Python is a powerful and easy to use programming language. It has a large community of developers and given its open source nature, you can find many solutions, scripts, and help all over the web. It is easy to learn and code, and faster than other high-level programming languages...and did I mention it is free because it is open-source
IPython is a very powerful extension to Python that provides: Powerful interactive shells (terminal, Qt-based and Notebooks based on Jupyter).
Jupyter is an open-source project that provides open-standards, and services for interactive computing across dozens of programming languages, including Python
, R
, Stata
and many others used by economists.
You can download and install Python
and its packages for free for your computer from Python.org. While this is the official site, which offers the basic installer and you can try do add any packages you require yourself, a much easier approach, which is almost foolproof is to use Continuum Anaconda or Enthought Canopy. Both of these distributions offer academic licenses (Canopy), which allow you to use a larger set of packages. Similarly, you can download R
from the r-project website.
I personally have switched to using Continuum Anaconda since it make installing all the packages and software I use much easier. You can follow the instructions below or better yet follow the instructions on the Computation Page of my Economic Growth and Comparative Development Course.
The easiest and most convenient way to install a working version of IPython with all the required packages and tools is using Continuum's Anaconda Distribution. You can install following the instructions in that website, or if you can just run this script (Mac/Linux). After installing the latest version of Anaconda, add the Anaconda/bin
directory to your PATH
variable.
To create an environment useful for these notebooks, in your terminal execute
conda create --name GeoPython3env -c conda-forge python=3.6 geopandas georasters pandas numpy matplotlib seaborn jupyter scikit-image scikit-learn scipy r rstudio r-irkernel ipykernel statsmodels pycountry networkx rpy2 rasterio r-tidyr r-tibble r-dplyr pandana urbanaccess dill xlrd pandas-datareader rise jupyterlab cython numba
This should create an environment with most of the packages we need. We can always install others down the road.
To start using one of the environment you will need to exectute the following command
source activate GeoPython3env
Once you have your Python distribution installed you'll be ready to start working. You have various options:
Canopy
program and work thereAnaconda Navigator
and open one of the apps from there (python
, ipython
, jupyter console
, jupyter notebook
, jupyter lab
, R
, Stata
ipython
jupyter console
jupyter qtconsole
jupyter notebook
jupyter lab
While theses last are all using IPython, each has its advantages and disadvantages. You should play with them to get a better feeling of which you want to use for which purpose. In my own research I usually use a text editor (TextMate, Atom, Sublime) and the jupyter qtconsole
or the jupyter notebook
. To see the power of Jupter notebooks
(see this excellent and in-depth presentation by its creators). As you will see, this might prove an excellent environment to do research, homework, replicate papers, etc.
Let's start by running some simple commands at the prompt to do some simple computations.
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1+1-2
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3*2
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3**2
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-1**2
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3*(3-2)
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3*3-2
Notice that Python obeys the usual orders for operators, so exponentiation before multiplication/division, etc.
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1/2
If you are in Python 2.7
you will notice that this answer is wrong if $1,2\in\mathbb{R}$, but Python thinks they are integers, so it forces and integer. In order to have a more natural behavior of division we need
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from __future__ import division
1/2
So what else can we do? Where do we start if we are new? You can use ?
or help()
to get help.
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?
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help()
If you want information about a command, say mycommand
you can use help(mycommand)
, mycommand?
or mycommand??
to get information about how it is used or even see its code.
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help(sum)
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sum?
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sum??
We can print information
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print('Hello World!')
We can also create variables, which can be of various types
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a = 1
b = 2
a+b
a
and b
now hold numerical values we can use for computing
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c = [1,2]
d = [[1,2],[3,4]]
print('c=%s' % c)
print('d=%s' % d)
Notice that we have used %s
and %
to let Python know we are passing a string to the print function.
What kind of variables are c
and d
? They look like vectors and matrices, but...
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print('a*c=%s' % (a*c))
print('b*d=%s' % (b*d))
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c*d
Actually, Python does not have vectors or matrices directly available. Instead it has lists, sets, arrays, etc., each with its own set of operations. We defined c
and d
as list objects
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type(c)
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type(d)
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type(a)
Luckily Python has a powerful package for numerical computing called Numpy.
In order to use a package in Python or IPython, say mypackage
, you need to import it, by executing
import mypackage
After executing this command, you will have access to the functions and objects defined in mypackage
. For example, if mypackage
has a function squared
that takes a real number x
and computes its square, we can use this function by calling mypackage.squared(x)
. Since the name of some packages might be too long, your can give them a nickname by importing them instead as
import mypackage as myp
so now we could compute the square of x
by calling myp.squared(x)
.
We will see various packages that will be useful to do computations, statistics, plots, etc.
IPython has a command that imports Numpy and Matplotlib (Python's main plotting package). Numpy is imported as np
and Matplotlib as plt
. One could import these by hand by executing
import numpy as np
import matplotlib as plt
but the creators of IPython have optimized the interaction between these packages by running the following command:
%pylab
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%pylab?
