95 lines
2.3 KiB
JavaScript
95 lines
2.3 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';
|
|||
|
|
|
|||
|
|
// MAIN //
|
|||
|
|
|
|||
|
|
/**
|
|||
|
|
* Computes the variance of a double-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 {Float64Array} x - input array
|
|||
|
|
* @param {integer} stride - stride length
|
|||
|
|
* @returns {number} variance
|
|||
|
|
*
|
|||
|
|
* @example
|
|||
|
|
* var Float64Array = require( '@stdlib/array/float64' );
|
|||
|
|
*
|
|||
|
|
* var x = new Float64Array( [ 1.0, -2.0, NaN, 2.0 ] );
|
|||
|
|
* var N = x.length;
|
|||
|
|
*
|
|||
|
|
* var v = dnanvariancewd( N, 1, x, 1 );
|
|||
|
|
* // returns ~4.3333
|
|||
|
|
*/
|
|||
|
|
function dnanvariancewd( N, correction, x, stride ) {
|
|||
|
|
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[ 0 ];
|
|||
|
|
if ( v === v && N-correction > 0.0 ) {
|
|||
|
|
return 0.0;
|
|||
|
|
}
|
|||
|
|
return NaN;
|
|||
|
|
}
|
|||
|
|
if ( stride < 0 ) {
|
|||
|
|
ix = (1-N) * stride;
|
|||
|
|
} else {
|
|||
|
|
ix = 0;
|
|||
|
|
}
|
|||
|
|
M2 = 0.0;
|
|||
|
|
mu = 0.0;
|
|||
|
|
n = 0;
|
|||
|
|
for ( i = 0; i < N; i++ ) {
|
|||
|
|
v = x[ ix ];
|
|||
|
|
if ( v === v ) {
|
|||
|
|
delta = v - mu;
|
|||
|
|
n += 1;
|
|||
|
|
mu += delta / n;
|
|||
|
|
M2 += delta * ( v - mu );
|
|||
|
|
}
|
|||
|
|
ix += stride;
|
|||
|
|
}
|
|||
|
|
nc = n - correction;
|
|||
|
|
if ( nc <= 0.0 ) {
|
|||
|
|
return NaN;
|
|||
|
|
}
|
|||
|
|
return M2 / nc;
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
|
|||
|
|
// EXPORTS //
|
|||
|
|
|
|||
|
|
module.exports = dnanvariancewd;
|