
SPPSV(l) ) SPPSV(l)
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
NbyN symmetric positive definite matrix stored in packed format and X and B are Nby
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 jth column of A is stored in the array AP as follows: if
UPLO = 'U', AP(i + (j1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i +
(j1)*(2nj)/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 NbyNRHS right hand side matrix B. On exit, if INFO = 0, the Nby
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 ith 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':
Twodimensional 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(l) 
