NAME

dpptrf - compute the Cholesky factorization of a real symmetric positive definite matrix A stored in packed format

SYNOPSIS

  SUBROUTINE DPPTRF( UPLO, N, A, INFO)
  CHARACTER * 1 UPLO
  INTEGER N, INFO
  DOUBLE PRECISION A(*)

  SUBROUTINE DPPTRF_64( UPLO, N, A, INFO)
  CHARACTER * 1 UPLO
  INTEGER*8 N, INFO
  DOUBLE PRECISION A(*)

  SUBROUTINE PPTRF( UPLO, N, A, [INFO])
  CHARACTER(LEN=1) :: UPLO
  INTEGER :: N, INFO
  REAL(8), DIMENSION(:) :: A

  SUBROUTINE PPTRF_64( UPLO, N, A, [INFO])
  CHARACTER(LEN=1) :: UPLO
  INTEGER(8) :: N, INFO
  REAL(8), DIMENSION(:) :: A

#include <sunperf.h>

void dpptrf(char uplo, int n, double *a, int *info);

void dpptrf_64(char uplo, long n, double *a, long *info);

dpptrf computes the Cholesky factorization of a real symmetric positive definite matrix A stored in packed format.

The factorization has the form

   A = U**T * U,  if UPLO = 'U', or

   A = L  * L**T,  if UPLO = 'L',

where U is an upper triangular matrix and L is lower triangular.

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)
On entry, the upper or lower triangle of the symmetric 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**T*U or A = L*L**T, 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
positive definite, and the factorization could not be
completed.

The packed storage scheme is illustrated by the following example when N = 4, UPLO = 'U':

Two-dimensional storage of the symmetric matrix A:

   a11 a12 a13 a14

       a22 a23 a24

           a33 a34     (aij  = aji)

a44

Packed storage of the upper triangle of A:

A = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]