sppsv(3)

NAME

SPPSV - compute the solution to a real system of linear

equations A * X = B,

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 def

inite 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 sym

metric 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 de

tails.

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 ille

gal 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 ]

LAPACK version 3.0 15 June 2000

SPPSV(3)