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dnrm2

README.md

dnrm2

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

The L2-norm is defined as

L2-norm definition.

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