npm package: @stdlib/stats-strided-distances-dsquared-euclidean
Description: Compute the squared Euclidean distance between two double-precision floating-point strided arrays.
Author: The Stdlib Authors
Latest version: 0.1.1

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# dsquaredEuclidean

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> Compute the squared Euclidean distance between two double-precision floating-point strided arrays.

<section class="intro">

The [squared Euclidean distance][wikipedia-squared-euclidean-distance] is defined as

<!-- <equation class="equation" label="eq:squared_euclidean_distance" align="center" raw="d(X,Y) = \sum_{i=0}^{N-1} (y_i - x_i)^2" alt="Equation for the squared Euclidean distance."> -->

<!-- </equation> -->

where `x_i` and `y_i` are the _ith_ components of vectors **X** and **Y**, respectively.

</section>

<!-- /.intro -->

<section class="installation">

## Installation

```bash
npm install @stdlib/stats-strided-distances-dsquared-euclidean
```

</section>

<section class="usage">

## Usage

```javascript
var dsquaredEuclidean = require( '@stdlib/stats-strided-distances-dsquared-euclidean' );
```

#### dsquaredEuclidean( N, x, strideX, y, strideY )

Computes the squared Euclidean distance between two double-precision floating-point strided arrays.

```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 z = dsquaredEuclidean( x.length, x, 1, y, 1 );
// returns 72.0
```

The function has the following parameters:

-   **N**: number of indexed elements.
-   **x**: input [`Float64Array`][@stdlib/array/float64].
-   **strideX**: stride length of `x`.
-   **y**: input [`Float64Array`][@stdlib/array/float64].
-   **strideY**: stride length of `y`.

The `N` and stride parameters determine which elements in the strided arrays are accessed at runtime. For example, to calculate the squared Euclidean distance between every other element in `x` and the first `N` elements of `y` in reverse order,

```javascript
var Float64Array = require( '@stdlib/array-float64' );

var x = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
var y = new Float64Array( [ 1.0, 1.0, 1.0, 1.0, 1.0, 1.0 ] );

var z = dsquaredEuclidean( 3, x, 2, y, -1 );
// returns 20.0
```

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' );

// Initial arrays...
var x0 = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
var y0 = new Float64Array( [ 7.0, 8.0, 9.0, 10.0, 11.0, 12.0 ] );

// Create offset views...
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*3 ); // start at 4th element

var z = dsquaredEuclidean( 3, x1, 1, y1, 1 );
// returns 192.0
```

#### dsquaredEuclidean.ndarray( N, x, strideX, offsetX, y, strideY, offsetY )

Computes the squared Euclidean distance between two double-precision floating-point strided arrays using alternative indexing semantics.

```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 z = dsquaredEuclidean.ndarray( x.length, x, 1, 0, y, 1, 0 );
// returns 72.0
```

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 squared Euclidean distance between every other element in `x` starting from the second element with the last 3 elements in `y` in reverse order

```javascript
var Float64Array = require( '@stdlib/array-float64' );

var x = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
var y = new Float64Array( [ 7.0, 8.0, 9.0, 10.0, 11.0, 12.0 ] );

var z = dsquaredEuclidean.ndarray( 3, x, 2, 1, y, -1, y.length-1 );
// returns 165.0
```

</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 dsquaredEuclidean = require( '@stdlib/stats-strided-distances-dsquared-euclidean' );

var opts = {
    'dtype': 'float64'
};
var x = discreteUniform( 10, 0, 100, opts );
console.log( x );

var y = discreteUniform( x.length, 0, 10, opts );
console.log( y );

var out = dsquaredEuclidean.ndarray( x.length, x, 1, 0, y, -1, y.length-1 );
console.log( out );
```

</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/distances/dsquared_euclidean.h"
```

#### stdlib_strided_dsquared_euclidean( N, \*X, strideX, \*Y, strideY )

Computes the squared Euclidean distance between two double-precision floating-point strided arrays.

```c
const double x[] = { 1.0, 2.0, 2.0, -7.0, -2.0, 3.0, 4.0, 2.0 };
const double y[] = { 2.0, 1.0, 2.0, 1.0, -2.0, 2.0, 3.0, 4.0 };

double v = stdlib_strided_dsquared_euclidean( 8, x, 1, y, 1 );
// returns 72.0
```

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 of `X`.
-   **Y**: `[in] double*` second input array.
-   **strideY**: `[in] CBLAS_INT` stride length of `Y`.

```c
double stdlib_strided_dsquared_euclidean( const CBLAS_INT N, const double *X, const CBLAS_INT strideX, const double *Y, const CBLAS_INT strideY );
```

<!--lint disable maximum-heading-length-->

#### stdlib_strided_dsquared_euclidean_ndarray( N, \*X, strideX, offsetX, \*Y, strideY, offsetY )

<!--lint enable maximum-heading-length-->

Computes the squared Euclidean distance between two double-precision floating-point strided arrays using alternative indexing semantics.

```c
const double x[] = { 4.0, 2.0, -3.0, 5.0, -1.0 };
const double y[] = { 2.0, 6.0, -1.0, -4.0, 8.0 };

double v = stdlib_strided_dsquared_euclidean_ndarray( 5, x, -1, 4, y, -1, 4 );
// returns 186.0
```

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 of `X`.
-   **offsetX**: `[in] CBLAS_INT` starting index for `X`.
-   **Y**: `[in] double*` second input array.
-   **strideY**: `[in] CBLAS_INT` stride length of `Y`.
-   **offsetY**: `[in] CBLAS_INT` starting index for `Y`.

```c
double stdlib_strided_dsquared_euclidean_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/distances/dsquared_euclidean.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 squared Euclidean distance between `x` and `y`:
    double d = stdlib_strided_dsquared_euclidean( N, x, strideX, y, strideY );

    // Print the result:
    printf( "Squared Euclidean distance: %lf\n", d );

    // Compute the squared Euclidean distance between `x` and `y` with offsets:
    d = stdlib_strided_dsquared_euclidean_ndarray( N, x, strideX, 0, y, strideY, N-1 );

    // Print the result:
    printf( "Squared Euclidean distance: %lf\n", d );
}
```

</section>

<!-- /.examples -->

</section>

<!-- /.c -->

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<section class="related">

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<section class="main-repo" >

* * *

## Notice

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For more information on the project, filing bug reports and feature requests, and guidance on how to develop [stdlib][stdlib], see the main project [repository][stdlib].

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---

## License

See [LICENSE][stdlib-license].


## Copyright

Copyright &copy; 2016-2026. The Stdlib [Authors][stdlib-authors].

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