time-to-botec

Benchmark sampling in different programming languages
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nanvariancepn.js (2804B)

      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 nansumpw = require( './nansumpw.js' );
     24 
     25 
     26 // VARIABLES //
     27 
     28 var WORKSPACE = [ 0.0, 0 ];
     29 
     30 
     31 // MAIN //
     32 
     33 /**
     34 * Computes the variance of a strided array ignoring `NaN` values and using a two-pass algorithm.
     35 *
     36 * ## Method
     37 *
     38 * -   This implementation uses a two-pass approach, as suggested by Neely (1966).
     39 *
     40 * ## References
     41 *
     42 * -   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).
     43 * -   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).
     44 *
     45 * @param {PositiveInteger} N - number of indexed elements
     46 * @param {number} correction - degrees of freedom adjustment
     47 * @param {NumericArray} x - input array
     48 * @param {integer} stride - stride length
     49 * @returns {number} variance
     50 *
     51 * @example
     52 * var x = [ 1.0, -2.0, NaN, 2.0 ];
     53 *
     54 * var v = nanvariancepn( x.length, 1, x, 1 );
     55 * // returns ~4.3333
     56 */
     57 function nanvariancepn( N, correction, x, stride ) {
     58 	var mu;
     59 	var ix;
     60 	var M2;
     61 	var nc;
     62 	var M;
     63 	var d;
     64 	var v;
     65 	var n;
     66 	var i;
     67 
     68 	if ( N <= 0 ) {
     69 		return NaN;
     70 	}
     71 	if ( N === 1 || stride === 0 ) {
     72 		v = x[ 0 ];
     73 		if ( v === v && N-correction > 0.0 ) {
     74 			return 0.0;
     75 		}
     76 		return NaN;
     77 	}
     78 	if ( stride < 0 ) {
     79 		ix = (1-N) * stride;
     80 	} else {
     81 		ix = 0;
     82 	}
     83 	// Compute an estimate for the mean...
     84 	WORKSPACE[ 0 ] = 0.0;
     85 	WORKSPACE[ 1 ] = 0;
     86 	nansumpw( N, WORKSPACE, x, stride, ix );
     87 	n = WORKSPACE[ 1 ];
     88 	nc = n - correction;
     89 	if ( nc <= 0.0 ) {
     90 		return NaN;
     91 	}
     92 	mu = WORKSPACE[ 0 ] / n;
     93 
     94 	// Compute the variance...
     95 	M2 = 0.0;
     96 	M = 0.0;
     97 	for ( i = 0; i < N; i++ ) {
     98 		v = x[ ix ];
     99 		if ( v === v ) {
    100 			d = v - mu;
    101 			M2 += d * d;
    102 			M += d;
    103 		}
    104 		ix += stride;
    105 	}
    106 	return (M2/nc) - ((M/n)*(M/nc));
    107 }
    108 
    109 
    110 // EXPORTS //
    111 
    112 module.exports = nanvariancepn;