stdlib-js
<summary>
About stdlib...
</summary>
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sum-series
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Compute the sum of an [infinite series][infinite-series].
bash
npm install @stdlib/math-base-tools-sum-series
javascript
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][es6-generator] or a function which returns successive elements of the series at each invocation.
Using an ES6 [Generator object][es6-generator]:
javascript
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:
javascript
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.
javascript
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.
javascript
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.
javascript
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 );
}
}
javascript
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 ) ) );
