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# Learn More
**This content is from the *Scientific Python QuickStart* by [Thomas J. Sargent](http://www.tomsargent.com/) and [John
Stachurski](https://johnstachurski.net/), originally published as the [JupyterBook example](https://executablebooks.github.io/quantecon-mini-example/docs/index.html).
We will be gradually adding more introductory Python materials by actuarial contributors. In the meantime, consider also referring to the [Python Study Group microsite](https://actuaries.asn.au/microsites/actuaries-in-data-analytics/knowledge/python-study-group) for materials from the 2021 YDAWG-organised sessions.**
We're about ready to wrap up this brief course on Python for scientific
computing.
In this last lecture we give some pointers to the major scientific libraries
and suggestions for further reading.
## NumPy
Fundamental matrix and array processing capabilities are provided by the
excellent [NumPy](http://www.numpy.org/) library.
For example, let\'s build some arrays
```{code-cell} ipython3
import numpy as np # Load the library
a = np.linspace(-np.pi, np.pi, 100) # Create even grid from -π to π
b = np.cos(a) # Apply cosine to each element of a
c = np.sin(a) # Apply sin to each element of a
```
Now let\'s take the inner product
```{code-cell} ipython3
b @ c
```
The number you see here might vary slightly due to floating point arithmetic
but it\'s essentially zero.
As with other standard NumPy operations, this inner product calls into highly
optimized machine code.
It is as efficient as carefully hand-coded FORTRAN or C.
## SciPy
The [SciPy](http://www.scipy.org) library is built on top of NumPy and
provides additional functionality.
(tuple_unpacking_example)=
For example, let\'s calculate $\int_{-2}^2 \phi(z) dz$ where $\phi$ is
the standard normal density.
```{code-cell} ipython3
from scipy.stats import norm
from scipy.integrate import quad
ϕ = norm()
value, error = quad(ϕ.pdf, -2, 2) # Integrate using Gaussian quadrature
value
```
SciPy includes many of the standard routines used in
- [linear algebra](http://docs.scipy.org/doc/scipy/reference/linalg.html)
- [integration](http://docs.scipy.org/doc/scipy/reference/integrate.html)
- [interpolation](http://docs.scipy.org/doc/scipy/reference/interpolate.html)
- [optimization](http://docs.scipy.org/doc/scipy/reference/optimize.html)
- [distributions and random number generation](http://docs.scipy.org/doc/scipy/reference/stats.html)
- [signal processing](http://docs.scipy.org/doc/scipy/reference/signal.html)
See them all [here](http://docs.scipy.org/doc/scipy/reference/index.html).
## Graphics
The most popular and comprehensive Python library for creating figures
and graphs is [Matplotlib](http://matplotlib.org/), with functionality
including
- plots, histograms, contour images, 3D graphs, bar charts etc.
- output in many formats (PDF, PNG, EPS, etc.)
- LaTeX integration
Example 2D plot with embedded LaTeX annotations
```{figure} /_static/lecture_specific/about_py/qs.png
:scale: 55%
```
Example contour plot
```{figure} /_static/lecture_specific/about_py/bn_density1.png
:scale: 55%
```
Example 3D plot
```{figure} /_static/lecture_specific/about_py/career_vf.png
:scale: 80%
```
More examples can be found in the [Matplotlib thumbnail
gallery](http://matplotlib.org/gallery.html).
Other graphics libraries include
- [Plotly](https://plot.ly/python/)
- [Bokeh](http://bokeh.pydata.org/en/latest/)
## Symbolic Algebra
It\'s useful to be able to manipulate symbolic expressions, as in
Mathematica or Maple.
The [SymPy](http://www.sympy.org/) library provides this functionality
from within the Python shell.
```{code-cell} ipython3
from sympy import Symbol
x, y = Symbol('x'), Symbol('y') # Treat 'x' and 'y' as algebraic symbols
x + x + x + y
```
We can manipulate expressions
```{code-cell} ipython3
expression = (x + y)**2
expression.expand()
```
solve polynomials
```{code-cell} ipython3
from sympy import solve
solve(x**2 + x + 2)
```
and calculate limits, derivatives and integrals
```{code-cell} ipython3
from sympy import limit, sin, diff
limit(1 / x, x, 0)
```
```{code-cell} ipython3
limit(sin(x) / x, x, 0)
```
```{code-cell} ipython3
diff(sin(x), x)
```
The beauty of importing this functionality into Python is that we are
working within a fully fledged programming language.
We can easily create tables of derivatives, generate LaTeX output, add
that output to figures and so on.
## Pandas
One of the most popular libraries for working with data is
[pandas](http://pandas.pydata.org/).
Pandas is fast, efficient, flexible and well designed.
Here\'s a simple example, using some dummy data generated with Numpy\'s
excellent `random` functionality.
```{code-cell} ipython3
import pandas as pd
np.random.seed(1234)
data = np.random.randn(5, 2) # 5x2 matrix of N(0, 1) random draws
dates = pd.date_range('28/12/2010', periods=5)
df = pd.DataFrame(data, columns=('price', 'weight'), index=dates)
print(df)
```
```{code-cell} ipython3
df.mean()
```
## Further Reading
These lectures were originally taken from a longer and more complete lecture
series on Python programming hosted by [QuantEcon](https://quantecon.org).
The [full set of lectures](https://python-programming.quantecon.org/) might be
useful as the next step of your study.