale, &work[1], &c__1);
}
goto L10;
}
/* Compute the estimate of the reciprocal condition number. */
if (ainvnm != 0.f) {
*rcond = 1.f / anorm / ainvnm;
}
}
L20:
return 0;
/* End of STBCON */
} /* stbcon_ */
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