SYNOPSIS

SUBROUTINE SPOSV(

UPLO, N, NRHS, A, LDA, B, LDB, INFO )

    

CHARACTER UPLO

    

INTEGER INFO, LDA, LDB, N, NRHS

    

REAL A( LDA, * ), B( LDB, * )

PURPOSE

SPOSV computes the solution to a real system of linear equations
   A * X = B, where A is an N-by-N symmetric positive definite 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 matrix and L is a lower triangular matrix. The factored form of A is then used to solve the system of equations A * X = B.

ARGUMENTS

UPLO (input) CHARACTER*1

= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.

N (input) INTEGER

The number of linear equations, i.e., the order of the matrix A. N >= 0.

NRHS (input) INTEGER

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

A (input/output) REAL array, dimension (LDA,N)

On entry, the symmetric matrix A. If UPLO = 'U', the leading N-by-N upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced. On exit, if INFO = 0, the factor U or L from the Cholesky factorization A = U**T*U or A = L*L**T.

LDA (input) INTEGER

The leading dimension of the array A. LDA >= max(1,N).

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

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) 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
> 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.