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

# In[ ]:


get_ipython().run_line_magic('matplotlib', 'inline')


# # Binning
# 
# ## Binning2D
# 
# Statistical data binning is a way to group several more or less
# continuous values into a smaller number of *bins*. For example, if you
# have irregularly distributed data over the oceans, you can organize
# these observations into a lower number of geographical intervals (for
# example, by grouping them all five degrees into latitudes and
# longitudes).
# 
# In this example, we will calculate drifter velocity statistics on the
# Black Sea over a period of 9 years.

# In[ ]:


import cartopy.crs
import matplotlib
import matplotlib.pyplot
import numpy
import pyinterp
import pyinterp.backends.xarray
import pyinterp.tests


# The first step is to load the data into memory and create the
# interpolator object:

# In[ ]:


ds = pyinterp.tests.load_aoml()


# Let's start by calculating the standard for vectors u and v.

# In[ ]:


norm = (ds.ud**2 + ds.vd**2)**0.5


# Now, we will describe the grid used to calculate our
# [binned](https://pangeo-pyinterp.readthedocs.io/en/latest/generated/pyinterp.Binning2D.html#pyinterp.Binning2D)
# statistics.

# In[ ]:


binning = pyinterp.Binning2D(
    pyinterp.Axis(numpy.arange(27, 42, 0.3), is_circle=True),
    pyinterp.Axis(numpy.arange(40, 47, 0.3)))
binning


# We push the loaded data into the different defined bins using [simple
# binning](https://pangeo-pyinterp.readthedocs.io/en/latest/generated/pyinterp.Binning2D.push.html#bilinear-binning).

# In[ ]:


binning.clear()
binning.push(ds.lon, ds.lat, norm, True)


# It is possible to retrieve other statistical
# [variables](https://pangeo-pyinterp.readthedocs.io/en/latest/generated/pyinterp.Binning2D.variable.html#pyinterp.Binning2D.variable)
# such as variance, minimum, maximum, etc.

# In[ ]:


nearest = binning.variable('mean')


# Then, we push the loaded data into the different defined bins using
# [linear binning](https://pangeo-pyinterp.readthedocs.io/en/latest/generated/pyinterp.Binning2D.push.html#bilinear-binning)

# In[ ]:


binning.clear()
binning.push(ds.lon, ds.lat, norm, False)
linear = binning.variable('mean')


# We visualize our result

# In[ ]:


fig = matplotlib.pyplot.figure(figsize=(10, 8))
ax1 = fig.add_subplot(211, projection=cartopy.crs.PlateCarree())
lon, lat = numpy.meshgrid(binning.x, binning.y, indexing='ij')
pcm = ax1.pcolormesh(lon,
                     lat,
                     nearest,
                     cmap='jet',
                     shading='auto',
                     vmin=0,
                     vmax=1,
                     transform=cartopy.crs.PlateCarree())
ax1.coastlines()
ax1.set_title("Simple binning.")

ax2 = fig.add_subplot(212, projection=cartopy.crs.PlateCarree())
lon, lat = numpy.meshgrid(binning.x, binning.y, indexing='ij')
pcm = ax2.pcolormesh(lon,
                     lat,
                     linear,
                     cmap='jet',
                     shading='auto',
                     vmin=0,
                     vmax=1,
                     transform=cartopy.crs.PlateCarree())
ax2.coastlines()
ax2.set_title("Linear binning.")
fig.colorbar(pcm, ax=[ax1, ax2], shrink=0.8)
fig.show()


# ## Histogram2D
# 
# This class, like the previous one, allows calculating a binning using
# histograms. In addition, this approach calculates the quantiles of the
# distribution and obtains the median value of the pixels.
# 
# Note that the algorithm used defines a maximum size of the number of bins
# handled by each histogram. If the number of observations is greater than the
# capacity of the histogram, the histogram will be compressed to best present
# this distribution in limited memory size. The description of the exact
# algorithm is in the article [A Streaming Parallel Decision Tree Algorithm](
# (http://jmlr.org/papers/v11/ben-haim10a.html).

# In[ ]:


hist2d = pyinterp.Histogram2D(
    pyinterp.Axis(numpy.arange(27, 42, 0.3), is_circle=True),
    pyinterp.Axis(numpy.arange(40, 47, 0.3)))
hist2d


# We push the loaded data into the different defined bins using the method
# `push`.

# In[ ]:


hist2d.push(ds.lon, ds.lat, norm)


# We visualize the mean vs median of the distribution.

# In[ ]:


fig = matplotlib.pyplot.figure(figsize=(10, 8))
ax1 = fig.add_subplot(211, projection=cartopy.crs.PlateCarree())
lon, lat = numpy.meshgrid(binning.x, binning.y, indexing='ij')
pcm = ax1.pcolormesh(lon,
                     lat,
                     hist2d.variable("mean"),
                     cmap='jet',
                     shading='auto',
                     vmin=0,
                     vmax=1,
                     transform=cartopy.crs.PlateCarree())
ax1.coastlines()
ax1.set_title("Mean")

ax2 = fig.add_subplot(212, projection=cartopy.crs.PlateCarree())
lon, lat = numpy.meshgrid(binning.x, binning.y, indexing='ij')
pcm = ax2.pcolormesh(lon,
                     lat,
                     hist2d.variable("quantile", 0.5),
                     cmap='jet',
                     shading='auto',
                     vmin=0,
                     vmax=1,
                     transform=cartopy.crs.PlateCarree())
ax2.coastlines()
ax2.set_title("Median")
fig.colorbar(pcm, ax=[ax1, ax2], shrink=0.8)
fig.show()