time-to-botec

Benchmark sampling in different programming languages
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main.js (4604B)

      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 var sqrt = require( '@stdlib/math/base/special/sqrt' );
     26 
     27 
     28 // MAIN //
     29 
     30 /**
     31 * Returns an accumulator function which incrementally computes an arithmetic mean and corrected sample standard deviation.
     32 *
     33 * ## Method
     34 *
     35 
     36 *
     37 * -   This implementation uses Welford's algorithm for efficient computation, which can be derived as follows. Let
     38 *
     39 *     ```tex
     40 *     \begin{align*}
     41 *     S_n &= n \sigma_n^2 \\
     42 *         &= \sum_{i=1}^{n} (x_i - \mu_n)^2 \\
     43 *         &= \biggl(\sum_{i=1}^{n} x_i^2 \biggr) - n\mu_n^2
     44 *     \end{align*}
     45 *     ```
     46 *
     47 *     Accordingly,
     48 *
     49 *     ```tex
     50 *     \begin{align*}
     51 *     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 \\
     52 *                   &= x_n^2 - n\mu_n^2 + (n-1)\mu_{n-1}^2 \\
     53 *                   &= x_n^2 - \mu_{n-1}^2 + n(\mu_{n-1}^2 - \mu_n^2) \\
     54 *                   &= x_n^2 - \mu_{n-1}^2 + n(\mu_{n-1} - \mu_n)(\mu_{n-1} + \mu_n) \\
     55 *                   &= x_n^2 - \mu_{n-1}^2 + (\mu_{n-1} - x_n)(\mu_{n-1} + \mu_n) \\
     56 *                   &= 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} \\
     57 *                   &= x_n^2 - x_n\mu_n - x_n\mu_{n-1} + \mu_n\mu_{n-1} \\
     58 *                   &= (x_n - \mu_{n-1})(x_n - \mu_n) \\
     59 *                   &= S_{n-1} + (x_n - \mu_{n-1})(x_n - \mu_n)
     60 *     \end{align*}
     61 *     ```
     62 *
     63 *     where we use the identity
     64 *
     65 *     ```tex
     66 *     x_n - \mu_{n-1} = n (\mu_n - \mu_{n-1})
     67 *     ```
     68 *
     69 * ## References
     70 *
     71 * -   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).
     72 * -   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).
     73 *
     74 * @param {Collection} [out] - output array
     75 * @throws {TypeError} output argument must be array-like
     76 * @returns {Function} accumulator function
     77 *
     78 * @example
     79 * var accumulator = incrmeanstdev();
     80 *
     81 * var ms = accumulator();
     82 * // returns null
     83 *
     84 * ms = accumulator( 2.0 );
     85 * // returns [ 2.0, 0.0 ]
     86 *
     87 * ms = accumulator( -5.0 );
     88 * // returns [ -1.5, ~4.95 ]
     89 *
     90 * ms = accumulator( 3.0 );
     91 * // returns [ 0.0, ~4.36 ]
     92 *
     93 * ms = accumulator( 5.0 );
     94 * // returns [ 1.25, ~4.35 ]
     95 *
     96 * ms = accumulator();
     97 * // returns [ 1.25, ~4.35 ]
     98 */
     99 function incrmeanstdev( out ) {
    100 	var meanstdev;
    101 	var delta;
    102 	var mu;
    103 	var M2;
    104 	var N;
    105 	if ( arguments.length === 0 ) {
    106 		meanstdev = [ 0.0, 0.0 ];
    107 	} else {
    108 		if ( !isArrayLike( out ) ) {
    109 			throw new TypeError( 'invalid argument. Output argument must be an array-like object. Value: `' + out + '`.' );
    110 		}
    111 		meanstdev = out;
    112 	}
    113 	M2 = 0.0;
    114 	mu = 0.0;
    115 	N = 0;
    116 	return accumulator;
    117 
    118 	/**
    119 	* If provided a value, the accumulator function returns updated results. If not provided a value, the accumulator function returns the current results.
    120 	*
    121 	* @private
    122 	* @param {number} [x] - input value
    123 	* @returns {(ArrayLikeObject|null)} output array or null
    124 	*/
    125 	function accumulator( x ) {
    126 		if ( arguments.length === 0 ) {
    127 			if ( N === 0 ) {
    128 				return null;
    129 			}
    130 			meanstdev[ 0 ] = mu; // Why? Because we cannot guarantee someone hasn't mutated the output array
    131 			if ( N === 1 ) {
    132 				if ( isnan( M2 ) ) {
    133 					meanstdev[ 1 ] = NaN;
    134 				} else {
    135 					meanstdev[ 1 ] = 0.0;
    136 				}
    137 				return meanstdev;
    138 			}
    139 			meanstdev[ 1 ] = sqrt( M2/(N-1) );
    140 			return meanstdev;
    141 		}
    142 		N += 1;
    143 		delta = x - mu;
    144 		mu += delta / N;
    145 		M2 += delta * ( x - mu );
    146 
    147 		meanstdev[ 0 ] = mu;
    148 		if ( N < 2 ) {
    149 			if ( isnan( M2 ) ) {
    150 				meanstdev[ 1 ] = NaN;
    151 			} else {
    152 				meanstdev[ 1 ] = 0.0;
    153 			}
    154 			return meanstdev;
    155 		}
    156 		meanstdev[ 1 ] = sqrt( M2/(N-1) );
    157 		return meanstdev;
    158 	}
    159 }
    160 
    161 
    162 // EXPORTS //
    163 
    164 module.exports = incrmeanstdev;