feat: add stats/strided/dpcorrwd

lib/node_modules/@stdlib/stats/strided/dpcorrwd/README.md

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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.
+
+-->
+
+# dpcorrwd
+
+> Calculate the [sample Pearson product-moment correlation coefficient][pearson-correlation] of two double-precision floating-point strided arrays using Welford algorithm.
+
+<section class="intro">
+
+The [Pearson product-moment correlation coefficient][pearson-correlation] (also known as Pearson's r) between random variables `X` and `Y` is defined as
+
+
+<!-- <equation class="equation" label="eq:pearson_correlation_coefficient" align="center" raw="\rho_{X,Y} = \frac{\operatorname{cov}(X,Y)}{\sigma_X \sigma_Y}" alt="Equation for the Pearson product-moment correlation coefficient."> -->
+
+```math
+\rho_{X,Y} = \frac{\mathop{\mathrm{cov}}(X,Y)}{\sigma_X \sigma_Y}
+```
+
+<!-- </equation> -->
+
+where the numerator is the [covariance][covariance] and the denominator is the product of the respective standard deviations.
+
+For a sample of size `n`, the [sample Pearson product-moment correlation coefficient][pearson-correlation] is defined as
+
+<!-- <equation class="equation" label="eq:sample_pearson_correlation_coefficient" align="center" raw="r = \frac{\displaystyle\sum_{i=0}^{N-1} (x_i - \bar{x})(y_i - \bar{y})}{\displaystyle\sqrt{\sum_{i=0}^{N-1} (x_i - \bar{x})^2} \sqrt{\sum_{i=0}^{N-1} (y_i - \bar{y})^2}}" alt="Equation for the sample Pearson product-moment correlation coefficient."> -->
+
+```math
+r_{xy} = \frac{\displaystyle\sum_{i=0}^{N-1} (x_i - \bar{x})(y_i - \bar{y})}{\displaystyle\sqrt{\sum_{i=0}^{N-1} (x_i - \bar{x})^2} \sqrt{\sum_{i=0}^{N-1} (y_i - \bar{y})^2}}
+```
+
+<!-- </equation> -->
+
+where `x_i` and `y_i` are the _ith_ components of vectors **X** and **Y**, respectively.
+
+The use of the term `n-1` is commonly referred to as Bessel's correction. Depending on the characteristics of the population distributions, other correction factors (e.g., `n-1.5`, `n+1`, etc) can yield better estimators.
+
+</section>
+
+<!-- /.intro -->
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var dpcorrwd = require( '@stdlib/stats/strided/dpcorrwd' );
+```
+
+#### dpcorrwd( N, x, strideX, y, strideY )
+
+Computes the [sample Pearson product-moment correlation coefficient][pearson-correlation] of two double-precision floating-point strided arrays using Welford algorithm.
+
+```javascript
+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 c = dpcorrwd( x.length, x, 1, y, 1 );
+// returns ~0.885
+```
+
+The function has the following parameters:
+
+-   **N**: number of indexed elements.
+-   **x**: first input [`Float64Array`][@stdlib/array/float64].
+-   **strideX**: stride length for `x`.
+-   **y**: second input [`Float64Array`][@stdlib/array/float64].
+-   **strideY**: stride length for `y`.
+
+The `N` and stride parameters determine which elements in the strided arrays are accessed at runtime. For example, to compute the [sample Pearson product-moment correlation coefficient][pearson-correlation] of every other element in `x` and `y`,
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+
+var x = new Float64Array( [ 1.0, 2.0, 2.0, -7.0, -2.0, 3.0, 4.0, 2.0 ] );
+var y = new Float64Array( [ 2.0, 1.0, 2.0, 1.0, -2.0, 2.0, 3.0, 4.0 ] );
+
+var c = dpcorrwd( 4, x, 2, y, 2 );
+// returns ~0.947
+```
+
+Note that indexing is relative to the first index. To introduce an offset, use [`typed array`][mdn-typed-array] views.
+
+<!-- eslint-disable stdlib/capitalized-comments -->
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+
+var x0 = new Float64Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ] );
+var y0 = new Float64Array( [ 2.0, -2.0, 2.0, 1.0, -2.0, 4.0, 3.0, 2.0 ] );
+
+var x1 = new Float64Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
+var y1 = new Float64Array( y0.buffer, y0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
+
+var c = dpcorrwd( 4, x1, 2, y1, 2 );
+// returns ~0.307
+```
+
+#### dpcorrwd.ndarray( N, x, strideX, offsetX, y, strideY, offsetY )
+
+Computes the [sample Pearson product-moment correlation coefficient][pearson-correlation] of two double-precision floating-point strided arrays using Welford algorithm and alternative indexing semantics.
+
+```javascript
+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 c = dpcorrwd.ndarray( x.length, x, 1, 0, y, 1, 0 );
+// returns ~0.885
+```
+
+The function has the following additional parameters:
+
+-   **offsetX**: starting index for `x`.
+-   **offsetY**: starting index for `y`.
+
+While [`typed array`][mdn-typed-array] views mandate a view offset based on the underlying buffer, the offset parameters support indexing semantics based on starting indices. For example, to calculate the [sample Pearson product-moment correlation coefficient][pearson-correlation] for every other element in `x` and `y` starting from the second element
+
+```javascript
+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 ] );
+var y = new Float64Array( [ -7.0, 2.0, 2.0, 1.0, -2.0, 2.0, 3.0, 4.0 ] );
+
+var c = dpcorrwd.ndarray( 4, x, 2, 1, y, 2, 1 );
+// returns ~0.927
+```
+
+</section>
+
+<!-- /.usage -->
+
+<section class="notes">
+
+## Notes
+
+-   If `N <= 0`, both functions return `NaN`.
