cabs2

Compute the squared absolute value of a double-precision complex floating-point 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( z )

Computes the squared absolute value of a double-precision complex floating-point number.

var Complex128 = require( '@stdlib/complex/float64/ctor' );

var y = cabs2( new Complex128( 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/ctor' );
var discreteUniform = require( '@stdlib/random/base/discrete-uniform' ).factory;
var cabs2 = require( '@stdlib/math/base/special/cabs2' );

// Create a PRNG to generate uniformly distributed pseudorandom integers:
var rand = discreteUniform( -50, 50 );

// Compute the squared absolute value for a set of random numbers...
var z;
var i;
for ( i = 0; i < 100; i++ ) {
    z = new Complex128( rand(), rand() );
    console.log( 'cabs2(%s) = %d', z.toString(), cabs2( z ) );
}

C APIs

Usage

#include "stdlib/math/base/special/cabs2.h"

stdlib_base_cabs2( z )

Computes the squared absolute value of a double-precision complex floating-point number.

#include "stdlib/complex/float64/ctor.h"

stdlib_complex128_t z = stdlib_complex128( 5.0, 3.0 );

double y = stdlib_base_cabs2( z );
// returns 34.0

The function accepts the following arguments:

z: [in] stdlib_complex128_t input value.

double stdlib_base_cabs2( const stdlib_complex128_t z );

Examples

#include "stdlib/math/base/special/cabs2.h"
#include "stdlib/complex/float64/ctor.h"
#include "stdlib/complex/float64/reim.h"
#include <stdio.h>

int main( void ) {
    const stdlib_complex128_t x[] = {
        stdlib_complex128( 3.14, 1.0 ),
        stdlib_complex128( -3.14, -1.0 ),
        stdlib_complex128( 0.0, 0.0 ),
        stdlib_complex128( 0.0/0.0, 0.0/0.0 )
    };

    stdlib_complex128_t v;
    double re;
    double im;
    double y;
    int i;
    for ( i = 0; i < 4; i++ ) {
        v = x[ i ];
        y = stdlib_base_cabs2( v );
        stdlib_complex128_reim( v, &re, &im );
        printf( "f(%lf + %lf) = %lf\n", re, im, y );
    }
}