Divide two complex numbers.
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> Divide two double-precision complex floating-point numbers.
``bash`
npm install @stdlib/complex-float64-base-div
`javascript`
var cdiv = require( '@stdlib/complex-float64-base-div' );
#### cdiv( z1, z2 )
Divides two double-precision complex floating-point numbers.
`javascript
var Complex128 = require( '@stdlib/complex-float64-ctor' );
var z1 = new Complex128( -13.0, -1.0 );
var z2 = new Complex128( -2.0, 1.0 );
var v = cdiv( z1, z2 );
// returns
`
#### cdiv.assign( re1, im1, re2, im2, out, strideOut, offsetOut )
Divides two double-precision complex floating-point numbers and assigns results to a provided output array.
`javascript
var Float64Array = require( '@stdlib/array-float64' );
var out = new Float64Array( 2 );
var v = cdiv.assign( -13.0, -1.0, -2.0, 1.0, out, 1, 0 );
// returns
var bool = ( out === v );
// returns true
`
The function supports the following parameters:
- re1: real component of the first complex number.
- im1: imaginary component of the first complex number.
- re2: real component of the second complex number.
- im2: imaginary component of the second complex number.
- out: output array.
- strideOut: stride length for out.out
- offsetOut: starting index for .
#### cdiv.strided( z1, sz1, oz1, z2, sz2, oz2, out, so, oo )
Divides two double-precision complex floating-point numbers stored in real-valued strided array views and assigns results to a provided strided output array.
`javascript
var Float64Array = require( '@stdlib/array-float64' );
var z1 = new Float64Array( [ -13.0, -1.0 ] );
var z2 = new Float64Array( [ -2.0, 1.0 ] );
var out = new Float64Array( 2 );
var v = cdiv.strided( z1, 1, 0, z2, 1, 0, out, 1, 0 );
// returns
var bool = ( out === v );
// returns true
`
The function supports the following parameters:
- z1: first complex number strided array view.
- sz1: stride length for z1.z1
- oz1: starting index for .z2
- z2: second complex number strided array view.
- sz2: stride length for .z2
- oz2: starting index for .out
- out: output array.
- so: stride length for .out
- oo: starting index for .
`javascript
var Complex128Array = require( '@stdlib/array-complex128' );
var discreteUniform = require( '@stdlib/random-array-discrete-uniform' );
var logEachMap = require( '@stdlib/console-log-each-map' );
var cdiv = require( '@stdlib/complex-float64-base-div' );
// Generate arrays of random values:
var z1 = new Complex128Array( discreteUniform( 200, -50, 50 ) );
var z2 = new Complex128Array( discreteUniform( 200, -50, 50 ) );
// Perform element-wise division:
logEachMap( '(%s) / (%s) = %s', z1, z2, cdiv );
`
*
`c`
#include "stdlib/complex/float64/base/div.h"
#### stdlib_base_complex128_div( 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_complex128_div( 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_complex128_div( const stdlib_complex128_t z1, const stdlib_complex128_t z2 );
`c
#include "stdlib/complex/float64/base/div.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_complex128_div( 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/complex-float64/base/sub][@stdlib/complex/float64/base/sub]: 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/complex/float64/base/sub]: https://www.npmjs.com/package/@stdlib/complex-float64-base-sub