Neighborly Package Megalodon

# npm

## @stdlib/math-base-special-cinv

0.0.5 • Public • Published

# inv

Compute the inverse of a complex number.

The inverse (or reciprocal) of a non-zero complex number `z = a + bi` is defined as

## Installation

`npm install @stdlib/math-base-special-cinv`

## 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>.

## 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.

## Keywords

### Install

`npm i @stdlib/math-base-special-cinv`

### Repository

github.com/stdlib-js/math-base-special-cinv

stdlib.io

0

0.0.5

Apache-2.0

48.6 kB

11