time-to-botec

README.md (6222B)

---

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 @license Apache-2.0
 
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 # gdot
 
 > Calculate the dot product of two vectors.
 
 <section class="intro">
 
 The [dot product][dot-product] (or scalar product) is defined as
 
 <!-- <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."> -->
 
 <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">
     <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@6cf4829ce9c06ba9fa207a2ea3b395266f86a259/lib/node_modules/@stdlib/blas/base/gdot/docs/img/equation_dot_product.svg" alt="Dot product definition.">
     <br>
 </div>
 
 <!-- </equation> -->
 
 </section>
 
 <!-- /.intro -->
 
 <section class="usage">
 
 ## Usage
 
 ```javascript
 var gdot = require( '@stdlib/blas/base/gdot' );
 ```
 
 #### gdot( N, x, strideX, y, strideY )
 
 Calculates the dot product of vectors `x` and `y`.
 
 ```javascript
 var x = [ 4.0, 2.0, -3.0, 5.0, -1.0 ];
 var y = [ 2.0, 6.0, -1.0, -4.0, 8.0 ];
 
 var z = gdot( x.length, x, 1, y, 1 );
 // returns -5.0
 ```
 
 The function has the following parameters:
 
 -   **N**: number of indexed elements.
 -   **x**: first input [`Array`][mdn-array] or [`typed array`][mdn-typed-array].
 -   **strideX**: index increment for `x`.
 -   **y**: second input [`Array`][mdn-array] or [`typed array`][mdn-typed-array].
 -   **strideY**: index increment for `y`.
 
 The `N` and `stride` parameters determine which elements in `x` and `y` are accessed at runtime. For example, to calculate the dot product of every other value in `x` and the first `N` elements of `y` in reverse order,
 
 ```javascript
 var floor = require( '@stdlib/math/base/special/floor' );
 
 var x = [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ];
 var y = [ 1.0, 1.0, 1.0, 1.0, 1.0, 1.0 ];
 
 var N = floor( x.length / 2 );
 
 var z = gdot( N, x, 2, y, -1 );
 // returns 9.0
 ```
 
 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' );
 var floor = require( '@stdlib/math/base/special/floor' );
 
 // 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 N = floor( x0.length / 2 );
 
 var z = gdot( N, x1, -2, y1, 1 );
 // returns 128.0
 ```
 
 #### gdot.ndarray( N, x, strideX, offsetX, y, strideY, offsetY )
 
 Calculates the dot product of `x` and `y` using alternative indexing semantics.
 
 ```javascript
 var x = [ 4.0, 2.0, -3.0, 5.0, -1.0 ];
 var y = [ 2.0, 6.0, -1.0, -4.0, 8.0 ];
 
 var z = gdot.ndarray( x.length, x, 1, 0, y, 1, 0 );
 // returns -5.0
 ```
 
 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 `offsetX` and `offsetY` parameters support indexing semantics based on starting indices. For example, to calculate the dot product of every other value in `x` starting from the second value with the last 3 elements in `y` in reverse order
 
 ```javascript
 var floor = require( '@stdlib/math/base/special/floor' );
 
 var x = [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ];
 var y = [ 7.0, 8.0, 9.0, 10.0, 11.0, 12.0 ];
 
 var N = floor( x.length / 2 );
 
 var z = gdot.ndarray( N, x, 2, 1, y, -1, y.length-1 );
 // returns 128.0
 ```
 
 </section>
 
 <!-- /.usage -->
 
 <section class="notes">
 
 ## Notes
 
 -   If `N <= 0` both functions return `0.0`.
 -   `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. Depending on the environment, the typed versions ([`ddot`][@stdlib/blas/base/ddot], [`sdot`][@stdlib/blas/base/sdot], etc.) are likely to be significantly more performant.
 
 </section>
 
 <!-- /.notes -->
 
 <section class="examples">
 
 ## Examples
 
 <!-- eslint no-undef: "error" -->
 
 ```javascript
 var randu = require( '@stdlib/random/base/randu' );
 var round = require( '@stdlib/math/base/special/round' );
 var Float64Array = require( '@stdlib/array/float64' );
 var Uint8ClampedArray = require( '@stdlib/array/uint8c' );
 var gdot = require( '@stdlib/blas/base/gdot' );
 
 var x;
 var y;
 var i;
 
 x = new Float64Array( 10 );
 y = new Uint8ClampedArray( 10 );
 for ( i = 0; i < x.length; i++ ) {
     x[ i ] = round( randu()*500.0 );
     y[ i ] = round( randu()*255.0 );
 }
 console.log( x );
 console.log( y );
 
 // Compute the dot product:
 var dot = gdot.ndarray( x.length, x, 1, 0, y, -1, y.length-1 );
 console.log( dot );
 ```
 
 </section>
 
 <!-- /.examples -->
 
 <section class="links">
 
 [dot-product]: https://en.wikipedia.org/wiki/Dot_product
 
 [blas]: http://www.netlib.org/blas
 
 [ddot]: http://www.netlib.org/lapack/explore-html/de/da4/group__double__blas__level1.html
 
 [mdn-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Array
 
 [mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray
 
 [@stdlib/blas/base/ddot]: https://www.npmjs.com/package/@stdlib/blas/tree/main/base/ddot
 
 [@stdlib/blas/base/sdot]: https://www.npmjs.com/package/@stdlib/blas/tree/main/base/sdot
 
 </section>
 
 <!-- /.links -->