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)

 = 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, NSUB = 2, NSUPER = 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.