time-to-botec

Benchmark sampling in different programming languages
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main.js (4177B)

      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 isNumber = require( '@stdlib/assert/is-number' ).isPrimitive;
     24 var isnan = require( '@stdlib/math/base/assert/is-nan' );
     25 
     26 
     27 // MAIN //
     28 
     29 /**
     30 * Returns an accumulator function which incrementally computes a variance-to-mean ratio (VMR).
     31 *
     32 * ## Method
     33 *
     34 * -   This implementation uses [Welford's method][algorithms-variance] for efficient computation, which can be derived as follows. Let
     35 *
     36 *     ```tex
     37 *     \begin{align*}
     38 *     S_n &= n \sigma_n^2 \\
     39 *         &= \sum_{i=1}^{n} (x_i - \mu_n)^2 \\
     40 *         &= \biggl(\sum_{i=1}^{n} x_i^2 \biggr) - n\mu_n^2
     41 *     \end{align*}
     42 *     ```
     43 *
     44 *     Accordingly,
     45 *
     46 *     ```tex
     47 *     \begin{align*}
     48 *     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 \\
     49 *                   &= x_n^2 - n\mu_n^2 + (n-1)\mu_{n-1}^2 \\
     50 *                   &= x_n^2 - \mu_{n-1}^2 + n(\mu_{n-1}^2 - \mu_n^2) \\
     51 *                   &= x_n^2 - \mu_{n-1}^2 + n(\mu_{n-1} - \mu_n)(\mu_{n-1} + \mu_n) \\
     52 *                   &= x_n^2 - \mu_{n-1}^2 + (\mu_{n-1} - x_n)(\mu_{n-1} + \mu_n) \\
     53 *                   &= 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} \\
     54 *                   &= x_n^2 - x_n\mu_n - x_n\mu_{n-1} + \mu_n\mu_{n-1} \\
     55 *                   &= (x_n - \mu_{n-1})(x_n - \mu_n) \\
     56 *                   &= S_{n-1} + (x_n - \mu_{n-1})(x_n - \mu_n)
     57 *     \end{align*}
     58 *     ```
     59 *
     60 *     where we use the identity
     61 *
     62 *     ```tex
     63 *     x_n - \mu_{n-1} = n (\mu_n - \mu_{n-1})
     64 *     ```
     65 *
     66 * [algorithms-variance]: https://en.wikipedia.org/wiki/Algorithms_for_calculating_variance
     67 *
     68 * @param {number} [mean] - mean value
     69 * @throws {TypeError} must provide a number primitive
     70 * @returns {Function} accumulator function
     71 *
     72 * @example
     73 * var accumulator = incrvmr();
     74 *
     75 * var D = accumulator();
     76 * // returns null
     77 *
     78 * D = accumulator( 2.0 );
     79 * // returns 0.0
     80 *
     81 * D = accumulator( 1.0 );
     82 * // returns ~0.33
     83 *
     84 * D = accumulator();
     85 * // returns ~0.33
     86 *
     87 * @example
     88 * var accumulator = incrvmr( 3.14 );
     89 */
     90 function incrvmr( mean ) {
     91 	var delta;
     92 	var mu;
     93 	var M2;
     94 	var N;
     95 
     96 	M2 = 0.0;
     97 	N = 0;
     98 	if ( arguments.length ) {
     99 		if ( !isNumber( mean ) ) {
    100 			throw new TypeError( 'invalid argument. Must provide a number primitive. Value: `' + mean + '`.' );
    101 		}
    102 		mu = mean;
    103 		return accumulator2;
    104 	}
    105 	mu = 0.0;
    106 	return accumulator1;
    107 
    108 	/**
    109 	* If provided a value, the accumulator function returns an updated accumulated value. If not provided a value, the accumulator function returns the current accumulated value.
    110 	*
    111 	* @private
    112 	* @param {number} [x] - new value
    113 	* @returns {(number|null)} accumulated value or null
    114 	*/
    115 	function accumulator1( x ) {
    116 		if ( arguments.length === 0 ) {
    117 			if ( N === 0 ) {
    118 				return null;
    119 			}
    120 			if ( N === 1 ) {
    121 				return ( isnan( M2 ) ) ? NaN : 0.0/mu;
    122 			}
    123 			return ( M2/(N-1) ) / mu;
    124 		}
    125 		N += 1;
    126 		delta = x - mu;
    127 		mu += delta / N;
    128 		M2 += delta * ( x - mu );
    129 		if ( N < 2 ) {
    130 			return ( isnan( M2 ) ) ? NaN : 0.0/mu;
    131 		}
    132 		return ( M2/(N-1) ) / mu;
    133 	}
    134 
    135 	/**
    136 	* If provided a value, the accumulator function returns an updated accumulated value. If not provided a value, the accumulator function returns the current accumulated value.
    137 	*
    138 	* @private
    139 	* @param {number} [x] - new value
    140 	* @returns {(number|null)} accumulated value or null
    141 	*/
    142 	function accumulator2( x ) {
    143 		if ( arguments.length === 0 ) {
    144 			if ( N === 0 ) {
    145 				return null;
    146 			}
    147 			return ( M2/N ) / mu;
    148 		}
    149 		N += 1;
    150 		delta = x - mu;
    151 		M2 += delta * delta;
    152 		return ( M2/N ) / mu;
    153 	}
    154 }
    155 
    156 
    157 // EXPORTS //
    158 
    159 module.exports = incrvmr;