83 lines
2.1 KiB
JavaScript
83 lines
2.1 KiB
JavaScript
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/**
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* @license Apache-2.0
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*
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* Copyright (c) 2020 The Stdlib Authors.
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*
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* Licensed under the Apache License, Version 2.0 (the "License");
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* you may not use this file except in compliance with the License.
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* You may obtain a copy of the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS,
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* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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*/
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'use strict';
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// MAIN //
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/**
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* Computes the variance of a strided array using a one-pass algorithm proposed by Youngs and Cramer.
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*
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* ## Method
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*
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* - This implementation uses a one-pass algorithm, as proposed by Youngs and Cramer (1971).
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*
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* ## References
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*
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* - 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).
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*
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* @param {PositiveInteger} N - number of indexed elements
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* @param {number} correction - degrees of freedom adjustment
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* @param {NumericArray} x - input array
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* @param {integer} stride - stride length
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* @param {NonNegativeInteger} offset - starting index
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* @returns {number} variance
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*
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* @example
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* var floor = require( '@stdlib/math/base/special/floor' );
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*
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* var x = [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ];
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* var N = floor( x.length / 2 );
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*
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* var v = varianceyc( N, 1, x, 2, 1 );
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* // returns 6.25
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*/
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function varianceyc( N, correction, x, stride, offset ) {
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var sum;
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var ix;
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var S;
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var v;
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var d;
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var n;
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var i;
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n = N - correction;
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if ( N <= 0 || n <= 0.0 ) {
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return NaN;
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}
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if ( N === 1 || stride === 0 ) {
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return 0.0;
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}
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sum = x[ offset ];
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ix = offset + stride;
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S = 0.0;
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for ( i = 2; i <= N; i++ ) {
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v = x[ ix ];
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sum += v;
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d = (i*v) - sum;
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S += (1.0/(i*(i-1))) * d * d;
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ix += stride;
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}
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return S / n;
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}
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// EXPORTS //
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module.exports = varianceyc;
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