time-to-botec

Benchmark sampling in different programming languages
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dvariancepn.js (2602B)

      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 // MODULES //
     22 
     23 var dsumpw = require( '@stdlib/blas/ext/base/dsumpw' );
     24 
     25 
     26 // MAIN //
     27 
     28 /**
     29 * Computes the variance of a double-precision floating-point strided array using a two-pass algorithm.
     30 *
     31 * ## Method
     32 *
     33 * -   This implementation uses a two-pass approach, as suggested by Neely (1966).
     34 *
     35 * ## References
     36 *
     37 * -   Neely, Peter M. 1966. "Comparison of Several Algorithms for Computation of Means, Standard Deviations and Correlation Coefficients." _Communications of the ACM_ 9 (7). Association for Computing Machinery: 496–99. doi:[10.1145/365719.365958](https://doi.org/10.1145/365719.365958).
     38 * -   Schubert, Erich, and Michael Gertz. 2018. "Numerically Stable Parallel Computation of (Co-)Variance." In _Proceedings of the 30th International Conference on Scientific and Statistical Database Management_. New York, NY, USA: Association for Computing Machinery. doi:[10.1145/3221269.3223036](https://doi.org/10.1145/3221269.3223036).
     39 *
     40 * @param {PositiveInteger} N - number of indexed elements
     41 * @param {number} correction - degrees of freedom adjustment
     42 * @param {Float64Array} x - input array
     43 * @param {integer} stride - stride length
     44 * @returns {number} variance
     45 *
     46 * @example
     47 * var Float64Array = require( '@stdlib/array/float64' );
     48 *
     49 * var x = new Float64Array( [ 1.0, -2.0, 2.0 ] );
     50 * var N = x.length;
     51 *
     52 * var v = dvariancepn( N, 1, x, 1 );
     53 * // returns ~4.3333
     54 */
     55 function dvariancepn( N, correction, x, stride ) {
     56 	var mu;
     57 	var ix;
     58 	var M2;
     59 	var M;
     60 	var d;
     61 	var n;
     62 	var i;
     63 
     64 	n = N - correction;
     65 	if ( N <= 0 || n <= 0.0 ) {
     66 		return NaN;
     67 	}
     68 	if ( N === 1 || stride === 0 ) {
     69 		return 0.0;
     70 	}
     71 	// Compute an estimate for the mean:
     72 	mu = dsumpw( N, x, stride ) / N;
     73 
     74 	if ( stride < 0 ) {
     75 		ix = (1-N) * stride;
     76 	} else {
     77 		ix = 0;
     78 	}
     79 	// Compute the variance...
     80 	M2 = 0.0;
     81 	M = 0.0;
     82 	for ( i = 0; i < N; i++ ) {
     83 		d = x[ ix ] - mu;
     84 		M2 += d * d;
     85 		M += d;
     86 		ix += stride;
     87 	}
     88 	return (M2/n) - ((M/N)*(M/n));
     89 }
     90 
     91 
     92 // EXPORTS //
     93 
     94 module.exports = dvariancepn;