fgivenx 2.4.2
fgivenx: Functional Posterior Plotter
License: MIT

=====================================
fgivenx: Functional Posterior Plotter  
=====================================
:fgivenx:  Functional Posterior Plotter 
:Author: Will Handley
:Version: 2.4.2
:Homepage: https://github.com/handley-lab/fgivenx
:Documentation: http://fgivenx.readthedocs.io/

.. image:: https://github.com/handley-lab/fgivenx/workflows/CI/badge.svg?branch=master
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   :target: https://codecov.io/gh/handley-lab/fgivenx
   :alt: Test Coverage Status
.. image:: https://badge.fury.io/py/fgivenx.svg
   :target: https://badge.fury.io/py/fgivenx
   :alt: PyPi location
.. image:: https://readthedocs.org/projects/fgivenx/badge/?version=latest
   :target: https://fgivenx.readthedocs.io/en/latest/?badge=latest
   :alt: Documentation Status
.. image:: http://joss.theoj.org/papers/cf6f8ac309d6a18b6d6cf08b64aa3f62/status.svg
   :target: http://joss.theoj.org/papers/cf6f8ac309d6a18b6d6cf08b64aa3f62
   :alt: Review Status
.. image:: https://zenodo.org/badge/100947684.svg
   :target: https://zenodo.org/badge/latestdoi/100947684
   :alt: Permanent DOI
.. image:: https://img.shields.io/badge/arXiv-1908.01711-b31b1b.svg
   :target: https://arxiv.org/abs/1908.01711
   :alt: Open-access paper

Description
===========

``fgivenx`` is a python package for plotting posteriors of functions. It is
currently used in astronomy, but will be of use to any scientists performing
Bayesian analyses which have predictive posteriors that are functions.

This package allows one to plot a predictive posterior of a function,
dependent on sampled parameters. We assume one has a Bayesian posterior
``Post(theta|D,M)`` described by a set of posterior samples ``{theta_i}~Post``.
If there is a function parameterised by theta ``y=f(x;theta)``, then this script
will produce a contour plot of the conditional posterior ``P(y|x,D,M)`` in the
``(x,y)`` plane.

The driving routines are ``fgivenx.plot_contours``, ``fgivenx.plot_lines`` and
``fgivenx.plot_dkl``. The code is compatible with getdist, and has a loading function
provided by ``fgivenx.samples_from_getdist_chains``.

|image0|

Getting Started
===============

Users can install using pip:

.. code:: bash

   pip install fgivenx

from source:

.. code:: bash

   git clone https://github.com/handley-lab/fgivenx
   cd fgivenx
   python setup.py install --user

or for those on `Arch linux <https://www.archlinux.org/>`__ it is
available on the
`AUR <https://aur.archlinux.org/packages/python-fgivenx/>`__

You can check that things are working by running the test suite (You may
encounter warnings if the optional dependency ``joblib`` is not installed):

.. code:: bash

   pip install pytest pytest-runner pytest-mpl
   export MPLBACKEND=Agg
   pytest <fgivenx-install-location>

   # or, equivalently
   git clone https://github.com/handley-lab/fgivenx
   cd fgivenx
   python setup.py test

Check the dependencies listed in the next section are installed. You can then use the
``fgivenx`` module from your scripts.

Some users of OSX or `Anaconda <https://en.wikipedia.org/wiki/Anaconda_(Python_distribution)>`__ may find ``QueueManagerThread`` errors if `Pillow <https://pypi.org/project/Pillow/>`__ is not installed (run ``pip install pillow``).

If you want to use parallelisation, have progress bars or getdist compatibility
you should install the additional optional dependencies:

.. code:: bash

   pip install joblib tqdm getdist
   # or, equivalently
   pip install -r  requirements.txt

You may encounter warnings if you don't have the optional dependency ``joblib``
installed.

Dependencies
=============
Basic requirements:

* Python 2.7+ or 3.4+
* `matplotlib <https://pypi.org/project/matplotlib/>`__
* `numpy <https://pypi.org/project/numpy/>`__
* `scipy <https://pypi.org/project/scipy/>`__

Documentation:

* `sphinx <https://pypi.org/project/Sphinx/>`__
* `numpydoc <https://pypi.org/project/numpydoc/>`__

Tests:

* `pytest <https://pypi.org/project/pytest/>`__
* `pytest-mpl <https://pypi.org/project/pytest-mpl/>`__

Optional extras:

* `joblib <https://pypi.org/project/joblib/>`__ (parallelisation) [`+ pillow <https://pypi.org/project/Pillow/>`__ on some systems]
* `tqdm <https://pypi.org/project/tqdm/>`__ (progress bars)
* `getdist <https://pypi.org/project/GetDist/>`__ (reading of getdist compatible files)


Documentation
=============

Full Documentation is hosted at
`ReadTheDocs <http://fgivenx.readthedocs.io/>`__.
To build your own local copy of the documentation you'll need to install
`sphinx <https://pypi.org/project/Sphinx/>`__. You can then run:

.. code:: bash

   cd docs
   make html

Citation
========

If you use ``fgivenx`` to generate plots for a publication, please cite
as: ::

   Handley, (2018). fgivenx: A Python package for functional posterior
   plotting . Journal of Open Source Software, 3(28), 849,
   https://doi.org/10.21105/joss.00849

or using the BibTeX:

