rat
===

Floating point rational approximation



Calling Sequence
~~~~~~~~~~~~~~~~


::

    [N,D]=rat(X [,tol])
    Y=rat(X [,tol])




Arguments
~~~~~~~~~

:X real vector or matrix
: :tol real positive scalar, the tolerance (see below). Default value
  is 1d-6.
: :N integer vector or matrix
: :D integer vector or matrix
: :Y real vector or matrix
:



Description
~~~~~~~~~~~

`[N,D] = rat(X,tol)` returns two integer matrices so that `N./D` is
close to `X` in the sense that `abs(N./D - X) <=
tol*norm(X,1)*abs(X)`.

`y=rat(x,tol)` return the quotient `N./D`

The rational approximations are generated by truncating continued
fraction expansions.



Examples
~~~~~~~~


::

    [n,d]=rat([3.5, 1.333333,-0.8])
    [n,d]=rat(%pi)
    [n,d]=rat(%pi,1.d-12)
    n/d-%pi




See Also
~~~~~~~~


+ `int`_ round towards zero
+ `round`_ round to nearest integer


.. _int: int.html
.. _round: round.html