# p?gecon

Estimates the reciprocal of the condition number of a general distributed matrix in either the 1-norm or the infinity-norm.

## Syntax

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

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

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

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

## Description

This routine estimates the reciprocal of the condition number of a general distributed real/complex matrix `sub(A) = A(ia:ia+n-1, ja:ja+n-1)` in either the 1-norm or infinity-norm, using the LU factorization computed by p?getrf.

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

## Input Parameters

norm

  (global) CHARACTER*1. Must be '1' or 'O' or 'I'.

  Specifies whether the 1-norm condition number or the infinity-norm condition number is required.

  If `norm = '1'` or 'O', then the 1-norm is used;

  If `norm = 'I'`, then the infinity-norm is used.

n

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

a

  (local)

  REAL for psgecon

  DOUBLE PRECISION for pdgecon

  COMPLEX for pcgecon

  DOUBLE COMPLEX for pzgecon.

  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 and U from the factorization sub(A) = P*L*U; the unit diagonal elements of L are not stored.

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.

  If `norm = '1'` or 'O', the 1-norm of the original distributed matrix sub(A);

  If `norm = 'I'`, the infinity-norm of the original distributed matrix sub(A).

work

  (local)

  REAL for psgecon

  DOUBLE PRECISION for pdgecon

  COMPLEX for pcgecon

  DOUBLE COMPLEX for pzgecon.

  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*max(1, ceil(NPROW-1, NPCOL))`, `LOCc(n+mod(ja-1,nb_a))+nb_a*max(1, 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*ceil(NPROW-1, NPCOL)`, `LOCc(n+mod(ja-1,nb_a))+ nb_a*ceil(NPCOL-1, NPROW)))`.

  LOCr and LOCc values can be computed using the ScaLAPACK tool function numroc; NPROW and NPCOL can be determined by calling the subroutine blacs_gridinfo.

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 pcgecon

  DOUBLE PRECISION for pzgecon

  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). See Description.

`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 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.

Parent topic: Routines for Estimating the Condition Number