A generalized continued fraction has the form

If a_i = 1 for all i, the above expression reduces to a simple continued fraction.

where the values b_i are called the coefficients or terms of the continued fraction.

Installation

npm install @stdlib/math-iter-utils-continued-fraction

Usage

var iterContinuedFraction = require( '@stdlib/math-iter-utils-continued-fraction' );

iterContinuedFraction( iterator[, options] )

Evaluates the terms of a continued fraction.

var array2iterator = require( '@stdlib/array-to-iterator' );

var arr = array2iterator( [ 3, 4, 12, 4 ] );

var v = iterContinuedFraction( arr );
// returns ~3.245

The function supports the following options:

• iter: maximum number of iterations. Default: 1e308.
• tol: tolerance at which to terminate further evaluation of the continued fraction. Default: floating-point epsilon.

To explicitly cap the maximum number of iterations, set the iter option.

var array2iterator = require( '@stdlib/array-to-iterator' );

var arr = array2iterator( [ 3, 4, 12, 4 ] );

var opts = {
    'iter': 2
};
var v = iterContinuedFraction( arr, opts );
// returns 3.25

The function terminates continued fraction evaluation once the difference between continued fraction approximations is sufficiently small. The default tolerance is floating-point epsilon (~2.22e-16). Once an update to a continued fraction approximation is less than or equal to this tolerance, the function terminates evaluation. To adjust the tolerance (e.g., to return a rough approximation), set the tol option.

var iterContinuedFractionSeq = require( '@stdlib/math-iter-sequences-continued-fraction' );

var opts = {
    'tol': 1.0e-7
};
var it = iterContinuedFractionSeq( 3.141592653589793, opts );
// returns <Object>

var v = iterContinuedFraction( it );
// returns ~3.14159292

Notes

• If an iterated value is non-numeric (including NaN), the function returns NaN. If non-numeric iterated values are possible, you are advised to provide an iterator which type checks and handles non-numeric values accordingly.

Examples

var iterContinuedFractionSeq = require( '@stdlib/math-iter-sequences-continued-fraction' );
var PI = require( '@stdlib/constants-float64-pi' );
var iterContinuedFraction = require( '@stdlib/math-iter-utils-continued-fraction' );

// Create an iterator for returning the list of continued fraction terms:
var it = iterContinuedFractionSeq( PI );

// Reconstitute the original value:
var v = iterContinuedFraction( it );
// returns <number>

console.log( 'Value: %d.', v );

See Also

• @stdlib/math-iter/sequences/continued-fraction: create an iterator which generates a list of all continued fraction terms which can be obtained given the precision of a provided number.

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

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