Sunday, 5 January 2014

Typical degree problem & Python: Part 1

Recently I've been forced to use Matlab for solving some algebra exercises for my degree.
Matlab drives me mad in several ways and even before typing the first line of code, I've been thinking about solving the problems with python.

Let's start.

Problem 1 formulation:

Draw an ellipse with its semi axes measuring a=5 and b=2, then create a script that plots a number n of ellipses equal in size with common center, solve for n=30. Each ellipse should be rotated an angle of pi/n radian from the previous one. The output of the script should look like this:

Solution:

##### Libraries #####

from numpy import *


from math import *


import pyqtgraph as pg


#####################


##### Input Variables


a=7  # semi axis X value


b=2  # semi axis Y value


n=30 # number of ellipses


#####################


window=pg.plot(title="Concentric Ellipses") #Creates plot window called window


alpha=linspace(0,2*pi) # Creates line matrix with values from 0 to 2*pi


SA=size(alpha) # Gets the size of alpha matrix


E=zeros([2,SA]) # Creates a 2xSA matrix filled with zeros


for i in range(SA): # Gets X,Y values of the ellipse and stores them in E

  E[0,i]=a*cos(alpha[i])
  E[1,i]=b*sin(alpha[i])

beta=0 # Ellipse angle variable inicialization


for i in range(n): # Generates n concentric ellipses angled pi/n radians 

  
  TM=[[cos(beta),-sin(beta)],[sin(beta),cos(beta)]] # Transformation matrix
     
  RE=dot(TM,E) # RE contains the coordinates of the rotated ellipse
  
  REX=RE[0,:] # RE X values extraction
  REY=RE[1,:] # RE Y values extraction
  
  window.plot(REX,REY) # Plots the current rotated ellipse
  
  beta+=pi/n # Increases beta by pi/n steps
  


To see it working, open a terminal (ctrl+alt+t), type "python" and then copy-paste the code.
(you need to have installed the pyqtgraph module in order to plot, see this post)

The main difference between python and matlab scripts for this exercise is the library import header, being the rest of them very mimetic.


Second exercise on the next post, bye!