2431-Using Octave as simple Calculator.sagews

Using Octave as simple Calculator

%octave
1+1

ans = 2

3*4

ans = 12

2^2

ans = 4

3/4

ans = 0.75

Using arrays:

Defining an array:

x = [1,2,3]

x = 1 2 3

using the ":" operator

y = [1:3]

y = 1 2 3

vectors can be added:

x+y

ans = 2 4 6

vectors can be multiplied/diviede by scalars:

x*2

ans = 2 4 6

x/2

ans = 0.5 1 1.5

We can do elementwise operations with help of "." :

x.*y

ans = 1 4 9

x.^2

ans = 1 4 9

x./y

ans = 1 1 1

Matrices

Everything is a Matrix....

Defining a Matrix is quite the same as with vectors:

A = [5 1 0;1 5 1; 0 1 5]

A = 5 1 0 1 5 1 0 1 5

There are several other ways to build a Matrix:

B1 = zeros(2,3)
B2 = ones(3)
B3 = rand(3,4)
Identity = eye(3)

B1 = 0 0 0 0 0 0 B2 = 1 1 1 1 1 1 1 1 1 B3 = 0.842419 0.474979 0.873249 0.579034 0.474746 0.920388 0.899179 0.558687 0.981904 0.403228 0.258319 0.15043 Identity = 1 0 0 0 1 0 0 0 1

A Matrix can also build as vector of vectors:

A = [[1,5,0];[1 5 1];[0,1,5]]

A = 1 5 0 1 5 1 0 1 5

We can multiply a matrix with another matrix:

A*B3

ans = 3.21615 5.07692 5.36914 3.37247 4.19805 5.48015 5.62746 3.5229 5.38427 2.93653 2.19077 1.31084

or with a vector:

x*A

ans = 3 18 17

but we have to be careful with dimensions!

A*x

error: operator *: nonconformant arguments (op1 is 3x3, op2 is 1x3)

use ' for adjoint and .' for transpose:

A*x.'

ans = 11 14 17

(I*B3)'

ans = (0,-0.842419) (0,-0.474746) (0,-0.981904) (0,-0.474979) (0,-0.920388) (0,-0.403228) (0,-0.873249) (0,-0.899179) (0,-0.258319) (0,-0.579034) (0,-0.558687) (0,-0.15043)

(I*B3).'

ans = (0,0.842419) (0,0.474746) (0,0.981904) (0,0.474979) (0,0.920388) (0,0.403228) (0,0.873249) (0,0.899179) (0,0.258319) (0,0.579034) (0,0.558687) (0,0.15043)

Programming

Comparisons

3==4

ans = 0

3<1

ans = 0

3>2

ans = 1

3!=4

ans = 1

the if statement

if condition
  blabla
endif

if condition
  bla bla
else
  bli bli
endif

for loop:

for k = 1:N
  bla bla
endfor

while:

while condition
  bla bla
endwhile

defining of functions

function [val1,...valn] = my_func(input1,...,inputm)
bla bla
endfunction

examples:

function y = foo(x)
y = x^2;
endfunction

foo(2)

ans = 4

Let's do more complicated ones:

function y = my_sign(x)
if x > 0
  y = 1;
else
  y = -1;
endif
endfunction

if x endif

my_sign(2)

ans = 1

my_sign(-1)

ans = -1

function y = add(n)
  y = 0;
  for k = 1:n
    y++;
  endfor
endfunction

ans = -1 y = 0;

add(5)

ans = 5

Remark: The ++ Statement above is something, which differs octave from matlab. In matlab you would have to write y = y+1

Octave also supports the +=, -=, *=, /= statements

Another important difference: In Matlab every loop or function is closed with "end", in octave you can use end also, but the provided endif, endwhile, endfor etc. statements make the code more readible!

Of course octave has also disadvanteges, especially matlab has more features like simulink included!

To call a function in octave/matlab save it to an *.m file with the name of the function. If you start octave in the folder you can call the function just with it's name.

Another thing: Matlab has it's own nice interface. But for octave there are also some nice interfaces like QOctave which is written in Qt, or the good old emacs also supports octave.

Have Fun!