93 lines
2.7 KiB
JavaScript
93 lines
2.7 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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// MODULES //
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var dssum = require( '@stdlib/blas/ext/base/dssum' ).ndarray;
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// MAIN //
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/**
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* Computes the variance of a single-precision floating-point strided array using a two-pass algorithm with extended accumulation and returning an extended precision result.
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*
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* ## Method
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*
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* - This implementation uses a two-pass approach, as suggested by Neely (1966).
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*
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* ## References
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*
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* - 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).
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* - 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).
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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 {Float32Array} 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 Float32Array = require( '@stdlib/array/float32' );
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* var floor = require( '@stdlib/math/base/special/floor' );
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*
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* var x = new Float32Array( [ 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 = dsvariancepn( N, 1, x, 2, 1 );
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* // returns 6.25
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*/
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function dsvariancepn( N, correction, x, stride, offset ) {
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var mu;
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var ix;
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var M2;
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var M;
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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 ) {
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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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// Compute an estimate for the mean:
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mu = dssum( N, x, stride, offset ) / N;
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// Compute the variance...
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ix = offset;
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M2 = 0.0;
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M = 0.0;
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for ( i = 0; i < N; i++ ) {
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d = x[ ix ] - mu;
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M2 += d * d;
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M += d;
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ix += stride;
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}
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return (M2/n) - ((M/N)*(M/n));
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}
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// EXPORTS //
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module.exports = dsvariancepn;
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