4th GouTP | Date : 18 Jan 2018 | Lilian Besson

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## 4th 2017/18 GouTP @ SCEE

- *About:* **Python introduction for MATLAB users**

- *Date:* 18th of January 2018

- *Who:* Lilian Besson

---

## What's a *"GouTP"* ?

- **Internal monthly technical training session** 📅
- Usually: *Thursday 3pm - 3:30pm*
- With ☕ coffee and 🍪 sweets : we relax while training !

> Initiative of Quentin and Vincent 👏 in last January...
  > Continued by Rémi and Lilian 👌 !

#### Not only @ SCEE ?
- Currently open to the *FAST* and *AUT* teams

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## Agenda for today [30 min]

1. What is Python [5 min]
2. Main differences in syntax and concepts [5 min]
3. Examples of problems solved Python [10 min]
4. Where can you find more information ?  [5 min]

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## 1. What is Python 🐍 ?

- developed and popular from the last 25 years
- Open-source and free programming language
- Interpreted, multi-platform, imperative and object-oriented
- Designed and acknowledged as *simple to learn and use*
- Used worldwide: research, data science, web applications etc

##### Ressources
- **Website**: python.org for the language & pypi.org for packages
- Documentation : docs.python.org (:fr: [docs.python.org/fr/3](https://docs.python.org/fr/3) translation in progress)

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## Comparison with MATLAB

---

> But Python don't have only advantages…

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## How to install Python ⬇
- On Linux and Mac OS : already installed!
- On Windows:
  + You can use the default installer from [python.org/downloads/windows](https://www.python.org/downloads/windows/) 🐍
  + Or the full installer from [anaconda.com/download](https://www.anaconda.com/download/) (✨)
- Takes about 10 minutes... and it's free !

> ⚠ Choose **Python 3** (currently 3.6.4) **not 2 !**
> ⚠ Python 2 will stop in less than 3 years (pythonclock.org)

---

## My suggestions for Python 🐍
- Use **Anaconda** to install (and upgrade) Python and packages
- Use **IPython** for the command line (✨ awesome features !)
- Use:
  + **Spyder** for your IDE if you like the MATLAB interface
    (installed in Anaconda, or  github.com/spyder-ide/spyder)
  + **PyCharm** if you want "the most powerful Python IDE ever"
  + Or a good generic text editor + a plugin for Python
    (Emacs, Vim, Atom, SublimeText, **Visual Studio Code**…)
- Use **Jupyter notebooks** to write or share your experiments
  (jupyter.org, eg. github.com/Naereen/notebooks)

> More suggestions: pierreh.eu/python-setup by Pierre Haessig

---

#### 📦 How to install modules in Python
- If you used Anaconda, use `conda install [name]` (in a terminal) to install module `[name]`,
- Or with the standard installer, use `pip install [name]`.

#### 🔍 How to find the module you need ?
- Ask your colleagues 😄 !
- Look on the Internet !
- Look directly on [pypi.org](https://pypi.org) (official) or [anaconda.org](https://anaconda.org)

---

## 📦 Overview of main Python modules
> Standard library is very rich, but not for scientific applications

- **Numpy** (numpy.org) for `numpy.array` for multi-dim arrays and linear algebra
- **Scipy** (scipy.org) for numerical computations (signal processing, integration, ODE integration, optimization etc)
- **Matplotlib** (matplotlib.org) for MATLAB-like 2D and 3D plots
- **pandas** for data manipulation (very powerful)
- **Scikit-Learn** (scikit-learn.org) for "classical" Machine Learning
- **Scikit-image** for 2D and generic image processing
- **Keras** (keras.io) for neural networks and deep learning

> And many others ! Check pypi.org

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## 2. Main differences in syntax between Python and MATLAB
> Ref: mathesaurus.sourceforge.net/matlab-python-xref.pdf

---

|  | Python | MATLAB
|:-|:-:|:-:|
| **Help** | `help(func)` or `func?` (IPython) | `help func`
| **And** | `a and b` | `a && b`
| **Or** | `a or b` | `a || b`
| **Datatype** | `np.array` of *any* type | multi-dim doubles array
| **Array** | `np.array([[1,2],[3,4]], dtype=float)` | `[1 2; 3 4]`
| **Size** | `np.size(a)` | `size(a)`
| **Nb Dim** | `np.ndim(a)` | `ndims(a)`
| **Last** | `a[-1]` | `a(end)`

