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* @license Apache-2.0
*
* Copyright (c) 2026 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 sqrt = require( '@stdlib/math/base/special/sqrt' );
// MAIN //
/**
* Computes the sample Pearson product-moment correlation coefficient of two double-precision floating-point strided arrays using Welford algorithm.
*
* @param {PositiveInteger} N - number of indexed elements
* @param {Float64Array} x - first input array
* @param {integer} strideX - stride length of `x`
* @param {NonNegativeInteger} offsetX - starting index of `x`
* @param {Float64Array} y - second input array
* @param {integer} strideY - stride length of `y`
* @param {NonNegativeInteger} offsetY - starting index of `y`
* @returns {number} pearson correlation coefficient
*
* @example
* var Float64Array = require( '@stdlib/array/float64' );
*
* var x = new Float64Array( [ 1.0, -2.0, 2.0 ] );
* var y = new Float64Array( [ 2.0, -2.0, 1.0 ] );
*
* var v = dpcorrwd( x.length, x, 1, 0, y, 1, 0 );
* // returns ~0.885
*/
function dpcorrwd( N, x, strideX, offsetX, y, strideY, offsetY ) {
var M2x;
var M2y;
var dy1;
var dy2;
var dx;
var my;
var mx;
var ix;
var iy;
var sx;
var sy;
var C;
var i;
if ( N <= 0 ) {
return NaN;
}
ix = offsetX;
iy = offsetY;
C = 0.0;
mx = 0.0;
my = 0.0;
M2x = 0.0;
M2y = 0.0;
for ( i = 0; i < N; i++ ) {
dx = x[ ix ] - mx;
mx += dx / ( i+1 );
M2x += dx * ( x[ ix ] - mx );
dy1 = y[ iy ] - my;
my += dy1 / ( i+1 );
dy2 = y[ iy ] - my;
M2y += dy2 * dy1;
C += dx * dy2;
ix += strideX;
iy += strideY;
}
if ( M2x === 0.0 || M2y === 0.0 ) {
return NaN;
}
sx = sqrt( M2x/N );
sy = sqrt( M2y/N );
return ( C/N ) / ( sx*sy ); // Note: why all the dividing by `N`? To avoid overflow.
}
// EXPORTS //
module.exports = dpcorrwd;
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