time-to-botec/squiggle/node_modules/@stdlib/math/base/special/fresnel/README.md
NunoSempere b6addc7f05 feat: add the node modules
Necessary in order to clearly see the squiggle hotwiring.
2022-12-03 12:44:49 +00:00

3.1 KiB

fresnel

Compute the Fresnel integrals S(x) and C(x).

The Fresnel integrals are defined as

Fresnel integral

Some sources define the Fresnel integrals using t2 for the argument of the sine and cosine. To get these functions, multiply the computed integrals by √(π/2) and multiply the argument x by √(2/π).

Usage

var fresnel = require( '@stdlib/math/base/special/fresnel' );

fresnel( [out,] x )

Simultaneously computes the Fresnel integrals S(x) and C(x).

var v = fresnel( 0.0 );
// returns [ ~0.0, ~0.0 ]

v = fresnel( 1.0 );
// returns [ ~0.438, ~0.780 ]

v = fresnel( Infinity );
// returns [ ~0.5, ~0.5 ]

v = fresnel( -Infinity );
// returns [ ~-0.5, ~-0.5 ]

v = fresnel( NaN );
// returns [ NaN, NaN ]

By default, the function returns the S(x) and C(x) as a two-element array. To avoid extra memory allocation, the function supports providing an output (destination) object.

var Float64Array = require( '@stdlib/array/float64' );

var out = new Float64Array( 2 );

var v = fresnel( out, 0.0 );
// returns <Float64Array>[ ~0.0, ~0.0 ]

var bool = ( v === out );
// returns true

Examples

var linspace = require( '@stdlib/array/linspace' );
var fresnel = require( '@stdlib/math/base/special/fresnel' );

var x = linspace( 0.0, 10.0, 100 );
var i;

for ( i = 0; i < x.length; i++ ) {
    console.log( fresnel( x[ i ] ) );
}