zppsv(3P)

NAME

zppsv - compute the solution to a complex system of linear equations A ∗ X = B,

SYNOPSIS

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

void zppsv(char uplo, long int n, long int nrhs,
doublecomplex ∗zap, doublecomplex ∗zb, long int ldb, long int ∗info)

CHARACTER UPLO

INTEGER INFO, LDB, N, NRHS

COMPLEX∗16 AP( ∗ ), B( LDB, ∗ )

PURPOSE

ZPPSV computes the solution to a complex system of linear equations
   A ∗ X = 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
   A = U∗∗H∗ U, if UPLO = ’U’, or
   A = L ∗ L∗∗H, 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) COMPLEX∗16 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 = ’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∗∗H∗U or A = L∗L∗∗H, in the same storage format as A.

B (input/output) COMPLEX∗16 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 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 ]