stdlib-js/math-base-special-dirac-delta

Evaluate the Dirac delta function.

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Dirac Delta

Evaluate the Dirac delta function.

The Dirac delta function may be loosely defined as

$$\delta = \begin{cases} \infty & \textrm{if}\ x = 0 \\ 0 & \textrm{if}\ x \neq 0\end{cases}$$

and is constrained to satisfy the identity

$$\int^{+\infty}_{-\infty} \delta(x)\ dx = 1$$

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

Alternatively,

• To load the package in a website via a script tag without installation and bundlers, use the ES Module available on the esm branch (see README).
• If you are using Deno, visit the deno branch (see README for usage intructions).
• For use in Observable, or in browser/node environments, use the Universal Module Definition (UMD) build available on the umd branch (see README).

The branches.md file summarizes the available branches and displays a diagram illustrating their relationships.

To view installation and usage instructions specific to each branch build, be sure to explicitly navigate to the respective README files on each branch, as linked to above.

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 ] ) );
}

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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 );
    }
}

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See Also

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

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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

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License

See LICENSE.

Copyright

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