+
+</section>
+
+<!-- /.notes -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```javascript
+var discreteUniform = require( '@stdlib/random/array/discrete-uniform' );
+var dpcorrwd = require( '@stdlib/stats/strided/dpcorrwd' );
+
+var opts = {
+    'dtype': 'float64'
+};
+var x = discreteUniform( 10, -50, 50, opts );
+console.log( x );
+
+var y = discreteUniform( 10, -50, 50, opts );
+console.log( y );
+
+var c = dpcorrwd( x.length, x, 1, y, 1 );
+console.log( c );
+```
+
+</section>
+
+<!-- /.examples -->
+
+<!-- C interface documentation. -->
+
+* * *
+
+<section class="c">
+
+## C APIs
+
+<!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->
+
+<section class="intro">
+
+</section>
+
+<!-- /.intro -->
+
+<!-- C usage documentation. -->
+
+<section class="usage">
+
+### Usage
+
+```c
+#include "stdlib/stats/strided/dpcorrwd.h"
+```
+
+#### stdlib_strided_dpcorrwd( N, \*X, strideX, \*Y, strideY )
+
+Computes the [sample Pearson product-moment correlation coefficient][pearson-correlation] of two double-precision floating-point strided arrays using Welford algorithm.
+
+```c
+const double x[] = { 1.0, -2.0, 2.0 };
+const double y[] = { 2.0, -2.0, 1.0 };
+
+double c = stdlib_strided_dpcorrwd( 3, x, 1, y, 1 );
+// returns ~0.885
+```
+
+The function accepts the following arguments:
+
+-   **N**: `[in] CBLAS_INT` number of indexed elements.
+-   **X**: `[in] double*` first input array.
+-   **strideX**: `[in] CBLAS_INT` stride length for `X`.
+-   **Y**: `[in] double*` second input array.
+-   **strideY**: `[in] CBLAS_INT` stride length for `Y`.
+
+```c
+double stdlib_strided_dpcorrwd( const CBLAS_INT N, const double *X, const CBLAS_INT strideX, const double *Y, const CBLAS_INT strideY );
+```
+
+#### stdlib_strided_dpcorrwd_ndarray( N, \*X, strideX, offsetX, \*Y, strideY, offsetY )
+
+Computes the [sample Pearson product-moment correlation coefficient][pearson-correlation] of two double-precision floating-point strided arrays using Welford algorithm and alternative indexing semantics.
+
+```c
+const double x[] = { 1.0, -2.0, 2.0 };
+const double y[] = { 2.0, -2.0, 1.0 };
+
+double c = stdlib_strided_dpcorrwd_ndarray( 3, x, 1, 0, y, 1, 0 );
+// returns ~0.885
+```
+
+The function accepts the following arguments:
+
+-   **N**: `[in] CBLAS_INT` number of indexed elements.
+-   **X**: `[in] double*` first input array.
+-   **strideX**: `[in] CBLAS_INT` stride length for `X`.
+-   **offsetX**: `[in] CBLAS_INT` starting index for `X`.
+-   **Y**: `[in] double*` second input array.
+-   **strideY**: `[in] CBLAS_INT` stride length for `Y`.
+-   **offsetY**: `[in] CBLAS_INT` starting index for `Y`.
+
+```c
+double stdlib_strided_dpcorrwd_ndarray( const CBLAS_INT N, const double *X, const CBLAS_INT strideX, const CBLAS_INT offsetX, const double *Y, const CBLAS_INT strideY, const CBLAS_INT offsetY );
+```
+
+</section>
+
+<!-- /.usage -->
+
+<!-- C API usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
+
+<section class="notes">
+
+</section>
+
+<!-- /.notes -->
+
+<!-- C API usage examples. -->
+
+<section class="examples">
+
+### Examples
+
+```c
+#include "stdlib/stats/strided/dpcorrwd.h"
+#include <stdio.h>
+
+int main( void ) {
+    // Create strided arrays:
+    const double x[] = { 1.0, -2.0, 3.0, -4.0, 5.0, -6.0, 7.0, -8.0 };
+    const double y[] = { 1.0, -2.0, 3.0, -4.0, 5.0, -6.0, 7.0, -8.0 };
+
+    // Specify the number of elements:
+    const int N = 8;
+
+    // Specify strides:
+    const int strideX = 1;
+    const int strideY = -1;
+
+    // Compute the Pearson product-moment correlation coefficient between `x` and `y`:
+    double d = stdlib_strided_dpcorrwd( N, x, strideX, y, strideY );
+
+    // Print the result:
+    printf( "Pearson Correlation Coefficient: %lf\n", d );
+
+    // Compute the Pearson product-moment correlation coefficient between `x` and `y` with offsets:
+    d = stdlib_strided_dpcorrwd_ndarray( N, x, strideX, 0, y, strideY, N-1 );
+
+    // Print the result:
+    printf( "Pearson Correlation Coefficient: %lf\n", d );
+}
+```
+
+</section>
+
+<!-- /.examples -->
+
+</section>
+
+<!-- /.c -->
+
+<section class="references">
+
+</section>
+
+<!-- /.references -->
+
+<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->
+
+<section class="related">
+
+</section>
+
+<!-- /.related -->
+
+<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
+
+<section class="links">
+
+[pearson-correlation]: https://en.wikipedia.org/wiki/Pearson_correlation_coefficient
+
+[covariance]: https://en.wikipedia.org/wiki/Covariance
+
+[@stdlib/array/float64]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/array/float64
+
+[mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray
+
+</section>
+
+<!-- /.links -->