p?trcon

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 12/16/2022

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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)

Include Files

Description

The p?trconroutine 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 matrix 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 size (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 matrix A indicating the first row and the first column of the matrix sub(A), respectively.

desca

(global and local) INTEGER array of size 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 size lwork is a workspace array.

lwork

(local or global) INTEGER. The size 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,iceil(NPROW-1, NPCOL)),

LOCc(n+mod(ja-1,nb_a))+nb_a*max(1,iceil(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*iceil(NPROW-1, NPCOL),

LOCc(n+mod(ja-1,nb_a))+nb_a*iceil(NPCOL-1, NPROW))).

NOTE:

iceil(x,y) is the ceiling of x/y, and mod(x,y) is the integer remainder of x/y.

iwork

(local) INTEGER. Workspace array of size liwork. Used in real flavors only.

liwork

(local or global) INTEGER. The size 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 of size lrwork. Used in complex flavors only.

lrwork

(local or global) INTEGER. The size 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: Estimating the Condition Number: ScaLAPACK Computational Routines

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