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feat: add stats/strided/distances/dcosine-similarity
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‎lib/node_modules/@stdlib/stats/strided/distances/dcosine-similarity/README.md‎

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<!--
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@license Apache-2.0
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Copyright (c) 2019 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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# dcosine-similarity
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> Computes the cosine similarity of two double-precision floating-point vectors.
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<section class="intro">
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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 dcosineSimilarity = require( '@stdlib/stats/strided/distances/dcosine-similarity' );
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```
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#### dcosineSimilarity( N, x, strideX, y, strideY )
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Calculates the cosine similarity of vectors `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( [ 4.0, 2.0, -3.0, 5.0, -1.0 ] );
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var y = new Float64Array( [ 2.0, 6.0, -1.0, -4.0, 8.0 ] );
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var z = dcosineSimilarity( x.length, x, 1, y, 1 );
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// returns ~-0.061
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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**: input [`Float64Array`][@stdlib/array/float64].
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- **strideX**: stride length of `x`.
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- **y**: input [`Float64Array`][@stdlib/array/float64].
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- **strideY**: stride length of `y`.
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The `N` and strides parameters determine which elements in the strided arrays are accessed at runtime. For example, to calculate the cosine similarity of every other value in `x` and the first `N` elements of `y` in reverse order,
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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, 3.0, 4.0, 5.0, 6.0 ] );
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var y = new Float64Array( [ 1.0, 1.0, 1.0, 1.0, 1.0, 1.0 ] );
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var z = dcosineSimilarity( 3, x, 2, y, -1 );
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// returns ~0.878
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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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// Initial arrays...
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var x0 = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
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var y0 = new Float64Array( [ 7.0, 8.0, 9.0, 10.0, 11.0, 12.0 ] );
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// Create offset views...
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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*3 ); // start at 4th element
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var z = dcosineSimilarity( 3, x1, 1, y1, 1 );
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// returns ~0.982
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```
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#### dcosineSimilarity.ndarray( N, x, strideX, offsetX, y, strideY, offsetY )
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Calculates the cosine similarity of `x` and `y` 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( [ 4.0, 2.0, -3.0, 5.0, -1.0 ] );
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var y = new Float64Array( [ 2.0, 6.0, -1.0, -4.0, 8.0 ] );
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var z = dcosineSimilarity.ndarray( x.length, x, 1, 0, y, 1, 0 );
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// returns ~-0.061
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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 cosine similarity of every other value in `x` starting from the second value with the last 3 elements in `y` in reverse order
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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, 3.0, 4.0, 5.0, 6.0 ] );
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var y = new Float64Array( [ 7.0, 8.0, 9.0, 10.0, 11.0, 12.0 ] );
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var z = dcosineSimilarity.ndarray( 3, x, 2, 1, y, -1, y.length-1 );
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// returns ~0.895
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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 <= 0`, both functions return `0.0`.
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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 dcosineSimilarity = require( '@stdlib/stats/strided/distances/dcosine-similarity' );
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var opts = {
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'dtype': 'float64'
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};
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var x = discreteUniform( 10, 0, 100, opts );
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console.log( x );
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var y = discreteUniform( x.length, 0, 10, opts );
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console.log( y );
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var out = dcosineSimilarity.ndarray( x.length, x, 1, 0, y, -1, y.length-1 );
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console.log( out );
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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/dcosine_similarity.h"
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```
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#### stdlib_strided_dcosine_similarity( N, \*X, strideX, \*Y, strideY )
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Computes the cosine similarity of two double-precision floating-point vectors.
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```c
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const double x[] = { 4.0, 2.0, -3.0, 5.0, -1.0 };
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const double y[] = { 2.0, 6.0, -1.0, -4.0, 8.0 };
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double v = stdlib_strided_dcosine_similarity( 5, x, 1, y, 1 );
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// returns ~-0.061
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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 of `X`.
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- **Y**: `[in] double*` second input array.
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- **strideY**: `[in] CBLAS_INT` stride length of `Y`.
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```c
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double stdlib_strided_dcosine_similarity( 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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<!--lint ignore maximum-heading-length-->
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#### stdlib_strided_dcosine_similarity_ndarray( N, \*X, strideX, offsetX, \*Y, strideY, offsetY )
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<!--lint ignore maximum-heading-length-->
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Computes the cosine similarity of two double-precision floating-point vectors using alternative indexing semantics.
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```c
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const double x[] = { 4.0, 2.0, -3.0, 5.0, -1.0 };
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const double y[] = { 2.0, 6.0, -1.0, -4.0, 8.0 };
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double v = stdlib_strided_dcosine_similarity_ndarray( 5, x, -1, 4, y, -1, 4 );
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// returns ~0.061
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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 of `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 of `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_dcosine_similarity_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/dcosine_similarity.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 cosine similarity of `x` and `y`:
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double sim = stdlib_strided_dcosine_similarity( N, x, strideX, y, strideY );
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// Print the result:
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printf( "cosine similarity: %lf\n", sim );
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// Compute the cosine similarity of `x` and `y` with offsets:
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sim = stdlib_strided_dcosine_similarity_ndarray( N, x, strideX, 0, y, strideY, N-1 );
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// Print the result:
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printf( "cosine similarity: %lf\n", sim );
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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 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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[@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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<!-- <related-links> -->
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<!-- </related-links> -->
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</section>
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<!-- /.links -->

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