161 lines
5.6 KiB
C
161 lines
5.6 KiB
C
#include "blaswrap.h"
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#ifdef _cpluscplus
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extern "C" {
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#endif
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#include "f2c.h"
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/* Subroutine */ int dgbsv_(integer *n, integer *kl, integer *ku, integer *
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nrhs, doublereal *ab, integer *ldab, integer *ipiv, doublereal *b,
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integer *ldb, integer *info)
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{
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/* -- LAPACK driver routine (version 3.0) --
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Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
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Courant Institute, Argonne National Lab, and Rice University
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March 31, 1993
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Purpose
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=======
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DGBSV computes the solution to a real system of linear equations
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A * X = B, where A is a band matrix of order N with KL subdiagonals
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and KU superdiagonals, and X and B are N-by-NRHS matrices.
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The LU decomposition with partial pivoting and row interchanges is
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used to factor A as A = L * U, where L is a product of permutation
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and unit lower triangular matrices with KL subdiagonals, and U is
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upper triangular with KL+KU superdiagonals. The factored form of A
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is then used to solve the system of equations A * X = B.
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Arguments
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=========
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N (input) INTEGER
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The number of linear equations, i.e., the order of the
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matrix A. N >= 0.
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KL (input) INTEGER
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The number of subdiagonals within the band of A. KL >= 0.
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KU (input) INTEGER
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The number of superdiagonals within the band of A. KU >= 0.
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NRHS (input) INTEGER
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The number of right hand sides, i.e., the number of columns
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of the matrix B. NRHS >= 0.
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AB (input/output) DOUBLE PRECISION array, dimension (LDAB,N)
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On entry, the matrix A in band storage, in rows KL+1 to
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2*KL+KU+1; rows 1 to KL of the array need not be set.
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The j-th column of A is stored in the j-th column of the
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array AB as follows:
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AB(KL+KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+KL)
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On exit, details of the factorization: U is stored as an
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upper triangular band matrix with KL+KU superdiagonals in
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rows 1 to KL+KU+1, and the multipliers used during the
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factorization are stored in rows KL+KU+2 to 2*KL+KU+1.
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See below for further details.
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LDAB (input) INTEGER
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The leading dimension of the array AB. LDAB >= 2*KL+KU+1.
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IPIV (output) INTEGER array, dimension (N)
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The pivot indices that define the permutation matrix P;
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row i of the matrix was interchanged with row IPIV(i).
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B (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS)
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On entry, the N-by-NRHS right hand side matrix B.
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On exit, if INFO = 0, the N-by-NRHS solution matrix X.
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LDB (input) INTEGER
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The leading dimension of the array B. LDB >= max(1,N).
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INFO (output) INTEGER
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= 0: successful exit
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< 0: if INFO = -i, the i-th argument had an illegal value
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> 0: if INFO = i, U(i,i) is exactly zero. The factorization
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has been completed, but the factor U is exactly
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singular, and the solution has not been computed.
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Further Details
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===============
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The band storage scheme is illustrated by the following example, when
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M = N = 6, KL = 2, KU = 1:
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On entry: On exit:
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* * * + + + * * * u14 u25 u36
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* * + + + + * * u13 u24 u35 u46
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* a12 a23 a34 a45 a56 * u12 u23 u34 u45 u56
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a11 a22 a33 a44 a55 a66 u11 u22 u33 u44 u55 u66
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a21 a32 a43 a54 a65 * m21 m32 m43 m54 m65 *
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a31 a42 a53 a64 * * m31 m42 m53 m64 * *
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Array elements marked * are not used by the routine; elements marked
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+ need not be set on entry, but are required by the routine to store
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elements of U because of fill-in resulting from the row interchanges.
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=====================================================================
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Test the input parameters.
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Parameter adjustments */
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/* System generated locals */
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integer ab_dim1, ab_offset, b_dim1, b_offset, i__1;
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/* Local variables */
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extern /* Subroutine */ int dgbtrf_(integer *, integer *, integer *,
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integer *, doublereal *, integer *, integer *, integer *),
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xerbla_(char *, integer *), dgbtrs_(char *, integer *,
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integer *, integer *, integer *, doublereal *, integer *, integer
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*, doublereal *, integer *, integer *);
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ab_dim1 = *ldab;
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ab_offset = 1 + ab_dim1 * 1;
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ab -= ab_offset;
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--ipiv;
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b_dim1 = *ldb;
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b_offset = 1 + b_dim1 * 1;
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b -= b_offset;
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/* Function Body */
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*info = 0;
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if (*n < 0) {
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*info = -1;
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} else if (*kl < 0) {
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*info = -2;
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} else if (*ku < 0) {
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*info = -3;
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} else if (*nrhs < 0) {
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*info = -4;
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} else if (*ldab < (*kl << 1) + *ku + 1) {
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*info = -6;
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} else if (*ldb < max(*n,1)) {
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*info = -9;
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}
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if (*info != 0) {
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i__1 = -(*info);
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xerbla_("DGBSV ", &i__1);
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return 0;
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}
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/* Compute the LU factorization of the band matrix A. */
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dgbtrf_(n, n, kl, ku, &ab[ab_offset], ldab, &ipiv[1], info);
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if (*info == 0) {
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/* Solve the system A*X = B, overwriting B with X. */
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dgbtrs_("No transpose", n, kl, ku, nrhs, &ab[ab_offset], ldab, &ipiv[
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1], &b[b_offset], ldb, info);
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}
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return 0;
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/* End of DGBSV */
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} /* dgbsv_ */
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#ifdef _cpluscplus
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}
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#endif
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