# Octave: A Free, High-Level Language for Mathematics

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A quick look at a language designed to manipulate matrices and provide other numerical functions.

For numerical computing, high level languages offer advantages over more traditional languages, such as FORTRAN or C. Built-in graphics capabilities, automatic variable typing and flexible data structures combine to provide an environment in which it is easy to develop your ideas without having to fight with the language. That's not to say that FORTRAN and C are of no use, just that sometimes you want to make life a bit easier.

Matlab is a one such language. It is available on many platforms (including Linux) and provides powerful facilities for manipulating matrices, as well as other numerical functions. Unfortunately, Matlab is commercial software and wasn't available for Linux until recently (in the last twelve months or so). However, there are other, freely-available alternatives, and Octave is one such alternative.

Superficially, Octave looks very much like Matlab, and the description in its LSM entry reads “GNU Matlab—A numerical matrix mathematics program.” To begin, type octave at the shell prompt, and Octave greets you with its own prompt. Now we can start doing math.

Matrix Operations

As you might expect, entering and manipulating matrices is one of Octave's strengths. (In order to differentiate Octave commands from the output, the prompt octave:number of the command precedes the commands in the examples below.) We can enter a matrix with the command:

```octave:1 a=[1 2 ; 3 4]
```

Octave then reports the result of the command, namely:

```a =
1  2
3  4
```
To suppress output, simply place a semicolon after the command. Note that we didn't have to worry about declaring the size or type of the matrix a, we just type it in and start working with it. For example, we can get the transpose of a by typing:
```octave:2 a'
ans =
1  3
2  4
```
Arithmetic operators such as +, - and * act as matrix operators unless they are preceded by a period, in which case they act in an element by element sense. Octave also provides the forward and backward slash operators that perform matrix right and left division. Again, these can be used in an element-wise fashion. So, given another matrix:
```octave:3 b=[1 0; 3 2]
b =
1  0
3  2
```
we can find the matrix product of a and b with the command:
```octave:4 a*b
ans =
7   4
15   8
```
Or define the (i,j)th entry of the product is the product of the (i,j) entries in a and b with the command:
```octave:5 a.*b
ans =
1  0
9  8
```
Matrix elements can easily be selected by index, so to get the (1,1) entry of a, type:
```octave:6 a(1,1)
ans=1
```
We can select a row or column using the colon operator, exactly as in Matlab. Thus, to select the first column of a type the command:
```octave:7 a(:,1)
ans =
1
3
```
And to select the first row of a type:
```octave:8 a(1,:)
ans =
1  2
```
As well as these elementary operations, Octave provides functions that perform higher-level operations, such as finding the eigenvalues of a matrix, by using a command like the following:
```octave:9 eig(a)
ans =
5.37228
-0.37228
```
Alternatively, you can find the eigenvalues and eigenvectors by giving the following command:
```octave:10 [v,d]=eig(a)
v =
0.41597  -0.82456
0.90938   0.56577
d =
5.37228   0.00000
0.00000  -0.37228
```
This is a demonstration of one of the main advantages of using a high level language like Octave. Writing a FORTRAN or C program to find the eigenvalues of a matrix would take a lot more time and effort than it does in Octave. Moreover, Octave routines are usually based on well-known, high quality algorithms, so you can have faith in the results.

Octave provides many other matrix routines, which are detailed in the manual and in the on-line help system.

User-Defined Functions

Octave also lets the user define his own functions via the function keyword. A function definition looks like this:

```function [output values] = name (input values)
sequence of commands
endfunction
```

