gnrm2

Calculate the L2-norm of a vector.

The L2-norm is defined as

Installation

npm install @stdlib/blas-base-gnrm2

Usage

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

gnrm2( N, x, stride )

Computes the L2-norm of a vector.

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: stride length.

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

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 N 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.

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 the strided array 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.
• Both functions support array-like objects having getter and setter accessors for array element access (e.g., @stdlib/array-base/accessor).

Examples

var discreteUniform = require( '@stdlib/random-array-discrete-uniform' );
var gnrm2 = require( '@stdlib/blas-base-gnrm2' );

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

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

References

• Blue, James L. 1978. "A Portable Fortran Program to Find the Euclidean Norm of a Vector." ACM Transactions on Mathematical Software 4 (1). New York, NY, USA: Association for Computing Machinery: 15–23. doi:10.1145/355769.355771.
• Anderson, Edward. 2017. "Algorithm 978: Safe Scaling in the Level 1 BLAS." ACM Transactions on Mathematical Software 44 (1). New York, NY, USA: Association for Computing Machinery: 1–28. doi:10.1145/3061665.

See Also

• @stdlib/blas-base/dnrm2: calculate the L2-norm of a double-precision floating-point vector.
• @stdlib/blas-base/snrm2: calculate the L2-norm of a single-precision floating-point vector.

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.

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License

See LICENSE.

Copyright

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