=====================
Tutorial: Basic plots
=====================

In this tutorial, the basic plot types of trianglechain are introduced

.. code:: python

    from trianglechain import TriangleChain, LineChain, RectangleChain
    from trianglechain.TriangleChain import ensure_rec
    import numpy as np

.. code:: python

    def get_samples(n_samples=100000, n_dims=3):
        covmat = np.random.normal(size=(n_dims, n_dims))
        covmat = np.dot(covmat.T, covmat)
        mean = np.random.uniform(size=(n_dims))
        samples = np.random.multivariate_normal(mean=mean, cov=covmat, size=(n_samples))
        return samples

    np.random.seed(42)
    samples = get_samples()
    samples = ensure_rec(samples, names=["a", "b", "c"])

Contour plot
============

.. code:: python

    tri = TriangleChain()
    tri.contour_cl(samples);

.. image:: output_4_1.png


Density image
=============

.. code:: python

    tri = TriangleChain()
    tri.density_image(samples);

.. image:: output_6_1.png


Scatter plot
============

.. code:: python

    tri = TriangleChain()
    tri.scatter(samples[:1000]);

.. image:: output_8_1.png


Scatter density
===============

.. code:: python

    # scatter, color corresponds to density
    tri = TriangleChain()
    tri.scatter_density(samples);


.. image:: output_10_1.png


Axlines
=======

.. code:: python

    lines = {"a": 0, "b": 0, "c": 0}

    tri = TriangleChain()
    tri.contour_cl(samples);
    tri.axlines(lines, color="k", axlines_kwargs={"ls": "--", "lw": 1});


.. image:: output_12_2.png


LineChain
=========

All the plotting types from above can also be used in the LineChain
environment. And the different plotting types can also be combined

.. code:: python

    line = LineChain()
    line.contour_cl(samples);
    line.density_image(samples);
    line.axlines(lines, color="white");



.. image:: output_15_0.png


RectangleChain
==============

Another option is RectangleChain, here you have to define the x and y
parameters

.. code:: python

    samples_rec = get_samples(n_dims=6)
    samples_rec = ensure_rec(samples_rec, names=["a", "b", "c", "d", "e", "f"])

.. code:: python

    rec = RectangleChain(params_x=["a", "b", "c", "d"], params_y=["e", "f"], fill=True)
    rec.contour_cl(samples_rec);
    rec.axlines(samples_rec[5])
    rec.scatter(samples_rec[:20]);



.. image:: output_19_0.png


Samples with probability
========================

To plot a sample where the probability of the sample is given, the
``prob`` argument can be used (for all ``contour_cl``, ``density_image``
and ``scatter_density``)

.. code:: python

    n_dims = 3
    n_samples = 1000000

    # Initalize grid
    sample = np.random.uniform(-5, 5, size=(n_samples, n_dims))

    # loglikelihood
    def loglike(x, mean, covmat):
        return -0.5 * np.dot(np.dot((x - mean).T, np.linalg.inv(covmat)), (x - mean))

    # Generate the covariance matrix
    covmat = np.random.normal(size=(n_dims, n_dims))
    covmat = np.identity(n_dims)

    # Generate the mean vector
    mean = np.zeros(3)

    # Compute the probability for each generated sample
    prob = np.zeros(n_samples)
    for i in range(n_samples):
        prob[i] = loglike(sample[i], mean, covmat)

    # Transform and normalize to probabilites
    prob = np.exp(prob)
    prob /= sum(prob)

.. code:: python

    tri = TriangleChain(names=["a", "b", "c"])
    tri.contour_cl(sample, prob=prob);

.. image:: output_23_1.png