# p?pocon

Estimates the reciprocal of the condition number (in the 1 - norm) of a symmetric / Hermitian positive-definite distributed matrix.

## Syntax

call pspocon( uplo, n, a, ia, ja, desca, anorm, rcond, work, lwork, iwork, liwork, info)

call pdpocon( uplo, n, a, ia, ja, desca, anorm, rcond, work, lwork, iwork, liwork, info)

call pcpocon( uplo, n, a, ia, ja, desca, anorm, rcond, work, lwork, rwork, lrwork, info)

call pzpocon( uplo, n, a, ia, ja, desca, anorm, rcond, work, lwork, rwork, lrwork, info)

## Description

This routine estimates the reciprocal of the condition number (in the 1 - norm) of a real symmetric or complex Hermitian positive definite distributed matrix `sub(A) = A(ia:ia+n-1, ja:ja+n-1)`, using the Cholesky factorization `sub(A) = UH*U` or `sub(A) = L*LH` computed by p?potrf.

An estimate is obtained for `||(sub(A))-1||`, and the reciprocal of the condition number is computed as

## Input Parameters

uplo

  (global) CHARACTER*1. Must be 'U' or 'L'.

  Specifies whether the factor stored in sub(A) is upper or lower triangular.

  If `uplo = 'U'`, sub(A) stores the upper triangular factor U of the Cholesky factorization `sub(A) = UH*U`.

  If `uplo = 'L'`, sub(A) stores the lower triangular factor L of the Cholesky factorization `sub(A) = L*LH`.

n

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

a

  (local)

  REAL for pspocon

  DOUBLE PRECISION for pdpocon

  COMPLEX for pcpocon

  DOUBLE COMPLEX for pzpocon.

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

  The array a contains the local pieces of the factors L or U from the Cholesky factorization `sub(A) = UH*U`, or `sub(A) = L*LH`, as computed by p?potrf.

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.

anorm

  (global) REAL for single precision flavors,

  DOUBLE PRECISION for double precision flavors.

  The 1-norm of the symmetric/Hermitian distributed matrix sub(A).

work

  (local)

  REAL for pspocon

  DOUBLE PRECISION for pdpocon

  COMPLEX for pcpocon

  DOUBLE COMPLEX for pzpocon.

  The array work of dimension (lwork) is a workspace array.

lwork

  (local or global) INTEGER. The dimension of the array work.

  For real flavors:

  lwork must be at least

  `lwork ≥ 2*LOCr(n+mod(ia-1,mb_a))+` `2*LOCc(n+mod(ja-1,nb_a))+` `max(2, max(nb_a*ceil(NPROW-1, NPCOL)`, `LOCc(n+mod(ja-1,nb_a))+`

  `nb_a*ceil(NPCOL-1, NPROW)))`.

  For complex flavors:

  lwork must be at least

  `lwork ≥ 2*LOCr(n+mod(ia-1,mb_a))+` `max(2, max(nb_a*max(1,ceil(NPROW-1, NPCOL))`, `LOCc(n+mod(ja-1,nb_a))+` `nb_a*max(1,ceil(NPCOL-1, NPROW))))`.

iwork

  (local) INTEGER. Workspace array, DIMENSION (liwork). Used in real flavors only.

liwork

  (local or global) INTEGER. The dimension of the array iwork; used in real flavors only. Must be at least `liwork ≥ LOCr(n+mod(ia-1,mb_a))`.

rwork

  (local) REAL for pcpocon

  DOUBLE PRECISION for pzpocon

  Workspace array, DIMENSION (lrwork). Used in complex flavors only.

lrwork

  (local or global) INTEGER. The dimension of the array rwork; used in complex flavors only. Must be at least `lrwork ≥ 2*LOCc(n+mod(ja-1,nb_a))`.

## Output Parameters

rcond

  (global) REAL for single precision flavors.

  DOUBLE PRECISION for double precision flavors.

  The reciprocal of the condition number of the distributed matrix sub(A).

`work(1)`

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

`iwork(1)`

  On exit, `iwork(1)` contains the minimum value of liwork required for optimum performance (for real flavors).

`rwork(1)`

  On exit, `rwork(1)` contains the minimum value of lrwork required for optimum performance (for complex flavors).

info

  (global) INTEGER. If `info=0`, the execution is successful.

  `info < 0`:

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

Parent topic: Routines for Estimating the Condition Number