Motivation

• Programming is important in almost every field!
• Important for automating.
• There will be a knowledge gap in the society.

Programming in other courses

• FYS1120: Electromagnetism
• MAT1120: Linear algebra
• AST1100: Introduction to Astrophysics
• Other courses: FYS2130, FYS2140, FYS2160,....

Goals

• To provide a good practical background to preform calculations in Python and MATLAB relevant to FYS-MEK1110.
• You learn programming by doing it, not by just reading how to do it.

Terminal Basics

Commands

>> date
Wed Jan  9 17:31:05 CET 2013

                        

Useful Commands

Working directory

>> pwd
/home/milad/documents
                        

List files

>> ls
folder1 folder2
                        

Change working directory

>> cd folder1
>> pwd
/home/milad/documents/folder1
>> cd ..
>> pwd
/home/milad/documents
                        

Make directory/folder

>> mkdir folder3
>> ls 
folder1 folder2 folder3

                        

Remove directory/folder

>> rm -r folder3
>> ls
folder1 folder2
                        

Make an empty file

>> touch file
>> ls 
folder1 folder2 file

                        

Remove file

>> rm file
>> ls
folder1 folder2
                        

Move files

>> mv name_of_file destination
                        

Copy files

>> cp name_of_file destination

                        

Python vs MATLAB

from pylab import *
n = 1000
x = zeros((n,3))
v = zeros((n,3))
a = zeros((n,3))

m = 1
q = 1

B = array([0,0,1])
omega = q * linalg.norm(B)/m
                        

n = 1000;
x = zeros(n,3);
v = zeros(n,3);
a = zeros(n,3);

m = 1;
q = 1;

B = [0 0 1];
omega = q*norm(B)/m;
                        

Equal qualities

Both are easy to learn

Both are useful for maths and physics

Both give a quick way to do programming

Both are very easy to use

Differences

Python is free

(as in both speech and beer)

MATLAB costs money

MATLAB may be easier to install

Python can be easy

(but it can have a bad day...)

Python is able to do tons of stuff

(from physics and maths to games and applications, using modules...)

MATLAB is more limited

MATLAB comes with a strong editor

Python does not

(but you can install great editors such as Spyder...)

What to choose?

We recommend Python

But teach both ;)

Getting down and dirty

echo export PATH=/mn/felt/u9/svennard/mayavi/epd-latest/bin/:$PATH >> ~/.bashrc && source ~/.bashrc

idle

matlab

It's a calculator!

>>> 9*4
36

>> 9*4
36

It's a calculator!

>>> 9/5
1
>>> 9./5.
1.8

>> 9/5
1.8

Maths

>>> from pylab import *
>>> 4*pi
12.566370614359172

>> 4*pi
12.567

Variables

>>> TC = 40.
>>> print TC
40.0

>> TC = 40
40
>> TC
40

Temperature conversion

>>> TF = 9./5. * TC + 32.
>>> print TF
104.0

>> TF = 9/5 * TC + 32
104

Changing variable values

>>> TC = 12.
>>> print TC
12.0
>>> print TF
104.0

>> TC = 12
12
>> TF
104

Ooops! What went wrong?

Push the ↑ button on your keyboard a couple of times and calculate TF again...

Scripting

Python

MATLAB

Temperature conversion script

TC = 12.
TF = 9./5. * TC + 32.
print TF

TC = 12;
TF = 9/5 * TC + 32;

Run with F5.

(Note the semicolons for MATLAB...)

Testing behaviour

Type a new value for TC on the command line and re-run the script. Did anything change?

Functions

Temperature conversion function

def convertF(TC):
    TF = 9./5.*TC + 32.
    return TF

# different ways of printing
print convertF(10)
TF = convertF(30)
print TF

function TF=convertF(TC);
TF = 9/5*TC + 32;
return

% different ways of printing
convertF(10)
TF = convertF(30);
TF

Arrays

>>> TC = array([0, 10, 15.5, 20])
>>> print TC
[  0.   10.   15.5  20. ]

>> TC = [0 10 15.5 20]
TC =

         0   10.0000   15.5000   20.0000

Arrays and functions

>>> TC = array([0, 10, 15.5, 20])
>>> print convertF(TC)
[ 32.   50.   59.9  68. ] 