> With `import numpy as np`

---

|  | Python | MATLAB
|:-|:-:|:-:|
| **Tranpose** | `a.T` | `a.'`
| **Conj. transpose** | `a.conj().T` | `a'`
| **Matrix** x | `a.dot(b)` or `a @ b` | `a * b`
| **Element-wise** x | `a * b` | `a .* b`
| **Element-wise** / | `a / b` | `a ./ b`
| **Element-wise** ^ | `a ** 3` | `a .^ 3`
| **Zeros** | `numpy.zeros((2,3,5))` | `zeros(2,3,5)`
| **Ones** | `numpy.ones((2,3,5))` | `ones(2,3,5)`
| **Identity** | `numpy.eye(10)` | `eye(10)`
| **Range** for loops | `range(0, 100, 2)` | `1:2:100`
| **Range** for arrays | `numpy.arange(0, 100, 2)` | `1:2:100`

---

> With `import numpy as np; import numpy.linalg as L`

---

## 3. Scientific problems solved with Python
> Just to give examples of syntax and modules

1. 1D numerical integration and plot
3. Solving a 2D Ordinary Differential Equation
2. Solving a constraint optimization problem and plotting solution
4. A simple neural network
5. Symbolic computations

---

## 3.1. 1D numerical integration and plot

> Goal : evaluate and plot the function on [-1, 1] :
> $$\mathrm{Ei}(x) := \int_{-\infty}^x \frac{\mathrm{e}^u}{u} \;\mathrm{d}u$$

#### How to?
Use modules!

- `numpy` for maths functions and arrays
- `scipy.integrate.quad` function for numerical integration
- `matplotlib.pyplot.plot` for 2D plotting

---

```python
import numpy as np                # standard convention
import matplotlib.pyplot as plt   # standard convention
from scipy.integrate import quad  # need only 1 function

def Ei(x, minfloat=1e-6, maxfloat=1000):
    def f(t):
        return np.exp(-t) / t
    if x > 0:
        return -1.0 * (quad(f, -x, -minfloat)[0]
                     + quad(f, minfloat, maxfloat)[0])
    else:
        return -1.0 * quad(f, -x, maxfloat)[0]

X = np.linspace(-1, 1, 1000) # 1000 points
Y = np.vectorize(Ei)(X)      # or [Ei(x) for x in X]
plt.plot(X, Y)               # MATLAB-like interface
plt.title("The function Ei(x)")
plt.xlabel("x"); plt.ylabel("y")
plt.savefig("figures/Ei_integral.png")
plt.show()
```

---

---

## 3.2. Solving a 2D Ordinary Differential Equation

> Goal : solve and plot the differential equation of a pendulum :
> $$\theta''(t) + b \,\theta'(t) + c \,\sin(\theta(t)) = 0$$

#### How to?
Use modules!

- `scipy.integrate.odeint` function for ODE integration
- `matplotlib.pyplot.plot` for 2D plotting

---

```python
import numpy as np
import matplotlib.pyplot as plt
from scipy.integrate import odeint  # use Runge-Kutta 4

def pend(y, t, b, c):  # function definition
    return np.array([y[1], -b*y[1] - c*np.sin(y[0])])

b, c = 0.25, 5.0  # tuple assignment
y0 = np.array([np.pi - 0.1, 0.0])
t = np.linspace(0, 10, 101)  # on [0,10] with 101 points

sol = odeint(pend, y0, t, args=(b, c))

plt.plot(t, sol[:, 0], 'b', label=r'$\theta(t)$')# blue
plt.plot(t, sol[:, 1], 'g', label=r'$\omega(t)$')# green
plt.legend(loc='best')
plt.xlabel('t')
plt.grid()
plt.savefig("figures/Pendulum_solution.png")
plt.show()
```

