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

# In[1]:


import numpy as np
import matplotlib.pyplot as plt


# In[2]:


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


# The population of Hares, Lynxes and carrots in Canada is in the file [population.txt](http://www.scipy-lectures.org/_downloads/populations.txt). Download that file and place it in this directory.

# Once this is done, execute the code below to load the data in the variable `data`.

# Important remark: **you should not use any `for` loop in this exercise!** :-)

# In[3]:


data = np.loadtxt('populations.txt')


# In[4]:


year, hares, lynxes, carrots = data.T  # trick: columns to variables


# In[5]:


year, hares, lynxes, carrots = data.T
populations = data[:,1:]


# In[6]:


data


# Plot the data (year vs each population item), using `label` and `legend`.

# In[7]:


for elt, name in zip(populations.T, ["hares", "lynxes", "carrots"]):
    plt.plot(year, elt, label=name, lw=.5)
plt.legend()
plt.grid(ls='-', alpha=.2)


# Compute the mean (`np.mean?`) and standard deviation (`np.std?`) of each piece of data

# In[8]:


np.mean(data, axis=0)


# In[9]:


np.std(data, axis=0)


# Which year each species had the largest population? (`np.argmax?` and use fancy indexing)

# In[10]:


year[np.argmax(data[:,1:], axis=0)]


# Which year any of the population is over 50000?

# In[11]:


mask = data[:,1:] > 50000


# In[12]:


year[np.any(mask, axis=1)]


# The top two years for each species when they had the lowest population

# You may use `argsort`, which gives the indices for which the array value would be sorted.

# In[13]:


get_ipython().run_line_magic('pinfo', 'np.argsort')


# In[14]:


year[np.argsort(data[:,1:], axis=0)[:2]]


# Compare (plot) the change in hare population (see `np.gradient?`) and the number of lynxes.

# In[15]:


np.gradient(hares)


# In[16]:


dhares = np.gradient(hares)
plt.plot(dhares, lynxes, 'o', mfc='gray', mec='black')
plt.grid(ls='-', alpha=.2)


# In[17]:


plt.plot(year, -dhares, lw=.5)
plt.plot(year, lynxes, lw=.5)
plt.grid(ls='-', alpha=.2)


# In[ ]: