# dpptrf (l) - Linux Manuals

## NAME

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

## SYNOPSIS

SUBROUTINE DPPTRF(
UPLO, N, AP, INFO )

CHARACTER UPLO

INTEGER INFO, N

DOUBLE PRECISION AP( * )

## PURPOSE

DPPTRF computes the Cholesky factorization of a real symmetric positive definite matrix A stored in packed format. The factorization has the form

U**T U,  if UPLO aqUaq, or

L**T,  if UPLO aqLaq,
where U is an upper triangular matrix and L is lower triangular.

## ARGUMENTS

UPLO (input) CHARACTER*1
= aqUaq: Upper triangle of A is stored;
= aqLaq: Lower triangle of A is stored.
N (input) INTEGER
The order of the matrix A. N >= 0.
AP (input/output) DOUBLE PRECISION array, dimension (N*(N+1)/2)
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 AP as follows: if UPLO = aqUaq, AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = aqLaq, 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 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) 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 is not positive definite, and the factorization could not be completed.

## FURTHER DETAILS

The packed storage scheme is illustrated by the following example when N = 4, UPLO = aqUaq:
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:
AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]