The input and output values are optional, so it is possible to write a function that takes no arguments and returns no values, such as

```octave:11 function hello
printf("hello\n")
endfunction
```
The printf statement prints the quoted string to the screen, and the \n is interpreted as a newline. Invoke the function by typing its name:
```octave:12 hello
hello
```
Obviously, functions that don't take arguments or return values aren't all that useful. To accept arguments, list them after the function name in the following manner:
```octave:13 function add(x,y)
x+y
endfunction
ans = 3
```
The output came from the statement x+y--if we had ended the line with a semicolon, there wouldn't have been any output from the add command. To assign the output to a variable, define the function in this way:
```octave:15 function sum=add(x,y)
sum=x+y;
endfunction
```
Now, if we type add(1,2), we get exactly the same result as before. However, by defining an output variable, we can assign the result of the add function to a variable in this way:
```octave:16 fred=add(1,2)
fred=3
```
A very powerful feature of Octave is the ability to return multiple values from a function. This feature exists in Matlab, but not in FORTRAN. For example, the following function:
```octave:17 function [sum,diff]=sumdiff(x,y)
sum=x+y;
diff=x-y;
endfunction
```
returns multiple values when invoked as:
```octave:18 ns,d]=sumdiff(1,2)
s = 3
d = -1
```
Functions can be defined at the keyboard, as we did in these examples, or stored in a file and used again. This lets you build a suite of routines for whatever tasks you want. All you have to do is put the files (identified with a .m suffix) somewhere where Octave can find them. The built-in variable LOADPATH specifies where Octave should look for the .m files. Many of Octave's standard functions are defined in .m files. You can also access user-supplied C++ routines within Octave, although this feature is not yet fully developed.

Octave also provides a full programming language, with flow control and looping constructs, as well as extensive input-output facilities. It is possible to write quite sophisticated programs in Octave, and development time is considerably shorter than you would expect using FORTRAN or C.

______________________

## Comment viewing options

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### I wish our university used

I wish our university used this as well as I have become used to it. The interface on Octave is a lot easier to use in my opinion. Matlab will just have to do sometimes though. college grants for students

### Matlab or octave

Where else could anyone get that kind of info written in such a perfect way?
Matlab or octave

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the best part of octave is it can parse matlab code , so it's very useful for students like me .however, matlab can not parse octave code .
another thing,you can type single quotes and double quotes in octave which like we know that's impossible with matlab(accept only singles quotes).
these are two big difference for me so I choose Octave over Matlab .
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### @windows version

Octave can be used on windows using cygwin.

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### Didn't know that

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### Great article. It's hard to

Great article. It's hard to say which one is the best.

### Fortran is my first programming language

When I was young, Fortran is my first programming language. Then I learned Matlab and Octave.. but I think Matlab is easier than Octave. thanks, Pampers Diapers

### disagree

Have to disagree Octave is far more intuitive. curtains and blinds

### Have used both, Octave and

Have used both, Octave and Matlab, but i prefer the latter, though i don't use matrixes that often. online sex cam live chat

### Thanks to your article, you

Thanks to your article, you don't know me and I live way too far away...
Why yes you can. m files work just fine with octave.

### Matlab's return is promising

Matlab's return is promising it will help in Computer Aided Designing
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### There is difference between

There is difference between Matlab and Octave. Octave is open source whereas Matlab is proprietary. Matlab surly is more comfortable working whereas Octave is free, that's why I love to work with Octave.
Sam

### user friendly

which one that give you more user friendly experience?
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### Doesn't this cause a conflict?

Great article but one quick question...?

"The input an' output values be optional, so it is possible t' write a function that takes no arguments an' returns no values, such as

octave:11 function hello
printf("hello\n")
endfunction"

How does this not result in conflict when compiling?

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### Octave: A Free, High-Level Language for Mathematics

Yeah, I wish we had this too in our university. I imagine calculating mathematical equations in just pressing some keys in the keyboard and not solving those problems with very long solutions by hands.
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### Wow...

Wow!I am pretty new to learn about this but would like to know which one in the end is the way to go?Is it Matlab or octave?I've read that Matlab can be more powerful, is that correct?
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### I have been learning computer

I have been learning computer languages but never even heard about Octave. May be because it is old now and isnt used much but it is always interesting to know more. I will be digging in deep to find more information on this. electric meat slicer

### That's all we need :)

That's all we need, another high-level Maths language. I find C difficult enough to deal with. My Dad was right, should have done law rather than engineering :)

### which one?

So in the end which one is the way to go? Matlab or octave? Both have benefits
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### I agree with David

I totally agree with David that it's almost mandatory that you also install the octave-forge package...

