Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

ID 766686
Date 3/22/2024
Public

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?la_porcond

Estimates the Skeel condition number for a symmetric positive-definite matrix.

Syntax

call sla_porcond( uplo, n, a, lda, af, ldaf, cmode, c, info, work, iwork )

call dla_porcond( uplo, n, a, lda, af, ldaf, cmode, c, info, work, iwork )

Include Files

  • mkl.fi

Description

The function estimates the Skeel condition number of

op(A) * op2(C)

where

the cmode parameter determines op2 as follows:

cmode Value

op2(C)

1

C

0

I

-1

inv(C)

The Skeel condition number

cond(A) = norminf(|inv(A)||A|)

is computed by computing scaling factors R such that

diag(R)*A*op2(C)

is row equilibrated and by computing the standard infinity-norm condition number.

Input Parameters

uplo

CHARACTER*1. Must be 'U' or 'L'.

Specifies the triangle of A to store:

If uplo = 'U', the upper triangle of A is stored,

If uplo = 'L', the lower triangle of A is stored.

n

INTEGER. The number of linear equations, that is, the order of the matrix A; n 0.

a, af, c, work

REAL for sla_porcond

DOUBLE PRECISION for dla_porcond

Arrays:

a (lda,*) contains the n-by-n matrix A.

af (ldaf,*) contains the triangular factor L or U from the Cholesky factorization

A = UT*U or A = L*LT,

as computed by ?potrf.

c, DIMENSIONn. The vector C in the formula op(A) * op2(C).

work is a workspace array of DIMENSION (3*n).

The second dimension of a and af must be at least max(1, n).

lda

INTEGER. The leading dimension of the array ab. ldamax(1,n).

ldaf

INTEGER. The leading dimension of af. ldafmax(1,n).

cmode

INTEGER. Determines op2(C) in the formula op(A) * op2(C) as follows:

If cmode = 1, op2(C) = C.

If cmode = 0, op2(C) = I.

If cmode = -1, op2(C) = inv(C).

iwork

INTEGER. Workspace array with DIMENSIONn.

Output Parameters

info

INTEGER.

If info = 0, the execution is successful.

If i > 0, the i-th parameter is invalid.

See Also