sppsv (l)  Linux Manuals
sppsv: computes the solution to a real system of linear equations A * X = B,
NAME
SPPSV  computes 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 equationsA
The Cholesky decomposition is used to factor A as
A
A
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

= aqUaq: Upper triangle of A is stored;
= aqLaq: 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 = aqUaq, AP(i + (j1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = aqLaq, 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 NbyNRHS 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 = aqUaq:Twodimensional storage of the symmetric matrix A:
a11 a12 a13 a14
Packed storage of the upper triangle of A:
AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]