>> TC = [0 10 15.5 20];
>> convertF(TC)

ans =

   32.0000   50.0000   59.9000   68.0000

Plotting

Plotting

>>> m = [1, 2, 4, 6, 9, 11]
>>> V = [0.13, 0.26, 0.50, 0.77, 1.15, 1.36]
>>> print V[3]
0.77
>>> plot(m,V,'o')
>>> xlabel('m [kg]')
>>> ylabel('V [l]')
>>> show()


>>> m = [1, 2, 4, 6, 9, 11]
>>> V = [0.13, 0.26, 0.50, 0.77, 1.15, 1.36]
>>> print V[3]
0.77
>>> plot(m,V,'o')
>>> xlabel('m [kg]')
>>> ylabel('V [l]')
>>> show()
>>> m = [1, 2, 4, 6, 9, 11]
>>> V = [0.13, 0.26, 0.50, 0.77, 1.15, 1.36]
>>> print V[3]
0.77
>>> plot(m,V,'o')
>>> xlabel('m [kg]')
>>> ylabel('V [l]')
>>> show()
>>> m = [1, 2, 4, 6, 9, 11]
>>> V = [0.13, 0.26, 0.50, 0.77, 1.15, 1.36]
>>> print V[3]
0.77
>>> plot(m,V,'o')
>>> xlabel('m [kg]')
>>> ylabel('V [l]')
>>> show()

>> m = [1 2 4 6 9 11];
>> V = [0.13 0.26 0.50 0.77 1.15 1.36];
>> V(4)
ans =     0.7700
>> plot(m,V,'o')
>> xlabel('m [kg]')
>> ylabel('V [l]')

Reptition

Start your editors!

echo export PATH=/mn/felt/u9/svennard/mayavi/epd-latest/bin/:$PATH >> ~/.bashrc && source ~/.bashrc

idle

matlab

It's a calculator!

>>> 9*4
36

>> 9*4
36

>>> 9/5
1
>>> 9./5.
1.8

>> 9/5
1.8

Maths

>>> from pylab import *
>>> 4*pi
12.566370614359172

>> 4*pi
12.567

Temperature conversion

>>> TC = 40.
>>> print TC
40.0
>>> TF = 9./5. * TC + 32.
>>> print TF
104.0

>> TC = 40
40
>> TC
40
>> TF = 9/5 * TC + 32
104

Changing variable values

>>> TC = 12.
>>> print TC
12.0
>>> print TF
104.0

>> TC = 12
12
>> TF
104

Ooops! What went wrong?

Push the ↑ button on your keyboard a couple of times and calculate TF again...

Reptition

Scripting

Python

MATLAB

Temperature conversion function

def convertF(TC):
    TF = 9./5.*TC + 32.
    return TF

function TF=convertF(TC);
TF = 9/5*TC + 32;
return

>>> print convertF(40)
104.0

>> convertF(40)
104.0

Run with F5.

(Note the semicolons for MATLAB...)

Reptition

Arrays

>>> TC = array([0, 10, 15.5, 20])
>>> print TC
[  0.   10.   15.5  20. ]

>> TC = [0 10 15.5 20]
TC =

         0   10.0000   15.5000   20.0000

Arrays and functions

>>> TC = array([0, 10, 15.5, 20])
>>> print convertF(TC)
[ 32.   50.   59.9  68. ] 

>> TC = [0 10 15.5 20];
>> convertF(TC)

ans =

   32.0000   50.0000   59.9000   68.0000

Plotting

>>> m = [1, 2, 4, 6, 9, 11]
>>> V = [0.13, 0.26, 0.50, 0.77, 1.15, 1.36]
>>> print V[3]
0.77
>>> plot(m,V,'o')
>>> xlabel('m [kg]')
>>> ylabel('V [l]')
>>> show()

>> m = [1 2 4 6 9 11];
>> V = [0.13 0.26 0.50 0.77 1.15 1.36];
>> V(4)
ans =     0.7700
>> plot(m,V,'o')
>> xlabel('m [kg]')
>> ylabel('V [l]')

This is what we are going to do today!

