zpptrf - itive definite matrix A stored in packed format
SUBROUTINE ZPPTRF(UPLO, N, A, INFO) CHARACTER*1 UPLO DOUBLE COMPLEX A(*) INTEGER N, INFO SUBROUTINE ZPPTRF_64(UPLO, N, A, INFO) CHARACTER*1 UPLO DOUBLE COMPLEX A(*) INTEGER*8 N, INFO F95 INTERFACE SUBROUTINE PPTRF(UPLO, N, A, INFO) CHARACTER(LEN=1) :: UPLO COMPLEX(8), DIMENSION(:) :: A INTEGER :: N, INFO SUBROUTINE PPTRF_64(UPLO, N, A, INFO) CHARACTER(LEN=1) :: UPLO COMPLEX(8), DIMENSION(:) :: A INTEGER(8) :: N, INFO C INTERFACE #include <sunperf.h> void zpptrf(char uplo, int n, doublecomplex *a, int *info); void zpptrf_64(char uplo, long n, doublecomplex *a, long *info);
Oracle Solaris Studio Performance Library zpptrf(3P) NAME zpptrf - compute the Cholesky factorization of a complex Hermitian pos- itive definite matrix A stored in packed format SYNOPSIS SUBROUTINE ZPPTRF(UPLO, N, A, INFO) CHARACTER*1 UPLO DOUBLE COMPLEX A(*) INTEGER N, INFO SUBROUTINE ZPPTRF_64(UPLO, N, A, INFO) CHARACTER*1 UPLO DOUBLE COMPLEX A(*) INTEGER*8 N, INFO F95 INTERFACE SUBROUTINE PPTRF(UPLO, N, A, INFO) CHARACTER(LEN=1) :: UPLO COMPLEX(8), DIMENSION(:) :: A INTEGER :: N, INFO SUBROUTINE PPTRF_64(UPLO, N, A, INFO) CHARACTER(LEN=1) :: UPLO COMPLEX(8), DIMENSION(:) :: A INTEGER(8) :: N, INFO C INTERFACE #include <sunperf.h> void zpptrf(char uplo, int n, doublecomplex *a, int *info); void zpptrf_64(char uplo, long n, doublecomplex *a, long *info); PURPOSE zpptrf 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*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 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 ] 7 Nov 2015 zpptrf(3P)