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feat: add stats/strided/distances/dcorrelation
PR-URL: #11917 Co-authored-by: Athan Reines <kgryte@gmail.com> Reviewed-by: Athan Reines <kgryte@gmail.com>
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‎lib/node_modules/@stdlib/stats/strided/distances/dcorrelation/README.md‎

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<!--
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@license Apache-2.0
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Copyright (c) 2026 The Stdlib Authors.
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Licensed under the Apache License, Version 2.0 (the "License");
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you may not use this file except in compliance with the License.
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You may obtain a copy of the License at
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http://www.apache.org/licenses/LICENSE-2.0
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Unless required by applicable law or agreed to in writing, software
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distributed under the License is distributed on an "AS IS" BASIS,
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WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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See the License for the specific language governing permissions and
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limitations under the License.
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-->
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# dcorrelation
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> Calculate the [correlation distance][correlation-distance] between two double-precision floating-point strided arrays.
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<section class="intro">
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The [correlation distance][correlation-distance] between random variables `X` and `Y` is defined as
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<!-- <equation class="equation" label="eq:sample_correlation_distance" align="center" raw="D(X, Y) = 1 - \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 correlation distance."> -->
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```math
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D(X, Y) = 1 - \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}}
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```
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<!-- </equation> -->
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where `x_i` and `y_i` are the _ith_ components of vectors **X** and **Y**, respectively.
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<!-- </equation> -->
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</section>
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<!-- /.intro -->
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<section class="usage">
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## Usage
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```javascript
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var dcorrelation = require( '@stdlib/stats/strided/distances/dcorrelation' );
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```
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#### dcorrelation( N, x, strideX, y, strideY )
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Computes the [correlation distance][correlation-distance] of two double-precision floating-point strided arrays.
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```javascript
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var Float64Array = require( '@stdlib/array/float64' );
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var x = new Float64Array( [ 1.0, -2.0, 2.0 ] );
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var y = new Float64Array( [ 2.0, -2.0, 1.0 ] );
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var c = dcorrelation( x.length, x, 1, y, 1 );
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// returns ~0.115
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```
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The function has the following parameters:
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- **N**: number of indexed elements.
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- **x**: first input [`Float64Array`][@stdlib/array/float64].
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- **strideX**: stride length for `x`.
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- **y**: second input [`Float64Array`][@stdlib/array/float64].
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- **strideY**: stride length for `y`.
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The `N` and stride parameters determine which elements in the strided arrays are accessed at runtime. For example, to compute the [correlation distance][correlation-distance] of every other element in `x` and `y`,
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```javascript
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var Float64Array = require( '@stdlib/array/float64' );
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var x = new Float64Array( [ 1.0, 2.0, 2.0, -7.0, -2.0, 3.0, 4.0, 2.0 ] );
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var y = new Float64Array( [ 2.0, 1.0, 2.0, 1.0, -2.0, 2.0, 3.0, 4.0 ] );
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var c = dcorrelation( 4, x, 2, y, 2 );
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// returns ~0.053
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```
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Note that indexing is relative to the first index. To introduce an offset, use [`typed array`][mdn-typed-array] views.
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<!-- eslint-disable stdlib/capitalized-comments -->
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```javascript
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var Float64Array = require( '@stdlib/array/float64' );
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var x0 = new Float64Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ] );
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var y0 = new Float64Array( [ 2.0, -2.0, 2.0, 1.0, -2.0, 4.0, 3.0, 2.0 ] );
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var x1 = new Float64Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
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var y1 = new Float64Array( y0.buffer, y0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
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var c = dcorrelation( 4, x1, 2, y1, 2 );
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// returns ~0.693
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```
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#### dcorrelation.ndarray( N, x, strideX, offsetX, y, strideY, offsetY )
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Computes the [correlation distance][correlation-distance] of two double-precision floating-point strided arrays using alternative indexing semantics.
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```javascript
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var Float64Array = require( '@stdlib/array/float64' );
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var x = new Float64Array( [ 1.0, -2.0, 2.0 ] );
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var y = new Float64Array( [ 2.0, -2.0, 1.0 ] );
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var c = dcorrelation.ndarray( x.length, x, 1, 0, y, 1, 0 );
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// returns ~0.115
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```
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The function has the following additional parameters:
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- **offsetX**: starting index for `x`.
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- **offsetY**: starting index for `y`.
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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 [correlation distance][correlation-distance] for every other element in `x` and `y` starting from the second element
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```javascript
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var Float64Array = require( '@stdlib/array/float64' );
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var x = new Float64Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ] );
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var y = new Float64Array( [ -7.0, 2.0, 2.0, 1.0, -2.0, 2.0, 3.0, 4.0 ] );
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var c = dcorrelation.ndarray( 4, x, 2, 1, y, 2, 1 );
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// returns ~0.073
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```
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</section>
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<!-- /.usage -->
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<section class="notes">
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## Notes
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- If `N <= 1`, both functions return `NaN`.
