rcond inverse condition number

## Syntax

    r = rcond(X)

## Arguments

X

  real or complex square matrix

r

  real positive number

## Description

`rcond(X)` is an estimate for the reciprocal of the condition of `X` in the 1-norm.

If `X` is well conditioned, `rcond(X)` is close to 1. If not, `rcond(X)` is close to 0.

Estimating the 1-norm inverse condition number with `rcond` is much faster than computing the 2-norm condition number with `cond`. As a trade-off, `rcond` may be less reliable.

Algorithm: We compute the 1-norm of X with Lapack/DLANGE, compute its LU decomposition with Lapack/DGETRF, and finally estimate the condition with Lapack/DGECON.

`rcond([])` yields `%inf`.

## Examples

    A = diag([1:10]);
    rcond(A)
    A(1,1) = 0.000001;
    rcond(A)

Comparative benchmark:

        A = ones(1000, 1000);
        timer(); cond(A);    timer()
        timer(); 1/rcond(A); timer()

## See also

- svd
- cond
- inv

## History

6.0.2 rcond([]) now yields %inf = 1/cond([]) instead of [].