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

Compute the inverse of a complex number.
https://github.com/stdlib-js/math-base-special-cinv

arithmetic cinv cmplx complex inv inverse javascript math mathematics node node-js nodejs number reciprocal stdlib

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Compute the inverse of a complex number.

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README 

        



  

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# cinv



[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url] 



> Compute the inverse of a double-precision complex floating-point number.



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





    Complex Inverse

    





## Installation



```bash

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

```



Alternatively,



-   To load the package in a website via a `script` tag without installation and bundlers, use the [ES Module][es-module] available on the [`esm`][esm-url] branch (see [README][esm-readme]).

-   If you are using Deno, visit the [`deno`][deno-url] branch (see [README][deno-readme] for usage intructions).

-   For use in Observable, or in browser/node environments, use the [Universal Module Definition (UMD)][umd] build available on the [`umd`][umd-url] branch (see [README][umd-readme]).



The [branches.md][branches-url] 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



```javascript

var cinv = require( '@stdlib/math-base-special-cinv' );

```



#### cinv( z )



Computes the inverse of a double-precision complex floating-point number.



```javascript

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

var real = require( '@stdlib/complex-float64-real' );

var imag = require( '@stdlib/complex-float64-imag' );



var v = cinv( new Complex128( 2.0, 4.0 ) );

// returns 



var re = real( v );

// returns 0.1



var im = imag( v );

// returns -0.2

```



## Examples



```javascript

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

var uniform = require( '@stdlib/random-base-uniform' );

var cinv = require( '@stdlib/math-base-special-cinv' );



var z1;

var z2;

var i;



for ( i = 0; i < 100; i++ ) {

    z1 = new Complex128( uniform( -50.0, 50.0 ), uniform( -50.0, 50.0 ) );

    z2 = cinv( z1 );



    console.log( '1.0 / (%s) = %s', z1.toString(), z2.toString() );

}

```



* * *



## C APIs



### Usage



```c

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

```



#### stdlib_base_cinv( z )



Computes the inverse of a double-precision complex floating-point number.



```c

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

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

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



stdlib_complex128_t z = stdlib_complex128( 2.0, 4.0 );



stdlib_complex128_t out = stdlib_base_cinv( z );



double re = stdlib_complex128_real( out );

// returns 0.1



double im = stdlib_complex128_imag( out );

// returns -0.2

```



The function accepts the following arguments:



-   **z**: `[in] stdlib_complex128_t` input value.



```c

stdlib_complex128_t stdlib_base_cinv( const stdlib_complex128_t z );

```



### Examples



```c

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

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

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

#include 



int main() {

    const stdlib_complex128_t x[] = {

        stdlib_complex128( 3.14, 1.5 ),

        stdlib_complex128( -3.14, -1.5 ),

        stdlib_complex128( 0.0, 0.0 ),

        stdlib_complex128( 0.0/0.0, 0.0/0.0 )

    };



    stdlib_complex128_t v;

    stdlib_complex128_t y;

    double re1;

    double im1;

    double re2;

    double im2;

    int i;

    for ( i = 0; i < 4; i++ ) {

        v = x[ i ];

        y = stdlib_base_cinv( v );

        stdlib_complex128_reim( v, &re1, &im1 );

        stdlib_complex128_reim( y, &re2, &im2 );

        printf( "cinv(%lf + %lfi) = %lf + %lfi\n", re1, im1, re2, im2 );

    }

}

```



* * *



## References



-   Smith, Robert L. 1962. "Algorithm 116: Complex Division." _Commun. ACM_ 5 (8). New York, NY, USA: ACM: 435. doi:[10.1145/368637.368661][@smith:1962a].

-   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][@stewart:1985a].

-   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][@priest:2004a].

-   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>][@baudin:2012a].



* * *



## See Also



-   [`@stdlib/math-base/ops/cdiv`][@stdlib/math/base/ops/cdiv]: divide two complex numbers.



* * *



## Notice



This package is part of [stdlib][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][stdlib], see the main project [repository][stdlib].



#### Community



[![Chat][chat-image]][chat-url]



---



## License



See [LICENSE][stdlib-license].



## Copyright



Copyright © 2016-2024. The Stdlib [Authors][stdlib-authors].



[npm-image]: http://img.shields.io/npm/v/@stdlib/math-base-special-cinv.svg

[npm-url]: https://npmjs.org/package/@stdlib/math-base-special-cinv



[test-image]: https://github.com/stdlib-js/math-base-special-cinv/actions/workflows/test.yml/badge.svg?branch=main

[test-url]: https://github.com/stdlib-js/math-base-special-cinv/actions/workflows/test.yml?query=branch:main



[coverage-image]: https://img.shields.io/codecov/c/github/stdlib-js/math-base-special-cinv/main.svg

[coverage-url]: https://codecov.io/github/stdlib-js/math-base-special-cinv?branch=main



[chat-image]: https://img.shields.io/gitter/room/stdlib-js/stdlib.svg

[chat-url]: https://app.gitter.im/#/room/#stdlib-js_stdlib:gitter.im



[stdlib]: https://github.com/stdlib-js/stdlib



[stdlib-authors]: https://github.com/stdlib-js/stdlib/graphs/contributors



[umd]: https://github.com/umdjs/umd

[es-module]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Modules



[deno-url]: https://github.com/stdlib-js/math-base-special-cinv/tree/deno

[deno-readme]: https://github.com/stdlib-js/math-base-special-cinv/blob/deno/README.md

[umd-url]: https://github.com/stdlib-js/math-base-special-cinv/tree/umd

[umd-readme]: https://github.com/stdlib-js/math-base-special-cinv/blob/umd/README.md

[esm-url]: https://github.com/stdlib-js/math-base-special-cinv/tree/esm

[esm-readme]: https://github.com/stdlib-js/math-base-special-cinv/blob/esm/README.md

[branches-url]: https://github.com/stdlib-js/math-base-special-cinv/blob/main/branches.md



[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/math-base-special-cinv/main/LICENSE



[@smith:1962a]: https://doi.org/10.1145/368637.368661



[@stewart:1985a]: https://doi.org/10.1145/214408.214414



[@priest:2004a]: https://doi.org/10.1145/1039813.1039814



[@baudin:2012a]: https://arxiv.org/abs/1210.4539



[@stdlib/math/base/ops/cdiv]: https://github.com/stdlib-js/math-base-ops-cdiv