dnrm2

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

The L2-norm is defined as

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 N = 3;

var z = dnrm2( N, 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 floor = require( '@stdlib/math/base/special/floor' );

var x = new Float64Array( [ 1.0, 2.0, 2.0, -7.0, -2.0, 3.0, 4.0, 2.0 ] );
var N = floor( x.length / 2 );

var z = dnrm2( 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 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 = 4;

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

If either N or stride 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 N = 3;

var z = dnrm2.ndarray( N, 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 floor = require( '@stdlib/math/base/special/floor' );

var x = new Float64Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ] );
var N = floor( x.length / 2 );

var z = dnrm2.ndarray( N, 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 randu = require( '@stdlib/random/base/randu' );
var round = require( '@stdlib/math/base/special/round' );
var Float64Array = require( '@stdlib/array/float64' );
var dnrm2 = require( '@stdlib/blas/base/dnrm2' );

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