time-to-botec

Benchmark sampling in different programming languages
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dnanvariancepn.js (2934B)

      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 dnansumpw = require( './dnansumpw.js' );
     24 
     25 
     26 // VARIABLES //
     27 
     28 var WORKSPACE = [ 0.0, 0 ];
     29 
     30 
     31 // MAIN //
     32 
     33 /**
     34 * Computes the variance of a double-precision floating-point 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 {Float64Array} x - input array
     48 * @param {integer} stride - stride length
     49 * @returns {number} variance
     50 *
     51 * @example
     52 * var Float64Array = require( '@stdlib/array/float64' );
     53 *
     54 * var x = new Float64Array( [ 1.0, -2.0, NaN, 2.0 ] );
     55 * var N = x.length;
     56 *
     57 * var v = dnanvariancepn( N, 1, x, 1 );
     58 * // returns ~4.3333
     59 */
     60 function dnanvariancepn( N, correction, x, stride ) {
     61 	var mu;
     62 	var ix;
     63 	var M2;
     64 	var nc;
     65 	var M;
     66 	var d;
     67 	var v;
     68 	var n;
     69 	var i;
     70 
     71 	if ( N <= 0 ) {
     72 		return NaN;
     73 	}
     74 	if ( N === 1 || stride === 0 ) {
     75 		v = x[ 0 ];
     76 		if ( v === v && N-correction > 0.0 ) {
     77 			return 0.0;
     78 		}
     79 		return NaN;
     80 	}
     81 	if ( stride < 0 ) {
     82 		ix = (1-N) * stride;
     83 	} else {
     84 		ix = 0;
     85 	}
     86 	// Compute an estimate for the mean...
     87 	WORKSPACE[ 0 ] = 0.0;
     88 	WORKSPACE[ 1 ] = 0;
     89 	dnansumpw( N, WORKSPACE, x, stride, ix );
     90 	n = WORKSPACE[ 1 ];
     91 	nc = n - correction;
     92 	if ( nc <= 0.0 ) {
     93 		return NaN;
     94 	}
     95 	mu = WORKSPACE[ 0 ] / n;
     96 
     97 	// Compute the variance...
     98 	M2 = 0.0;
     99 	M = 0.0;
    100 	for ( i = 0; i < N; i++ ) {
    101 		v = x[ ix ];
    102 		if ( v === v ) {
    103 			d = v - mu;
    104 			M2 += d * d;
    105 			M += d;
    106 		}
    107 		ix += stride;
    108 	}
    109 	return (M2/nc) - ((M/n)*(M/nc));
    110 }
    111 
    112 
    113 // EXPORTS //
    114 
    115 module.exports = dnanvariancepn;