cabs2

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

The absolute value of a complex number is defined as

|a + bi| = \sqrt{a^2 + b^2}

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

Installation

npm install @stdlib/math-base-special-cabs2

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 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 );
    }
}

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.