time-to-botec

Benchmark sampling in different programming languages
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dnanvariancewd.js (2359B)

      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 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 {Float64Array} x - input array
     34 * @param {integer} stride - stride length
     35 * @returns {number} variance
     36 *
     37 * @example
     38 * var Float64Array = require( '@stdlib/array/float64' );
     39 *
     40 * var x = new Float64Array( [ 1.0, -2.0, NaN, 2.0 ] );
     41 * var N = x.length;
     42 *
     43 * var v = dnanvariancewd( N, 1, x, 1 );
     44 * // returns ~4.3333
     45 */
     46 function dnanvariancewd( N, correction, x, stride ) {
     47 	var delta;
     48 	var mu;
     49 	var M2;
     50 	var ix;
     51 	var nc;
     52 	var v;
     53 	var n;
     54 	var i;
     55 
     56 	if ( N <= 0 ) {
     57 		return NaN;
     58 	}
     59 	if ( N === 1 || stride === 0 ) {
     60 		v = x[ 0 ];
     61 		if ( v === v && N-correction > 0.0 ) {
     62 			return 0.0;
     63 		}
     64 		return NaN;
     65 	}
     66 	if ( stride < 0 ) {
     67 		ix = (1-N) * stride;
     68 	} else {
     69 		ix = 0;
     70 	}
     71 	M2 = 0.0;
     72 	mu = 0.0;
     73 	n = 0;
     74 	for ( i = 0; i < N; i++ ) {
     75 		v = x[ ix ];
     76 		if ( v === v ) {
     77 			delta = v - mu;
     78 			n += 1;
     79 			mu += delta / n;
     80 			M2 += delta * ( v - mu );
     81 		}
     82 		ix += stride;
     83 	}
     84 	nc = n - correction;
     85 	if ( nc <= 0.0 ) {
     86 		return NaN;
     87 	}
     88 	return M2 / nc;
     89 }
     90 
     91 
     92 // EXPORTS //
     93 
     94 module.exports = dnanvariancewd;