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/**
* @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 dnansumpw = require( './dnansumpw.js' );
// VARIABLES //
var WORKSPACE = [ 0.0, 0 ];
// MAIN //
/**
* Computes the variance of a double-precision floating-point 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 {Float64Array} x - input array
* @param {integer} stride - stride length
* @param {NonNegativeInteger} offset - starting index
* @returns {number} variance
*
* @example
* var Float64Array = require( '@stdlib/array/float64' );
* var floor = require( '@stdlib/math/base/special/floor' );
*
* var x = new Float64Array( [ 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 = dnanvariancepn( N, 1, x, 2, 1 );
* // returns 6.25
*/
function dnanvariancepn( 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;
dnansumpw( 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 = dnanvariancepn;
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