# gss

Golden Section Search for javascript. (a line search technique used to minimize or maximize the output a function, also known as `argmax`

).

# Golden Section Search

A line search technique to help you find the minimum or maximum of a function. I've adapted the version from wikipedia to support async functions as well as synchronous ones :)

# How to use

```
npm install gss
```

The arguments are a bit bad, but here's how you'd use it:

```
gss(asyncFunctionToMinimize, lowerBound, middleNumber, upperBound, precision, callback(err, min))
```

`asyncFunctionToMinimize(x, cb)`

: takes one argument,`x`

, for which you are finding the argmax, and a callback that it calls when finished. It should call its callback like this:`cb(null, result)`

.`lowerBound`

: a number you think makes a lower bound to the solution`middleNumber`

: any number between the upper and lower bounds`upperBound`

: a number you think makes an upper bound to the solution`callback(err, min)`

: a function to receive the results of the line search

The synchronous version takes a function that returns the result, and when it finishes it returns the result, so you don't need a callback. See the example below.

# Async example:

```
var gss = require('gss').gss
// f(x) = x^2
var f = function(x, cb) { cb(null, Math.pow(x, 2)); }
gss(f, -10, -7, 1, Math.sqrt(1e-10), function(err, min) {
//
// Now we have the min!
//
console.log(min, 'this should be prettty close to zero.');
});
```

Sync example (you bad bad noder ;):

```
var gssSync = require('gss').gssSync
var f = function(x) { return Math.pow(x, 2); } // f(x) = x^2
var min = gssSync(_.memoize(f), -100, -50, 100, Math.sqrt(1e-10))
console.log(min, 'should be pretty darn close to zero.');
```

# Gotchas

I recommend you use `_.memoize`

to make the minimization go as quickly as possible. If you'd like to maximize instead, have your function multiply by -1 before returning.

# TODOs:

- tests
- automatically choose the
`middleNumber`

, to simplify API