divide

Divide two complex numbers.

Usage

var cdiv = require( '@stdlib/math/base/complex/divide' );

cdiv( [out,] re1, im1, re2, im2 )

Divides two complex numbers where each complex number is comprised of a real component re and an imaginary component im.

var v = cdiv( -13.0, -1.0, -2.0, 1.0 );
// returns [ 5.0, 3.0 ]

By default, the function returns real and imaginary components as a two-element array. To avoid unnecessary memory allocation, the function supports providing an output (destination) object.

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

var out = new Float64Array( 2 );

var v = cdiv( out, -13.0, -1.0, -2.0, 1.0 );
// returns <Float64Array>[ 5.0, 3.0 ]

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

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 cdiv = require( '@stdlib/math/base/complex/divide' );

var re;
var im;
var z1;
var z2;
var z3;
var o;
var i;

for ( i = 0; i < 100; i++ ) {
    re = round( randu()*100.0 ) - 50.0;
    im = round( randu()*100.0 ) - 50.0;
    z1 = new Complex128( re, im );

    re = round( randu()*100.0 ) - 50.0;
    im = round( randu()*100.0 ) - 50.0;
    z2 = new Complex128( re, im );

    o = cdiv( real(z1), imag(z1), real(z2), imag(z2) );
    z3 = new Complex128( o[ 0 ], o[ 1 ] );

    console.log( '(%s) / (%s) = %s', z1.toString(), z2.toString(), z3.toString() );
}

References

  • Smith, Robert L. 1962. "Algorithm 116: Complex Division." Commun. ACM 5 (8). New York, NY, USA: ACM: 435. doi:10.1145/368637.368661.
  • Stewart, G. W. 1985. "A Note on Complex Division." ACM Trans. Math. Softw. 11 (3). New York, NY, USA: ACM: 238–41. doi:10.1145/214408.214414.
  • Priest, Douglas M. 2004. "Efficient Scaling for Complex Division." ACM Trans. Math. Softw. 30 (4). New York, NY, USA: ACM: 389–401. doi:10.1145/1039813.1039814.
  • Baudin, Michael, and Robert L. Smith. 2012. "A Robust Complex Division in Scilab." arXiv abs/1210.4539 [cs.MS] (October): 1–25. <https://arxiv.org/abs/1210.4539>.