Quick demonstration of GNU Octave¶

in a Jupyter Notebook¶

This Jupyter Notebook was written by Lilian Besson.

TODO: finish this!
FIXME: something weird is going on...

Some basic plotting¶

In [30]:

% Some variables
N = 100
disp(['Number of values N =', num2str(N)])
h = 1 / N
disp(['Step h = ', num2str(h)])

N =  100
Number of values N =100
h =  0.010000
Step h = 0.01

In [29]:

% Some arrays
t = 0 : h : 2*pi;
x = cos(t);
y = sin(t);
length(t)
length(x)
length(y)

ans =  629
ans =  629
ans =  629

In [16]:

fig = figure();
plot(t, x, 'r*-')
grid on
hold on
plot(t, y, 'b+-')
legend(['\cos(t)', '\sin(t)'])
title('Cosinus and sinus on [0, 2 \pi]')
% whitebg(fig);

In [17]:

fig = figure();
grid on
plot(x, y)
title('\sin(t) as function of \cos(t)')
% whitebg(fig);

Some basic linear algebra¶

In [19]:

a = [[1 0 1]; [0 1 1]; [1 1 0]]

In [20]:

a'

In [21]:

b = 1 + a^5

b =

   12   11   12
   11   12   12
   12   12   11

eig gives the eigen values:

In [24]:

l_a = eig(a)
l_b = eig(b)

In [34]:

[Ua, Sa, Va] = svd(a)
[Ub, Sb, Vb] = svd(b)

Ua =

  -5.7735e-01   4.0825e-01  -7.0711e-01
  -5.7735e-01  -8.1650e-01  -7.8505e-17
  -5.7735e-01   4.0825e-01   7.0711e-01

Sa =

Diagonal Matrix

   2.00000         0         0
         0   1.00000         0
         0         0   1.00000

Va =

  -0.57735   0.81650  -0.00000
  -0.57735  -0.40825   0.70711
  -0.57735  -0.40825  -0.70711

Ub =

  -5.7735e-01   4.0825e-01  -7.0711e-01
  -5.7735e-01  -8.1650e-01  -1.6098e-15
  -5.7735e-01   4.0825e-01   7.0711e-01

Sb =

Diagonal Matrix

   35.00000          0          0
          0    1.00000          0
          0          0    1.00000

Vb =

  -0.57735   0.81650  -0.00000
  -0.57735  -0.40825   0.70711
  -0.57735  -0.40825  -0.70711

That's all for today, folks!