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

# <!--BOOK_INFORMATION-->
# <img align="left" style="padding-right:10px;" src="figures/PDSH-cover-small.png">
# 
# *This notebook contains an excerpt from the [Python Data Science Handbook](http://shop.oreilly.com/product/0636920034919.do) by Jake VanderPlas; the content is available [on GitHub](https://github.com/jakevdp/PythonDataScienceHandbook).*
# 
# *The text is released under the [CC-BY-NC-ND license](https://creativecommons.org/licenses/by-nc-nd/3.0/us/legalcode), and code is released under the [MIT license](https://opensource.org/licenses/MIT). If you find this content useful, please consider supporting the work by [buying the book](http://shop.oreilly.com/product/0636920034919.do)!*

# <!--NAVIGATION-->
# < [Computation on NumPy Arrays: Universal Functions](02.03-Computation-on-arrays-ufuncs.ipynb) | [Contents](Index.ipynb) | [Computation on Arrays: Broadcasting](02.05-Computation-on-arrays-broadcasting.ipynb) >
# 
# <a href="https://colab.research.google.com/github/jakevdp/PythonDataScienceHandbook/blob/master/notebooks/02.04-Computation-on-arrays-aggregates.ipynb"><img align="left" src="https://colab.research.google.com/assets/colab-badge.svg" alt="Open in Colab" title="Open and Execute in Google Colaboratory"></a>
# 

# # Aggregations: Min, Max, and Everything In Between

# Often when faced with a large amount of data, a first step is to compute summary statistics for the data in question.
# Perhaps the most common summary statistics are the mean and standard deviation, which allow you to summarize the "typical" values in a dataset, but other aggregates are useful as well (the sum, product, median, minimum and maximum, quantiles, etc.).
# 
# NumPy has fast built-in aggregation functions for working on arrays; we'll discuss and demonstrate some of them here.

# ## Summing the Values in an Array
# 
# As a quick example, consider computing the sum of all values in an array.
# Python itself can do this using the built-in ``sum`` function:

# In[1]:


import numpy as np


# In[2]:


L = np.random.random(100)
sum(L)


# The syntax is quite similar to that of NumPy's ``sum`` function, and the result is the same in the simplest case:

# In[3]:


np.sum(L)


# However, because it executes the operation in compiled code, NumPy's version of the operation is computed much more quickly:

# In[4]:


big_array = np.random.rand(1000000)
get_ipython().run_line_magic('timeit', 'sum(big_array)')
get_ipython().run_line_magic('timeit', 'np.sum(big_array)')


# Be careful, though: the ``sum`` function and the ``np.sum`` function are not identical, which can sometimes lead to confusion!
# In particular, their optional arguments have different meanings, and ``np.sum`` is aware of multiple array dimensions, as we will see in the following section.

# ## Minimum and Maximum
# 
# Similarly, Python has built-in ``min`` and ``max`` functions, used to find the minimum value and maximum value of any given array:

# In[5]:


min(big_array), max(big_array)


# NumPy's corresponding functions have similar syntax, and again operate much more quickly:

# In[6]:


np.min(big_array), np.max(big_array)


# In[7]:


get_ipython().run_line_magic('timeit', 'min(big_array)')
get_ipython().run_line_magic('timeit', 'np.min(big_array)')


# For ``min``, ``max``, ``sum``, and several other NumPy aggregates, a shorter syntax is to use methods of the array object itself:

# In[8]:


print(big_array.min(), big_array.max(), big_array.sum())


# Whenever possible, make sure that you are using the NumPy version of these aggregates when operating on NumPy arrays!

# ### Multi dimensional aggregates
# 
# One common type of aggregation operation is an aggregate along a row or column.
# Say you have some data stored in a two-dimensional array:

# In[9]:


M = np.random.random((3, 4))
print(M)


# By default, each NumPy aggregation function will return the aggregate over the entire array:

# In[10]:


M.sum()


# Aggregation functions take an additional argument specifying the *axis* along which the aggregate is computed. For example, we can find the minimum value within each column by specifying ``axis=0``:

# In[11]:


M.min(axis=0)


# The function returns four values, corresponding to the four columns of numbers.
# 
# Similarly, we can find the maximum value within each row:

# In[12]:


M.max(axis=1)


# The way the axis is specified here can be confusing to users coming from other languages.
# The ``axis`` keyword specifies the *dimension of the array that will be collapsed*, rather than the dimension that will be returned.
# So specifying ``axis=0`` means that the first axis will be collapsed: for two-dimensional arrays, this means that values within each column will be aggregated.

