time-to-botec

Benchmark sampling in different programming languages
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ndarray.js (2365B)

      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 strided array ignoring `NaN` values and using Welford's algorithm.
     25 *
     26 * ## References
     27 *
     28 * -   Welford, B. P. 1962. "Note on a Method for Calculating Corrected Sums of Squares and Products." _Technometrics_ 4 (3). Taylor & Francis: 419–20. doi:[10.1080/00401706.1962.10490022](https://doi.org/10.1080/00401706.1962.10490022).
     29 * -   van Reeken, A. J. 1968. "Letters to the Editor: Dealing with Neely's Algorithms." _Communications of the ACM_ 11 (3): 149–50. doi:[10.1145/362929.362961](https://doi.org/10.1145/362929.362961).
     30 *
     31 * @param {PositiveInteger} N - number of indexed elements
     32 * @param {number} correction - degrees of freedom adjustment
     33 * @param {NumericArray} x - input array
     34 * @param {integer} stride - stride length
     35 * @param {NonNegativeInteger} offset - starting index
     36 * @returns {number} variance
     37 *
     38 * @example
     39 * var floor = require( '@stdlib/math/base/special/floor' );
     40 *
     41 * var x = [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0, NaN, NaN ];
     42 * var N = floor( x.length / 2 );
     43 *
     44 * var v = nanvariancewd( N, 1, x, 2, 1 );
     45 * // returns 6.25
     46 */
     47 function nanvariancewd( N, correction, x, stride, offset ) {
     48 	var delta;
     49 	var mu;
     50 	var M2;
     51 	var ix;
     52 	var nc;
     53 	var v;
     54 	var n;
     55 	var i;
     56 
     57 	if ( N <= 0 ) {
     58 		return NaN;
     59 	}
     60 	if ( N === 1 || stride === 0 ) {
     61 		v = x[ offset ];
     62 		if ( v === v && N-correction > 0.0 ) {
     63 			return 0.0;
     64 		}
     65 		return NaN;
     66 	}
     67 	ix = offset;
     68 	M2 = 0.0;
     69 	mu = 0.0;
     70 	n = 0;
     71 	for ( i = 0; i < N; i++ ) {
     72 		v = x[ ix ];
     73 		if ( v === v ) {
     74 			delta = v - mu;
     75 			n += 1;
     76 			mu += delta / n;
     77 			M2 += delta * ( v - mu );
     78 		}
     79 		ix += stride;
     80 	}
     81 	nc = n - correction;
     82 	if ( nc <= 0.0 ) {
     83 		return NaN;
     84 	}
     85 	return M2 / nc;
     86 }
     87 
     88 
     89 // EXPORTS //
     90 
     91 module.exports = nanvariancewd;