sgbsv

NAME

sgbsv - compute 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

SYNOPSIS

  SUBROUTINE SGBSV( N, NSUB, NSUPER, NRHS, A, LDA, IPIVOT, B, LDB, 
 *      INFO)
  INTEGER N, NSUB, NSUPER, NRHS, LDA, LDB, INFO
  INTEGER IPIVOT(*)
  REAL A(LDA,*), B(LDB,*)
 
  SUBROUTINE SGBSV_64( N, NSUB, NSUPER, NRHS, A, LDA, IPIVOT, B, LDB, 
 *      INFO)
  INTEGER*8 N, NSUB, NSUPER, NRHS, LDA, LDB, INFO
  INTEGER*8 IPIVOT(*)
  REAL A(LDA,*), B(LDB,*)

F95 INTERFACE

  SUBROUTINE GBSV( [N], NSUB, NSUPER, [NRHS], A, [LDA], IPIVOT, B, 
 *       [LDB], [INFO])
  INTEGER :: N, NSUB, NSUPER, NRHS, LDA, LDB, INFO
  INTEGER, DIMENSION(:) :: IPIVOT
  REAL, DIMENSION(:,:) :: A, B
 
  SUBROUTINE GBSV_64( [N], NSUB, NSUPER, [NRHS], A, [LDA], IPIVOT, B, 
 *       [LDB], [INFO])
  INTEGER(8) :: N, NSUB, NSUPER, NRHS, LDA, LDB, INFO
  INTEGER(8), DIMENSION(:) :: IPIVOT
  REAL, DIMENSION(:,:) :: A, B

C INTERFACE

#include <sunperf.h>

void sgbsv(int n, int nsub, int nsuper, int nrhs, float *a, int lda, int *ipivot, float *b, int ldb, int *info);

void sgbsv_64(long n, long nsub, long nsuper, long nrhs, float *a, long lda, long *ipivot, float *b, long ldb, long *info);

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): The number of linear equations, i.e., the order of the matrix A. N >= 0.
* NSUB (input): The number of subdiagonals within the band of A. NSUB >= 0.
* NSUPER (input): The number of superdiagonals within the band of A. NSUPER >= 0.
* NRHS (input): The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.
* A (input/output): On entry, the matrix A in band storage, in rows NSUB+1 to 2*NSUB+NSUPER+1; rows 1 to NSUB of the array need not be set. The j-th column of A is stored in the j-th column of the array A as follows: A(NSUB+NSUPER+1+i-j,j) = A(i,j) for max(1,j-NSUPER)<=i<=min(N,j+NSUB) On exit, details of the factorization: U is stored as an upper triangular band matrix with NSUB+NSUPER superdiagonals in rows 1 to NSUB+NSUPER+1, and the multipliers used during the factorization are stored in rows NSUB+NSUPER+2 to 2*NSUB+NSUPER+1. See below for further details.
* LDA (input): The leading dimension of the array A. LDA >= 2*NSUB+NSUPER+1.
* IPIVOT (output): The pivot indices that define the permutation matrix P; row i of the matrix was interchanged with row IPIVOT(i).
* B (input/output): 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): The leading dimension of the array B. LDB >= max(1,N).
* INFO (output)