time-to-botec

Benchmark sampling in different programming languages
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ndarray.js (3004B)

      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 float64ToFloat32 = require( '@stdlib/number/float64/base/to-float32' );
     24 var ssumpw = require( '@stdlib/blas/ext/base/ssumpw' ).ndarray;
     25 
     26 
     27 // MAIN //
     28 
     29 /**
     30 * Computes the variance of a single-precision floating-point strided array using a two-pass algorithm.
     31 *
     32 * ## Method
     33 *
     34 * -   This implementation uses a two-pass approach, as suggested by Neely (1966).
     35 *
     36 * ## References
     37 *
     38 * -   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).
     39 * -   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).
     40 *
     41 * @param {PositiveInteger} N - number of indexed elements
     42 * @param {number} correction - degrees of freedom adjustment
     43 * @param {Float32Array} x - input array
     44 * @param {integer} stride - stride length
     45 * @param {NonNegativeInteger} offset - starting index
     46 * @returns {number} variance
     47 *
     48 * @example
     49 * var Float32Array = require( '@stdlib/array/float32' );
     50 * var floor = require( '@stdlib/math/base/special/floor' );
     51 *
     52 * var x = new Float32Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ] );
     53 * var N = floor( x.length / 2 );
     54 *
     55 * var v = svariancepn( N, 1, x, 2, 1 );
     56 * // returns 6.25
     57 */
     58 function svariancepn( N, correction, x, stride, offset ) {
     59 	var mu;
     60 	var ix;
     61 	var M2;
     62 	var M;
     63 	var d;
     64 	var n;
     65 	var i;
     66 
     67 	n = N - correction;
     68 	if ( N <= 0 || n <= 0.0 ) {
     69 		return NaN;
     70 	}
     71 	if ( N === 1 || stride === 0 ) {
     72 		return 0.0;
     73 	}
     74 	// Compute an estimate for the mean:
     75 	mu = ssumpw( N, x, stride, offset ) / N;
     76 
     77 	// Compute the variance...
     78 	ix = offset;
     79 	M2 = 0.0;
     80 	M = 0.0;
     81 	for ( i = 0; i < N; i++ ) {
     82 		d = float64ToFloat32( x[ ix ] - mu );
     83 		M2 = float64ToFloat32( M2 + float64ToFloat32( d*d ) );
     84 		M = float64ToFloat32( M + d );
     85 		ix += stride;
     86 	}
     87 	return float64ToFloat32( float64ToFloat32(M2/n) - float64ToFloat32( float64ToFloat32(M/N)*float64ToFloat32(M/n) ) ); // eslint-disable-line max-len
     88 }
     89 
     90 
     91 // EXPORTS //
     92 
     93 module.exports = svariancepn;