# p?pttrf

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

## Syntax

call pspttrf(n, d, e, ja, desca, af, laf, work, lwork, info)

call pdpttrf(n, d, e, ja, desca, af, laf, work, lwork, info)

call pcpttrf(n, d, e, ja, desca, af, laf, work, lwork, info)

call pzpttrf(n, d, e, ja, desca, af, laf, work, lwork, info)

## Description

This routine computes the Cholesky factorization of an n-by-n real symmetric or complex hermitian positive-definite tridiagonal distributed matrix `A(1:n, ja:ja+n-1)`.

The resulting factorization is not the same factorization as returned from LAPACK. Additional permutations are performed on the matrix for the sake of parallelism.

The factorization has the form:

`A(1:n, ja:ja+n-1) = P*L*D*LH*PT`, or

`A(1:n, ja:ja+n-1) = P*UH*D*U*PT`,

where P is a permutation matrix, and U and L are tridiagonal upper and lower triangular matrices, respectively.

## Input Parameters

n

  (global) INTEGER. The order of the distributed submatrix `A(1:n, ja:ja+n-1)`

  `(n ≥ 0)`.

d, e

  (local)

  REAL for pspttrf

  DOUBLE PRECISON for pdpttrf

  COMPLEX for pcpttrf

  DOUBLE COMPLEX for pzpttrf.

  Pointers into the local memory to arrays of dimension `(desca(nb_))` each.

  On entry, the array d contains the local part of the global vector storing the main diagonal of the distributed matrix A.

  On entry, the array e contains the local part of the global vector storing the upper diagonal of the distributed matrix A.

ja

  (global) INTEGER. The index in the global array A that points to the start of the matrix to be operated on (which may be either all of A or a submatrix of A).

desca

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

  If `desca(dtype_) = 501`, then `dlen_ ≥ 7`;

  else if `desca(dtype_) = 1`, then `dlen_ ≥ 9`.

laf

  (local) INTEGER. The dimension of the array af.

  Must be `laf ≥ NB+2`.

  If laf is not large enough, an error code will be returned and the minimum acceptable size will be returned in af(1).

work

  (local) Same type as d and e. Workspace array of dimension lwork .

lwork

  (local or global) INTEGER. The size of the work array, must be at least

  `lwork ≥ 8*NPCOL`.

## Output Parameters

d, e

  On exit, overwritten by the details of the factorization.

af

  (local)

  REAL for pspttrf

  DOUBLE PRECISION for pdpttrf

  COMPLEX for pcpttrf

  DOUBLE COMPLEX for pzpttrf.

  Array, dimension (laf).

  Auxiliary Fillin space. Fillin is created during the factorization routine p?pttrf and this is stored in af.

  Note that if a linear system is to be solved using p?pttrs after the factorization routine, af must not be altered.

`work(1)`

  On exit, `work(1)` contains the minimum value of lwork required for optimum performance.

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`.

  `info > 0`:

  If `info = k ≤ NPROCS`, the submatrix stored on processor info and factored locally was not positive definite, and the factorization was not completed.

  If `info = k > NPROCS`, the submatrix stored on processor `info-NPROCS` representing interactions with other processors was not nonsingular, and the factorization was not completed.

Parent topic: Routines for Matrix Factorization