# rat

Floating point rational approximation

### Syntax

[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)`

.

`y = rat(x, tol)`

returns 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

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