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- If all values in either `x` or `y` are constant, the [correlation distance][correlation-distance] is not defined.
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</section>
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<!-- /.notes -->
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<section class="examples">
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## Examples
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<!-- eslint no-undef: "error" -->
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```javascript
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var discreteUniform = require( '@stdlib/random/array/discrete-uniform' );
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var dcorrelation = require( '@stdlib/stats/strided/distances/dcorrelation' );
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var opts = {
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'dtype': 'float64'
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};
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var x = discreteUniform( 10, -50, 50, opts );
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console.log( x );
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var y = discreteUniform( 10, -50, 50, opts );
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console.log( y );
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var c = dcorrelation( x.length, x, 1, y, 1 );
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console.log( c );
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```
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</section>
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<!-- /.examples -->
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<!-- C interface documentation. -->
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* * *
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<section class="c">
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## C APIs
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<!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->
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<section class="intro">
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</section>
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<!-- /.intro -->
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<!-- C usage documentation. -->
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<section class="usage">
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### Usage
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```c
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#include "stdlib/stats/strided/distances/dcorrelation.h"
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```
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#### stdlib_strided_dcorrelation( N, \*X, strideX, \*Y, strideY )
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Computes the [correlation distance][correlation-distance] between two double-precision floating-point strided arrays.
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```c
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const double x[] = { 1.0, -2.0, 2.0 };
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const double y[] = { 2.0, -2.0, 1.0 };
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double c = stdlib_strided_dcorrelation( 3, x, 1, y, 1 );
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// returns ~0.115
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```
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The function accepts the following arguments:
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- **N**: `[in] CBLAS_INT` number of indexed elements.
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- **X**: `[in] double*` first input array.
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- **strideX**: `[in] CBLAS_INT` stride length for `X`.
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- **Y**: `[in] double*` second input array.
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- **strideY**: `[in] CBLAS_INT` stride length for `Y`.
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```c
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double stdlib_strided_dcorrelation( const CBLAS_INT N, const double *X, const CBLAS_INT strideX, const double *Y, const CBLAS_INT strideY );
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```
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#### stdlib_strided_dcorrelation_ndarray( N, \*X, sx, ox, \*Y, sy, oy )
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Computes the [correlation distance][correlation-distance] between two double-precision floating-point strided arrays using alternative indexing semantics.
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```c
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const double x[] = { 1.0, -2.0, 2.0 };
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const double y[] = { 2.0, -2.0, 1.0 };
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double c = stdlib_strided_dcorrelation_ndarray( 3, x, 1, 0, y, 1, 0 );
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// returns ~0.115
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```
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The function accepts the following arguments:
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- **N**: `[in] CBLAS_INT` number of indexed elements.
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- **X**: `[in] double*` first input array.
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- **strideX**: `[in] CBLAS_INT` stride length for `X`.
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- **offsetX**: `[in] CBLAS_INT` starting index for `X`.
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- **Y**: `[in] double*` second input array.
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- **strideY**: `[in] CBLAS_INT` stride length for `Y`.
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- **offsetY**: `[in] CBLAS_INT` starting index for `Y`.
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```c
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double stdlib_strided_dcorrelation_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 );
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```
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</section>
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<!-- /.usage -->
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<!-- C API usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
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<section class="notes">
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</section>
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<!-- /.notes -->
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<!-- C API usage examples. -->
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<section class="examples">
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### Examples
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```c
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#include "stdlib/stats/strided/distances/dcorrelation.h"
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#include <stdio.h>
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int main( void ) {
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// Create strided arrays:
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const double x[] = { 1.0, -2.0, 3.0, -4.0, 5.0, -6.0, 7.0, -8.0 };
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const double y[] = { 1.0, -2.0, 3.0, -4.0, 5.0, -6.0, 7.0, -8.0 };
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// Specify the number of elements:
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const int N = 8;
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// Specify strides:
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const int strideX = 1;
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const int strideY = -1;
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// Compute the correlation distance between `x` and `y`:
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double d = stdlib_strided_dcorrelation( N, x, strideX, y, strideY );
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// Print the result:
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printf( "Correlation Distance: %lf\n", d );
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// Compute the correlation distance between `x` and `y` with offsets:
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d = stdlib_strided_dcorrelation_ndarray( N, x, strideX, 0, y, strideY, N-1 );
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// Print the result:
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printf( "Correlation Distance: %lf\n", d );
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}
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```
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</section>
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<!-- /.examples -->
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</section>
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<!-- /.c -->
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<section class="references">
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</section>
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<!-- /.references -->
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<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->
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<section class="related">
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</section>
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<!-- /.related -->
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<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
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<section class="links">
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[correlation-distance]: https://en.wikipedia.org/wiki/Pearson_correlation_coefficient#Pearson's_distance
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[@stdlib/array/float64]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/array/float64
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[mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray
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</section>
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<!-- /.links -->

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