# p?potf2

Computes the Cholesky factorization of a symmetric/Hermitian positive definite matrix (local unblocked algorithm).

## Syntax

call pspotf2(uplo, n, a, ia, ja, desca, info)

call pdpotf2(uplo, n, a, ia, ja, desca, info)

call pcpotf2(uplo, n, a, ia, ja, desca, info)

call pzpotf2(uplo, n, a, ia, ja, desca, info)

## Description

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

The factorization has the form

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

where U is an upper triangular matrix, L is lower triangular. X' denotes transpose (conjugate transpose) of X.

## Input Parameters

uplo

  (global) CHARACTER.

  Specifies whether the upper or lower triangular part of the symmetric/Hermitian matrix A is stored.

  = 'U': upper triangle of sub (A) is stored;

  = 'L': lower triangle of sub (A) is stored.

n

  (global) INTEGER.

  The number of rows and columns to be operated on, that is, the order of the distributed submatrix sub (A). `n ≥ 0`.

a

  (local)

  REAL for pspotf2

  DOUBLE PRECISION or pdpotf2

  COMPLEX for pcpotf2

  COMPLEX*16 for pzpotf2.

  Pointer into the local memory to an array of DIMENSION`(lld_a, LOCc(ja+n-1))` containing the local pieces of the n-by-n symmetric distributed matrix sub(A) to be factored.

  If `uplo = 'U'`, the leading n-by-n upper triangular part of sub(A) contains the upper triangular matrix and the strictly lower triangular part of this matrix is not referenced.

  If `uplo = 'L'`, the leading n-by-n lower triangular part of sub(A) contains the lower triangular matrix and the strictly upper triangular part of sub(A) is not referenced.

ia, ja

  (global) INTEGER.

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

desca

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

## Output Parameters

a

  (local)

  On exit,

  if `uplo = 'U'`, the upper triangular part of the distributed matrix contains the Cholesky factor U;

  if `uplo = 'L'`, the lower triangular part of the distributed matrix contains the Cholesky factor L.

info

  (local) INTEGER.

  `= 0`: successful exit

  `< 0`: if the i-th argument is an array and the j-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`.

  `> 0`: `if info = k`, the leading minor of order k is not positive definite, and the factorization could not be completed.

Parent topic: Auxiliary Routines