**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).

- A browser-based notebook with support for code, text, mathematical expressions, inline plots and other rich media.
- Support for interactive data visualization and use of GUI toolkits.
- Flexible, embeddable interpreters to load into your own projects.
- Easy to use, high performance tools for parallel computing.

**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 -c r -c mro --override-channels python=3.9 georasters geopandas pandas spatialpandas statsmodels xlrd networkx ipykernel ipyparallel ipython ipython_genutils ipywidgets jupyter jupyterlab kiwisolver matplotlib-base matplotlib scikit-image scikit-learn scipy seaborn geoplot geopy geotiff pycountry nb_conda_kernels stata_kernel nltk
```

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
```

I assume you have followed the steps above and have installed `Anaconda`

. Everything that is done should work on any distribution that has the required packages, since the Python scripts should run (in principle) on any of these distributions.

We will use IPython as our computing environment.

Once you have your Python distribution installed you'll be ready to start working. You have various options:

- Open the
`Canopy`

program and work there - Open
`Anaconda Navigator`

and open one of the apps from there (`python`

,`ipython`

,`jupyter console`

,`jupyter notebook`

,`jupyter lab`

,`R`

,`Stata`

- From the Terminal prompt (command-line in Windows) execute one of the following commands:
`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.

You can pass some additional commands to `ipython`

in order to change colors and rendering of plots. I usually use `jupyter qtconsole --color=linux --pylab=inline`

. You can create profiles to manage many options within `IPython`

and `JuPyter`

.

Let's start by running some simple commands at the prompt to do some simple computations.

In [ ]:

```
1+1-2
```

In [ ]:

```
3*2
```

In [ ]:

```
3**2
```

In [ ]:

```
-1**2
```

In [ ]:

```
3*(3-2)
```

In [ ]:

```
3*3-2
```

In [ ]:

```
1/2
```

`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

In [ ]:

```
from __future__ import division
1/2
```

It is a good idea to include this among the packages to be imported by default

So what else can we do? Where do we start if we are new? You can use `?`

or `help()`

to get help.

In [ ]:

```
?
```

In [ ]:

```
help()
```

`mycommand`

you can use `help(mycommand)`

, `mycommand?`

or `mycommand??`

to get information about how it is used or even see its code.

In [ ]:

```
help(sum)
```

In [ ]:

```
sum?
```

In [ ]:

```
sum??
```

We can print information

In [ ]:

```
print('Hello World!')
```

We can also create variables, which can be of various types

In [ ]:

```
a = 1
b = 2
a+b
```

`a`

and `b`

now hold numerical values we can use for computing

In [ ]:

```
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...

In [ ]:

```
print(' a * c = %s' % (a * c))
print(' b * d = %s' % (b * d))
```

In [ ]:

```
c*d
```

`c`

and `d`

as list objects

In [ ]:

```
type(c)
```

In [ ]:

```
type(d)
```

In [ ]:

```
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
```

In [ ]:

```
%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
```

In [ ]:

```
%matplotlib?
```

In [ ]:

```
%pylab --no-import-all
%matplotlib inline
```

In [ ]:

```
np?
```

Let us now recreate `c`

and `d`

, but as Numpy arrays instead.

In [ ]:

```
ca = np.array(c)
da = np.array(d)
print('c = %s' % c)
print('d = %s' % d)
print('ca = %s' % ca)
print('da = %s' % da)
```

In [ ]:

```
cm = np.matrix(c)
dm = np.matrix(d)
print('cm = %s' % cm)
print('dm = %s' % dm)
```

*wonderful* feature of IPython, which is not avalable if Python)

In [ ]:

```
cm.shape
```

In [ ]:

```
ca.shape
```

In [ ]:

```
dm.diagonal()
```

In [ ]:

```
da.cumsum()
```

Let's try again some operations on our new arrays and matrices

In [ ]:

```
cm*dm
```

In [ ]:

```
ca
```

In [ ]:

```
da
```

In [ ]:

```
ca*da
```

In [ ]:

```
ca.dot(da)
```

We can create special matrices using Numpy's functions and classes

In [ ]:

```
print(np.ones((3,4)))
print(np.zeros((2,2)))
print(np.eye(2))
print(np.ones_like(cm))
```

In [ ]:

```
np.random.uniform(-1,1,10)
```

In [ ]:

```
#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:

In [ ]:

```
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 $\sigma\in\{0.5,1,1.5\}$

In [ ]:

```
# Create vector
c = np.linspace(0.1, 5, 100)
# Evaluate utilities for different CRRA parameters
u1 = u(c, .5)
u2 = u(c, 1)
u3 = u(c, 1.5)
# Plot
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.savefig('./CRRA.jpg', dpi=150)
plt.savefig('./CRRA.pdf', dpi=150)
plt.savefig('./CRRA.png', dpi=150)
plt.show()
```

In [ ]:

```
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
```

In [ ]:

```
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()
```

Write the function for the Cobb-Douglas production function. Can you generalize it so that we can use it for aggregate, per capita, and per efficiency units without having to write a function for each?

Remember aggregate production is $$ Y = F(K, AL) = K^\alpha (A L)^{1-\alpha}, $$

per capita is

$$ \hat y=\frac{F(K, AL)}{L} = \frac{K^\alpha (A L)^{1-\alpha}}{L} = Ak^\alpha, $$and per effective worker

$$ y = \frac{F(K, AL)}{AL} = \frac{K^\alpha (A L)^{1-\alpha}}{AL} = k^\alpha, $$where $k=K/AL$.

`lambda`

notation, which allows you to define functions in one line or without giving the function a name.

In [ ]:

```
squared = lambda x: x**2
squared(2)
```

Let's write a script that prints "Hello World!"

In [ ]:

```
%%file?
```

In [ ]:

```
%%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

In [ ]:

```
%run helloworld.py
```

Write a simple script `randomwalk.py`

that simulates and plots random walks. In particular, create a function `randomwalk(x0, T, mu, sigma)`

that simulates the random walk starting at $x_0=x0$ until $t=T$ where the shock is distributed $\mathcal{N}(\mu,\sigma^2)$

In [ ]:

```
import randomwalk as rw
```

In [ ]:

```
rw.randomwalk(0, 500, 0, 1)
```

In [ ]:

```
from randomwalk import randomwalk
```

In [ ]:

```
randomwalk??
```

In [ ]:

```
import time
time.sleep(10)
print("It's time")
```