SYNOPSIS

SUBROUTINE SPBTRS(

UPLO, N, KD, NRHS, AB, LDAB, B, LDB, INFO )

    

CHARACTER UPLO

    

INTEGER INFO, KD, LDAB, LDB, N, NRHS

    

REAL AB( LDAB, * ), B( LDB, * )

PURPOSE

SPBTRS solves a system of linear equations A*X = B with a symmetric positive definite band matrix A using the Cholesky factorization A = U**T*U or A = L*L**T computed by SPBTRF.

ARGUMENTS

UPLO (input) CHARACTER*1

= 'U': Upper triangular factor stored in AB;
= 'L': Lower triangular factor stored in AB.

N (input) INTEGER

The order of the matrix A. N >= 0.

KD (input) INTEGER

The number of superdiagonals of the matrix A if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. KD >= 0.

NRHS (input) INTEGER

The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.

AB (input) REAL array, dimension (LDAB,N)

The triangular factor U or L from the Cholesky factorization A = U**T*U or A = L*L**T of the band matrix A, stored in the first KD+1 rows of the array. The j-th column of U or L is stored in the j-th column of the array AB as follows: if UPLO ='U', AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j; if UPLO ='L', AB(1+i-j,j) = L(i,j) for j<=i<=min(n,j+kd).

LDAB (input) INTEGER

The leading dimension of the array AB. LDAB >= KD+1.

B (input/output) REAL array, dimension (LDB,NRHS)

On entry, the right hand side matrix B. On exit, the 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