136 lines
3.4 KiB
Markdown
136 lines
3.4 KiB
Markdown
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<!--
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@license Apache-2.0
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Copyright (c) 2020 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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# gdot
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> Calculate the dot product of two vectors.
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<section class="intro">
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The [dot product][dot-product] (or scalar product) is defined as
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<!-- <equation class="equation" label="eq:dot_product" align="center" raw="\mathbf{x}\cdot\mathbf{y} = \sum_{i=0}^{N-1} x_i y_i = x_0 y_0 + x_1 y_1 + \ldots + x_{N-1} y_{N-1}" alt="Dot product definition."> -->
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<div class="equation" align="center" data-raw-text="\mathbf{x}\cdot\mathbf{y} = \sum_{i=0}^{N-1} x_i y_i = x_0 y_0 + x_1 y_1 + \ldots + x_{N-1} y_{N-1}" data-equation="eq:dot_product">
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<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@b7a453f335bade718a3f48a61658d1564dc3f786/lib/node_modules/@stdlib/blas/gdot/docs/img/equation_dot_product.svg" alt="Dot product definition.">
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<br>
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</div>
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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 gdot = require( '@stdlib/blas/gdot' );
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```
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#### gdot( x, y )
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Calculates the dot product of vectors `x` and `y`.
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```javascript
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var Int32Array = require( '@stdlib/array/int32' );
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var array = require( '@stdlib/ndarray/array' );
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var x = array( new Int32Array( [ 4.0, 2.0, -3.0, 5.0, -1.0 ] ) );
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var y = array( new Int32Array( [ 2.0, 6.0, -1.0, -4.0, 8.0 ] ) );
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var z = gdot( x, y );
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// returns -5.0
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```
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The function has the following parameters:
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- **x**: a 1-dimensional [`ndarray`][@stdlib/ndarray/array] or an array-like object.
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- **y**: a 1-dimensional [`ndarray`][@stdlib/ndarray/array] or an array-like object.
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If provided empty vectors, the function returns `0.0`.
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```javascript
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var z = gdot( [], [] );
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// returns 0.0
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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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- `gdot()` corresponds to the [BLAS][blas] level 1 function [`ddot`][ddot] with the exception that this implementation works with any array type, not just Float64Arrays.
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- In general, for best performance, especially for large vectors, provide 1-dimensional [`ndarrays`][@stdlib/ndarray/array] whose underlying data type is either `float64` or `float32`.
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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/base/discrete-uniform' );
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var gdot = require( '@stdlib/blas/gdot' );
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var rand1 = discreteUniform.factory( 0, 100 );
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var rand2 = discreteUniform.factory( 0, 10 );
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var x = [];
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var y = [];
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var i;
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for ( i = 0; i < 10; i++ ) {
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x.push( rand1() );
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y.push( rand2() );
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}
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console.log( x );
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console.log( y );
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var z = gdot( x, y );
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console.log( z );
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```
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</section>
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<!-- /.examples -->
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<section class="links">
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[dot-product]: https://en.wikipedia.org/wiki/Dot_product
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[blas]: http://www.netlib.org/blas
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[ddot]: http://www.netlib.org/lapack/explore-html/df/d28/group__single__blas__level1.html
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[@stdlib/ndarray/array]: https://www.npmjs.com/package/@stdlib/ndarray-array
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</section>
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<!-- /.links -->
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