inv
Compute the inverse of a complex number.
The inverse (or reciprocal) of a non-zero complex number z = a + bi is defined as
Usage
var cinv = require( '@stdlib/math/base/special/cinv' );
cinv( [out,] re1, im1 )
Computes the inverse of a complex number comprised of a real component re and an imaginary component im.
var v = cinv( 2.0, 4.0 );
// returns [ 0.1, -0.2 ]
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 = cinv( out, 2.0, 4.0 );
// returns <Float64Array>[ 0.1, -0.2 ]
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 cinv = require( '@stdlib/math/base/special/cinv' );
var re;
var im;
var z1;
var z2;
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 );
o = cinv( real(z1), imag(z1) );
z2 = new Complex128( o[ 0 ], o[ 1 ] );
console.log( '1.0 / (%s) = %s', z1.toString(), z2.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>.