113 lines
2.9 KiB
JavaScript
113 lines
2.9 KiB
JavaScript
|
/**
|
|||
|
|
* @license Apache-2.0
|
|||
|
|
*
|
|||
|
|
* Copyright (c) 2020 The Stdlib Authors.
|
|||
|
|
*
|
|||
|
|
* Licensed under the Apache License, Version 2.0 (the "License");
|
|||
|
|
* you may not use this file except in compliance with the License.
|
|||
|
|
* You may obtain a copy of the License at
|
|||
|
|
*
|
|||
|
|
* http://www.apache.org/licenses/LICENSE-2.0
|
|||
|
|
*
|
|||
|
|
* Unless required by applicable law or agreed to in writing, software
|
|||
|
|
* distributed under the License is distributed on an "AS IS" BASIS,
|
|||
|
|
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
|
|||
|
|
* See the License for the specific language governing permissions and
|
|||
|
|
* limitations under the License.
|
|||
|
|
*/
|
|||
|
|
|
|||
|
|
'use strict';
|
|||
|
|
|
|||
|
|
// MODULES //
|
|||
|
|
|
|||
|
|
var nansumpw = require( './nansumpw.js' );
|
|||
|
|
|
|||
|
|
|
|||
|
|
// VARIABLES //
|
|||
|
|
|
|||
|
|
var WORKSPACE = [ 0.0, 0 ];
|
|||
|
|
|
|||
|
|
|
|||
|
|
// MAIN //
|
|||
|
|
|
|||
|
|
/**
|
|||
|
|
* Computes the variance of a strided array ignoring `NaN` values and using a two-pass algorithm.
|
|||
|
|
*
|
|||
|
|
* ## Method
|
|||
|
|
*
|
|||
|
|
* - This implementation uses a two-pass approach, as suggested by Neely (1966).
|
|||
|
|
*
|
|||
|
|
* ## References
|
|||
|
|
*
|
|||
|
|
* - 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).
|
|||
|
|
* - 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).
|
|||
|
|
*
|
|||
|
|
* @param {PositiveInteger} N - number of indexed elements
|
|||
|
|
* @param {number} correction - degrees of freedom adjustment
|
|||
|
|
* @param {NumericArray} x - input array
|
|||
|
|
* @param {integer} stride - stride length
|
|||
|
|
* @param {NonNegativeInteger} offset - starting index
|
|||
|
|
* @returns {number} variance
|
|||
|
|
*
|
|||
|
|
* @example
|
|||
|
|
* var floor = require( '@stdlib/math/base/special/floor' );
|
|||
|
|
*
|
|||
|
|
* var x = [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0, NaN, NaN ];
|
|||
|
|
* var N = floor( x.length / 2 );
|
|||
|
|
*
|
|||
|
|
* var v = nanvariancepn( N, 1, x, 2, 1 );
|
|||
|
|
* // returns 6.25
|
|||
|
|
*/
|
|||
|
|
function nanvariancepn( N, correction, x, stride, offset ) {
|
|||
|
|
var mu;
|
|||
|
|
var ix;
|
|||
|
|
var M2;
|
|||
|
|
var nc;
|
|||
|
|
var M;
|
|||
|
|
var d;
|
|||
|
|
var v;
|
|||
|
|
var n;
|
|||
|
|
var i;
|
|||
|
|
|
|||
|
|
if ( N <= 0 ) {
|
|||
|
|
return NaN;
|
|||
|
|
}
|
|||
|
|
if ( N === 1 || stride === 0 ) {
|
|||
|
|
v = x[ offset ];
|
|||
|
|
if ( v === v && N-correction > 0.0 ) {
|
|||
|
|
return 0.0;
|
|||
|
|
}
|
|||
|
|
return NaN;
|
|||
|
|
}
|
|||
|
|
// Compute an estimate for the mean...
|
|||
|
|
WORKSPACE[ 0 ] = 0.0;
|
|||
|
|
WORKSPACE[ 1 ] = 0;
|
|||
|
|
nansumpw( N, WORKSPACE, x, stride, offset );
|
|||
|
|
n = WORKSPACE[ 1 ];
|
|||
|
|
nc = n - correction;
|
|||
|
|
if ( nc <= 0.0 ) {
|
|||
|
|
return NaN;
|
|||
|
|
}
|
|||
|
|
mu = WORKSPACE[ 0 ] / n;
|
|||
|
|
|
|||
|
|
// Compute the variance...
|
|||
|
|
ix = offset;
|
|||
|
|
M2 = 0.0;
|
|||
|
|
M = 0.0;
|
|||
|
|
for ( i = 0; i < N; i++ ) {
|
|||
|
|
v = x[ ix ];
|
|||
|
|
if ( v === v ) {
|
|||
|
|
d = v - mu;
|
|||
|
|
M2 += d * d;
|
|||
|
|
M += d;
|
|||
|
|
}
|
|||
|
|
ix += stride;
|
|||
|
|
}
|
|||
|
|
return (M2/nc) - ((M/n)*(M/nc));
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
|
|||
|
|
// EXPORTS //
|
|||
|
|
|
|||
|
|
module.exports = nanvariancepn;
|