sum-series

Compute the sum of an infinite series.

Installation

npm install @stdlib/math-base-tools-sum-series

Usage

var sumSeries = require( '@stdlib/math-base-tools-sum-series' );

sumSeries( generator[, options ] )

Computes the sum of the series given by the supplied generator argument. generator can be either an ES6 Generator object or a function which returns successive elements of the series at each invocation.

Using an ES6 Generator object:

var pow = require( '@stdlib/math-base-special-pow' );
var gen = geometricSeriesGenerator( 0.9 );
var out = sumSeries( gen );
// returns 10

function* geometricSeriesGenerator( x ) {
    var exponent = 0;
    while ( true ) {
        yield pow( x, exponent );
        exponent += 1;
    }
}

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

var pow = require( '@stdlib/math-base-special-pow' );
var gen = geometricSeriesClosure( 0.9 );
var out = sumSeries( gen );
// returns 10

function geometricSeriesClosure( x ) {
    var exponent = -1;
    return gen;

    function gen() {
        exponent += 1;
        return pow( x, exponent );
    }
}

The function accepts the following options:

• maxTerms: integer denoting the maximum number of terms to be summed. Default: 1000000.
• tolerance: number specifying the tolerance used to assess convergence. Default: 2.22e-16.
• initialValue: number specifying the initial value of the returned sum. Default: 0.

By default, the initial value of the sum is 0. To choose a different one, use the initialValue option.

var pow = require( '@stdlib/math-base-special-pow' );

var out = sumSeries( geometricSeriesClosure( 0.5 ), {
    'initialValue': 1
});
// returns 3

function geometricSeriesClosure( x ) {
    var exponent = -1;
    return gen;

    function gen() {
        exponent += 1;
        return pow( x, exponent );
    }
}

To change the maximum number of terms to be summed, set the maxTerms option.

var pow = require( '@stdlib/math-base-special-pow' );

// Note: infinite sum is 2
var out = sumSeries( geometricSeriesClosure( 0.5 ), {
    'maxTerms': 10
});
// returns ~1.998

function geometricSeriesClosure( x ) {
    var exponent = -1;
    return gen;

    function gen() {
        exponent += 1;
        return pow( x, exponent );
    }
}

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

var pow = require( '@stdlib/math-base-special-pow' );

var out = sumSeries( geometricSeriesClosure( 0.5 ), {
    'tolerance': 1e-3
});
// returns ~1.998

function geometricSeriesClosure( x ) {
    var exponent = -1;
    return gen;

    function gen() {
        exponent += 1;
        return pow( x, exponent );
    }
}

Examples

var log1p = require( '@stdlib/math-base-special-log1p' );
var sumSeries = require( '@stdlib/math-base-tools-sum-series' );

function* log1pSeries( x ) {
    var mMult = -x;
    var mProd = -1;
    var k = 0;
    while ( true ) {
        mProd *= mMult;
        k += 1;
        yield ( mProd / k );
    }
}

console.log( 'log1p(0.5) evaluated via math-log1p module: %d', log1p( 0.5 ) );
console.log( 'log1p(0.5) evaluated via infinite series expansion: %d', sumSeries( log1pSeries( 0.5 ) ) );

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.