rational

From MASS v7.3-25 by Brian Ripley

Rational Approximation

Find rational approximations to the components of a real numeric object using a standard continued fraction method.

Keywords: math

Usage

rational(x, cycles = 10, max.denominator = 2000, ...)

Arguments

x: Any object of mode numeric. Missing values are now allowed.
cycles: The maximum number of steps to be used in the continued fraction approximation process.
max.denominator: An early termination criterion. If any partial denominator exceeds max.denominator the continued fraction stops at that point.
...: arguments passed to or from other methods.

Details

Each component is first expanded in a continued fraction of the form

x = floor(x) + 1/(p1 + 1/(p2 + ...)))

where p1, p2, ...are positive integers, terminating either at cycles terms or when a pj > max.denominator. The continued fraction is then re-arranged to retrieve the numerator and denominator as integers and the ratio returned as the value.

Value

A numeric object with the same attributes as x but with entries rational approximations to the values. This effectively rounds relative to the size of the object and replaces very small entries by zero.

Examples

X <- matrix(runif(25), 5, 5)
zapsmall(solve(X, X/5)) # print near-zeroes as zero
rational(solve(X, X/5))

Documentation reproduced from package MASS, version 7.3-25, License: GPL-2 | GPL-3

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