complex-sqrt/README.md

Floating point complex square root

# complex-sqrt

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Floating point complex square root

## Intro

Calculating the complex square root requires some care. The naive method may encounter overflow, underflow, or loss of precision due to the intermediate floating point results. A simple remedy[[1]](#references) is:

![Complex w](docs/images/w.png)

Then using w,

![Complex sqrt](docs/images/sqrt.png)

## Usage

##### `require('complex-sqrt')( a, b [, result] )`

Calculates sqrt(a + ib) and returns a two-element JS array with the real and imaginary components of the answer.

`result` is an optional to-element `Array` or typed array into which output is passed, if provided.

## Example

```javascript
var sqrt = require('complex-sqrt');

var result = sqrt( 1, 2 );

// result = [ 1.272019649514069, 0.7861513777574233 ]
```

## References

[1] Press, William H. *[Numerical Recipes 3rd Edition: The Art of Scientific Computing](https://books.google.com/books?id=1aAOdzK3FegC&pg=PA226&lpg=PA226&dq=complex+division+underflow&source=bl&ots=3jPhF9Irii&sig=JwEAckqmfBNd8dIQTrUD-Pk9dzE&hl=en&sa=X&ei=-VZQVYDpJImRyATAoYCwBg&ved=0CDwQ6AEwBA#v=onepage&q=complex%20division%20underflow&f=false)*. Cambridge University Press, 2007.

## Credits
(c) 2015 Ricky Reusser. MIT License