# ### Other aggregation functions
# 
# NumPy provides many other aggregation functions, but we won't discuss them in detail here.
# Additionally, most aggregates have a ``NaN``-safe counterpart that computes the result while ignoring missing values, which are marked by the special IEEE floating-point ``NaN`` value (for a fuller discussion of missing data, see [Handling Missing Data](03.04-Missing-Values.ipynb)).
# Some of these ``NaN``-safe functions were not added until NumPy 1.8, so they will not be available in older NumPy versions.
# 
# The following table provides a list of useful aggregation functions available in NumPy:
# 
# |Function Name      |   NaN-safe Version  | Description                                   |
# |-------------------|---------------------|-----------------------------------------------|
# | ``np.sum``        | ``np.nansum``       | Compute sum of elements                       |
# | ``np.prod``       | ``np.nanprod``      | Compute product of elements                   |
# | ``np.mean``       | ``np.nanmean``      | Compute mean of elements                      |
# | ``np.std``        | ``np.nanstd``       | Compute standard deviation                    |
# | ``np.var``        | ``np.nanvar``       | Compute variance                              |
# | ``np.min``        | ``np.nanmin``       | Find minimum value                            |
# | ``np.max``        | ``np.nanmax``       | Find maximum value                            |
# | ``np.argmin``     | ``np.nanargmin``    | Find index of minimum value                   |
# | ``np.argmax``     | ``np.nanargmax``    | Find index of maximum value                   |
# | ``np.median``     | ``np.nanmedian``    | Compute median of elements                    |
# | ``np.percentile`` | ``np.nanpercentile``| Compute rank-based statistics of elements     |
# | ``np.any``        | N/A                 | Evaluate whether any elements are true        |
# | ``np.all``        | N/A                 | Evaluate whether all elements are true        |
# 
# We will see these aggregates often throughout the rest of the book.

# ## Example: What is the Average Height of US Presidents?

# Aggregates available in NumPy can be extremely useful for summarizing a set of values.
# As a simple example, let's consider the heights of all US presidents.
# This data is available in the file *president_heights.csv*, which is a simple comma-separated list of labels and values:

# In[13]:


get_ipython().system('head -4 data/president_heights.csv')


# We'll use the Pandas package, which we'll explore more fully in [Chapter 3](03.00-Introduction-to-Pandas.ipynb), to read the file and extract this information (note that the heights are measured in centimeters).

# In[14]:


import pandas as pd
data = pd.read_csv('data/president_heights.csv')
heights = np.array(data['height(cm)'])
print(heights)


# Now that we have this data array, we can compute a variety of summary statistics:

# In[15]:


print("Mean height:       ", heights.mean())
print("Standard deviation:", heights.std())
print("Minimum height:    ", heights.min())
print("Maximum height:    ", heights.max())


# Note that in each case, the aggregation operation reduced the entire array to a single summarizing value, which gives us information about the distribution of values.
# We may also wish to compute quantiles:

# In[16]:


print("25th percentile:   ", np.percentile(heights, 25))
print("Median:            ", np.median(heights))
print("75th percentile:   ", np.percentile(heights, 75))


# We see that the median height of US presidents is 182 cm, or just shy of six feet.
# 
# Of course, sometimes it's more useful to see a visual representation of this data, which we can accomplish using tools in Matplotlib (we'll discuss Matplotlib more fully in [Chapter 4](04.00-Introduction-To-Matplotlib.ipynb)). For example, this code generates the following chart:

# In[17]:


get_ipython().run_line_magic('matplotlib', 'inline')
import matplotlib.pyplot as plt
import seaborn; seaborn.set()  # set plot style


# In[18]:


plt.hist(heights)
plt.title('Height Distribution of US Presidents')
plt.xlabel('height (cm)')
plt.ylabel('number');


# These aggregates are some of the fundamental pieces of exploratory data analysis that we'll explore in more depth in later chapters of the book.

# <!--NAVIGATION-->
# < [Computation on NumPy Arrays: Universal Functions](02.03-Computation-on-arrays-ufuncs.ipynb) | [Contents](Index.ipynb) | [Computation on Arrays: Broadcasting](02.05-Computation-on-arrays-broadcasting.ipynb) >
# 
# <a href="https://colab.research.google.com/github/jakevdp/PythonDataScienceHandbook/blob/master/notebooks/02.04-Computation-on-arrays-aggregates.ipynb"><img align="left" src="https://colab.research.google.com/assets/colab-badge.svg" alt="Open in Colab" title="Open and Execute in Google Colaboratory"></a>
#