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Calculate the L2-norm of a vector.

The L2-norm is defined as

L2-norm definition.


npm install @stdlib/blas-base-gnrm2


var gnrm2 = require( '@stdlib/blas-base-gnrm2' );

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 floor = require( '@stdlib/math-base-special-floor' );

var x = [ 1.0, 2.0, 2.0, -7.0, -2.0, 3.0, 4.0, 2.0 ];
var N = floor( x.length / 2 );

var z = gnrm2( N, 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 floor = require( '@stdlib/math-base-special-floor' );

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 N = floor( x0.length / 2 );

var z = gnrm2( N, 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 floor = require( '@stdlib/math-base-special-floor' );

var x = [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ];
var N = floor( x.length / 2 );

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


  • 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.


var randu = require( '@stdlib/random-base-randu' );
var round = require( '@stdlib/math-base-special-round' );
var Float64Array = require( '@stdlib/array-float64' );
var gnrm2 = require( '@stdlib/blas-base-gnrm2' );

var x;
var i;

x = new Float64Array( 10 );
for ( i = 0; i < x.length; i++ ) {
    x[ i ] = round( randu()*100.0 );
console.log( x );

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

See Also


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.





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