SYNOPSIS

SUBROUTINE SPPSV(

UPLO, N, NRHS, AP, B, LDB, INFO )

    

CHARACTER UPLO

    

INTEGER INFO, LDB, N, NRHS

    

REAL AP( * ), B( LDB, * )

PURPOSE

SPPSV computes the solution to a real system of linear equations
   A * X = B, where A is an N-by-N symmetric positive definite matrix stored in packed format 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.

AP (input/output) REAL array, dimension (N*(N+1)/2)

On entry, the upper or lower triangle of the symmetric matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array AP as follows: if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. See below for further details. On exit, if INFO = 0, the factor U or L from the Cholesky factorization A = U**T*U or A = L*L**T, in the same storage format as A.

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.

FURTHER DETAILS

The packed storage scheme is illustrated by the following example when N = 4, UPLO = 'U':
Two-dimensional storage of the symmetric matrix A:

   a11 a12 a13 a14

       a22 a23 a24

           a33 a34     (aij = conjg(aji))

               a44
Packed storage of the upper triangle of A:
AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]