113 lines
2.7 KiB
JavaScript
113 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 nansumpw = require( './nansumpw.js' );
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// VARIABLES //
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var WORKSPACE = [ 0.0, 0 ];
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// MAIN //
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/**
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* Computes the variance of a strided array ignoring `NaN` values and using a two-pass algorithm.
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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 {NumericArray} x - input array
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* @param {integer} stride - stride length
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* @returns {number} variance
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*
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* @example
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* var x = [ 1.0, -2.0, NaN, 2.0 ];
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*
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* var v = nanvariancepn( x.length, 1, x, 1 );
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* // returns ~4.3333
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*/
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function nanvariancepn( N, correction, x, stride ) {
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var mu;
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var ix;
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var M2;
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var nc;
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var M;
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var d;
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var v;
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var n;
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var i;
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if ( 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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v = x[ 0 ];
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if ( v === v && N-correction > 0.0 ) {
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return 0.0;
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}
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return NaN;
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}
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if ( stride < 0 ) {
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ix = (1-N) * stride;
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} else {
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ix = 0;
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}
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// Compute an estimate for the mean...
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WORKSPACE[ 0 ] = 0.0;
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WORKSPACE[ 1 ] = 0;
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nansumpw( N, WORKSPACE, x, stride, ix );
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n = WORKSPACE[ 1 ];
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nc = n - correction;
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if ( nc <= 0.0 ) {
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return NaN;
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}
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mu = WORKSPACE[ 0 ] / n;
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// Compute the variance...
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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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v = x[ ix ];
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if ( v === v ) {
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d = v - mu;
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M2 += d * d;
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M += d;
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}
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ix += stride;
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}
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return (M2/nc) - ((M/n)*(M/nc));
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}
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// EXPORTS //
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module.exports = nanvariancepn;
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