# ?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 )

• 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 AT*X = B (Transpose).

If `trans = 'C'`, the system has the form AH*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, DIMENSION n. 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 DIMENSION n. 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 DIMENSION n.

## Output Parameters

info

INTEGER.

If info = 0, the execution is successful.

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