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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 float64ToFloat32 = require( '@stdlib/number/float64/base/to-float32' );
// MAIN //
/**
* Computes the variance of a single-precision floating-point strided array ignoring `NaN` values and using Welford's algorithm.
*
* ## References
*
* - Welford, B. P. 1962. "Note on a Method for Calculating Corrected Sums of Squares and Products." _Technometrics_ 4 (3). Taylor & Francis: 419–20. doi:[10.1080/00401706.1962.10490022](https://doi.org/10.1080/00401706.1962.10490022).
* - van Reeken, A. J. 1968. "Letters to the Editor: Dealing with Neely's Algorithms." _Communications of the ACM_ 11 (3): 149–50. doi:[10.1145/362929.362961](https://doi.org/10.1145/362929.362961).
*
* @param {PositiveInteger} N - number of indexed elements
* @param {number} correction - degrees of freedom adjustment
* @param {Float32Array} x - input array
* @param {integer} stride - stride length
* @param {NonNegativeInteger} offset - starting index
* @returns {number} variance
*
* @example
* var Float32Array = require( '@stdlib/array/float32' );
* var floor = require( '@stdlib/math/base/special/floor' );
*
* var x = new Float32Array( [ 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 = snanvariancewd( N, 1, x, 2, 1 );
* // returns 6.25
*/
function snanvariancewd( N, correction, x, stride, offset ) {
var delta;
var mu;
var M2;
var ix;
var nc;
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;
}
ix = offset;
M2 = 0.0;
mu = 0.0;
n = 0;
for ( i = 0; i < N; i++ ) {
v = x[ ix ];
if ( v === v ) {
delta = float64ToFloat32( v - mu );
n += 1;
mu = float64ToFloat32( mu + float64ToFloat32( delta/n ) );
M2 = float64ToFloat32( M2 + float64ToFloat32( delta*float64ToFloat32( v-mu ) ) ); // eslint-disable-line max-len
}
ix += stride;
}
nc = n - correction;
if ( nc <= 0.0 ) {
return NaN;
}
return float64ToFloat32( M2 / nc );
}
// EXPORTS //
module.exports = snanvariancewd;
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