@stdlib/math-base-tools-sum-series/lib/basic.js

Compute the sum of an infinite series.

/**
* @license Apache-2.0
*
* Copyright (c) 2018 The Stdlib Authors.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
*    http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/

'use strict';

// MODULES //

var abs = require( '@stdlib/math-base-special-abs' );
var EPS = require( '@stdlib/constants-float64-eps' );


// VARIABLES //

var MAX_TERMS = 1000000;


// MAIN //

/**
* Sum the elements of the series given by the supplied function.
*
* @param {Function} generator - series function
* @param {Object} [options] - function options
* @param {PositiveInteger} [options.maxTerms=1000000] - maximum number of terms to be added
* @param {PositiveNumber} [options.tolerance=2.22e-16] - further terms are only added as long as the next term is greater than current term times the tolerance
* @param {number} [options.initialValue=0] - initial value of the resulting sum
* @returns {number} sum of all series terms
*
* @example
* var gen = geometricSeriesClosure( 0.9 )
* var out = sumSeries( gen );
* // returns 10.0
*
* function geometricSeriesClosure( x ) {
*     var exponent = -1;
*     return function() {
*         exponent += 1;
*         return Math.pow( x, exponent );
*     };
* }
*/
function sumSeries( generator, options ) {
	var tolerance;
	var nextTerm;
	var counter;
	var result;
	var opts;

	opts = {};

	if ( arguments.length > 1 ) {
		opts = options;
	}
	tolerance = opts.tolerance || EPS;
	counter = opts.maxTerms || MAX_TERMS;
	result = opts.initialValue || 0;

	// Repeatedly call function...
	do {
		nextTerm = generator();
		result += nextTerm;
	}
	while ( ( abs(tolerance * result) < abs(nextTerm) ) && --counter ); // eslint-disable-line no-plusplus

	return result;
}


// EXPORTS //

module.exports = sumSeries;