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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';
// MAIN //
/**
* Computes the variance of a double-precision floating-point strided array ignoring `NaN` values and using a one-pass algorithm proposed by Youngs and Cramer.
*
* ## Method
*
* - This implementation uses a one-pass algorithm, as proposed by Youngs and Cramer (1971).
*
* ## References
*
* - Youngs, Edward A., and Elliot M. Cramer. 1971. "Some Results Relevant to Choice of Sum and Sum-of-Product Algorithms." _Technometrics_ 13 (3): 657–65. doi:[10.1080/00401706.1971.10488826](https://doi.org/10.1080/00401706.1971.10488826).
*
* @param {PositiveInteger} N - number of indexed elements
* @param {number} correction - degrees of freedom adjustment
* @param {Float64Array} x - input array
* @param {integer} strideX - stride length
* @param {NonNegativeInteger} offsetX - starting index
* @returns {number} variance
*
* @example
* var Float64Array = require( '@stdlib/array/float64' );
*
* var x = new Float64Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0, NaN, NaN ] );
*
* var v = dnanvarianceyc( 5, 1, x, 2, 1 );
* // returns 6.25
*/
function dnanvarianceyc( N, correction, x, strideX, offsetX ) {
var sum;
var ix;
var nc;
var S;
var v;
var d;
var n;
var i;
if ( N <= 0 ) {
return NaN;
}
if ( N === 1 || strideX === 0 ) {
v = x[ offsetX ];
if ( v === v && N-correction > 0.0 ) {
return 0.0;
}
return NaN;
}
ix = offsetX;
// Find the first non-NaN element...
for ( i = 0; i < N; i++ ) {
v = x[ ix ];
if ( v === v ) {
break;
}
ix += strideX;
}
if ( i === N ) {
return NaN;
}
ix += strideX;
sum = v;
S = 0.0;
i += 1;
n = 1;
for ( i; i < N; i++ ) {
v = x[ ix ];
if ( v === v ) {
n += 1;
sum += v;
d = (n*v) - sum;
S += (1.0/(n*(n-1))) * d * d;
}
ix += strideX;
}
nc = n - correction;
if ( nc <= 0.0 ) {
return NaN;
}
return S / nc;
}
// EXPORTS //
module.exports = dnanvarianceyc;
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