#!/usr/bin/env python
# coding: utf-8

# # Special histograms in physt
# 
# Sometimes, it is necessary to bin values in transformed coordinates (e.g. *polar*). In principle,
# it is possible to create histograms from already transformed values (i.e. *r* and *φ*). However,
# this is not always the best way to go as each set of coordinates has its own peculiarities (e.g.
# *the typical range of values for azimuthal angle*)
# 
# Physt provides a general framework for constructing the **transformed histograms** (see a dedicated 
# section of this document) and a couple of most frequently used variants:
# 
# * **PolarHistogram**
# * **SphericalHistogram**
# * **CylindricalHistogram**

# In[1]:


# Necessary import evil
from physt import cylindrical, polar, spherical
import numpy as np


# In[2]:


# Generate some points in the Cartesian coordinates
np.random.seed(42)

x = np.random.rand(1000)  
y = np.random.rand(1000)
z = np.random.rand(1000)


# ## Polar histogram
# 
# This histograms maps values to **radius** (r) and **azimuthal angle** (φ, ranging from 0 to 2π).
# 
# By default (unless you specify the `phi_bins` parameter), the whole azimuthal range is spanned (even if there are no values that fall in parts of the circle).

# In[3]:


# Create a polar histogram with default parameters
hist = polar(x, y)
ax = hist.plot.polar_map()
hist


# In[4]:


hist.bins


# In[5]:


# Create a polar histogram with different binning
hist2 = polar(x+.3, y+.3, radial_bins="pretty", phi_bins="pretty")
ax = hist2.plot.polar_map(density=True)


# In[6]:


# Default axes names
hist.axis_names


# When working with *any* transformed histograms, you can fill values in the **original**, or **transformed**
# coordinates. All methods working with coordinates understand the parameter `transformed` which (if True)
# says that the method parameter are already in the transformed coordinated; otherwise, all values are considered to be in the original coordinates and transformed on inserting (creating, searching).

# In[7]:


# Using transformed / untransformed values
print("Non-transformed", hist.find_bin((0.1, 1)))
print("Transformed", hist.find_bin((0.1, 1), transformed=True))

print("Non-transformed", hist.find_bin((0.1, 2.7)))     # Value
print("Transformed", hist.find_bin((0.1, 2.7), transformed=True))


# In[8]:


# Simple plotting, similar to Histogram2D
hist.plot.polar_map(density=True, show_zero=False, cmap="Wistia", lw=0.5, figsize=(5, 5));


# ### Adding new values

# In[9]:


# Add a single, untransformed value
hist.fill((-.5, -.5), weight=12)
hist.plot.polar_map(density=True, show_zero=True, cmap="Reds", lw=0.5, figsize=(5, 5));


# In[10]:


# Add a couple of values, transformed
data = [[.5, 3.05], [.5, 3.2], [.7, 3.3]]
weights = [1, 5, 20]

hist.fill_n(data, weights=weights, transformed=True)
hist.plot.polar_map(density=True, show_zero=True, cmap="Reds", lw=0.5, figsize=(5, 5));


# ### Projections
# 
# The projections are stored using specialized Histogram1D subclasses that keep (in the case of radial) information about the proper bin sizes.

# In[11]:


radial = hist.projection("r")
radial.plot(density=True, color="red", alpha=0.5).set_title("Density")
radial.plot(label="absolute", color="blue", alpha=0.5).set_title("Absolute")
radial.plot(label="cumulative", cumulative=True, density=True, color="green", alpha=0.5).set_title("Cumulative")
radial


# In[12]:


hist.projection("phi").plot(cmap="rainbow")


# ## Cylindrical histogram
# To be implemented

# In[13]:


data = np.random.rand(100, 3)
h = cylindrical(data)
h


# In[14]:


# %matplotlib qt
proj = h.projection("rho", "phi")
proj.plot.polar_map()
proj


# In[15]:


proj = h.projection("phi", "z")
ax = proj.plot.cylinder_map(show_zero=False)
ax.view_init(50, 70)
proj


# ## Spherical histogram
# To be implemented

# In[16]:


n = 1000000
data = np.empty((n, 3))
data[:,0] = np.random.normal(0, 1, n)
data[:,1] = np.random.normal(0, 1.3, n)
data[:,2] = np.random.normal(1, 1.2, n)
h = spherical(data)
h


# In[17]:


globe = h.projection("theta", "phi")
# globe.plot()
globe.plot.globe_map(density=True, figsize=(7, 7), cmap="rainbow") 
globe.plot.globe_map(density=False, figsize=(7, 7))
globe


# ## Implementing custom transformed histogram
# 
# **TO BE WRITTEN**