Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

ID 766686
Date 3/22/2024
Public

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?la_syrcond

Estimates the Skeel condition number for a symmetric indefinite matrix.

Syntax

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

call dla_syrcond( uplo, n, a, lda, af, ldaf, ipiv, 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_syrcond

DOUBLE PRECISION for dla_syrcond

Arrays:

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

af (ldaf,*) contains the The block diagonal matrix D and the multipliers used to obtain the factor L or U as computed by ?sytrf.

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

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

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

lda

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

ldaf

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

ipiv

INTEGER.

Array with DIMENSIONn. Details of the interchanges and the block structure of D as determined by ?sytrf.

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