time-to-botec

Benchmark sampling in different programming languages
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dvarianceyc.js (2122B)

      1 /**
      2 * @license Apache-2.0
      3 *
      4 * Copyright (c) 2020 The Stdlib Authors.
      5 *
      6 * Licensed under the Apache License, Version 2.0 (the "License");
      7 * you may not use this file except in compliance with the License.
      8 * You may obtain a copy of the License at
      9 *
     10 *    http://www.apache.org/licenses/LICENSE-2.0
     11 *
     12 * Unless required by applicable law or agreed to in writing, software
     13 * distributed under the License is distributed on an "AS IS" BASIS,
     14 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
     15 * See the License for the specific language governing permissions and
     16 * limitations under the License.
     17 */
     18 
     19 'use strict';
     20 
     21 // MAIN //
     22 
     23 /**
     24 * Computes the variance of a double-precision floating-point strided array using a one-pass algorithm proposed by Youngs and Cramer.
     25 *
     26 * ## Method
     27 *
     28 * -   This implementation uses a one-pass algorithm, as proposed by Youngs and Cramer (1971).
     29 *
     30 * ## References
     31 *
     32 * -   Youngs, Edward A., and Elliot M. Cramer. 1971. "Some Results Relevant to Choice of Sum and Sum-of-Product Algorithms." _Technometrics_ 13 (3): 657–65. doi:[10.1080/00401706.1971.10488826](https://doi.org/10.1080/00401706.1971.10488826).
     33 *
     34 * @param {PositiveInteger} N - number of indexed elements
     35 * @param {number} correction - degrees of freedom adjustment
     36 * @param {Float64Array} x - input array
     37 * @param {integer} stride - stride length
     38 * @returns {number} variance
     39 *
     40 * @example
     41 * var Float64Array = require( '@stdlib/array/float64' );
     42 *
     43 * var x = new Float64Array( [ 1.0, -2.0, 2.0 ] );
     44 * var N = x.length;
     45 *
     46 * var v = dvarianceyc( N, 1, x, 1 );
     47 * // returns ~4.3333
     48 */
     49 function dvarianceyc( N, correction, x, stride ) {
     50 	var sum;
     51 	var ix;
     52 	var S;
     53 	var v;
     54 	var d;
     55 	var n;
     56 	var i;
     57 
     58 	n = N - correction;
     59 	if ( N <= 0 || n <= 0.0 ) {
     60 		return NaN;
     61 	}
     62 	if ( N === 1 || stride === 0 ) {
     63 		return 0.0;
     64 	}
     65 	if ( stride < 0 ) {
     66 		ix = (1-N) * stride;
     67 	} else {
     68 		ix = 0;
     69 	}
     70 	sum = x[ ix ];
     71 	ix += stride;
     72 	S = 0.0;
     73 	for ( i = 2; i <= N; i++ ) {
     74 		v = x[ ix ];
     75 		sum += v;
     76 		d = (i*v) - sum;
     77 		S += (1.0/(i*(i-1))) * d * d;
     78 		ix += stride;
     79 	}
     80 	return S / n;
     81 }
     82 
     83 
     84 // EXPORTS //
     85 
     86 module.exports = dvarianceyc;