Table of Contents

1  Quick demonstration of GNU Octave

1.1  Some basic plotting

1.2  Some basic linear algebra

1.3  3D plotting

1.4  Conclusion

Quick demonstration of GNU Octave

In a Jupyter Notebook

• This Jupyter Notebook was written by Lilian Besson.
• It uses the unofficial Octave kernel for Jupyter by @Calysto.

---

Some basic plotting

Let show some basic use of GNU Octave for computations, and plotting.

% 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

% 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

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

fig = figure();
plot(x, y);
title('sin(t) as function of cos(t)')

---

Some basic linear algebra

We can also easily work with matrices and showcase a little bit of linear algebra.

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

a =

   1   0   1
   0   1   1
   1   1   0

a'  # a transpose

ans =

   1   0   1
   0   1   1
   1   1   0

b = 1 + a^5

b =

   12   11   12
   11   12   12
   12   12   11

eig gives the eigen values:

Test of notes.

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

l_a =

  -1.00000
   1.00000
   2.00000

l_b =

   -1.00000
    1.00000
   35.00000

[Ua, Sa, Va] = svd(a)

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, Sb, Vb] = svd(b)

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

---

3D plotting

Some basic 3D plotting:

x = linspace(-2, 2, 50);
y = linspace(-2, 2, 50);
[xx,yy] = meshgrid(x, y);
mesh(xx, yy, 4 - (xx.^2 + yy.^2))

x = linspace(-2, 2, 50);
y = linspace(-2, 2, 50);
[xx,yy] = meshgrid(x, y);
meshc(xx, yy, 4 - (xx.^2 + yy.^2))

# From https://octave.sourceforge.io/octave/function/plot3.html
z = [0:0.05:5];
plot3(cos (2*pi*z), sin (2*pi*z), z, ";helix;");
plot3(z, exp (2i*pi*z), ";complex sinusoid;");

clf;
z = [0:0.05:5];
plot3 (cos (2*pi*z), sin (2*pi*z), z);
legend ("helix");
title ("plot3() of a helix");

clf;
colormap ("default");
[X, Y] = meshgrid (linspace (-3, 3, 40));
Z = sqrt (abs (X .* Y)) ./ (1 + X.^2 + Y.^2);
meshc (X, Y, Z);
title ("meshc() combines mesh/contour plots");

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Conclusion

We showed a little bit how to use a Jupyter notebook with GNU Octave (or GNU Octave with a Jupyter notebook?).

That's all for today, folks!