and here is all the code we need

from pylab import *
from time import sleep
ion()
line, = plot(0,0)
xlim(-4,4)
ylim(-4,4)
show()
for maxt in arange(-50,50,0.2):
    t = arange(-50,maxt,0.01)
    x = sin(t) * (exp(cos(t)) - 2*cos(4*t) - pow(sin(t/12.), 5))
    y = cos(t) * (exp(cos(t)) - 2*cos(4*t) - pow(sin(t/12.), 5))
    line.set_xdata(x)
    line.set_ydata(y)
    draw()
    sleep(0.01)

Don't worry, we'll explain it all to you ;)

Why for loops?

for-loops

Let's say you want to plot

$f(x)=sin(x)$ for

$x=0, 0.1, 0.2, 0.3, ...9.9, 10$

We need to make an array which is a list of all x-values

It would be really boring to type every element in this array!

>>> x = array([0, 0.1, 0.2, 0.3])

>> x = [0, 0.1, 0.2, 0.3]

Fortunately, there is a more efficient way of doing this:

by using a for-loop!

Going from $0.0$ to $10.0$ in steps of $0.1$ we need:

zeros((n,m)) function:
makes an array with dimention $n \times m$, where all elements are zero.

>>> zeros((1,10))
array([[ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.]])

>>> zeros((10,1))
array([[ 0.],
       [ 0.],
       [ 0.],
       [ 0.],
       [ 0.],
       [ 0.],
       [ 0.],
       [ 0.],
       [ 0.],
       [ 0.]])

for-loop:

from pylab import *
x0 = 0.0
x1 = 10.0
dx = 0.1


n = ceil (( x1 - x0 ) / dx ) + 1

x = zeros (( n , 1) )

for i in range (int (n)) :
    x [ i ] = x0 + i * dx

plot (x , sin(x),'-o' )
show ()
print x, n

range-function

>>> range(10)
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]

>>> range(0,10)
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]

>>> range(1,10)
[1, 2, 3, 4, 5, 6, 7, 8, 9]

>>> range(1,10,1)
[1, 2, 3, 4, 5, 6, 7, 8, 9]

>>> range(1,10,2)
[1, 3, 5, 7, 9]

>>> range(0,10,0.1)

Vectorization

linspace(a,b,c)

>>> linspace(1,10,10)
array([  1.,   2.,   3.,   4.,   5.,   6.,   7.,   8.,   9.,  10.])

from pylab import *
x=linspace(0,10,100)
plot (x , sin(x),'-o' )
show ()

arange(a,b,c)

>>> arange(0,1,0.1)
array([ 0. ,  0.1,  0.2,  0.3,  0.4,  0.5,  0.6,  0.7,  0.8,  0.9])

from pylab import *
x=arange(0,10,0.1)
plot (x , sin(x),'-o' )
show ()

What if...

...we explore if-tests?

Dice throwing

Dice throwing

from pylab import *
points = 0
diceResult = randint(1,7)
if diceResult < 4:
    points = points + 1
else:
    points = points - 1
print points

Dice throwing

from pylab import *
points = 0
for i in range(1000):
    diceResult = randint(1,7)
    if diceResult < 4:
        points = points + 1
    else:
        points = points - 1
print points

Programming motion

Taking positions of objects through steps in time

Programming motion

Programming motion

$\vec r(t_i + \Delta t) = \vec r(t_i) + \Delta t \cdot \vec v(t_i)$

$\vec v(t_i + \Delta t) = \vec v(t_i) + \Delta t \cdot \vec a(t_i)$

Python example

from pylab import *
n = 100
dt = 0.10
x = zeros((n,1))
v = zeros((n,1))
a = zeros((n,1))
t = zeros((n,1))
a[0] = 300
x[0] = 0
v[0] = 0
for i in range(0,n-1):
   a[i+1] = a[i]
   v[i+1] = v[i] + a[i]*dt
   x[i+1] = x[i] + v[i+1]*dt
   t[i+1] = t[i] + dt
subplot(3,1,1)
plot(t,a)
xlabel('t')
ylabel('a')
subplot(3,1,2)
plot(t,v)
xlabel('t')
ylabel('v')
subplot(3,1,3)
plot(t,x)
xlabel('t')
ylabel('x')