I do recommend using the --no-import-all
option in order to ensure you do not contaminate the namespace. Instead it might be best to use
%pylab --no-import-all
%matplotlib
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%matplotlib?
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%pylab --no-import-all
%matplotlib inline
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np?
Let us now recreate c
and d
, but as Numpy arrays instead.
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ca = np.array(c)
da = np.array(d)
print('c=%s' % c)
print('d=%s' % d)
print('ca=%s' % ca)
print('da=%s' % da)
We could have created them as matrices intead. Again how you want to cerate them depends on what you will be doing with them. See here for an explanation of the differences between Numpy arrays and matrices.
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cm = np.matrix(c)
dm = np.matrix(d)
print('cm=%s' % cm)
print('dm=%s' % dm)
Let's see some information about these...(this is a good moment to show tab completion...a wonderful feature of IPython, which is not avalable if Python)
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cm.shape
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ca.shape
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dm.diagonal()
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da.cumsum()
Let's try again some operations on our new arrays and matrices
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cm*dm
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ca
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da
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ca*da
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ca.dot(da)
We can create special matrices using Numpy's functions and classes
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print(np.ones((3,4)))
print(np.zeros((2,2)))
print(np.eye(2))
print(np.ones_like(cm))
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np.random.uniform(-1,1,10)
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#np.random.seed(123456)
x0 = 0
x = [x0]
[x.append(x[-1] + np.random.normal() ) for i in range(500)]
plt.plot(x)
plt.title('A simple random walk')
plt.xlabel('Period')
plt.ylabel('Log Income')
plt.show()
We have used some of the functions in Python, Numpy and Matplotlib. But what if we wanted to create our own functions? It is very easy to do so in Python. There are two ways to define functions. Let's use them to define the CRRA utility function $u(c)=\frac{c^{1-\sigma}-1}{1-\sigma}$ and the production function $f(k)=Ak^\alpha$.
The first method is as follows:
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def u(c,sigma):
'''This function returns the value of utility when the CRRA
coefficient is sigma. I.e.
u(c,sigma)=(c**(1-sigma)-1)/(1-sigma) if sigma!=1
and
u(c,sigma)=ln(c) if sigma==1
Usage: u(c,sigma)
'''
if sigma!=1:
u = (c**(1-sigma) - 1) / (1-sigma)
else:
u = np.log(c)
return u
This defined the utility function. Let's plot it for $0< c\le5$ and $\sigma\in\{0.5,1,1.5\}$
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c = np.linspace(0.1,5,100)
u1 = u(c,.5)
u2 = u(c,1)
u3 = u(c,1.5)
plt.plot(c,u1,label=r'$\sigma=.5$')
plt.plot(c,u2,label=r'$\sigma=1$')
plt.plot(c,u3,label=r'$\sigma=1.5$')
plt.xlabel(r'$c_t$')
plt.ylabel(r'$u(c_t)$')
plt.title('CRRA Utility function')
plt.legend(loc=4)
plt.show()
While this is nice, it requires us to always have to put a value for the CRRA coefficient. Furthermore, we need to remember if $c$ is the first or second argument. Since we tend to use log-utilities a lot, let us change the definition of the utility function so that it has a default value for $\sigma$ equal to 1
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def u(c, sigma=1):
'''This function returns the value of utility when the CRRA
coefficient is sigma. I.e.
u(c,sigma)=(c**(1-sigma)-1)/(1-sigma) if sigma!=1
and
u(c,sigma)=ln(c) if sigma==1
Usage: u(c,sigma=value), where sigma=1 is the default
'''
if sigma!=1:
u = (c**(1-sigma) - 1) / (1-sigma)
else:
u = np.log(c)
return u
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sigma1 = .25
sigma3 = 1.25
u1 = u(c, sigma=sigma1)
u2 = u(c)
u3 = u(c, sigma=sigma3)
plt.plot(c, u1, label=r'$\sigma='+str(sigma1)+'$')
plt.plot(c, u2, label=r'$\sigma=1$')
plt.plot(c, u3, label=r'$\sigma='+str(sigma3)+'$')
plt.xlabel(r'$c_t$')
plt.ylabel(r'$u(c_t)$')
plt.title('CRRA Utility function')
plt.legend(loc=4)
plt.show()
The second method is to use the lambda
notation, which allows you to define functions in one line or without giving the function a name.
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squared = lambda x: x**2
squared(2)
Let's write a script that prints "Hello World!"
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%%file?
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%%file helloworld.py
#!/usr/bin/env python
# coding=utf-8
'''
My First script in Python
Author: Me
E-mail: me@me.com
Website: http://me.com
GitHub: https://github.com/me
Date: Today
This code computes Random Walks and graphs them
'''
'''
from __future__ import division
import numpy as np
import matplotlib.pyplot as plt
'''
print('Hello World!')
Let's run that script
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%run helloworld.py
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import time
time.sleep(10)
print("It's time")
Notebook written by Ömer Özak for his Ph.D. students in Economics at Southern Methodist University. Feel free to use, distribute, or contribute.