Dirac Delta

Evaluate the Dirac delta function.

The Dirac delta function may be loosely defined as

and is constrained to satisfy the identity

Note that the Dirac delta function is not a function in the traditional sense, as any real-valued function which is zero everywhere except at a single point, must have an integral equal to 0.

Installation

npm install @stdlib/math-base-special-dirac-delta

Usage

var diracDelta = require( '@stdlib/math-base-special-dirac-delta' );

diracDelta( x )

Evaluates the Dirac delta function.

var v = diracDelta( 0.0 );
// returns Infinity

v = diracDelta( 3.14 );
// returns 0.0

v = diracDelta( NaN );
// returns NaN

Examples

var linspace = require( '@stdlib/array-base-linspace' );
var diracDelta = require( '@stdlib/math-base-special-dirac-delta' );

var x = linspace( -1.0, 1.0, 101 );

var i;
for ( i = 0; i < x.length; i++ ) {
    console.log( 'dirac(%d) = %d', x[ i ], diracDelta( x[ i ] ) );
}

C APIs

Usage

#include "stdlib/math/base/special/dirac_delta.h"

stdlib_base_dirac_delta( x )

Evaluates the Dirac delta function.

double x = stdlib_base_dirac_delta( 0.0 );
// returns Infinity

x = stdlib_base_dirac_delta( 3.14 );
// returns 0.0

The function accepts the following arguments:

• x: [in] double input value.

double stdlib_base_dirac_delta( const double x );

Examples

#include "stdlib/math/base/special/dirac_delta.h"
#include <stdlib.h>
#include <stdio.h>

int main( void ) {
    const double x[] = { -1.0, -0.5, 0.0, 0.5, 1.0, 3.14, 2.0 };
    
    double v;
    int i;
    for ( i = 0; i < 7; i++ ) {
        v = stdlib_base_dirac_delta( x[ i ] );
        printf( "dirac(%lf) = %lf\n", x[ i ], v );
    }
}

See Also

• @stdlib/math-base/special/kronecker-delta: evaluate the Kronecker delta.

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 © 2016-2024. The Stdlib Authors.