dnrm2

Calculate the L2-norm of a double-precision floating-point vector.

The L2-norm is defined as

Installation

npm install @stdlib/blas-base-dnrm2

Usage

var dnrm2 = require( '@stdlib/blas-base-dnrm2' );

dnrm2( N, x, stride )

Computes the L2-norm of a double-precision floating-point vector x.

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

var x = new Float64Array( [ 1.0, -2.0, 2.0 ] );

var z = dnrm2( 3, x, 1 );
// returns 3.0

The function has the following parameters:

• N: number of indexed elements.
• x: input Float64Array.
• 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 Float64Array = require( '@stdlib/array-float64' );

var x = new Float64Array( [ 1.0, 2.0, 2.0, -7.0, -2.0, 3.0, 4.0, 2.0 ] );

var z = dnrm2( 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 = dnrm2( 4, x1, 2 );
// returns 5.0

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

dnrm2.ndarray( N, x, stride, offset )

Computes the L2-norm of a double-precision floating-point vector using alternative indexing semantics.

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

var x = new Float64Array( [ 1.0, -2.0, 2.0 ] );

var z = dnrm2.ndarray( 3, 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 Float64Array = require( '@stdlib/array-float64' );

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

var z = dnrm2.ndarray( 4, x, 2, 1 );
// returns 5.0

Notes

• If N <= 0, both functions return 0.0.
• dnrm2() corresponds to the BLAS level 1 function dnrm2.

Examples

var discreteUniform = require( '@stdlib/random-array-discrete-uniform' );
var dnrm2 = require( '@stdlib/blas-base-dnrm2' );

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

var out = dnrm2( x.length, x, 1 );
console.log( out );

C APIs

Usage

#include "stdlib/blas/base/dnrm2.h"

c_dnrm2( N, *X, stride )

Computes the L2-norm of a double-precision floating-point vector.

const double x[] = { 1.0, -2.0, 2.0 };

double v = c_dnrm2( 3, x, 1 );
// returns 3.0

The function accepts the following arguments:

• N: [in] CBLAS_INT number of indexed elements.
• X: [in] double* input array.
• stride: [in] CBLAS_INT index increment for X.

double c_dnrm2( const CBLAS_INT N, const double *X, const CBLAS_INT stride );

c_dnrm2_ndarray( N, *X, stride, offset )

Computes the L2-norm of a double-precision floating-point vector using alternative indexing semantics.

const double x[] = { 1.0, -2.0, 2.0 };

double v = c_dnrm2_ndarray( 3, x, -1, 2 );
// returns 3.0

The function accepts the following arguments:

• N: [in] CBLAS_INT number of indexed elements.
• X: [in] double* input array.
• stride: [in] CBLAS_INT index increment for X.
• offset: [in] CBLAS_INT starting index for X.

double c_dnrm2_ndarray( const CBLAS_INT N, const double *X, const CBLAS_INT stride, const CBLAS_INT offset );

Examples

#include "stdlib/blas/base/dnrm2.h"
#include <stdio.h>

int main( void ) {
    // Create a strided array:
    const double x[] = { 1.0, -2.0, 3.0, -4.0, 5.0, -6.0, 7.0, -8.0 };

    // Specify the number of elements:
    const int N = 8;

    // Specify a stride:
    const int strideX = 1;

    // Compute the L2-norm:
    double l2 = c_dnrm2( N, x, strideX );

    // Print the result:
    printf( "L2-norm: %lf\n", l2 );

    // Compute the L2-norm:
    l2 = c_dnrm2_ndarray( N, x, -strideX, N-1 );

    // Print the result:
    printf( "L2-norm: %lf\n", l2 );
}

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/gnrm2: calculate the L2-norm of a 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.

Community

License

See LICENSE.

Copyright

Copyright © 2016-2026. The Stdlib Authors.