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# Useful Utilities

## `UnionDict` – a dict with set like operations and keys as attributes

This object combines the key-element storage of a `dict` with the union operation of a `set()` object. It is used in the `cogent3.draw` module, primarily for the `figure` and `layout` attributes.

### Accessing elements of a `UnionDict`

Keys in a `UnionDict` can be accessed like attributes

### Updating a `UnionDict`

If you use the `|` bitwise operator to compare two dicts and the left one is a `UnionDict`, a union operation is performed.

This can also be done using the `union` method.

### Accessing a non-existent `UnionDict` key

But if accessing as an attribute, you get an attribute error.

## Using Cogent3’s optimisers for your own functions

You have a function that you want to maximise/minimise. The parameters in your function may be bounded (must lie in a specific interval) or not. The `cogent3` optimisers can be applied to these cases. The `Powell` (a local optimiser) and `SimulatedAnnealing` (a global optimiser) classes in particular have had their interfaces standardised for such use cases. We demonstrate for a very simple function below.

We write a simple factory function that uses a provided value for omega to compute the squared deviation from an estimate, then use it to create our optimisable function.

We then import the minimise function and use it to minimise the function, obtaining the fit statistic and the associated estimate of S. Note that we provide lower and upper bounds (which are optional) and an initial guess for our parameter of interest (`S`).

The minimise and maximise functions can also handle multidimensional optimisations, just make xinit (and the bounds) lists rather than scalar values.