#include "blaswrap.h"
#include "f2c.h"
/* Subroutine */ int zgbsv_(integer *n, integer *kl, integer *ku, integer *
nrhs, doublecomplex *ab, integer *ldab, integer *ipiv, doublecomplex *
b, integer *ldb, integer *info)
{
/* -- LAPACK driver routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
February 29, 1992
Purpose
=======
ZGBSV computes the solution to a complex system of linear equations
A * X = B, where A is a band matrix of order N with KL subdiagonals
and KU superdiagonals, and X and B are N-by-NRHS matrices.
The LU decomposition with partial pivoting and row interchanges is
used to factor A as A = L * U, where L is a product of permutation
and unit lower triangular matrices with KL subdiagonals, and U is
upper triangular with KL+KU superdiagonals. The factored form of A
is then used to solve the system of equations A * X = B.
Arguments
=========
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.
NRHS (input) INTEGER
The number of right hand sides, i.e., the number of columns
of the matrix B. NRHS >= 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(N,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 (N)
The pivot indices that define the permutation matrix P;
row i of the matrix was interchanged with row IPIV(i).
B (input/output) COMPLEX*16 array, dimension (LDB,NRHS)
On entry, the N-by-NRHS right hand side matrix B.
On exit, if INFO = 0, the N-by-NRHS solution matrix X.
LDB (input) INTEGER
The leading dimension of the array B. LDB >= max(1,N).
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 the solution has not been computed.
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.
=====================================================================
Test the input parameters.
Parameter adjustments */
/* System generated locals */
integer ab_dim1, ab_offset, b_dim1, b_offset, i__1;
/* Local variables */
extern /* Subroutine */ int xerbla_(char *, integer *), zgbtrf_(
integer *, integer *, integer *, integer *, doublecomplex *,
integer *, integer *, integer *), zgbtrs_(char *, integer *,
integer *, integer *, integer *, doublecomplex *, integer *,
integer *, doublecomplex *, integer *, integer *);
ab_dim1 = *ldab;
ab_offset = 1 + ab_dim1 * 1;
ab -= ab_offset;
--ipiv;
b_dim1 = *ldb;
b_offset = 1 + b_dim1 * 1;
b -= b_offset;
/* Function Body */
*info = 0;
if (*n < 0) {
*info = -1;
} else if (*kl < 0) {
*info = -2;
} else if (*ku < 0) {
*info = -3;
} else if (*nrhs < 0) {
*info = -4;
} else if (*ldab < (*kl << 1) + *ku + 1) {
*info = -6;
} else if (*ldb < max(*n,1)) {
*info = -9;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZGBSV ", &i__1);
return 0;
}
/* Compute the LU factorization of the band matrix A. */
zgbtrf_(n, n, kl, ku, &ab[ab_offset], ldab, &ipiv[1], info);
if (*info == 0) {
/* Solve the system A*X = B, overwriting B with X. */
zgbtrs_("No transpose", n, kl, ku, nrhs, &ab[ab_offset], ldab, &ipiv[
1], &b[b_offset], ldb, info);
}
return 0;
/* End of ZGBSV */
} /* zgbsv_ */