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/* zla_gbrcond_x.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;
doublereal zla_gbrcond_x__(char *trans, integer *n, integer *kl, integer *ku,
doublecomplex *ab, integer *ldab, doublecomplex *afb, integer *ldafb,
integer *ipiv, doublecomplex *x, integer *info, doublecomplex *work,
doublereal *rwork, ftnlen trans_len)
{
/* System generated locals */
integer ab_dim1, ab_offset, afb_dim1, afb_offset, i__1, i__2, i__3, i__4;
doublereal ret_val, d__1, d__2;
doublecomplex z__1, z__2;
/* Builtin functions */
double d_imag(doublecomplex *);
void z_div(doublecomplex *, doublecomplex *, doublecomplex *);
/* Local variables */
integer i__, j, kd, ke;
doublereal tmp;
integer kase;
extern logical lsame_(char *, char *);
integer isave[3];
doublereal anorm;
extern /* Subroutine */ int zlacn2_(integer *, doublecomplex *,
doublecomplex *, doublereal *, integer *, integer *), xerbla_(
char *, integer *);
doublereal ainvnm;
extern /* Subroutine */ int zgbtrs_(char *, integer *, integer *, integer
*, integer *, doublecomplex *, integer *, integer *,
doublecomplex *, integer *, integer *);
logical notrans;
/* -- LAPACK routine (version 3.2.1) -- */
/* -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and -- */
/* -- Jason Riedy of Univ. of California Berkeley. -- */
/* -- April 2009 -- */
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
/* -- Univ. of California Berkeley and NAG Ltd. -- */
/* .. */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* Purpose */
/* ======= */
/* ZLA_GBRCOND_X Computes the infinity norm condition number of */
/* op(A) * diag(X) where X is a COMPLEX*16 vector. */
/* Arguments */
/* ========= */
/* TRANS (input) CHARACTER*1 */
/* Specifies the form of the system of equations: */
/* = 'N': A * X = B (No transpose) */
/* = 'T': A**T * X = B (Transpose) */
/* = 'C': A**H * X = B (Conjugate Transpose = Transpose) */
/* N (input) INTEGER */
/* The number of linear equations, i.e., 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) */
/* 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(N,j+kl) */
/* LDAB (input) INTEGER */
/* The leading dimension of the array AB. LDAB >= KL+KU+1. */
/* AFB (input) COMPLEX*16 array, dimension (LDAFB,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. */
/* LDAFB (input) INTEGER */
/* The leading dimension of the array AFB. LDAFB >= 2*KL+KU+1. */
/* IPIV (input) INTEGER array, dimension (N) */
/* The pivot indices from the factorization A = P*L*U */
/* as computed by ZGBTRF; row i of the matrix was interchanged */
/* with row IPIV(i). */
/* X (input) COMPLEX*16 array, dimension (N) */
/* The vector X in the formula op(A) * diag(X). */
/* INFO (output) INTEGER */
/* = 0: Successful exit. */
/* i > 0: The ith argument is invalid. */
/* WORK (input) COMPLEX*16 array, dimension (2*N). */
/* Workspace. */
/* RWORK (input) DOUBLE PRECISION array, dimension (N). */
/* Workspace. */
/* ===================================================================== */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Statement Functions .. */
/* .. */
/* .. Statement Function Definitions .. */
/* .. */
/* .. Executable Statements .. */
/* Parameter adjustments */
ab_dim1 = *ldab;
ab_offset = 1 + ab_dim1;
ab -= ab_offset;
afb_dim1 = *ldafb;
afb_offset = 1 + afb_dim1;
afb -= afb_offset;
--ipiv;
--x;
--work;
