time-to-botec/js/node_modules/@stdlib/math/base/special/cabs2/README.md

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@license Apache-2.0
Copyright (c) 2018 The Stdlib Authors.
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
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# abs2
> Compute the squared [absolute value][absolute-value] of a complex number.
<section class="intro">
The [absolute value][absolute-value] of a complex number is defined as
<!-- <equation class="equation" label="eq:absolute_value_complex" align="center" raw="|a + bi| = \sqrt{a^2 + b^2}" alt="Absolute value"> -->
<div class="equation" align="center" data-raw-text="|a + bi| = \sqrt{a^2 + b^2}" data-equation="eq:absolute_value_complex">
<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@d4edb68b52a6c646be5683023c5a24890300727f/lib/node_modules/@stdlib/math/base/special/cabs2/docs/img/equation_absolute_value_complex.svg" alt="Absolute value">
<br>
</div>
<!-- </equation> -->
which corresponds to the length of a vector from the origin to a complex value plotted in the complex plane.
</section>
<!-- /.intro -->
<section class="usage">
## Usage
```javascript
var cabs2 = require( '@stdlib/math/base/special/cabs2' );
```
#### cabs2( re, im )
Computes the squared [absolute value][absolute-value] of a `complex` number comprised of a **real** component `re` and an **imaginary** component `im`.
```javascript
var y = cabs2( 5.0, 3.0 );
// returns 34.0
```
</section>
<!-- /.usage -->
<section class="notes">
## Notes
- Be careful to avoid overflow and underflow.
- Depending on the environment, this function _may_ have better performance than computing the [absolute value][absolute-value] of a `complex` number and then squaring. Hence, where appropriate, consider using `cabs2()` over [`cabs()`][@stdlib/math/base/special/cabs].
</section>
<!-- /.notes -->
<section class="examples">
## Examples
<!-- eslint no-undef: "error" -->
```javascript
var Complex128 = require( '@stdlib/complex/float64' );
var randu = require( '@stdlib/random/base/randu' );
var round = require( '@stdlib/math/base/special/round' );
var real = require( '@stdlib/complex/real' );
var imag = require( '@stdlib/complex/imag' );
var cabs2 = require( '@stdlib/math/base/special/cabs2' );
var re;
var im;
var z;
var i;
for ( i = 0; i < 100; i++ ) {
re = round( randu()*100.0 ) - 50.0;
im = round( randu()*100.0 ) - 50.0;
z = new Complex128( re, im );
console.log( 'cabs2(%s) = %d', z.toString(), cabs2( real(z), imag(z) ) );
}
```
</section>
<!-- /.examples -->
<section class="links">
[absolute-value]: https://en.wikipedia.org/wiki/Absolute_value
[@stdlib/math/base/special/cabs]: https://www.npmjs.com/package/@stdlib/math/tree/main/base/special/cabs
</section>
<!-- /.links -->