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gasum

Compute the sum of absolute values (L1 norm).

The L1 norm is defined as

$$\|\mathbf{x}\|_1 = \sum_{i=0}^{n-1} \vert x_i \vert$$

Installation

npm install @stdlib/blas-base-gasum

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

gasum( N, x, stride )

Computes the sum of absolute values.

var x = [ -2.0, 1.0, 3.0, -5.0, 4.0, 0.0, -1.0, -3.0 ];

var sum = gasum( x.length, x, 1 );
// returns 19.0

The function has the following parameters:

• N: number of indexed elements.
• x: input Array or typed array.
• stride: index increment.

The N and stride parameters determine which elements in x are used to compute the sum. For example, to sum every other value,

var x = [ -2.0, 1.0, 3.0, -5.0, 4.0, 0.0, -1.0, -3.0 ];

var sum = gasum( 4, x, 2 );
// returns 10.0

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

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

// Initial array...
var x0 = new Float64Array( [ 1.0, -2.0, 3.0, -4.0, 5.0, -6.0 ] );

// Create an offset view...
var x1 = new Float64Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element

// Sum every other value...
var sum = gasum( 3, x1, 2 );
// returns 12.0

If either N or stride is less than or equal to 0, the function returns 0.

gasum.ndarray( N, x, stride, offset )

Computes the sum of absolute values using alternative indexing semantics.

var x = [ -2.0, 1.0, 3.0, -5.0, 4.0, 0.0, -1.0, -3.0 ];

var sum = gasum.ndarray( x.length, x, 1, 0 );
// returns 19.0

The function has the following additional parameters:

• offset: starting index.

While typed array views mandate a view offset based on the underlying buffer, the offset parameter supports indexing semantics based on a starting index. For example, to sum the last three elements,

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

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

var sum = gasum.ndarray( 3, x, 1, x.length-3 );
// returns 15.0

// Using a negative stride to sum from the last element:
sum = gasum.ndarray( 3, x, -1, x.length-1 );
// returns 15.0

Notes

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

Examples

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

var opts = {
    'dtype': 'generic'
};
var x = discreteUniform( 10, -100, 100, opts );
console.log( x );

var y = gasum( x.length, x, 1 );
console.log( y );

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See Also

• @stdlib/blas-base/dasum: compute the sum of absolute values (L1 norm).
• @stdlib/blas-base/sasum: compute the sum of absolute values (L1 norm).

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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

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License

See LICENSE.

Copyright

Copyright © 2016-2024. The Stdlib Authors.