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

# # Plotting with Matplotlib
# 
# Matplotlib is the "standard" Python plotting package (although there are a few other good contenders).
# 
# Let's get on to that all important step of visualizing data. We will be using the matplotlib Python package for that. Let's start by plotting the function $f(x) = x^2$.
# 
# First, let's generate the numbers using Numpy:

# In[23]:


x = np.arange(0,10,0.4)
f = x ** 2


# Now let's create a noisy version of $f$ by adding some random Gaussian noise:

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mu, sigma = 0, 5 # mean and standard deviation
f_noisy = f + np.random.normal(mu, sigma, len(f))
f_noisy


# To plot the data, first import the **pyplot** module of matplotlib:

# In[30]:


import matplotlib.pyplot as plt
get_ipython().run_line_magic('matplotlib', 'inline')


# In[37]:


plt.plot(x, f, '-k', label="f(x)")           # plot the function using a black line
plt.plot(x, f_noisy, 'ob', label="noisy f")  # plot the noisy version using blue circles


# We can add additional features to the plot such as a legend and axis labels, and note the use of semi-colons to suppress the output of the commands:

# In[44]:


plt.plot(x, f, '-k', label="f(x)");           # plot the function using a black line
plt.plot(x, f_noisy, 'ob', label="noisy f");  # plot the noisy version using blue circles
plt.xlabel("x", size="xx-large");
plt.ylabel("f(x)", size="xx-large");
plt.ylim(-5, 100);
plt.legend(loc="upper left");


# ### Example 2:  histograms
# 
# Let's generate two datasets from a normal distribution and plot their histograms:

# In[45]:


mu = 100    # mean of distribution
sigma = 15  # standard deviation of distribution
x1 = mu + sigma * np.random.randn(10000)
x2 = mu + 10 + sigma * np.random.randn(10000)


# Next, we'll generate a histogram of the two datasets, showing some features of Matplotlib's hist function.  The 'normed' flag normalizes the bin heights such that it represents a probability distribution.  'alpha' is the opacity.

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num_bins = 50
# the histogram of the data
plt.hist(x1, num_bins, normed=True, facecolor='green', alpha=0.4, label='first');
plt.hist(x2, num_bins, normed=True, facecolor='blue', alpha=0.4, label='second');
plt.xlabel('x',size="xx-large");
plt.ylabel('normalized counts', size="xx-large");
plt.legend(loc='upper right');