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@stdlib/math-base-tools-sum-series
Advanced tools
Compute the sum of an infinite series.
npm install @stdlib/math-base-tools-sum-series
var sumSeries = require( '@stdlib/math-base-tools-sum-series' );
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
:
1000000
.2.22e-16
.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' );
var out = sumSeries( geometricSeriesClosure( 0.5 ), {
'maxTerms': 10
});
// returns ~1.998 (infinite sum is 2)
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 );
}
}
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 ) ) );
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.
See LICENSE.
Copyright © 2016-2022. The Stdlib Authors.
FAQs
Compute the sum of an infinite series.
We found that @stdlib/math-base-tools-sum-series demonstrated a healthy version release cadence and project activity because the last version was released less than a year ago. It has 0 open source maintainers collaborating on the project.
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