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# cidentity

> Evaluate the [identity function][identity-function] of a double-precision [complex][@stdlib/complex/float64] floating-point number.

<section class="intro">

The [identity-function][identity-function] is defined as

<!-- <equation class="equation" label="eq:identity_function" align="center" raw="f(z) = z" alt="Identity function"> -->

<div class="equation" align="center" data-raw-text="f(z) = z" data-equation="eq:identity_function">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@3ac3ef7b03afae265d5c85a664dc22e0a373c0c2/lib/node_modules/@stdlib/math/base/special/cidentity/docs/img/equation_identity_function.svg" alt="Identity function">
    <br>
</div>

<!-- </equation> -->

for all `z`.

</section>

<!-- /.intro -->

<section class="usage">

## Usage

```javascript
var cidentity = require( '@stdlib/math/base/special/cidentity' );
```

#### cidentity( z )

Evaluates the [identity function][identity-function] for a double-precision [complex][@stdlib/complex/float64] floating-point number.

```javascript
var Complex128 = require( '@stdlib/complex/float64' );
var real = require( '@stdlib/complex/real' );
var imag = require( '@stdlib/complex/imag' );

var v = cidentity( new Complex128( -1.0, 2.0 ) );
// returns <Complex128>

var re = real( v );
// returns -1.0

var im = imag( v );
// returns 2.0
```

</section>

<!-- /.usage -->

<section class="examples">

## Examples

<!-- eslint-disable max-len -->

<!-- eslint no-undef: "error" -->

```javascript
var discreteUniform = require( '@stdlib/random/base/discrete-uniform' );
var Complex128 = require( '@stdlib/complex/float64' );
var cidentity = require( '@stdlib/math/base/special/cidentity' );

var z;
var i;
for ( i = 0; i < 100; i++ ) {
    z = new Complex128( discreteUniform( -50, 50 ), discreteUniform( -50, 50 ) );
    console.log( 'identity(%s) = %s', z, cidentity( z ) );
}
```

</section>

<!-- /.examples -->

<!-- C interface documentation. -->

* * *

<section class="c">

## C APIs

<!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->

<section class="intro">

</section>

<!-- /.intro -->

<!-- C usage documentation. -->

<section class="usage">

### Usage

```c
#include "stdlib/math/base/special/cidentity.h"
```

#### stdlib_base_cidentity( z )

Evaluates the identity function for a double-precision complex floating-point number.

```c
#include "stdlib/complex/float64.h"
#include "stdlib/complex/real.h"
#include "stdlib/complex/imag.h"

stdlib_complex128_t z = stdlib_complex128( 2.5, -1.5 );
stdlib_complex128_t out = stdlib_base_cidentity( z );

double re = stdlib_real( out );
// returns 2.5

double im = stdlib_imag( out );
// returns -1.5
```

The function accepts the following arguments:

-   **z**: `[in] stdlib_complex128_t` input value.

```c
stdlib_complex128_t stdlib_base_cidentity( const stdlib_complex128_t z );
```

</section>

<!-- /.usage -->

<!-- C API usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->

<section class="notes">

</section>

<!-- /.notes -->

<!-- C API usage examples. -->

<section class="examples">

### Examples

```c
#include "stdlib/math/base/special/cidentity.h"
#include "stdlib/complex/float64.h"
#include "stdlib/complex/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_cidentity( v );
        stdlib_reim( v, &re1, &im1 );
        stdlib_reim( y, &re2, &im2 );
        printf( "cidentity(%lf + %lfi) = %lf + %lfi\n", re1, im1, re2, im2 );
    }
}
```

</section>

<!-- /.examples -->

</section>

<!-- /.c -->

<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->

<section class="related">

* * *

## See Also

-   <span class="package-name">[`@stdlib/math/base/special/cidentityf`][@stdlib/math/base/special/cidentityf]</span><span class="delimiter">: </span><span class="description">evaluate the identity function for a single-precision complex floating-point number.</span>
-   <span class="package-name">[`@stdlib/math/base/special/identity`][@stdlib/math/base/special/identity]</span><span class="delimiter">: </span><span class="description">evaluate the identity function for a double-precision floating-point number.</span>

</section>

<!-- /.related -->

<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->

<section class="links">

[identity-function]: https://en.wikipedia.org/wiki/Identity_function

[@stdlib/complex/float64]: https://www.npmjs.com/package/@stdlib/complex-float64

<!-- <related-links> -->

[@stdlib/math/base/special/cidentityf]: https://github.com/stdlib-js/math/tree/main/base/special/cidentityf

[@stdlib/math/base/special/identity]: https://github.com/stdlib-js/math/tree/main/base/special/identity

<!-- </related-links> -->

</section>

<!-- /.links -->