.. code:: bibtex

   @article{fgivenx,
       doi = {10.21105/joss.00849},
       url = {http://dx.doi.org/10.21105/joss.00849},
       year  = {2018},
       month = {Aug},
       publisher = {The Open Journal},
       volume = {3},
       number = {28},
       author = {Will Handley},
       title = {fgivenx: Functional Posterior Plotter},
       journal = {The Journal of Open Source Software}
   }

Example Usage
=============



Plot user-generated samples
---------------------------

.. code:: python

    import numpy
    import matplotlib.pyplot as plt
    from fgivenx import plot_contours, plot_lines, plot_dkl


    # Model definitions
    # =================
    # Define a simple straight line function, parameters theta=(m,c)
    def f(x, theta):
        m, c = theta
        return m * x + c


    numpy.random.seed(1)

    # Posterior samples
    nsamples = 1000
    ms = numpy.random.normal(loc=-5, scale=1, size=nsamples)
    cs = numpy.random.normal(loc=2, scale=1, size=nsamples)
    samples = numpy.array([(m, c) for m, c in zip(ms, cs)]).copy()

    # Prior samples
    ms = numpy.random.normal(loc=0, scale=5, size=nsamples)
    cs = numpy.random.normal(loc=0, scale=5, size=nsamples)
    prior_samples = numpy.array([(m, c) for m, c in zip(ms, cs)]).copy()

    # Set the x range to plot on
    xmin, xmax = -2, 2
    nx = 100
    x = numpy.linspace(xmin, xmax, nx)

    # Set the cache
    cache = 'cache/test'
    prior_cache = cache + '_prior'

    # Plotting
    # ========
    fig, axes = plt.subplots(2, 2)

    # Sample plot
    # -----------
    ax_samples = axes[0, 0]
    ax_samples.set_ylabel(r'$c$')
    ax_samples.set_xlabel(r'$m$')
    ax_samples.plot(prior_samples.T[0], prior_samples.T[1], 'b.')
    ax_samples.plot(samples.T[0], samples.T[1], 'r.')

    # Line plot
    # ---------
    ax_lines = axes[0, 1]
    ax_lines.set_ylabel(r'$y = m x + c$')
    ax_lines.set_xlabel(r'$x$')
    plot_lines(f, x, prior_samples, ax_lines, color='b', cache=prior_cache)
    plot_lines(f, x, samples, ax_lines, color='r', cache=cache)

    # Predictive posterior plot
    # -------------------------
    ax_fgivenx = axes[1, 1]
    ax_fgivenx.set_ylabel(r'$P(y|x)$')
    ax_fgivenx.set_xlabel(r'$x$')
    cbar = plot_contours(f, x, prior_samples, ax_fgivenx,
                         colors=plt.cm.Blues_r, lines=False,
                         cache=prior_cache)
    cbar = plot_contours(f, x, samples, ax_fgivenx, cache=cache)

    # DKL plot
    # --------
    ax_dkl = axes[1, 0]
    ax_dkl.set_ylabel(r'$D_\mathrm{KL}$')
    ax_dkl.set_xlabel(r'$x$')
    ax_dkl.set_ylim(bottom=0, top=2.0)
    plot_dkl(f, x, samples, prior_samples, ax_dkl,
             cache=cache, prior_cache=prior_cache)

    ax_lines.get_shared_x_axes().join(ax_lines, ax_fgivenx, ax_samples)

    fig.tight_layout()
    fig.savefig('plot.png')

|image0|

Plot GetDist chains
-------------------

.. code:: python

    import numpy
    import matplotlib.pyplot as plt
    from fgivenx import plot_contours, samples_from_getdist_chains

    file_root = './plik_HM_TT_lowl/base_plikHM_TT_lowl'
    samples, weights = samples_from_getdist_chains(['logA', 'ns'], file_root)

    def PPS(k, theta):
        logA, ns = theta
        return logA + (ns - 1) * numpy.log(k)
        
    k = numpy.logspace(-4,1,100)
    cbar = plot_contours(PPS, k, samples, weights=weights)
    cbar = plt.colorbar(cbar,ticks=[0,1,2,3])
    cbar.set_ticklabels(['',r'$1\sigma$',r'$2\sigma$',r'$3\sigma$'])
    
    plt.xscale('log')
    plt.ylim(2,4)
    plt.ylabel(r'$\ln\left(10^{10}\mathcal{P}_\mathcal{R}\right)$')
    plt.xlabel(r'$k / {\rm Mpc}^{-1}$')
    plt.tight_layout()
    plt.savefig('planck.png')

|image1|

Contributing
============
Want to contribute to ``fgivenx``? Awesome!
There are many ways you can contribute via the 
[GitHub repository](https://github.com/handley-lab/fgivenx), 
see below.

Opening issues
--------------
Open an issue to report bugs or to propose new features.

Proposing pull requests
-----------------------
Pull requests are very welcome. Note that if you are going to propose drastic
changes, be sure to open an issue for discussion first, to make sure that your
PR will be accepted before you spend effort coding it.

.. |image0| image:: https://raw.githubusercontent.com/handley-lab/fgivenx/master/plot.png
.. |image1| image:: https://raw.githubusercontent.com/handley-lab/fgivenx/master/planck.png 

Changelog
=========
:v2.2.0:  Paper accepted
:v2.1.17: 100% coverage
:v2.1.16: Tests fixes
:v2.1.15: Additional plot tests
:v2.1.13: Further bug fix in test suite for image comparison
:v2.1.12: Bug fix in test suite for image comparison
:v2.1.11: Documentation upgrades
:v2.1.10: Added changelog