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    @stdlib/math-base-special-cinv
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    0.0.5 • Public • Published

    inv

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    Compute the inverse of a complex number.

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

    Complex Inverse

    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.

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    License

    See LICENSE.

    Copyright

    Copyright © 2016-2021. The Stdlib Authors.

    Install

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

    Homepage

    stdlib.io

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    Version

    0.0.5

    License

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    48.6 kB

    Total Files

    11

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    Collaborators

    • stdlib-bot
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