# firanka Release 0.1.12

Calculations on real functions

MIT
Install
``` pip install firanka==0.1.12 ```

# firanka

firanka is a Python library to perform calculations on particular kinds of functions. These functions have a domain, which is a single continuous subset of the real number line. These functions can have any values.

firanka allows you do define two classes of such functions or series.

First are the DiscreteSeries. DiscreteSeries further divide the function domain into slices (left-closed, right-open) that have constant values. Manipulating DiscreteSeries and performing calculations on them is cheap.

Then you have FunctionSeries. These are simply defined by user-supplied Python callable.

Best part is, you can join series together (given a joining operator), slice them and so on.

# Usage

## Series

Can be imported from sai.series. A generic abstract superclass for series - `Series` can be imported for checking if given object is a series.

Series are immutable, but non-hashable.

Read the source code of the base class to get to know more about series operations.

### Applying and joining

Applying requires a callable(index: float, value: current value) -> value. Joining requires a callable(index: float, valueSelf, valueOther: values from self and other table) -> value.

### DiscreteSeries

To use a DiscreteSeries you must give it a set of data to work with. These will define intervals with given values, left-closed, right-open. as in:

```fs = DiscreteSeries([(0,1), (3, 4), (5, 6)])
fs[0.5] == 1
fs[3] == 4
fs[5] == 6
fs.domain == '<0;5>'
# fs[6] - NotInDomainError's```

Datapoints given must be already sorted!. By default, the domain will be both sides closed, from minimum to maximum given in data, but you can specify a custom one:

```fs = DiscreteSeries([(0,1), (3, 4), (5, 6)], '(0; 8>')
# fs[0] - NotInDomainError's !
fs[6] == 6```

Although you can't specify a domain where it would be impossible to compute the value. (ie. starting at smaller than zero). Doing so will throw a ValueError.

Note that when using `join_discrete()` sometimes other series might get calls from beyond their domain. This can be seen for example here:

```logs = FunctionSeries(math.log, '(0;5>')
dirs = DiscreteSeries([(0,1)], '<0;5>')

# Raises ValueError due to math.log being called with 0
dirs.join_discrete(logs, lambda x, y: x+y)   ```

### FunctionSeries

Using FunctionSeries is straightforward. Just give them a callable and a domain:

`fs = FunctionSeries(lambda x: x**2, '<-2;2>')`

### ModuloSeries

ModuloSeries allow you to wrap a finite series in repetition.

`fs = ModuloSeries(someOtherSeries)`

By definition, ModuloSeries has the domain of all real numbers.

Note that someOtherSeries's domain length must be non-zero and finite. Otherwise ValueError will be thrown.

## LinearInterpolationSeries

These are discretes, but allow you to define an operator that will take its neighbours into account and let you return a custom value.

By default, it will assumes that values can be added, subbed, multed and dived, and will do classical linear interpolation.

They can either utilize an existing discrete series, or be created just as any other discrete series would be.

## DiscreteSeriesBuilder

Sometimes you just need to update a DiscreteSeries, or to blang a brand new one. This little fella will help you out.

You can pass a DiscreteSeries to build on or start from stratch:

```kb = DiscreteSeriesBuilder(series)
kb = DiscreteSeriesBuilder()

kb.put(1,2)

series = kb.as_series()
isinstance(series, DiscreteSeries)```

By calling `as_series()` you get a new DiscreteSeries instance returned.

## Intervals

Can be imported from sai.intervals.

Interval is a continuous subset of the real number line.

You can create Intervals as follows:

`Interval(-5, 5, True, False) == Interval('<-5;5)')`

For more information use the source Interval's are immutable and hashable. They can be sliced:

`Interval('<-5;5>')[0:] == Interval('<0;5>')`

Slices work as a both-sides-closed range if both sides are shown!

You can check whether an interval contains a point

`5 not in Interval('<-1;5)')`

Or you can check for strict inclusion

`Interval('<-1;1>') in Interval('<-2;2>')`