# rat

Returns a rational approximation of the input using a continued fraction approximation.

## Syntax

[n,d] = rat(X)

[n,d] = rat(X, tol)

str = rat(...)

## Inputs

`X`- Values to be approximated.
`tol`- Relative tolerance (default: 1.0e-6).

## Outputs

- n
- The numerator of the rational apprxoimation.
- d
- The denominator of the rational apprxoimation.
- str
- The continued fraction.

## Examples

Compute the rational fraction.

`[n,d] = rat(2.31304347826)`

```
n = 266
d = 115
```

Compute the continued fraction.

`str = rat(2.31304347826)`

`str = 2 + 1/(3 + 1/(5 + 1/7))`

## Comments

rat computes terms of the continued fraction until the relative
tolerance is acheived.

Note: The result may not be the fraction within the allowed tolerance
with the smallest possible integers.

When `X` is a matrix and the output is str, the results are
stored as a column of strings, as if the inputs had been X(:).