time-to-botec

Benchmark sampling in different programming languages
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dnanvarianceyc.js (2484B)

      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 // MAIN //
     22 
     23 /**
     24 * Computes the variance of a double-precision floating-point strided array ignoring `NaN` values and using a one-pass algorithm proposed by Youngs and Cramer.
     25 *
     26 * ## Method
     27 *
     28 * -   This implementation uses a one-pass algorithm, as proposed by Youngs and Cramer (1971).
     29 *
     30 * ## References
     31 *
     32 * -   Youngs, Edward A., and Elliot M. Cramer. 1971. "Some Results Relevant to Choice of Sum and Sum-of-Product Algorithms." _Technometrics_ 13 (3): 657–65. doi:[10.1080/00401706.1971.10488826](https://doi.org/10.1080/00401706.1971.10488826).
     33 *
     34 * @param {PositiveInteger} N - number of indexed elements
     35 * @param {number} correction - degrees of freedom adjustment
     36 * @param {Float64Array} x - input array
     37 * @param {integer} stride - stride length
     38 * @returns {number} variance
     39 *
     40 * @example
     41 * var Float64Array = require( '@stdlib/array/float64' );
     42 *
     43 * var x = new Float64Array( [ 1.0, -2.0, NaN, 2.0 ] );
     44 * var N = x.length;
     45 *
     46 * var v = dnanvarianceyc( N, 1, x, 1 );
     47 * // returns ~4.3333
     48 */
     49 function dnanvarianceyc( N, correction, x, stride ) {
     50 	var sum;
     51 	var ix;
     52 	var nc;
     53 	var S;
     54 	var v;
     55 	var d;
     56 	var n;
     57 	var i;
     58 
     59 	if ( N <= 0 ) {
     60 		return NaN;
     61 	}
     62 	if ( N === 1 || stride === 0 ) {
     63 		v = x[ 0 ];
     64 		if ( v === v && N-correction > 0.0 ) {
     65 			return 0.0;
     66 		}
     67 		return NaN;
     68 	}
     69 	if ( stride < 0 ) {
     70 		ix = (1-N) * stride;
     71 	} else {
     72 		ix = 0;
     73 	}
     74 	// Find the first non-NaN element...
     75 	for ( i = 0; i < N; i++ ) {
     76 		v = x[ ix ];
     77 		if ( v === v ) {
     78 			break;
     79 		}
     80 		ix += stride;
     81 	}
     82 	if ( i === N ) {
     83 		return NaN;
     84 	}
     85 	ix += stride;
     86 	sum = v;
     87 	S = 0.0;
     88 	i += 1;
     89 	n = 1;
     90 	for ( i; i < N; i++ ) {
     91 		v = x[ ix ];
     92 		if ( v === v ) {
     93 			n += 1;
     94 			sum += v;
     95 			d = (n*v) - sum;
     96 			S += (1.0/(n*(n-1))) * d * d;
     97 		}
     98 		ix += stride;
     99 	}
    100 	nc = n - correction;
    101 	if ( nc <= 0.0 ) {
    102 		return NaN;
    103 	}
    104 	return S / nc;
    105 }
    106 
    107 
    108 // EXPORTS //
    109 
    110 module.exports = dnanvarianceyc;