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cinv

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

Installation

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 available on the esm branch (see README).
• If you are using Deno, visit the deno branch (see README for usage intructions).
• For use in Observable, or in browser/node environments, use the Universal Module Definition (UMD) build available on the umd branch (see README).

The branches.md 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

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

cinv( z )

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

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 <Complex128>

var re = real( v );
// returns 0.1

var im = imag( v );
// returns -0.2

Examples

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() );
}

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C APIs

Usage

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

stdlib_base_cinv( z )

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

#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.

stdlib_complex128_t stdlib_base_cinv( const stdlib_complex128_t z );

Examples

#include "stdlib/math/base/special/cinv.h"
#include "stdlib/complex/float64/ctor.h"
#include "stdlib/complex/float64/reim.h"
#include <stdio.h>

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 );
    }
}

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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>.

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See Also

• @stdlib/math-base/ops/cdiv: divide two complex numbers.

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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.

Community

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License

See LICENSE.

Copyright

Copyright © 2016-2024. The Stdlib Authors.