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/* sgbsv.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"
/* Subroutine */ int sgbsv_(integer *n, integer *kl, integer *ku, integer *
nrhs, real *ab, integer *ldab, integer *ipiv, real *b, integer *ldb,
integer *info)
{
/* System generated locals */
integer ab_dim1, ab_offset, b_dim1, b_offset, i__1;
/* Local variables */
extern /* Subroutine */ int xerbla_(char *, integer *), sgbtrf_(
integer *, integer *, integer *, integer *, real *, integer *,
integer *, integer *), sgbtrs_(char *, integer *, integer *,
integer *, integer *, real *, integer *, integer *, real *,
integer *, integer *);
/* -- LAPACK driver routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* SGBSV computes the solution to a real 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) REAL 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) REAL 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. */
/* ===================================================================== */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input parameters. */
/* Parameter adjustments */
ab_dim1 = *ldab;
ab_offset = 1 + ab_dim1;
ab -= ab_offset;
--ipiv;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
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_("SGBSV ", &i__1);
return 0;
}
/* Compute the LU factorization of the band matrix A. */
sgbtrf_(n, n, kl, ku, &ab[ab_offset], ldab, &ipiv[1], info);
if (*info == 0) {
/* Solve the system A*X = B, overwriting B with X. */
sgbtrs_("No transpose", n, kl, ku, nrhs, &ab[ab_offset], ldab, &ipiv[
1], &b[b_offset], ldb, info);
}
return 0;
/* End of SGBSV */
} /* sgbsv_ */
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