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

StartFraction 1 Over z EndFraction equals StartFraction z overbar Over z z overbar EndFraction equals StartFraction a Over a squared plus b squared EndFraction minus StartFraction b Over a squared plus b squared EndFraction i period

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() );
}

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 );
    }
}

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>.

See Also

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