--rwork;
/* Function Body */
ret_val = 0.;
*info = 0;
notrans = lsame_(trans, "N");
if (! notrans && ! lsame_(trans, "T") && ! lsame_(
trans, "C")) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*kl < 0 || *kl > *n - 1) {
*info = -3;
} else if (*ku < 0 || *ku > *n - 1) {
*info = -4;
} else if (*ldab < *kl + *ku + 1) {
*info = -6;
} else if (*ldafb < (*kl << 1) + *ku + 1) {
*info = -8;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZLA_GBRCOND_X", &i__1);
return ret_val;
}
/* Compute norm of op(A)*op2(C). */
kd = *ku + 1;
ke = *kl + 1;
anorm = 0.;
if (notrans) {
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
tmp = 0.;
/* Computing MAX */
i__2 = i__ - *kl;
/* Computing MIN */
i__4 = i__ + *ku;
i__3 = min(i__4,*n);
for (j = max(i__2,1); j <= i__3; ++j) {
i__2 = kd + i__ - j + j * ab_dim1;
i__4 = j;
z__2.r = ab[i__2].r * x[i__4].r - ab[i__2].i * x[i__4].i,
z__2.i = ab[i__2].r * x[i__4].i + ab[i__2].i * x[i__4]
.r;
z__1.r = z__2.r, z__1.i = z__2.i;
tmp += (d__1 = z__1.r, abs(d__1)) + (d__2 = d_imag(&z__1),
abs(d__2));
}
rwork[i__] = tmp;
anorm = max(anorm,tmp);
}
} else {
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
tmp = 0.;
/* Computing MAX */
i__3 = i__ - *kl;
/* Computing MIN */
i__4 = i__ + *ku;
i__2 = min(i__4,*n);
for (j = max(i__3,1); j <= i__2; ++j) {
i__3 = ke - i__ + j + i__ * ab_dim1;
i__4 = j;
z__2.r = ab[i__3].r * x[i__4].r - ab[i__3].i * x[i__4].i,
z__2.i = ab[i__3].r * x[i__4].i + ab[i__3].i * x[i__4]
.r;
z__1.r = z__2.r, z__1.i = z__2.i;
tmp += (d__1 = z__1.r, abs(d__1)) + (d__2 = d_imag(&z__1),
abs(d__2));
}
rwork[i__] = tmp;
anorm = max(anorm,tmp);
}
}
/* Quick return if possible. */
if (*n == 0) {
ret_val = 1.;
return ret_val;
} else if (anorm == 0.) {
return ret_val;
}
/* Estimate the norm of inv(op(A)). */
ainvnm = 0.;
kase = 0;
L10:
zlacn2_(n, &work[*n + 1], &work[1], &ainvnm, &kase, isave);
if (kase != 0) {
if (kase == 2) {
/* Multiply by R. */
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__;
i__3 = i__;
i__4 = i__;
z__1.r = rwork[i__4] * work[i__3].r, z__1.i = rwork[i__4] *
work[i__3].i;
work[i__2].r = z__1.r, work[i__2].i = z__1.i;
}
if (notrans) {
zgbtrs_("No transpose", n, kl, ku, &c__1, &afb[afb_offset],
ldafb, &ipiv[1], &work[1], n, info);
} else {
zgbtrs_("Conjugate transpose", n, kl, ku, &c__1, &afb[
afb_offset], ldafb, &ipiv[1], &work[1], n, info);
}
/* Multiply by inv(X). */
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__;
z_div(&z__1, &work[i__], &x[i__]);
work[i__2].r = z__1.r, work[i__2].i = z__1.i;
}
} else {
/* Multiply by inv(X'). */
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__;
z_div(&z__1, &work[i__], &x[i__]);
work[i__2].r = z__1.r, work[i__2].i = z__1.i;
}
if (notrans) {
zgbtrs_("Conjugate transpose", n, kl, ku, &c__1, &afb[
afb_offset], ldafb, &ipiv[1], &work[1], n, info);
} else {
zgbtrs_("No transpose", n, kl, ku, &c__1, &afb[afb_offset],
ldafb, &ipiv[1], &work[1], n, info);
}
/* Multiply by R. */
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__;
i__3 = i__;
i__4 = i__;
z__1.r = rwork[i__4] * work[i__3].r, z__1.i = rwork[i__4] *
work[i__3].i;
work[i__2].r = z__1.r, work[i__2].i = z__1.i;
}
}
goto L10;
}
/* Compute the estimate of the reciprocal condition number. */
if (ainvnm != 0.) {
ret_val = 1. / ainvnm;
}
return ret_val;
} /* zla_gbrcond_x__ */
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