# cppsv (l) - Linux Man Pages

## NAME

CPPSV - computes the solution to a complex system of linear equations A * X = B,

## SYNOPSIS

SUBROUTINE CPPSV(
UPLO, N, NRHS, AP, B, LDB, INFO )

CHARACTER UPLO

INTEGER INFO, LDB, N, NRHS

COMPLEX AP( * ), B( LDB, * )

## PURPOSE

CPPSV computes the solution to a complex system of linear equations
B, where A is an N-by-N Hermitian 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

U**H* U,  if UPLO aqUaq, or

L**H,  if UPLO aqLaq,
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) COMPLEX array, dimension (N*(N+1)/2)
On entry, the upper or lower triangle of the Hermitian matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array AP as follows: if UPLO = aqUaq, AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = aqLaq, 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**H*U or A = L*L**H, in the same storage format as A.
B (input/output) COMPLEX 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 = aqUaq:
Two-dimensional storage of the Hermitian 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 ]