cpptrf (3p)

Name

cpptrf - 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);

Description

Oracle Solaris Studio Performance Library                           cpptrf(3P)



NAME
       cpptrf - 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);



PURPOSE
       cpptrf 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 ]




                                  7 Nov 2015                        cpptrf(3P)