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cinvf

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

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

$${\frac {1}{z}}=\frac{\bar{z}}{z{\bar{z}}} = \frac{a}{a^{2}+b^{2}} - \frac{b}{a^2+b^2}i.$$

Installation

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

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

cinvf( z )

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

var Complex64 = require( '@stdlib/complex-float32-ctor' );
var realf = require( '@stdlib/complex-float32-real' );
var imagf = require( '@stdlib/complex-float32-imag' );

var v = cinvf( new Complex64( 2.0, 4.0 ) );
// returns <Complex64>

var re = realf( v );
// returns ~0.1

var im = imagf( v );
// returns ~-0.2

Examples

var Complex64Array = require( '@stdlib/array-complex64' );
var uniform = require( '@stdlib/random-array-uniform' );
var logEachMap = require( '@stdlib/console-log-each-map' );
var cinvf = require( '@stdlib/math-base-special-cinvf' );

// Create an array of random numbers:
var arr = new Complex64Array( uniform( 200, -100.0, 100.0 ) );

// Compute the inverse of each number in the array:
logEachMap( '1.0 / (%s) = %s', arr, cinvf );

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C APIs

Usage

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

stdlib_base_cinvf( z )

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

#include "stdlib/complex/float32/ctor.h"
#include "stdlib/complex/float32/real.h"
#include "stdlib/complex/float32/imag.h"

stdlib_complex64_t z = stdlib_complex64( 2.0f, 4.0f );

stdlib_complex64_t out = stdlib_base_cinvf( z );

float re = stdlib_complex64_real( out );
// returns 0.1f

float im = stdlib_complex64_imag( out );
// returns -0.2f

The function accepts the following arguments:

• z: [in] stdlib_complex64_t input value.

stdlib_complex64_t stdlib_base_cinvf( const stdlib_complex64_t z );

Examples

#include "stdlib/math/base/special/cinvf.h"
#include "stdlib/complex/float32/ctor.h"
#include "stdlib/complex/float32/reim.h"
#include <stdio.h>

int main( void ) {
    const stdlib_complex64_t x[] = {
        stdlib_complex64( 3.14f, 1.5f ),
        stdlib_complex64( -3.14f, -1.5f ),
        stdlib_complex64( 0.0f, 0.0f ),
        stdlib_complex64( 0.0f/0.0f, 0.0f/0.0f )
    };

    stdlib_complex64_t v;
    stdlib_complex64_t y;
    float re1;
    float im1;
    float re2;
    float im2;
    int i;
    for ( i = 0; i < 4; i++ ) {
        v = x[ i ];
        y = stdlib_base_cinvf( v );
        stdlib_complex64_reim( v, &re1, &im1 );
        stdlib_complex64_reim( y, &re2, &im2 );
        printf( "cinvf(%f + %fi) = %f + %fi\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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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 © 2016-2025. The Stdlib Authors.