npm package: @stdlib/stats-strided-distances-dcosine-distance
Description: Compute the cosine distance between two double-precision floating-point strided arrays.
Author: The Stdlib Authors
Latest version: 0.0.1

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# dcosineDistance

[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url] <!-- [![dependencies][dependencies-image]][dependencies-url] -->

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

<section class="intro">

The [cosine distance][wikipedia-cosine-distance] is defined as

<!-- <equation class="equation" label="eq:cosine_similarity" align="center" raw="D_C(A, B) = 1 - S_C(A, B) = 1 - \cos(\theta) = 1 - \frac{A \cdot B}{\lVert A \rVert \, \lVert B \rVert} = 1 - \frac{\sum_{i=0}^{N-1} A_i B_i}{\sqrt{\sum_{i=0}^{N-1} A_i^2} \cdot \sqrt{\sum_{i=0}^{N-1} B_i^2}}" alt="Equation for cosine distance."> -->

<!-- </equation> -->

where `S_C` is the [cosine similarity][wikipedia-cosine-similarity] and `A_i` and `B_i` are the _ith_ components of vectors **A** and **B**, respectively.

</section>

<!-- /.intro -->

<section class="installation">

## Installation

```bash
npm install @stdlib/stats-strided-distances-dcosine-distance
```

</section>

<section class="usage">

## Usage

```javascript
var dcosineDistance = require( '@stdlib/stats-strided-distances-dcosine-distance' );
```

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

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

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

var x = new Float64Array( [ 4.0, 2.0, -3.0, 5.0, -1.0 ] );
var y = new Float64Array( [ 2.0, 6.0, -1.0, -4.0, 8.0 ] );

var z = dcosineDistance( x.length, x, 1, y, 1 );
// returns ~1.061
```

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 cosine distance between every other value 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 = dcosineDistance( 3, x, 2, y, -1 );
// returns ~0.122
```

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 = dcosineDistance( 3, x1, 1, y1, 1 );
// returns ~0.018
```

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

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

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

var x = new Float64Array( [ 4.0, 2.0, -3.0, 5.0, -1.0 ] );
var y = new Float64Array( [ 2.0, 6.0, -1.0, -4.0, 8.0 ] );

var z = dcosineDistance.ndarray( x.length, x, 1, 0, y, 1, 0 );
// returns ~1.061
```

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 cosine 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 = dcosineDistance.ndarray( 3, x, 2, 1, y, -1, y.length-1 );
// returns ~0.105
```

</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 dcosineDistance = require( '@stdlib/stats-strided-distances-dcosine-distance' );

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 = dcosineDistance.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/dcosine_distance.h"
```

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

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

```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_dcosine_distance( 5, x, 1, y, 1 );
// returns ~1.061
```

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_dcosine_distance( 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_dcosine_distance_ndarray( N, \*X, strideX, offsetX, \*Y, strideY, offsetY )

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

Computes the cosine 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_dcosine_distance_ndarray( 5, x, -1, 4, y, -1, 4 );
// returns ~1.061
```

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_dcosine_distance_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/dcosine_distance.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 cosine distance between `x` and `y`:
    double c = stdlib_strided_dcosine_distance( N, x, strideX, y, strideY );

    // Print the result:
    printf( "cosine distance: %lf\n", c );

    // Compute the cosine distance between `x` and `y` with offsets:
    c = stdlib_strided_dcosine_distance_ndarray( N, x, strideX, 0, y, strideY, N-1 );

    // Print the result:
    printf( "cosine distance: %lf\n", c );
}
```

</section>

<!-- /.examples -->

</section>

<!-- /.c -->

<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->

<section class="related">

</section>

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<section class="main-repo" >

* * *

## Notice

This package is part of [stdlib][stdlib], a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.

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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[wikipedia-cosine-similarity]: https://en.wikipedia.org/wiki/Cosine_similarity

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