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# Introduction
`tabulation` is a Python module that provides the `Tabulation` class. The `Tabulation`
class represents a mathematical function by a sequence of linear interpolations between
points defined by arrays of *x* and *y* coordinates.
`tabulation` is a product of the [PDS Ring-Moon Systems Node](https://pds-rings.seti.org).
# Installation
The `tabulation` module is available via the `rms-tabulation` package on PyPI and can be
installed with:
```sh
pip install rms-tabulation
```
# Getting Started
The `Tabulation` class models a mathematical function by a series of (*x*,*y*) points and
performs linear interpolation between them. Although optimized to model filter bandpasses
and spectral flux, the class is sufficiently general to be used in a wide range of
applications.
The mathematical function is treated as equal to zero outside the domain of the *x*
coordinates, with a step at the provided leading and trailing *x* coordinates. In general,
zero values (either supplied or computed) at either the leading or trailing ends are
removed. However, if explicitly supplied, one leading and/or trailing zero value is
considered significant because it anchors the interpolation of a ramp at the beginning or
end of the domain.
A variety of mathematical operations can be performed on `Tabulation` objects, including
addition, subtraction, multiplication, division, integration, and finding the X mean,
FWHM, and square width. See the [module
documentation](https://rms-tabulation.readthedocs.io/en/latest/module.html) for details.
Here are some examples to get you started:
>>> t2 = Tabulation([0, 2, 4], [0, 5, 5]) # Ramp on leading edge
>>> t2.domain()
(0., 4.)
>>> t2([0, 1, 1.9, 2, 3, 3.9, 4, 5, 6])
```python
>>> from tabulation import Tabulation
>>> t1 = Tabulation([2, 4], [10, 10]) # Leading&trailing step function
>>> t1.domain()
(2., 4.)
>>> r1 = t1([0, 1, 1.9, 2, 3, 3.9, 4, 5, 6])
array([ 0., 0., 0., 10., 10., 10., 10., 0., 0.])
>>> t1.x_mean()
3.0
>>> t1.integral()
20.0
>>> t2 = Tabulation([0, 2, 4], [0, 5, 5]) # Ramp on leading edge
>>> t2.domain()
(0., 4.)
>>> r2 = t2([0, 1, 1.9, 2, 3, 3.9, 4, 5, 6])
array([ 0., 2.5, 4.75, 5., 5., 5. , 5., 0., 0.])
>>> t2.x_mean()
2.6666666666666665
>>> t2.integral()
15.0
>>> t3 = t2-t1
>>> t3.domain()
(0.0, 4.0)
>>> r2-r1
array([ 0. , 2.5 , 4.75, -5. , -5. , -5. , -5. , 0. , 0. ])
>>> t3([0, 1, 1.9, 2, 3, 3.9, 4, 5, 6])
array([ 0. , 2.5 , 4.75, -5. , -5. , -5. , -5. , 0. , 0. ])
>>> t3.integral()
-5.000000000000001
```
# Contributing
Information on contributing to this package can be found in the
[Contributing Guide](https://github.com/SETI/rms-tabulation/blob/main/CONTRIBUTING.md).
# Links
- [Documentation](https://rms-tabulation.readthedocs.io)
- [Repository](https://github.com/SETI/rms-tabulation)
- [Issue tracker](https://github.com/SETI/rms-tabulation/issues)
- [PyPi](https://pypi.org/project/rms-tabulation)
# Licensing
This code is licensed under the [Apache License v2.0](https://github.com/SETI/rms-tabulation/blob/main/LICENSE).
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