Commands, strings, loops and logic
There is a complete documentation of Octave at http://www.gnu.org/software/octave/doc/interpreter/
Formatting numbers
You can format numbers in three different ways; format long
, format
short
and format bank
(2 decimals)
>>> format long >>> pi ans = 3.14159265358979 >>> format short >>> pi ans = 3.1416 >>> format bank >>> pi ans = 3.14
Just writing the command format
will give you the default format
short
.
String variables
When handling text instead of numbers you use strings. A string is enclosed in either "signs or 'signs.
>>> my_string_variable="Hello World!" my_string_variable = Hello World! >>> my_string_variable='Hello World!' my_string_variable = Hello World!
The help command
If you want to find information about a command or a function you can use the
help
command.
>>> help asin `asin' is a builtin function  Mapping Function: asin (X) Compute the inverse sine in radians for each element of X. See also: sin, asind
The disp command
You can use the disp
command together with an argument enclosed
in brackets to display data. When using disp
the output is displayed
without the ans=
.
>>> disp(pi) 3.1416 >>> disp(my_string_variable) Hello World! >>> disp("The value of pi is:"), disp(pi) The value of pi is: 3.1416
Date and time
When measuring time on a computer it is a convention to measure the time since
00:00:00 UTC
1 January 1970. The command time
will give you the number of seconds since then;
the command now
will give you the number of days. The command date
will give
you the current date as a string. The command clock
will give you the current
yearmonthdayhourminutesecond as a rowmatrix.
>>> time ans = 1.2737e+009 >>> now ans = 7.3427e+005 >>> date ans = 12May2010 >>> clock ans = 2010.0000 5.0000 12.0000 15.0000 41.0000 40.3795
mfiles
You can store a number of commands in a so called mfile. You enter the commands in an editor and run the mfile from Octave.
Working directory
All mfiles should be stored in the so called working directory. Write pwd
(print working directory)
to see the current working directory of Octave. If you prefer to store your files at some other directory, go there by using the
command cd
(change directory). For more information about cd
see
http://www.computerhope.com/unix/ucd.htm.
Write your mfiles in any editor that can handle pure text without adding fileextensions such as .txt
. Some examples are
Notepad++ for Windows, Sublime Text 2 for Mac (install from App Store), and gedit for Linux. Save the mfiles
in the working directory of Octave.
A first mfile
Save following lines:
a=1; b=2; disp('a+b=') disp(a+b)
in a file called test1.m in your Octave working directory. Write test1
in Octave to see the output.
The forstatement
Repeating the same operation over and over again is called iterating.
One way to iterate when programming is to use a for
statement.
A for
statement in its simplest form uses a variable representing
an index that is increased by 1 in each step.
In the code below, the index is called i
. The command
between for
and end
is repeated 10 times. The first
time row 2 is executed, i
is equal to 0, the second time i
is equal to 1, and so on.
Row 4 starts with a %
sign, everything to the right of the %
sign
is ignored when the program is run; this is a comment intended
for those reading the actual code.
for i=0:9 disp(i) end %the numbers 0, 1,...,9 are displayed
You can increment your index with something else than 1 by adding a number between the starting index and the last index.
for i=0:0.1:2 disp(i) end %21 numbers are displayed, the numbers 0,0.1,0.2,...,2
Sequences, Continued
Exercise 1
Write for
statements in mfiles to solve following exercises.
Use format long
.
 The recurrence equation
\[
\left\{
\begin{align}
a_0 &=c \\
a_{n+1} &=1+\frac{1}{a_n}, n\geq0
\end{align}
\right.
\]
has two fixpoints \(x_1=\dfrac{1+\sqrt{5}}{2}\) and \(x_2=\dfrac{1\sqrt{5}}{2}\).
Write afor
statement to iterate the recurrence equation 10 times.
What happens if you start with \(c=x_1\) and \(c=x_2\) respectively?
What happens if you iterate 50 times? 100 times?  Write a recurrence equation for the continued fraction
\[
1 + \cfrac{1}{2
+ \cfrac{1}{2
+ \cfrac{1}{2
+ \cfrac{1}{2+\cdots } } }}
\]
Hint: it is easier to write a recurrence equation for the continued fraction
plus 1.
 Find the limit of the recurrence equation by iterating in Octave.
 Find the exact value of the continued fraction by first finding the fixpoints of the recurrence equation you used in a and then subtracting 1.
Some series
A series \(\sum a_i\) is said to converge if \(\sum_{i=0}^{n}a_i\) has a finite limit as \(n\rightarrow\infty\).
Exercise 2
 Use Octave to make a conjecture about the convergence of \[ \sum_{i=1}^{n}\left(\frac{1}{i}\right)^2 \] as \(n\rightarrow\infty\).
 Use Octave to make a conjecture about the convergence of \[ \sum_{i=1}^{n}\frac{1}{i} \] as \(n\rightarrow\infty\).

