Merge branch 'master' of gitlab.unige.ch:Thibaut.Lunet/python-math

examples/scipy/README.md

@@ -17,4 +17,4 @@ f(u) = c_x \frac{\partial u}{\partial x}
 ```
 
 It compute it in 1D, 2D, 3D, and extract the eigenvalues for each cases.
-in particular, it uses the [eigvals](https://docs.scipy.org/doc/scipy/reference/generated/scipy.linalg.eigvals.html) of the scipy package.
\ No newline at end of file
+In particular, it uses the [eigvals](https://docs.scipy.org/doc/scipy/reference/generated/scipy.linalg.eigvals.html) of the scipy package.

examples/sympy/README.md

+# Sympy examples
+
+This directory contains several script that show how sympy can be used for particular scientific applications.
+Also, you can look at an [extended list of Sympy Tutorials](http://docs.sympy.org/latest/tutorial/index.html) to go further ...
+
+## [solve-diff-eqns.py](solve-diff-eqns.py)
+
+This script is a basic example of how to solve a differential equation using sympy.
+
+In particular, the equation u''(t) - u(t) = exp(t) is solved, using the sympy function dsolve [minimize](http://docs.sympy.org/latest/modules/solvers/ode.html).

examples/sympy/solve-diff-eqns.py

+#!/usr/bin/env python2
+# -*- coding: utf-8 -*-
+"""
+Sympy example: How to solve a differential equation using sympy 
+
+@author: a.perez
+"""
+
+import sympy as sy
+
+# Define a generic function u and its variable, t
+u = sy.Function('u')
+t = sy.symbols('t')
+
+# We want to solve the differential equation u''(t) - u(t) = exp(t)
+
+u_tt = sy.diff(u(t), t, t)  # Second derivative of u wrt t
+                            # (symbolic, since u is a generic function)
+
+lhs = u_tt - u(t)           # Left hand-side of the equation
+rhs = sy.exp(t)             # Right hand-side of the equation
+
+eq = sy.Eq(lhs, rhs)        # We create the equation
+
+
+sol = sy.dsolve(eq, u(t))   # And we solve it using the function dsolve,
+                            # wrt the function u(t)
+                            
+                            
+# Now sol is the equation:
+#   u(t) = C2*exp(-t) + (C1 + t/2)*exp(t)

exercises/4-Numpy/numpy1-chessboard-solution.py

@@ -3,7 +3,8 @@
 
 # Exercise 4.1: Numpy chessboard - Solution
 #
-# Create a 8x8 matrix with a chessboard pattern with numbers 1 and 0.
+# Create a 8x8 matrix with a chessboard pattern with numbers 1 and 0,
+# then visualize it with the function imshow from matplotlib.
 
 import numpy as np
 import matplotlib.pyplot as plt
@@ -19,5 +20,4 @@ def chessboard():
 
 
 M = chessboard()
-print(M)
 plt.imshow(M, cmap='binary')

exercises/4-Numpy/numpy1-chessboard.py

@@ -3,12 +3,16 @@
 
 # Exercise 4.1: Numpy chessboard
 #
-# Create a 8x8 matrix with a chessboard pattern with numbers 1 and 0.
+# Create a 8x8 matrix with a chessboard pattern with numbers 1 and 0,
+# then visualize it with the function imshow from matplotlib.
 
 import numpy as np
+import matplotlib.pyplot as plt
+
 
 def chessboard():
     pass # Your code here
 
 
-print(chessboard())
+M = chessboard()
+plt.imshow(M, cmap='binary')