# p?trcon

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

## Syntax

call pstrcon( norm, uplo, diag, n, a, ia, ja, desca, rcond, work, lwork, iwork, liwork, info)

call pdtrcon( norm, uplo, diag, n, a, ia, ja, desca, rcond, work, lwork, iwork, liwork, info)

call pctrcon( norm, uplo, diag, n, a, ia, ja, desca, rcond, work, lwork, rwork, lrwork, info)

call pztrcon( norm, uplo, diag, n, a, ia, ja, desca, rcond, work, lwork, rwork, lrwork, info)

## Description

This routine estimates the reciprocal of the condition number of a triangular distributed matrix `sub(A) = A(ia:ia+n-1, ja:ja+n-1)`, in either the 1-norm or the infinity-norm.

The norm of sub(A) is computed and an estimate is obtained for `||(sub(A))-1||`, then 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.

uplo

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

  If `uplo = 'U'`, `sub(A)` is upper triangular. If `uplo = 'L'`, `sub(A)` is lower triangular.

diag

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

  If `diag = 'N'`, `sub(A)` is non-unit triangular. If `diag = 'U'`, `sub(A)` is unit triangular.

n

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

a

  (local)

  REAL for pstrcon

  DOUBLE PRECISION for pdtrcon

  COMPLEX for pctrcon

  DOUBLE COMPLEX for pztrcon.

  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 triangular distributed matrix sub(A).

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

  If `uplo = 'L'`, the leading n-by-n lower triangular part of this distributed matrix contains the lower triangular matrix, and its strictly upper triangular part is not referenced.

  If `diag = 'U'`, the diagonal elements of sub(A) are also not referenced and are assumed to be 1.

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.

work

  (local)

  REAL for pstrcon

  DOUBLE PRECISION for pdtrcon

  COMPLEX for pctrcon

  DOUBLE COMPLEX for pztrcon.

  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))+` `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)))`.

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 ≥ 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 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