Download and install Octave
There are a number of Open Source alternatives to the program MatLab, one of the most known alternatives is GNU Octave. When using Octave you use a command line to enter commands. Octave can be downloaded and installed from GNU Octave.
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Install on Mac
If using Mac:
Install Homebrew.
Install XCode from App Store.
Open and run the XCode app to agree to the License Agreement.
Install XQuartz.
Stamps com for mac. Import science packages, open the terminal and enter:
Install Octave (this takes time):
Update:
At the end of the process a summary is shown displaying the path to Octave. If following is shown:
then the path to Octave is
/usr/local/Cellar/octave/3.8.1/bin/Octave
Open AppleScript Editor and make a New Document. Write following:where
/path/to/octave
is the path. Save the script as Octave.app, select Application when saving.For more information see Octave for MacOS X.
As a calculator
The easiest way to get started, is to use Octave as a calculator.
The arithmetic operators are:
There are predefined constants in Octave, some of them are listed below:
constant | explanation |
---|---|
pi , e , i | Make a wild guess! |
Inf (infinity) | Operations yielding numbers larger than the maximum floating point will give this answer. |
NaN (not a number) | Operations that can not be defined in any reasonably way will give this answer |
There are also a number of predefined mathematical functions in Octave, some of them are listed below:
function | explanation |
---|---|
sin, cos, tan | Trigonometric functions using radians |
asin, acos, atan | Inverse trigonometric functions |
exp, log, log10 | Exponential function, natural logarithm, logarithm to the base 10 |
sqrt | Square root |
abs | Absolute value |
round, floor, ceil | Round to nearest integer, round down, round up |
rem | Remainder when doing integer division |
Showing more decimals
You can show more decimals by typing
format long
. Go back to showing few decimals by typing format short
.Exercise 1
Calculate following expressions
- (sqrt[5]{200})
- (dfrac{3cdot 10^{-3}}{0.001+sqrt{0.2}})
- (dfrac{2^{3+sin{0.3}}+5}{10})
You should get these answers
ans = 2.8854
ans = 0.0066932
ans = 1.4819
You can see old commands by using up/down arrow keys.
Exercise 2
https://oospuy.weebly.com/final-cut-pro-for-mac.html. Guess the output of following commands, then check the answers given by Octave
1/0 0/0 tan(pi/2)
inf+inf inf-inf inf/inf inf*inf
nan+2 nan+nan
Exit Octave
Exit Octave by writing
exit
or quit
.Numerical variables
When evaluating the value of an expression, the result is stored in a variable called
ans
(answer). You can also introduce variables of your own.By writing
who
you can see all variables. If you write a semi colon at the end of the line, the output is not shown.Naming variables
Various programs have different rules for naming entities. Although some modern programs allow for all kind of characters in names, you may run into trouble if you use characters like '-' or blank. If you want to stay on the safe side, never having to bother about naming-rules for specific programs, follow these old-school rules:
- The first character must be an english letter :
a
-z
,A
-Z
Some programs can handle letters like å, Æ, Ç, ü; others cannot. Use english names when programming! - The name can include numbers :
0
-9
- The name can include underscore :
_
These rules apply to Octave and a number of other programs.
Assignments
When writing
a=5
at the command prompt, the equal-sign should not be thought of as a logical equality; a
is not equal to 5, it is assigned the value 5. Having that in mind, one can write assignments like thisThe statement above would be false if it was a logical statement, it is however not a logical statement but an assignment. The right-hand-side of the statement is calculated first, the result is then assigned to the variable on the left-hand-side.
Hiding the output and repeating previous commands
You can write several commands on one line by using comma, or semi colon. By using up-arrow, you can repeat the previous command, and alter it.
You can calculate a geometric series by using up-arrow several times.
Exercise 3
Calculate the series:
![Octave Octave](/uploads/1/3/4/0/134051352/271318089.png)
(The answer is 1.5962)
Exercises on Sequences
A sequence is a function with the domain being the natural numbers. A sequence can be written like this (a_0,a_1,a_2,..) or like this
[left( a_n right)_{n=0}^{infty} ] Recurrence equations
A geometric progression can be defined in different ways. Consider the infinite geometric progression (3, 3cdot 2, 3cdot 2^2,..).
You can describe the geometric progression in two ways.
How to put a watermark on word doc for mac. A recurrence equation:
[ left{ begin{align} a_0 &=3 a_{n+1} &=2cdot a_n, ngeq0 end{align} right. ] An explicit formula:
[a_n=3cdot 2^n, nin mathbb{n}] Exercise 4
Use Octave to find the limit as (nrightarrowinfty) of following sequences. Type
format long
to show more decimals. Try different initial values (c), do you get different limits?- [ left{ begin{align} a_0 &=c a_{n+1} &=1+frac{1}{a_n}, ngeq0 end{align} right. ]
- [ left{ begin{align} a_0 &=c a_{n+1} &=sqrt{1+a_n}, ngeq0 end{align} right. ]
Try to explain your answers. If you fail, do the exercises on Calculus - Fixpoints.
Find maximum values in the array x.
For a vector argument, return the maximum value. For a matrix argument,return a row vector with the maximum value of each column. For amulti-dimensional array,
max
operates along the first non-singletondimension.If the optional third argument dim is present then operate alongthis dimension. In this case the second argument is ignored and should beset to the empty matrix.
For two matrices (or a matrix and a scalar), return the pairwise maximum.
Thus,
returns the largest element of the 2-D matrix x, and
compares each element of the range
2:5
with pi
, and returns arow vector of the maximum values.For complex arguments, the magnitude of the elements are used forcomparison. If the magnitudes are identical, then the results are orderedby phase angle in the range (-pi, pi]. Hence,
because all entries have magnitude 1, but -1 has the largest phase anglewith value pi.
Octave For Mac Yosemite
If called with one input and two output arguments,
max
also returnsthe first index of the maximum value(s). Thus,Octave For Machine Learning
See also: min, cummax, cummin.