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.
Type: double
Dimension: scalar | matrix
tol
Relative tolerance (default: 1.0e-6).
Type: double
Dimension: scalar

Outputs

n
The numerator of the rational apprxoimation.
Type: integer
d
The denominator of the rational apprxoimation.
Type: integer
str
The continued fraction.
Type: string

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))

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(:).