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/* zgbcon.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 zgbcon_(char *norm, integer *n, integer *kl, integer *ku,
doublecomplex *ab, integer *ldab, integer *ipiv, doublereal *anorm,
doublereal *rcond, doublecomplex *work, doublereal *rwork, integer *
info)
{
/* System generated locals */
integer ab_dim1, ab_offset, i__1, i__2, i__3;
doublereal d__1, d__2;
doublecomplex z__1, z__2;
/* Builtin functions */
double d_imag(doublecomplex *);
/* Local variables */
integer j;
doublecomplex t;
integer kd, lm, jp, ix, kase, kase1;
doublereal scale;
extern logical lsame_(char *, char *);
integer isave[3];
extern /* Double Complex */ VOID zdotc_(doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *);
logical lnoti;
extern /* Subroutine */ int zaxpy_(integer *, doublecomplex *,
doublecomplex *, integer *, doublecomplex *, integer *), zlacn2_(
integer *, doublecomplex *, doublecomplex *, doublereal *,
integer *, integer *);
extern doublereal dlamch_(char *);
extern /* Subroutine */ int xerbla_(char *, integer *);
doublereal ainvnm;
extern integer izamax_(integer *, doublecomplex *, integer *);
logical onenrm;
extern /* Subroutine */ int zlatbs_(char *, char *, char *, char *,
integer *, integer *, doublecomplex *, integer *, doublecomplex *,
doublereal *, doublereal *, integer *), zdrscl_(integer *, doublereal *, doublecomplex *,
integer *);
char normin[1];
doublereal smlnum;
/* -- LAPACK routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* Modified to call ZLACN2 in place of ZLACON, 10 Feb 03, SJH. */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* ZGBCON estimates the reciprocal of the condition number of a complex */
/* general band matrix A, in either the 1-norm or the infinity-norm, */
/* using the LU factorization computed by ZGBTRF. */
/* An estimate is obtained for norm(inv(A)), and 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. */
/* N (input) INTEGER */
/* The order 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) COMPLEX*16 array, dimension (LDAB,N) */
/* Details of the LU factorization of the band matrix A, as */
/* computed by ZGBTRF. U is stored as an upper triangular band */
/* matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and */
/* the multipliers used during the factorization are stored in */
/* rows KL+KU+2 to 2*KL+KU+1. */
/* LDAB (input) INTEGER */
/* The leading dimension of the array AB. LDAB >= 2*KL+KU+1. */
/* IPIV (input) INTEGER array, dimension (N) */
/* The pivot indices; for 1 <= i <= N, row i of the matrix was */
/* interchanged with row IPIV(i). */
/* ANORM (input) DOUBLE PRECISION */
/* If NORM = '1' or 'O', the 1-norm of the original matrix A. */
/* If NORM = 'I', the infinity-norm of the original matrix A. */
/* RCOND (output) DOUBLE PRECISION */
/* The reciprocal of the condition number of the matrix A, */
/* computed as RCOND = 1/(norm(A) * norm(inv(A))). */
/* WORK (workspace) COMPLEX*16 array, dimension (2*N) */
/* RWORK (workspace) DOUBLE PRECISION 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;
--ipiv;
--work;
--rwork;
/* Function Body */
*info = 0;
onenrm = *(unsigned char *)norm == '1' || lsame_(norm, "O");
if (! onenrm && ! lsame_(norm, "I")) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*kl < 0) {
*info = -3;
} else if (*ku < 0) {
*info = -4;
} else if (*ldab < (*kl << 1) + *ku + 1) {
*info = -6;
} else if (*anorm < 0.) {
*info = -8;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZGBCON", &i__1);
return 0;
}
/* Quick return if possible */
*rcond = 0.;
if (*n == 0) {
*rcond = 1.;
return 0;
} else if (*anorm == 0.) {
return 0;
}
smlnum = dlamch_("Safe minimum");
/* Estimate the norm of inv(A). */
ainvnm = 0.;
*(unsigned char *)normin = 'N';
if (onenrm) {
kase1 = 1;
} else {
kase1 = 2;
}
kd = *kl + *ku + 1;
lnoti = *kl > 0;
kase = 0;
L10:
zlacn2_(n, &work[*n + 1], &work[1], &ainvnm, &kase, isave);
if (kase != 0) {
if (kase == kase1) {
/* Multiply by inv(L). */
if (lnoti) {
i__1 = *n - 1;
for (j = 1; j <= i__1; ++j) {
/* Computing MIN */
i__2 = *kl, i__3 = *n - j;
lm = min(i__2,i__3);
jp = ipiv[j];
i__2 = jp;
t.r = work[i__2].r, t.i = work[i__2].i;
if (jp != j) {
i__2 = jp;
i__3 = j;
work[i__2].r = work[i__3].r, work[i__2].i = work[i__3]
.i;
i__2 = j;
work[i__2].r = t.r, work[i__2].i = t.i;
}
z__1.r = -t.r, z__1.i = -t.i;
zaxpy_(&lm, &z__1, &ab[kd + 1 + j * ab_dim1], &c__1, &
work[j + 1], &c__1);
/* L20: */
}
}
/* Multiply by inv(U). */
i__1 = *kl + *ku;
zlatbs_("Upper", "No transpose", "Non-unit", normin, n, &i__1, &
ab[ab_offset], ldab, &work[1], &scale, &rwork[1], info);
} else {
/* Multiply by inv(U'). */
i__1 = *kl + *ku;
zlatbs_("Upper", "Conjugate transpose", "Non-unit", normin, n, &
i__1, &ab[ab_offset], ldab, &work[1], &scale, &rwork[1],
info);
/* Multiply by inv(L'). */
if (lnoti) {
for (j = *n - 1; j >= 1; --j) {
/* Computing MIN */
i__1 = *kl, i__2 = *n - j;
lm = min(i__1,i__2);
i__1 = j;
i__2 = j;
zdotc_(&z__2, &lm, &ab[kd + 1 + j * ab_dim1], &c__1, &
work[j + 1], &c__1);
z__1.r = work[i__2].r - z__2.r, z__1.i = work[i__2].i -
z__2.i;
work[i__1].r = z__1.r, work[i__1].i = z__1.i;
jp = ipiv[j];
if (jp != j) {
i__1 = jp;
t.r = work[i__1].r, t.i = work[i__1].i;
i__1 = jp;
i__2 = j;
work[i__1].r = work[i__2].r, work[i__1].i = work[i__2]
.i;
i__1 = j;
work[i__1].r = t.r, work[i__1].i = t.i;
}
/* L30: */
}
}
}
/* Divide X by 1/SCALE if doing so will not cause overflow. */
*(unsigned char *)normin = 'Y';
if (scale != 1.) {
ix = izamax_(n, &work[1], &c__1);
i__1 = ix;
if (scale < ((d__1 = work[i__1].r, abs(d__1)) + (d__2 = d_imag(&
work[ix]), abs(d__2))) * smlnum || scale == 0.) {
goto L40;
}
zdrscl_(n, &scale, &work[1], &c__1);
}
goto L10;
}
/* Compute the estimate of the reciprocal condition number. */
if (ainvnm != 0.) {
*rcond = 1. / ainvnm / *anorm;
}
L40:
return 0;
/* End of ZGBCON */
} /* zgbcon_ */
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