cpptrf(3P) Sun Performance Library cpptrf(3P)NAMEcpptrf - compute the Cholesky factorization of a complex Hermitian pos‐
itive definite matrix A stored in packed format
SYNOPSIS
SUBROUTINE CPPTRF(UPLO, N, A, INFO)
CHARACTER * 1 UPLO
COMPLEX A(*)
INTEGER N, INFO
SUBROUTINE CPPTRF_64(UPLO, N, A, INFO)
CHARACTER * 1 UPLO
COMPLEX A(*)
INTEGER*8 N, INFO
F95 INTERFACE
SUBROUTINE PPTRF(UPLO, [N], A, [INFO])
CHARACTER(LEN=1) :: UPLO
COMPLEX, DIMENSION(:) :: A
INTEGER :: N, INFO
SUBROUTINE PPTRF_64(UPLO, [N], A, [INFO])
CHARACTER(LEN=1) :: UPLO
COMPLEX, DIMENSION(:) :: A
INTEGER(8) :: N, INFO
C INTERFACE
#include <sunperf.h>
void cpptrf(char uplo, int n, complex *a, int *info);
void cpptrf_64(char uplo, long n, complex *a, long *info);
PURPOSEcpptrf computes the Cholesky factorization of a complex Hermitian posi‐
tive definite matrix A stored in packed format.
The factorization has the form
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 lower triangular.
ARGUMENTS
UPLO (input)
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
N (input) The order of the matrix A. N >= 0.
A (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 A as follows: if UPLO = 'U', A(i +
(j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', A(i +
(j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. See below for further
details.
On exit, if INFO = 0, the triangular factor U or L from the
Cholesky factorization A = U**H*U or A = L*L**H, in the same
storage format as A.
INFO (output)
= 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 is not posi‐
tive definite, and the factorization could not be completed.
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:
A = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]
6 Mar 2009 cpptrf(3P)
