96 lines
2.8 KiB
JavaScript
96 lines
2.8 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 float64ToFloat32 = require( '@stdlib/number/float64/base/to-float32' );
|
||
var ssumpw = require( '@stdlib/blas/ext/base/ssumpw' );
|
||
|
||
|
||
// MAIN //
|
||
|
||
/**
|
||
* Computes the variance of a single-precision floating-point strided array 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 {Float32Array} x - input array
|
||
* @param {integer} stride - stride length
|
||
* @returns {number} variance
|
||
*
|
||
* @example
|
||
* var Float32Array = require( '@stdlib/array/float32' );
|
||
*
|
||
* var x = new Float32Array( [ 1.0, -2.0, 2.0 ] );
|
||
* var N = x.length;
|
||
*
|
||
* var v = svariancepn( N, 1, x, 1 );
|
||
* // returns ~4.3333
|
||
*/
|
||
function svariancepn( N, correction, x, stride ) {
|
||
var mu;
|
||
var ix;
|
||
var M2;
|
||
var M;
|
||
var d;
|
||
var n;
|
||
var i;
|
||
|
||
n = N - correction;
|
||
if ( N <= 0 || n <= 0.0 ) {
|
||
return NaN;
|
||
}
|
||
if ( N === 1 || stride === 0 ) {
|
||
return 0.0;
|
||
}
|
||
// Compute an estimate for the mean:
|
||
mu = ssumpw( N, x, stride ) / N;
|
||
|
||
if ( stride < 0 ) {
|
||
ix = (1-N) * stride;
|
||
} else {
|
||
ix = 0;
|
||
}
|
||
// Compute the variance...
|
||
M2 = 0.0;
|
||
M = 0.0;
|
||
for ( i = 0; i < N; i++ ) {
|
||
d = float64ToFloat32( x[ ix ] - mu );
|
||
M2 = float64ToFloat32( M2 + float64ToFloat32( d*d ) );
|
||
M = float64ToFloat32( M + d );
|
||
ix += stride;
|
||
}
|
||
return float64ToFloat32( float64ToFloat32(M2/n) - float64ToFloat32( float64ToFloat32(M/N)*float64ToFloat32(M/n) ) ); // eslint-disable-line max-len
|
||
}
|
||
|
||
|
||
// EXPORTS //
|
||
|
||
module.exports = svariancepn;
|