 Rewrite the series \[ 1\frac{1}{2}+\frac{1}{3}\frac{1}{4}+\frac{1}{5}\frac{1}{6}+\cdots \] using a \(\sum\).
 Use Octave to make a conjecture about the convergence of this series as \(n\rightarrow\infty\).
 Iterate to find the sum of the first 50 terms of \[ 1\frac{1}{3}+\frac{1}{5}\frac{1}{7}+\frac{1}{9}\frac{1}{11}+\cdots \] then multiply the result with 4. What happens when you iterate 500 times? 5000 times? 50000 times?
Boolean Logic
Boolean algebra
In Boolean algebra you represent the logical values true and false by the numbers 1 and 0 respectively.
>>> true ans = 1 >>> false ans = 0
and, or, not
The basic operators in logic are and, or and not, these are written using the symbols ∧, ∨ and ¬ respectively. If p and q are statements that are either true or false, then you get the truth table
p  q  p ∧ q  p ∨ q  ¬p 

true  true  true  true  false 
true  false  false  true  false 
false  true  false  true  true 
false  false  false  false  true 
The operators ∧ and ∨ are binary operators, they are applied to two operands. The operator ¬ is an unary operator, it applies to one operand.
In Octave (and most other programming languages) the operators ∧, ∨
and ¬ are written using the symbols &&
, 
and !
; giving the truth
table
p  q  p && q 
p  q 
!p 

1  1  1  1  0 
1  0  0  1  0 
0  1  0  1  1 
0  0  0  0  1 
In Octave (and most other programming languages) all numbers that are not 0 are thought of as being true.
>>> a=4.5; >>> b=0; >>> (a && b)  !b ans = 1
Note that you can perform logical operations by using arithmetics.
p &&
q = pq
p 
q = p+qpq
!p = 1p
Comparison Operators
When doing a comparison in Octave you apply a comparison operator on two numbers and the result is either true or false, represented by 1 or 0.
operation  operators  operands  result 

arithmetic operations  +  * / ^ 
numbers  a number 
logical operations  &&  ! 
logical values  a logical value 
comparisons  > >= < <= == != 
numbers  a logical value 
The comparison operators are:
operator  explanation 

>  greater than, > 
>=  greater than or equal to, ≥ 
<  less than, < 
<=  less than or equal to, ≤ 
==  equal to, = 
!=  not equal to, ≠ 
>>> a=1; b=2; c=2; d=3; >>> a>=b ans = 0 >>> b>=c ans = 1 >>> (a < b) && (c!=d) ans = 1 >>> a < b && c!=d >>>parse error: syntax error >>> a < b && c!=d ^
further info:
Harmonic
series
MadhavaLeibniz
series
Fuzzy Logics: This article was published in Scientific American 1993, A Partly True Story, by Ian Stewart
That is true → ← That is false
by Malin Christersson under a Creative Commons AttributionNoncommercialShare Alike 2.5 Sweden License