time-to-botec/squiggle/node_modules/@stdlib/math/base/special/cabs2/README.md

abs2

Compute the squared absolute value of a complex number.

The absolute value of a complex number is defined as

which corresponds to the length of a vector from the origin to a complex value plotted in the complex plane.

Usage

var cabs2 = require( '@stdlib/math/base/special/cabs2' );

cabs2( re, im )

Computes the squared absolute value of a complex number comprised of a real component re and an imaginary component im.

var y = cabs2( 5.0, 3.0 );
// returns 34.0

Notes

• Be careful to avoid overflow and underflow.
• Depending on the environment, this function may have better performance than computing the absolute value of a complex number and then squaring. Hence, where appropriate, consider using cabs2() over cabs().

Examples

var Complex128 = require( '@stdlib/complex/float64' );
var randu = require( '@stdlib/random/base/randu' );
var round = require( '@stdlib/math/base/special/round' );
var real = require( '@stdlib/complex/real' );
var imag = require( '@stdlib/complex/imag' );
var cabs2 = require( '@stdlib/math/base/special/cabs2' );

var re;
var im;
var z;
var i;

for ( i = 0; i < 100; i++ ) {
    re = round( randu()*100.0 ) - 50.0;
    im = round( randu()*100.0 ) - 50.0;
    z = new Complex128( re, im );
    console.log( 'cabs2(%s) = %d', z.toString(), cabs2( real(z), imag(z) ) );
}