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About stdlib...

We believe in a future in which the web is a preferred environment for numerical computation. To help realize this future, we've built stdlib. stdlib is a standard library, with an emphasis on numerical and scientific computation, written in JavaScript (and C) for execution in browsers and in Node.js.

The library is fully decomposable, being architected in such a way that you can swap out and mix and match APIs and functionality to cater to your exact preferences and use cases.

When you use stdlib, you can be absolutely certain that you are using the most thorough, rigorous, well-written, studied, documented, tested, measured, and high-quality code out there.

To join us in bringing numerical computing to the web, get started by checking us out on GitHub, and please consider financially supporting stdlib. We greatly appreciate your continued support!

gnrm2

NPM version Build Status Coverage Status

Calculate the L2-norm of a vector.

The L2-norm is defined as

L2-norm definition.

Usage

To use in Observable,

gnrm2 = require( 'https://cdn.jsdelivr.net/gh/stdlib-js/blas-base-gnrm2@umd/browser.js' )

To vendor stdlib functionality and avoid installing dependency trees for Node.js, you can use the UMD server build:

var gnrm2 = require( 'path/to/vendor/umd/blas-base-gnrm2/index.js' )

To include the bundle in a webpage,

<script type="text/javascript" src="https://cdn.jsdelivr.net/gh/stdlib-js/blas-base-gnrm2@umd/browser.js"></script>

If no recognized module system is present, access bundle contents via the global scope:

<script type="text/javascript">
(function () {
    window.gnrm2;
})();
</script>

gnrm2( N, x, stride )

Computes the L2-norm of a vector x.

var x = [ 1.0, -2.0, 2.0 ];

var z = gnrm2( x.length, x, 1 );
// returns 3.0

The function has the following parameters:

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

The N and stride parameters determine which elements in x are accessed at runtime. For example, to compute the L2-norm of every other element in x,

var x = [ 1.0, 2.0, 2.0, -7.0, -2.0, 3.0, 4.0, 2.0 ];

var z = gnrm2( 4, x, 2 );
// returns 5.0

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

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

var x0 = new Float64Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ] );
var x1 = new Float64Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element

var z = gnrm2( 4, x1, 2 );
// returns 5.0

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

gnrm2.ndarray( N, x, stride, offset )

Computes the L2-norm of a vector using alternative indexing semantics.

var x = [ 1.0, -2.0, 2.0 ];

var z = gnrm2.ndarray( x.length, x, 1, 0 );
// returns 3.0

The function has the following additional parameters:

  • offset: starting index for x.

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 calculate the L2-norm for every other value in x starting from the second value

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

var z = gnrm2.ndarray( 4, x, 2, 1 );
// returns 5.0

Notes

  • If N <= 0, both functions return 0.0.
  • gnrm2() corresponds to the BLAS level 1 function dnrm2 with the exception that this implementation works with any array type, not just Float64Arrays. Depending on the environment, the typed versions (dnrm2, snrm2, etc.) are likely to be significantly more performant.

Examples

<!DOCTYPE html>
<html lang="en">
<body>
<script type="text/javascript" src="https://cdn.jsdelivr.net/gh/stdlib-js/random-array-discrete-uniform@umd/browser.js"></script>
<script type="text/javascript" src="https://cdn.jsdelivr.net/gh/stdlib-js/blas-base-gnrm2@umd/browser.js"></script>
<script type="text/javascript">
(function () {

var opts = {
    'dtype': 'float64'
};
var x = discreteUniform( 10, -100, 100, opts );
console.log( x );

var out = gnrm2( x.length, x, 1 );
console.log( out );

})();
</script>
</body>
</html>

See Also

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.