TL: added sympy example, typo

examples/README.md

@@ -25,5 +25,9 @@ Contains scripts that use numpy python package for specific applications
 
 Contains scripts that use scipy python package for specific applications
 
+## [sympy](sympy/)
+
+Contains scripts that use sympy python package for symbolic computation
+
 [MarkDown documentation](https://docs.gitlab.com/ee/user/markdown.html) - General synthax for *.md* files
 

examples/numpy/README.md

@@ -12,8 +12,9 @@ in the [data.txt](data.txt) file, modify those and write the modified data into
 ## [callFortranRoutine.py](callFortranRoutine.py)
 
 Perform the [Rutishauser-Kahan-Pal-Walker algorithm](https://link.springer.com/content/pdf/10.1007/BF01405565.pdf) to transform an arrow matrix (with non-zero elements
-in the first row and column, and diagonal) into a symmetric trifdiagonal matrix.
-It uses the [f2py](https://www.numfys.net/howto/F2PY/) sub-module of numpy to compile a fortran subroutine that can be called in python. 
+in the first row and column, and diagonal) into a symmetric tridiagonal matrix.
+It uses the [f2py](https://www.numfys.net/howto/F2PY/) sub-module of numpy to compile a fortran subroutine (written in [libfor.f95](libfor.f95)) 
+that can be called in python. 
 
 
 ## [csv-read-interpol-plot.py](csv-read-interpol-plot.py)

examples/sympy/README.md

@@ -7,4 +7,9 @@ Also, you can look at an [extended list of Sympy Tutorials](http://docs.sympy.or
 
 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).
+In particular, the equation u''(t) - u(t) = exp(t) is solved, using the sympy function [dsolve](http://docs.sympy.org/latest/modules/solvers/ode.html).
+
+## [generalMidPointInterpolation.py](generalMidPointInterpolation.py)
+
+This script compute the general formula of mid-point interpolation on one-dimensionnal uniform grids.
+The interpolation can be computed for any order (1, 3, 5, ... always an odd number) 

examples/sympy/generalMidPointInterpolation.py

+#!/usr/bin/env python2
+# -*- coding: utf-8 -*-
+"""
+Created on Wed Oct 19 18:54:50 2016
+
+@author: t.lunet
+"""
+import sympy as sy
+from time import time
+sy.init_printing()
+
+# Interpolation order : 1, 3, 5, ... always odd number
+nP = 1
+
+# Setup computations
+i0 = (nP-1)//2
+A = sy.zeros(nP+1)
+e = sy.ones(1, nP+1)
+
+# Construction of dX symbols
+lDx = []
+for i in range(nP):
+    lDx.append(sy.Symbol('\\Delta x_{'+str(i-i0)+'}'))
+lPos = [0]*(nP+1)
+lPos[i0] = 0
+for i in range((nP-1)//2):
+    lPos[i0-i-1] = lPos[i0-i]-lDx[i0-i-1]
+for i in range((nP+1)//2):
+    lPos[i0+i+1] = lPos[i0+i]+lDx[i0+i]
+
+# Contruct vandermonde matrix
+for i in range(nP+1):
+    c = i-i0
+    for j in range(nP+1):
+        A[i, j] = c**j
+
+# Coordinate for middle point
+for i in range(nP+1):
+    e[0, i] /= 2**i
+
+
+print('Inverting A')
+t0 = time()
+coeff = e * A.inv()
+print(' -- computation time = {:.2f}'.format(time()-t0))
+
+print('Simplifying coeff')
+t0 = time()
+coeff.simplify()
+print(' -- computation time = {:.2f}'.format(time()-t0))

examples/sympy/solve-diff-eqns.py

 #!/usr/bin/env python2
 # -*- coding: utf-8 -*-
 """
-Sympy example: How to solve a differential equation using sympy 
+Sympy example: How to solve a differential equation using sympy
 
 @author: a.perez
 """
 
 import sympy as sy
+sy.init_printing()
 
 # Define a generic function u and its variable, t
 u = sy.Function('u')
@@ -25,7 +26,7 @@ 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)