continued-fraction

Continued fraction approximation.

Installation

npm install @stdlib/math-base-tools-continued-fraction

Usage

var continuedFraction = require( '@stdlib/math-base-tools-continued-fraction' );

continuedFraction( generator[, options ] )

Evaluates the continued fraction described by the supplied generator argument. generator can be either a function which returns an array with two elements, the a and b terms of the fraction, or an ES6 Generator object. By default, the function computes

Using an ES6 Generator object:

// Continued fraction for (e-1)^(-1):
var gen = generator();
var out = continuedFraction( gen );
// returns ~0.582

function* generator() {
    var i = 0;
    while ( true ) {
        i += 1;
        yield [ i, i ];
    }
}

Alternatively, one can use a closure to achieve the same goal:

// Continued fraction for (e-1)^(-1):
var gen = generator();
var out = continuedFraction( gen );
// returns ~0.582

function generator() {
    var i = 0;
    return gen;

    function gen() {
        i += 1;
        return [ i, i ];
    }
}

The function accepts the following options:

• maxIter: integer denoting the maximum number of times the supplied generator object will be called. Default: 1000000.
• tolerance: number primitive specifying the used tolerance to assess convergence. Default: 2.22e-16.
• keep: boolean primitive indicating whether to keep the b0 term in the continued fraction. Default: false.

To evaluate

set the keep option to true.

var out = continuedFraction( generator(), {
    'keep': true
});
// returns ~1.718

function generator() {
    var i = 0;
    return gen;

    function gen() {
        i += 1;
        return [ i, i ];
    }
}

To change the maximum number of iterations, set the maxIter option.

var out = continuedFraction( generator(), {
    'maxIter': 10
});
// returns ~0.582

function generator() {
    var i = 0;
    return gen;

    function gen() {
        i += 1;
        return [ i, i ];
    }
}

The default tolerance of 2.22e-16 to assess convergence can be changed via the tolerance option.

var out = continuedFraction( generator(), {
    'tolerance': 1e-1
});
// returns ~0.579

function generator() {
    var i = 0;
    return gen;

    function gen() {
        i += 1;
        return [ i, i ];
    }
}

Examples

var continuedFraction = require( '@stdlib/math-base-tools-continued-fraction' );
var out;

function* generator() {
    while ( true ) {
        yield [ 1, 1 ];
    }
}

function closure() {
    var ones = [ 1, 1 ];
    return gen;

    function gen() {
        return ones;
    }
}

out = continuedFraction( generator(), {
    'keep': true
});
console.log( 'Golden ratio (generator): %d,', out );

out = continuedFraction( closure(), {
    'keep': true
});
console.log( 'Golden ratio (closure): %d', out );

Notice

This package is part of stdlib, a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.

For more information on the project, filing bug reports and feature requests, and guidance on how to develop stdlib, see the main project repository.

Community

License

See LICENSE.

Copyright

Copyright © 2016-2024. The Stdlib Authors.