dznrm2

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

Installation

npm install @stdlib/blas-base-dznrm2

Usage

var dznrm2 = require( '@stdlib/blas-base-dznrm2' );

dznrm2( N, x, strideX )

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

var Complex128Array = require( '@stdlib/array-complex128' );

var x = new Complex128Array( [ 0.3, 0.1, 0.5, 0.0, 0.0, 0.5, 0.0, 0.2 ] );

var norm = dznrm2( 4, x, 1 );
// returns ~0.8

The function has the following parameters:

• N: number of indexed elements.
• x: input Complex128Array.
• strideX: index increment for x.

The N and stride parameters determine which elements in the strided array are accessed at runtime. For example, to traverse every other value,

var Complex128Array = require( '@stdlib/array-complex128' );

var x = new Complex128Array( [ -2.0, 1.0, 3.0, -5.0, 4.0, 0.0, -1.0, -3.0 ] );

var norm = dznrm2( 2, x, 2 );
// returns ~4.6

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

var Complex128Array = require( '@stdlib/array-complex128' );

// Initial array:
var x0 = new Complex128Array( [ 1.0, -2.0, 3.0, -4.0, 5.0, -6.0 ] );

// Create an offset view:
var x1 = new Complex128Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element

// Compute the L2-norm:
var norm = dznrm2( 2, x1, 1 );
// returns ~9.3

dznrm2.ndarray( N, x, strideX, offset )

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

var Complex128Array = require( '@stdlib/array-complex128' );

var x = new Complex128Array( [ 0.3, 0.1, 0.5, 0.0, 0.0, 0.5, 0.0, 0.2 ] );

var norm = dznrm2.ndarray( 4, x, 1, 0 );
// returns ~0.8

The function has the following additional parameters:

• offsetX: 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 start from the second index,

var Complex128Array = require( '@stdlib/array-complex128' );

var x = new Complex128Array( [ 1.0, -2.0, 3.0, -4.0, 5.0, -6.0 ] );

var norm = dznrm2.ndarray( 2, x, 1, 1 );
// returns ~9.3

Notes

• If N <= 0, both functions return 0.0.
• dznrm2() corresponds to the BLAS level 1 function dznrm2.

Examples

var discreteUniform = require( '@stdlib/random-base-discrete-uniform' );
var filledarrayBy = require( '@stdlib/array-filled-by' );
var Complex128 = require( '@stdlib/complex-float64-ctor' );
var dznrm2 = require( '@stdlib/blas-base-dznrm2' );

function rand() {
    return new Complex128( discreteUniform( 0, 10 ), discreteUniform( -5, 5 ) );
}

var x = filledarrayBy( 10, 'complex128', rand );
console.log( x.toString() );

// Computes the L2-norm:
var norm = dznrm2( x.length, x, 1 );
console.log( norm );

C APIs

Usage

#include "stdlib/blas/base/dznrm2.h"

c_dznrm2( N, *X, strideX )

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

const double X[] = { 0.3, 0.1, 0.5, 0.0, 0.0, 0.5, 0.0, 0.2 };

double norm = c_dznrm2( 4, (void *)X, 1 );
// returns 0.8

The function accepts the following arguments:

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

double c_dznrm2( const CBLAS_INT N, const void *X, const CBLAS_INT strideX );

c_dznrm2_ndarray( N, *X, strideX, offsetX )

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

const double X[] = { 0.3, 0.1, 0.5, 0.0, 0.0, 0.5, 0.0, 0.2 };

double norm = c_dznrm2_ndarray( 4, (void *)X, 1, 0 );
// returns 0.8

The function accepts the following arguments:

• N: [in] CBLAS_INT number of indexed elements.
• X: [in] void* input array.
• strideX: [in] CBLAS_INT index increment for X.
• offsetX: [in] CBLAS_INT starting index for X.

double c_dznrm2_ndarray( const CBLAS_INT N, const void *X, const CBLAS_INT strideX, const CBLAS_INT offsetX );

Examples

#include "stdlib/blas/base/dznrm2.h"
#include <stdio.h>

int main( void ) {
    // Create a strided array of interleaved real and imaginary components:
    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 = 4;

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

    // Compute the L2-norm:
    double norm = c_dznrm2( N, (void *)X, strideX );

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

    // Compute the L2-norm using alternative indexing semantics:
    norm = c_dznrm2_ndarray( N, (void *)X, -strideX, N-1 );

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

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.

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.