#include "blaswrap.h"
#include "f2c.h"
/* Subroutine */ int zppsv_(char *uplo, integer *n, integer *nrhs,
doublecomplex *ap, doublecomplex *b, integer *ldb, integer *info)
{
/* -- LAPACK driver routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
March 31, 1993
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 ]
=====================================================================
Test the input parameters.
Parameter adjustments */
/* System generated locals */
integer b_dim1, b_offset, i__1;
/* Local variables */
extern logical lsame_(char *, char *);
extern /* Subroutine */ int xerbla_(char *, integer *), zpptrf_(
char *, integer *, doublecomplex *, integer *), zpptrs_(
char *, integer *, integer *, doublecomplex *, doublecomplex *,
integer *, integer *);
--ap;
b_dim1 = *ldb;
b_offset = 1 + b_dim1 * 1;
b -= b_offset;
/* Function Body */
*info = 0;
if (! lsame_(uplo, "U") && ! lsame_(uplo, "L")) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*nrhs < 0) {
*info = -3;
} else if (*ldb < max(1,*n)) {
*info = -6;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZPPSV ", &i__1);
return 0;
}
/* Compute the Cholesky factorization A = U'*U or A = L*L'. */
zpptrf_(uplo, n, &ap[1], info);
if (*info == 0) {
/* Solve the system A*X = B, overwriting B with X. */
zpptrs_(uplo, n, nrhs, &ap[1], &b[b_offset], ldb, info);
}
return 0;
/* End of ZPPSV */
} /* zppsv_ */