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))

Comments

rat computes terms of the continued fraction until the relative tolerance is acheived.
NoteColonSymbol 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(:).