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/* zgbtf2.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 doublecomplex c_b1 = {1.,0.};
static integer c__1 = 1;
/* Subroutine */ int zgbtf2_(integer *m, integer *n, integer *kl, integer *ku,
doublecomplex *ab, integer *ldab, integer *ipiv, integer *info)
{
/* System generated locals */
integer ab_dim1, ab_offset, i__1, i__2, i__3, i__4;
doublecomplex z__1;
/* Builtin functions */
void z_div(doublecomplex *, doublecomplex *, doublecomplex *);
/* Local variables */
integer i__, j, km, jp, ju, kv;
extern /* Subroutine */ int zscal_(integer *, doublecomplex *,
doublecomplex *, integer *), zgeru_(integer *, integer *,
doublecomplex *, doublecomplex *, integer *, doublecomplex *,
integer *, doublecomplex *, integer *), zswap_(integer *,
doublecomplex *, integer *, doublecomplex *, integer *), xerbla_(
char *, integer *);
extern integer izamax_(integer *, doublecomplex *, integer *);
/* -- LAPACK routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* ZGBTF2 computes an LU factorization of a complex m-by-n band matrix */
/* A using partial pivoting with row interchanges. */
/* This is the unblocked version of the algorithm, calling Level 2 BLAS. */
/* 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) COMPLEX*16 array, dimension (LDAB,N) */
/* On entry, the matrix A in band storage, in rows KL+1 to */
/* 2*KL+KU+1; rows 1 to KL of the array need not be set. */
/* The j-th column of A is stored in the j-th column of the */
/* array AB as follows: */
/* AB(kl+ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(m,j+kl) */
/* On exit, details of the factorization: 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. */
/* See below for further details. */
/* LDAB (input) INTEGER */
/* The leading dimension of the array AB. LDAB >= 2*KL+KU+1. */
/* IPIV (output) INTEGER array, dimension (min(M,N)) */
/* The pivot indices; for 1 <= i <= min(M,N), row i of the */
/* matrix was interchanged with row IPIV(i). */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value */
/* > 0: if INFO = +i, U(i,i) is exactly zero. The factorization */
/* has been completed, but the factor U is exactly */
/* singular, and division by zero will occur if it is used */
/* to solve a system of equations. */
/* Further Details */
/* =============== */
/* The band storage scheme is illustrated by the following example, when */
/* M = N = 6, KL = 2, KU = 1: */
/* On entry: On exit: */
/* * * * + + + * * * u14 u25 u36 */
/* * * + + + + * * u13 u24 u35 u46 */
/* * a12 a23 a34 a45 a56 * u12 u23 u34 u45 u56 */
/* a11 a22 a33 a44 a55 a66 u11 u22 u33 u44 u55 u66 */
/* a21 a32 a43 a54 a65 * m21 m32 m43 m54 m65 * */
/* a31 a42 a53 a64 * * m31 m42 m53 m64 * * */
/* Array elements marked * are not used by the routine; elements marked */
/* + need not be set on entry, but are required by the routine to store */
/* elements of U, because of fill-in resulting from the row */
/* interchanges. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* KV is the number of superdiagonals in the factor U, allowing for */
/* fill-in. */
/* Parameter adjustments */
ab_dim1 = *ldab;
ab_offset = 1 + ab_dim1;
ab -= ab_offset;
--ipiv;
/* Function Body */
kv = *ku + *kl;
/* Test the input parameters. */
*info = 0;
if (*m < 0) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*kl < 0) {
*info = -3;
} else if (*ku < 0) {
*info = -4;
} else if (*ldab < *kl + kv + 1) {
*info = -6;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZGBTF2", &i__1);
return 0;
}
/* Quick return if possible */
if (*m == 0 || *n == 0) {
return 0;
}
/* Gaussian elimination with partial pivoting */
/* Set fill-in elements in columns KU+2 to KV to zero. */
i__1 = min(kv,*n);
for (j = *ku + 2; j <= i__1; ++j) {
i__2 = *kl;
for (i__ = kv - j + 2; i__ <= i__2; ++i__) {
i__3 = i__ + j * ab_dim1;
ab[i__3].r = 0., ab[i__3].i = 0.;
/* L10: */
}
/* L20: */
}
/* JU is the index of the last column affected by the current stage */
/* of the factorization. */
ju = 1;
i__1 = min(*m,*n);
for (j = 1; j <= i__1; ++j) {
/* Set fill-in elements in column J+KV to zero. */
if (j + kv <= *n) {
i__2 = *kl;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + (j + kv) * ab_dim1;
ab[i__3].r = 0., ab[i__3].i = 0.;
/* L30: */
}
}
/* Find pivot and test for singularity. KM is the number of */
/* subdiagonal elements in the current column. */
/* Computing MIN */
i__2 = *kl, i__3 = *m - j;
km = min(i__2,i__3);
i__2 = km + 1;
jp = izamax_(&i__2, &ab[kv + 1 + j * ab_dim1], &c__1);
ipiv[j] = jp + j - 1;
i__2 = kv + jp + j * ab_dim1;
if (ab[i__2].r != 0. || ab[i__2].i != 0.) {
/* Computing MAX */
/* Computing MIN */
i__4 = j + *ku + jp - 1;
i__2 = ju, i__3 = min(i__4,*n);
ju = max(i__2,i__3);
/* Apply interchange to columns J to JU. */
if (jp != 1) {
i__2 = ju - j + 1;
i__3 = *ldab - 1;
i__4 = *ldab - 1;
zswap_(&i__2, &ab[kv + jp + j * ab_dim1], &i__3, &ab[kv + 1 +
j * ab_dim1], &i__4);
}
if (km > 0) {
/* Compute multipliers. */
z_div(&z__1, &c_b1, &ab[kv + 1 + j * ab_dim1]);
zscal_(&km, &z__1, &ab[kv + 2 + j * ab_dim1], &c__1);
/* Update trailing submatrix within the band. */
if (ju > j) {
i__2 = ju - j;
z__1.r = -1., z__1.i = -0.;
i__3 = *ldab - 1;
i__4 = *ldab - 1;
zgeru_(&km, &i__2, &z__1, &ab[kv + 2 + j * ab_dim1], &
c__1, &ab[kv + (j + 1) * ab_dim1], &i__3, &ab[kv
+ 1 + (j + 1) * ab_dim1], &i__4);
}
}
} else {
/* If pivot is zero, set INFO to the index of the pivot */
/* unless a zero pivot has already been found. */
if (*info == 0) {
*info = j;
}
}
/* L40: */
}
return 0;
/* End of ZGBTF2 */
} /* zgbtf2_ */
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