NAME

spbsv - compute the solution to a real system of linear equations A * X = B,

SYNOPSIS

  SUBROUTINE SPBSV( UPLO, N, NDIAG, NRHS, A, LDA, B, LDB, INFO)
  CHARACTER * 1 UPLO
  INTEGER N, NDIAG, NRHS, LDA, LDB, INFO
  REAL A(LDA,*), B(LDB,*)

  SUBROUTINE SPBSV_64( UPLO, N, NDIAG, NRHS, A, LDA, B, LDB, INFO)
  CHARACTER * 1 UPLO
  INTEGER*8 N, NDIAG, NRHS, LDA, LDB, INFO
  REAL A(LDA,*), B(LDB,*)

F95 INTERFACE

  SUBROUTINE PBSV( UPLO, [N], NDIAG, [NRHS], A, [LDA], B, [LDB], [INFO])
  CHARACTER(LEN=1) :: UPLO
  INTEGER :: N, NDIAG, NRHS, LDA, LDB, INFO
  REAL, DIMENSION(:,:) :: A, B

  SUBROUTINE PBSV_64( UPLO, [N], NDIAG, [NRHS], A, [LDA], B, [LDB], 
 *       [INFO])
  CHARACTER(LEN=1) :: UPLO
  INTEGER(8) :: N, NDIAG, NRHS, LDA, LDB, INFO
  REAL, DIMENSION(:,:) :: A, B

C INTERFACE

#include <sunperf.h>

void spbsv(char uplo, int n, int ndiag, int nrhs, float *a, int lda, float *b, int ldb, int *info);

void spbsv_64(char uplo, long n, long ndiag, long nrhs, float *a, long lda, float *b, long ldb, long *info);

PURPOSE

spbsv computes the solution to a real system of linear equations A * X = B, where A is an N-by-N symmetric positive definite band matrix and X and B are N-by-NRHS matrices.

The Cholesky decomposition is used to factor A as

   A = U**T * U,  if UPLO = 'U', or

   A = L * L**T,  if UPLO = 'L',

where U is an upper triangular band matrix, and L is a lower triangular band matrix, with the same number of superdiagonals or subdiagonals as A. The factored form of A is then used to solve the system of equations A * X = B.

ARGUMENTS

UPLO (input)

 = 'U':  Upper triangle of A is stored;

 = 'L':  Lower triangle of A is stored.

N (input)
The number of linear equations, i.e., the order of the matrix A. N > = 0.
NDIAG (input)
The number of superdiagonals of the matrix A if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. NDIAG > = 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 upper or lower triangle of the symmetric band matrix A, stored in the first NDIAG+1 rows of the array. The j-th column of A is stored in the j-th column of the array A as follows: if UPLO = 'U', A(NDIAG+1+i-j,j) = A(i,j) for max(1,j-NDIAG) < =i < =j; if UPLO = 'L', A(1+i-j,j) = A(i,j) for j < =i < =min(N,j+NDIAG). See below for further details.
On exit, if INFO = 0, the triangular factor U or L from the Cholesky factorization A = U**T*U or A = L*L**T of the band matrix A, in the same storage format as A.
LDA (input)
The leading dimension of the array A. LDA > = NDIAG+1.
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, the leading minor of order i of A is not
positive definite, so the factorization could not be
completed, and the solution has not been computed.

FURTHER DETAILS

The band storage scheme is illustrated by the following example, when N = 6, NDIAG = 2, and UPLO = 'U':

On entry: On exit:

    *    *   a13  a24  a35  a46      *    *   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

Similarly, if UPLO = 'L' the format of A is as follows:

On entry: On exit:

   a11  a22  a33  a44  a55  a66     l11  l22  l33  l44  l55  l66
   a21  a32  a43  a54  a65   *      l21  l32  l43  l54  l65   *
   a31  a42  a53  a64   *    *      l31  l42  l53  l64   *    *

Array elements marked * are not used by the routine.