---

---

## 3.3. Constraint optimization problem

> Goal: minimize a function under inequality constraints
> $$f(x,y) := (x - 1)^2 + (y - 2.5)^2$$
> $$\text{such that } \begin{cases}x \geq 0 \text{ and } y \geq 0 \\ x - 2y + 2 \geq 0 \\ - x - 2y + 6 \geq 0 \\ x + 2y + 2 \geq 0\end{cases}$$

#### How to?

- `scipy.optimize.minimize` function for minimization
- `matplotlib.pyplot.plot` for 2D plotting

---

```python
import numpy as np
import matplotlib.pyplot as plt
from scipy.optimize import minimize

def obj(x):  return (x[0] - 1)**2 + (x[1] - 2.5)**2

x0 = (2, 0)  # first guess
bnds = ((0, None), (0, None))  # [0, +oo) for x and y
cons = ({'type': 'ineq', 'fun': lambda x: x[0]-2*x[1]+2},
        {'type': 'ineq', 'fun': lambda x:-x[0]-2*x[1]+6},
        {'type': 'ineq', 'fun': lambda x:-x[0]+2*x[1]+2})

res = minimize(obj, x0, method='SLSQP', bounds=bnds,
               constraints=cons)
print("Minimum is", res.x)  # (1.4, 1.7)
```

---

## 3.4. A simple neural network
> Using keras (keras.io) it's very simple and concise 😎 !

```python
from keras.models import Sequential
model = Sequential()

from keras.layers import Dense
model.add(Dense(units=64, activation='relu', input_dim=100))
model.add(Dense(units=10, activation='softmax'))

model.compile(loss='categorical_crossentropy',
              optimizer='sgd', metrics=['accuracy'])

## x_train and y_train are Numpy arrays
## just like in the Scikit-Learn API.
model.fit(x_train, y_train, epochs=5, batch_size=32)

## evaluate or predict using the model
loss_and_metrics = model.evaluate(x_test, y_test, batch_size=128)
classes = model.predict(x_test, batch_size=128)
```

---

## 3.5. Symbolic computations

- Almost impossible to do in MATLAB…
- Most Python code written for numerical values also works for symbolic values! Use **SymPy** module
- Powerful webtool like Wolfram|Alpha : [sympygamma.com](http://www.sympygamma.com/)
- An example from my latest article…
  + the same code works for numbers
  + or exact fractions
  + or symbols $\mu_1,\ldots,\mu_K$

---

##### Example : generated graph with numbers

> Graph saved a DOT file and to a TikZ graph with [dot2tex](https://github.com/Naereen/dot2tex)

---

##### Example : generated graph with fractions

> Source: [banditslilian.gforge.inria.fr/docs/complete_tree_exploration_for_MP_bandits.html](http://banditslilian.gforge.inria.fr/docs/complete_tree_exploration_for_MP_bandits.html)

---

##### Example : generated graph with symbols

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## Conclusion (1/3)

#### Sum-up
- I hope you got a good introduction to Python
  + Good tutorials: www.scipy-lectures.org
- It's not hard to migrate from MATLAB to Python
- More ressources:
  + official documentation : docs.scipy.org/doc/numpy-dev/user/numpy-for-matlab-users.html
  + a good 45-minute training video : youtu.be/YkCegjtoHFQ
  + mathesaurus.sourceforge.net/matlab-numpy.html and mathesaurus.sourceforge.net/matlab-python-xref.pdf

---

## Conclusion (2/3)

#### Next GouTP @ SCEE
> By Lilian
- Jupyter notebooks for teaching and research
  $\hookrightarrow$ jupyter.org

#### GouTP @ FAST or AUT ?
> By Pierre Haessig

- Julia programming language (~ between Python and Matlab)
  $\hookrightarrow$ julialang.org

> By you ? Any idea is welcome!

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## Conclusion (3/3)

> *Thanks for joining 👏 !* *Contact us if you want to do a GouTP!*

#### Your mission, if you accept it... 💥
1. *Padawan level:* Train yourself a little bit on Python 🐍
   $\hookrightarrow$ introtopython.org or learnpython.org
2. *Jedi level:* Try to solve a numerical system, from your research or teaching, in Python instead of MATLAB
3. *Master level:* From now on, try to use open-source tools for your research (Python and others)