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gdot

Calculate the dot product of two vectors.

The dot product (or scalar product) is defined as

$$\mathbf{x}\cdot\mathbf{y} = \sum_{i=0}^{N-1} x_i y_i = x_0 y_0 + x_1 y_1 + \ldots + x_{N-1} y_{N-1}$$

Installation

npm install @stdlib/blas-base-gdot

Alternatively,

To load the package in a website via a script tag without installation and bundlers, use the ES Module available on the esm branch (see README).
If you are using Deno, visit the deno branch (see README for usage intructions).
For use in Observable, or in browser/node environments, use the Universal Module Definition (UMD) build available on the umd branch (see README).

The branches.md file summarizes the available branches and displays a diagram illustrating their relationships.

To view installation and usage instructions specific to each branch build, be sure to explicitly navigate to the respective README files on each branch, as linked to above.

Usage

var gdot = require( '@stdlib/blas-base-gdot' );

gdot( N, x, strideX, y, strideY )

Calculates the dot product of vectors x and y.

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 or typed array.
strideX: index increment for x.
y: second input Array or typed array.
strideY: index increment for y.

The N and stride parameters determine which elements in the strided arrays 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,

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 z = gdot( 3, x, 2, y, -1 );
// returns 9.0

Note that indexing is relative to the first index. To introduce an offset, use typed array views.

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 = gdot( 3, 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.

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 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 dot product of every other value in x starting from the second value with the last 3 elements in y in reverse order

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 z = gdot.ndarray( 3, x, 2, 1, y, -1, y.length-1 );
// returns 128.0

Notes

If N <= 0 both functions return 0.0.
gdot() corresponds to the BLAS level 1 function ddot with the exception that this implementation works with any array type, not just Float64Arrays. Depending on the environment, the typed versions (ddot, sdot, etc.) are likely to be significantly more performant.

Examples

var discreteUniform = require( '@stdlib/random-array-discrete-uniform' );
var gdot = require( '@stdlib/blas-base-gdot' );

var opts = {
    'dtype': 'float64'
};
var x = discreteUniform( 10, 0, 500, opts );
console.log( x );

var y = discreteUniform( x.length, 0, 255, opts );
console.log( y );

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

Notice

This package is part of 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, see the main project repository.

Community

License

See LICENSE.

stdlib-js/blas-base-gdot