Divide two complex numbers.
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> Divide two double-precision complex floating-point numbers.
``bash`
npm install @stdlib/math-base-ops-cdiv
`javascript`
var cdiv = require( '@stdlib/math-base-ops-cdiv' );
#### cdiv( z1, z2 )
Divides two double-precision complex floating-point numbers.
`javascript
var Complex128 = require( '@stdlib/complex-float64-ctor' );
var real = require( '@stdlib/complex-float64-real' );
var imag = require( '@stdlib/complex-float64-imag' );
var z1 = new Complex128( -13.0, -1.0 );
var z2 = new Complex128( -2.0, 1.0 );
var v = cdiv( z1, z2 );
// returns
var re = real( v );
// returns 5.0
var im = imag( v );
// returns 3.0
`
`javascript
var Complex128 = require( '@stdlib/complex-float64-ctor' );
var discreteUniform = require( '@stdlib/random-base-discrete-uniform' );
var real = require( '@stdlib/complex-float64-real' );
var imag = require( '@stdlib/complex-float64-imag' );
var cdiv = require( '@stdlib/math-base-ops-cdiv' );
function randomComplex() {
var re = discreteUniform( -50, 50 );
var im = discreteUniform( -50, 50 );
return new Complex128( re, im );
}
var z1;
var z2;
var z3;
var i;
for ( i = 0; i < 100; i++ ) {
z1 = randomComplex();
z2 = randomComplex();
z3 = cdiv( z1, z2 );
console.log( '(%s) / (%s) = %s', z1.toString(), z2.toString(), z3.toString() );
}
`
*
`c`
#include "stdlib/math/base/ops/cdiv.h"
#### stdlib_base_cdiv( z1, z2 )
Divides two double-precision complex floating-point numbers.
`c
#include "stdlib/complex/float64/ctor.h"
#include "stdlib/complex/float64/real.h"
#include "stdlib/complex/float64/imag.h"
stdlib_complex128_t z1 = stdlib_complex128( -13.0, -1.0 );
stdlib_complex128_t z2 = stdlib_complex128( -2.0, 1.0 );
stdlib_complex128_t out = stdlib_base_cdiv( z1, z2 );
double re = stdlib_complex128_real( out );
// returns 5.0
double im = stdlib_complex128_imag( out );
// returns 3.0
`
The function accepts the following arguments:
- z1: [in] stdlib_complex128_t input value.[in] stdlib_complex128_t
- z2: input value.
`c`
stdlib_complex128_t stdlib_base_cdiv( const stdlib_complex128_t z1, const stdlib_complex128_t z2 );
`c
#include "stdlib/math/base/ops/cdiv.h"
#include "stdlib/complex/float64/ctor.h"
#include "stdlib/complex/float64/reim.h"
#include
int main( void ) {
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 re;
double im;
int i;
for ( i = 0; i < 4; i++ ) {
v = x[ i ];
stdlib_complex128_reim( v, &re, &im );
printf( "z = %lf + %lfi\n", re, im );
y = stdlib_base_cdiv( v, v );
stdlib_complex128_reim( y, &re, &im );
printf( "cdiv(z, z) = %lf + %lfi\n", re, im );
}
}
`
*
- 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].
*
- [@stdlib/complex-float64/base/add][@stdlib/complex/float64/base/add]: add two double-precision complex floating-point numbers.
- [@stdlib/complex-float64/base/mul][@stdlib/complex/float64/base/mul]: multiply two double-precision complex floating-point numbers.
- [@stdlib/math-base/ops/csub][@stdlib/math/base/ops/csub]: subtract two double-precision complex floating-point numbers.
*
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].
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[@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/complex/float64/base/add]: https://www.npmjs.com/package/@stdlib/complex-float64-base-add
[@stdlib/complex/float64/base/mul]: https://www.npmjs.com/package/@stdlib/complex-float64-base-mul
[@stdlib/math/base/ops/csub]: https://www.npmjs.com/package/@stdlib/math-base-ops-csub