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# 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

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