# p?potrf

Computes the Cholesky factorization of a symmetric (Hermitian) positive-definite distributed matrix.

## Syntax

call pspotrf(uplo, n, a, ia, ja, desca, info)

call pdpotrf(uplo, n, a, ia, ja, desca, info)

call pcpotrf(uplo, n, a, ia, ja, desca, info)

call pzpotrf(uplo, n, a, ia, ja, desca, info)

## Description

This routine computes the Cholesky factorization of a real symmetric or complex Hermitian positive-definite distributed n-by-n matrix `A(ia:ia+n-1, ja:ja+n-1)`, denoted below as sub(A).

The factorization has the form

`sub(A) = UH*U` if `uplo='U'`, or

`sub(A) = L*LH` if `uplo='L'`

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

## Input Parameters

uplo

  (global) CHARACTER*1.

  Indicates whether the upper or lower triangular part of sub(A) is stored. Must be 'U' or 'L'.

  If `uplo = 'U'`, the array a stores the upper triangular part of the matrix `sub(A)` that is factored as UH*U.

  If `uplo = 'L'`, the array a stores the lower triangular part of the matrix `sub(A)` that is factored as L*LH.

n

  (global) INTEGER. The order of the distributed submatrix sub(A) `(n≥0)`.

a

  (local)

  REAL for pspotrf

  DOUBLE PRECISON for pdpotrf

  COMPLEX for pcpotrf

  DOUBLE COMPLEX for pzpotrf.

  Pointer into the local memory to an array of dimension `(lld_a, LOCc(ja+n-1))`.

  On entry, this array contains the local pieces of the n-by-n symmetric/Hermitian distributed matrix `sub(A)` to be factored.

  Depending on uplo, the array a contains either the upper or the lower triangular part of the matrix `sub(A)` (see uplo).

ia, ja

  (global) INTEGER. The row and column indices in the global array A indicating the first row and the first column of the submatrix `sub(A)`, respectively.

desca

  (global and local) INTEGER array, dimension (dlen_). The array descriptor for the distributed matrix A.

## Output Parameters

a

  The upper or lower triangular part of a is overwritten by the Cholesky factor U or L, as specified by uplo.

info

  (global) INTEGER.

  If `info=0`, the execution is successful;

  `info < 0`: if the i-th argument is an array, and the j-th entry had an illegal value, then `info = -(i*100+j)`; if the i-th argument is a scalar and had an illegal value, then `info = -i`.

  If `info = k >0`, the leading minor of order `k, A(ia:ia+k-1, ja:ja+k-1)`, is not positive-definite, and the factorization could not be completed.

Parent topic: Routines for Matrix Factorization