?la_gercond

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 3/31/2023

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?la_gercond

Estimates the Skeel condition number for a general matrix.

Syntax

call sla_gercond( trans, n, a, lda, af, ldaf, ipiv, cmode, c, info, work, iwork )

call dla_gercond( trans, 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

trans

CHARACTER*1. Must be 'N' or 'T' or 'C'.

Specifies the form of the system of equations:

If trans = 'N', the system has the form A*X = B (No transpose).

If trans = 'T', the system has the form A^T*X = B (Transpose).

If trans = 'C', the system has the form A^H*X = B (Conjugate Transpose = Transpose).

n

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

a, af, c, work

REAL for sla_gercond

DOUBLE PRECISION for dla_gercond

Arrays:

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

af(ldaf,*) contains factors L and U from the factorization of the general matrix A=P*L*U, as returned by ?getrf.

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 a. lda≥max(1,n).

ldaf

INTEGER. The leading dimension of af. ldaf≥max(1, n).

ipiv

INTEGER.

Array with DIMENSIONn. The pivot indices from the factorization A = P*L*U as computed by ?getrf. Row i of the matrix was interchanged with row ipiv(i).

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.

Parent topic: LAPACK Auxiliary Routines

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

?la_gercond

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