time-to-botec

Benchmark sampling in different programming languages
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main.js (4488B)

      1 /**
      2 * @license Apache-2.0
      3 *
      4 * Copyright (c) 2018 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 isArrayLike = require( '@stdlib/assert/is-array-like-object' );
     24 var isnan = require( '@stdlib/math/base/assert/is-nan' );
     25 
     26 
     27 // MAIN //
     28 
     29 /**
     30 * Returns an accumulator function which incrementally computes an arithmetic mean and unbiased sample variance.
     31 *
     32 * ## Method
     33 *
     34 *
     35 * -   This implementation uses Welford's algorithm for efficient computation, which can be derived as follows. Let
     36 *
     37 *     ```tex
     38 *     \begin{align*}
     39 *     S_n &= n \sigma_n^2 \\
     40 *         &= \sum_{i=1}^{n} (x_i - \mu_n)^2 \\
     41 *         &= \biggl(\sum_{i=1}^{n} x_i^2 \biggr) - n\mu_n^2
     42 *     \end{align*}
     43 *     ```
     44 *
     45 *     Accordingly,
     46 *
     47 *     ```tex
     48 *     \begin{align*}
     49 *     S_n - S_{n-1} &= \sum_{i=1}^{n} x_i^2 - n\mu_n^2 - \sum_{i=1}^{n-1} x_i^2 + (n-1)\mu_{n-1}^2 \\
     50 *                   &= x_n^2 - n\mu_n^2 + (n-1)\mu_{n-1}^2 \\
     51 *                   &= x_n^2 - \mu_{n-1}^2 + n(\mu_{n-1}^2 - \mu_n^2) \\
     52 *                   &= x_n^2 - \mu_{n-1}^2 + n(\mu_{n-1} - \mu_n)(\mu_{n-1} + \mu_n) \\
     53 *                   &= x_n^2 - \mu_{n-1}^2 + (\mu_{n-1} - x_n)(\mu_{n-1} + \mu_n) \\
     54 *                   &= x_n^2 - \mu_{n-1}^2 + \mu_{n-1}^2 - x_n\mu_n - x_n\mu_{n-1} + \mu_n\mu_{n-1} \\
     55 *                   &= x_n^2 - x_n\mu_n - x_n\mu_{n-1} + \mu_n\mu_{n-1} \\
     56 *                   &= (x_n - \mu_{n-1})(x_n - \mu_n) \\
     57 *                   &= S_{n-1} + (x_n - \mu_{n-1})(x_n - \mu_n)
     58 *     \end{align*}
     59 *     ```
     60 *
     61 *     where we use the identity
     62 *
     63 *     ```tex
     64 *     x_n - \mu_{n-1} = n (\mu_n - \mu_{n-1})
     65 *     ```
     66 *
     67 * ## References
     68 *
     69 * -   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).
     70 * -   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).
     71 *
     72 * @param {Collection} [out] - output array
     73 * @throws {TypeError} output argument must be array-like
     74 * @returns {Function} accumulator function
     75 *
     76 * @example
     77 * var accumulator = incrmeanvar();
     78 *
     79 * var mv = accumulator();
     80 * // returns null
     81 *
     82 * mv = accumulator( 2.0 );
     83 * // returns [ 2.0, 0.0 ]
     84 *
     85 * mv = accumulator( -5.0 );
     86 * // returns [ -1.5, 24.5 ]
     87 *
     88 * mv = accumulator( 3.0 );
     89 * // returns [ 0.0, 19.0 ]
     90 *
     91 * mv = accumulator( 5.0 );
     92 * // returns [ 1.25, ~18.92 ]
     93 *
     94 * mv = accumulator();
     95 * // returns [ 1.25, ~18.92 ]
     96 */
     97 function incrmeanvar( out ) {
     98 	var meanvar;
     99 	var delta;
    100 	var mu;
    101 	var M2;
    102 	var N;
    103 	if ( arguments.length === 0 ) {
    104 		meanvar = [ 0.0, 0.0 ];
    105 	} else {
    106 		if ( !isArrayLike( out ) ) {
    107 			throw new TypeError( 'invalid argument. Output argument must be an array-like object. Value: `' + out + '`.' );
    108 		}
    109 		meanvar = out;
    110 	}
    111 	M2 = 0.0;
    112 	mu = 0.0;
    113 	N = 0;
    114 	return accumulator;
    115 
    116 	/**
    117 	* If provided a value, the accumulator function returns updated results. If not provided a value, the accumulator function returns the current results.
    118 	*
    119 	* @private
    120 	* @param {number} [x] - input value
    121 	* @returns {(ArrayLikeObject|null)} output array or null
    122 	*/
    123 	function accumulator( x ) {
    124 		if ( arguments.length === 0 ) {
    125 			if ( N === 0 ) {
    126 				return null;
    127 			}
    128 			meanvar[ 0 ] = mu; // Why? Because we cannot guarantee someone hasn't mutated the output array
    129 			if ( N === 1 ) {
    130 				if ( isnan( M2 ) ) {
    131 					meanvar[ 1 ] = NaN;
    132 				} else {
    133 					meanvar[ 1 ] = 0.0;
    134 				}
    135 				return meanvar;
    136 			}
    137 			meanvar[ 1 ] = M2 / (N-1);
    138 			return meanvar;
    139 		}
    140 		N += 1;
    141 		delta = x - mu;
    142 		mu += delta / N;
    143 		M2 += delta * ( x - mu );
    144 
    145 		meanvar[ 0 ] = mu;
    146 		if ( N < 2 ) {
    147 			if ( isnan( M2 ) ) {
    148 				meanvar[ 1 ] = NaN;
    149 			} else {
    150 				meanvar[ 1 ] = 0.0;
    151 			}
    152 			return meanvar;
    153 		}
    154 		meanvar[ 1 ] = M2 / (N-1);
    155 		return meanvar;
    156 	}
    157 }
    158 
    159 
    160 // EXPORTS //
    161 
    162 module.exports = incrmeanvar;