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/* cpbcon.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 cpbcon_(char *uplo, integer *n, integer *kd, complex *ab,
integer *ldab, real *anorm, real *rcond, complex *work, real *rwork,
integer *info)
{
/* System generated locals */
integer ab_dim1, ab_offset, i__1;
real r__1, r__2;
/* Builtin functions */
double r_imag(complex *);
/* Local variables */
integer ix, kase;
real scale;
extern logical lsame_(char *, char *);
integer isave[3];
logical upper;
extern /* Subroutine */ int clacn2_(integer *, complex *, complex *, real
*, integer *, integer *);
extern integer icamax_(integer *, complex *, integer *);
real scalel;
extern doublereal slamch_(char *);
extern /* Subroutine */ int clatbs_(char *, char *, char *, char *,
integer *, integer *, complex *, integer *, complex *, real *,
real *, integer *);
real scaleu;
extern /* Subroutine */ int xerbla_(char *, integer *);
real ainvnm;
extern /* Subroutine */ int csrscl_(integer *, real *, complex *, integer
*);
char normin[1];
real smlnum;
/* -- LAPACK routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* Modified to call CLACN2 in place of CLACON, 10 Feb 03, SJH. */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* CPBCON estimates the reciprocal of the condition number (in the */
/* 1-norm) of a complex Hermitian positive definite band matrix using */
/* the Cholesky factorization A = U**H*U or A = L*L**H computed by */
/* CPBTRF. */
/* An estimate is obtained for norm(inv(A)), and the reciprocal of the */
/* condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))). */
/* Arguments */
/* ========= */
/* UPLO (input) CHARACTER*1 */
/* = 'U': Upper triangular factor stored in AB; */
/* = 'L': Lower triangular factor stored in AB. */
/* N (input) INTEGER */
/* The order of the matrix A. N >= 0. */
/* KD (input) INTEGER */
/* The number of superdiagonals of the matrix A if UPLO = 'U', */
/* or the number of sub-diagonals if UPLO = 'L'. KD >= 0. */
/* AB (input) COMPLEX array, dimension (LDAB,N) */
/* The triangular factor U or L from the Cholesky factorization */
/* A = U**H*U or A = L*L**H of the band matrix A, stored in the */
/* first KD+1 rows of the array. The j-th column of U or L is */
/* stored in the j-th column of the array AB as follows: */
/* if UPLO ='U', AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j; */
/* if UPLO ='L', AB(1+i-j,j) = L(i,j) for j<=i<=min(n,j+kd). */
/* LDAB (input) INTEGER */
/* The leading dimension of the array AB. LDAB >= KD+1. */
/* ANORM (input) REAL */
/* The 1-norm (or infinity-norm) of the Hermitian band matrix A. */
/* RCOND (output) REAL */
/* The reciprocal of the condition number of the matrix A, */
/* computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an */
/* estimate of the 1-norm of inv(A) computed in this routine. */
/* WORK (workspace) COMPLEX array, dimension (2*N) */
/* RWORK (workspace) REAL 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 .. */
/* .. */
/* .. Statement Functions .. */
/* .. */
/* .. Statement Function definitions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input parameters. */
/* Parameter adjustments */
ab_dim1 = *ldab;
ab_offset = 1 + ab_dim1;
ab -= ab_offset;
--work;
--rwork;
/* Function Body */
*info = 0;
upper = lsame_(uplo, "U");
if (! upper && ! lsame_(uplo, "L")) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*kd < 0) {
*info = -3;
} else if (*ldab < *kd + 1) {
*info = -5;
} else if (*anorm < 0.f) {
*info = -6;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("CPBCON", &i__1);
return 0;
}
/* Quick return if possible */
*rcond = 0.f;
if (*n == 0) {
*rcond = 1.f;
return 0;
} else if (*anorm == 0.f) {
return 0;
}
smlnum = slamch_("Safe minimum");
/* Estimate the 1-norm of the inverse. */
kase = 0;
*(unsigned char *)normin = 'N';
L10:
clacn2_(n, &work[*n + 1], &work[1], &ainvnm, &kase, isave);
if (kase != 0) {
if (upper) {
/* Multiply by inv(U'). */
clatbs_("Upper", "Conjugate transpose", "Non-unit", normin, n, kd,
&ab[ab_offset], ldab, &work[1], &scalel, &rwork[1], info);
*(unsigned char *)normin = 'Y';
/* Multiply by inv(U). */
clatbs_("Upper", "No transpose", "Non-unit", normin, n, kd, &ab[
ab_offset], ldab, &work[1], &scaleu, &rwork[1], info);
} else {
/* Multiply by inv(L). */
clatbs_("Lower", "No transpose", "Non-unit", normin, n, kd, &ab[
ab_offset], ldab, &work[1], &scalel, &rwork[1], info);
*(unsigned char *)normin = 'Y';
/* Multiply by inv(L'). */
clatbs_("Lower", "Conjugate transpose", "Non-unit", normin, n, kd,
&ab[ab_offset], ldab, &work[1], &scaleu, &rwork[1], info);
}
/* Multiply by 1/SCALE if doing so will not cause overflow. */
scale = scalel * scaleu;
if (scale != 1.f) {
ix = icamax_(n, &work[1], &c__1);
i__1 = ix;
if (scale < ((r__1 = work[i__1].r, dabs(r__1)) + (r__2 = r_imag(&
work[ix]), dabs(r__2))) * smlnum || scale == 0.f) {
goto L20;
}
csrscl_(n, &scale, &work[1], &c__1);
}
goto L10;
}
/* Compute the estimate of the reciprocal condition number. */
if (ainvnm != 0.f) {
*rcond = 1.f / ainvnm / *anorm;
}
L20:
return 0;
/* End of CPBCON */
} /* cpbcon_ */
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