time-to-botec

Benchmark sampling in different programming languages
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dnanvariancech.js (3519B)

      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 ignoring `NaN` values and using a one-pass trial mean algorithm.
     25 *
     26 * ## Method
     27 *
     28 * -   This implementation uses a one-pass trial mean approach, as suggested by Chan et al (1983).
     29 *
     30 * ## References
     31 *
     32 * -   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).
     33 * -   Ling, Robert F. 1974. "Comparison of Several Algorithms for Computing Sample Means and Variances." _Journal of the American Statistical Association_ 69 (348). American Statistical Association, Taylor & Francis, Ltd.: 859–66. doi:[10.2307/2286154](https://doi.org/10.2307/2286154).
     34 * -   Chan, Tony F., Gene H. Golub, and Randall J. LeVeque. 1983. "Algorithms for Computing the Sample Variance: Analysis and Recommendations." _The American Statistician_ 37 (3). American Statistical Association, Taylor & Francis, Ltd.: 242–47. doi:[10.1080/00031305.1983.10483115](https://doi.org/10.1080/00031305.1983.10483115).
     35 * -   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).
     36 *
     37 * @param {PositiveInteger} N - number of indexed elements
     38 * @param {number} correction - degrees of freedom adjustment
     39 * @param {Float64Array} x - input array
     40 * @param {integer} stride - stride length
     41 * @returns {number} variance
     42 *
     43 * @example
     44 * var Float64Array = require( '@stdlib/array/float64' );
     45 *
     46 * var x = new Float64Array( [ 1.0, -2.0, NaN, 2.0 ] );
     47 * var N = x.length;
     48 *
     49 * var v = dnanvariancech( N, 1, x, 1 );
     50 * // returns ~4.3333
     51 */
     52 function dnanvariancech( N, correction, x, stride ) {
     53 	var mu;
     54 	var ix;
     55 	var M2;
     56 	var nc;
     57 	var M;
     58 	var d;
     59 	var v;
     60 	var n;
     61 	var i;
     62 
     63 	if ( N <= 0 ) {
     64 		return NaN;
     65 	}
     66 	if ( N === 1 || stride === 0 ) {
     67 		v = x[ 0 ];
     68 		if ( v === v && N-correction > 0.0 ) {
     69 			return 0.0;
     70 		}
     71 		return NaN;
     72 	}
     73 	if ( stride < 0 ) {
     74 		ix = (1-N) * stride;
     75 	} else {
     76 		ix = 0;
     77 	}
     78 	// Find an estimate for the mean...
     79 	for ( i = 0; i < N; i++ ) {
     80 		v = x[ ix ];
     81 		if ( v === v ) {
     82 			mu = v;
     83 			break;
     84 		}
     85 		ix += stride;
     86 	}
     87 	if ( i === N ) {
     88 		return NaN;
     89 	}
     90 	ix += stride;
     91 	i += 1;
     92 
     93 	// Compute the variance...
     94 	M2 = 0.0;
     95 	M = 0.0;
     96 	n = 1;
     97 	for ( i; i < N; i++ ) {
     98 		v = x[ ix ];
     99 		if ( v === v ) {
    100 			d = v - mu;
    101 			M2 += d * d;
    102 			M += d;
    103 			n += 1;
    104 		}
    105 		ix += stride;
    106 	}
    107 	nc = n - correction;
    108 	if ( nc <= 0.0 ) {
    109 		return NaN;
    110 	}
    111 	return (M2/nc) - ((M/n)*(M/nc));
    112 }
    113 
    114 
    115 // EXPORTS //
    116 
    117 module.exports = dnanvariancech;