### Octave is great

"I'd say there's a *big* difference between Matlab and Octave. Octave is Open Source, that means it's free as opposed to Matlab which you have to pay for. Very powerful."

Absolutely agree with this. I love Matlab but the flexibility that I have with Octave is awesome.

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### Octave VS Matlab - Big Difference

I'd say there's a *big* difference between Matlab and Octave. Octave is Open Source, that means it's free as opposed to Matlab which you have to pay for. Very powerful.

### Coding Style

I see about the Visual Basic notation like if .. else .. end, but Octave, like Matlab uses C oriented notations also, for example a ! in Octave is a NOT, as it is in C, instead of <> in VB. Also you can use all the C based = symbols like: `+=', `-=', `*=', `/=', `^=', `.*=', `./=', and `.^='.

### Octave Origins

From what I'm getting, James B. Rawlings and John W. Eaton at the University of Texas were the first to start development of Octave, clear back in 1988. In '92 James Rawlings started development full time. How does open source software put food on the table. I'm still puzzled.

### Almost VB Style

This is my first introduction to either Matlab or Octave. The format almost has a Visual Basic feel to it; not like C at all. Then again, maybe just the function definitions. For me, the advantage would be to do server side math, thereby not relying on flaky client side Javascript, which is anything but precision.

### Octave is no doubt an equally

Octave is no doubt an equally impressive piece of software and just as functional as Matlab. I've used both and have no preference either way as they both work in very similar manners. There is no doubt that Octave is a great alternative to Matlab and gets the job done just as well. backpacking Europe

As of August 1, 2010 the newest version 3.3.52 is available in BETA for people interested in helping test. Be sure to download it and give it a spin: Octave Downloads.

### Windows Version

MatLab is indeed a great high level program (language?) for doing precision math. It's available for Windows or Linux. I didn't see if Octave is also available for both.

### mathlab is still better

I have used both programs and I think mathlab is still much than octave.

### I am starting to learn about

I am starting to learn about this but would like to know that this will be used for quite some time down the road. I see this is dated 1997, has there been any changes to this, or is there any news of switching to a different system? custom t-shirts

### Changes

I see this is dated 1997, has there been any changes to this, or is there any news of switching to a different system? I am starting to learn about this but would like to know that this will be used for quite some time down the road. Outdoor Pool Furniture

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### You don't know me and I live

You don't know me and I live way too far away... but my name is Peter. I'm doing an undergrad I.T. degree and this semester I'm doing a subject on Pattern Recognition (eventually using Neural Networks). The subject demands use of Matlab and for some reason, our I.T. faculty seems to be fairly poor at supporting anything Linux (except for network admin and programming based subjects). iphone headphones

### Matlab OR Octave

the best part of octave is it can parse matlab code , so it's very useful for students like me .however, matlab can not parse octave code .
another thing,you can type single quotes and double quotes in octave which like we know that's impossible with matlab(accept only singles quotes).
these are two big difference for me so I choose Octave over Matlab .
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### I tried Octave

I tried Octave once , it's unbelievable .
very very useful for people who use Matrix (resolve Jordan and Gauss problem easily)

### I wish our university had

I wish our university had Octave installed. But most machines in Ottawa are Windows.

### I wish we had it too

Yeah, I wish we had this too in our university. I imagine calculating mathematical equations in just pressing some keys in the keyboard and not solving those problems with very long solutions by hands.

### Great

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### You have a lot of resources

I always consult linuxjournal so many things about my job, and my school.

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### What I like!

I like how it provides a convenient command line interface for solving linear and nonlinear problems numerically! Also great features are: Matrices as fundamental data type and Built-in support for complex numbers.

### Thank you!

I used Matlab exclusively in my MSc. never knew that there was a Gnu'able version. Installed from my GNU/Linux's distrobution and taking it for a spin. Thanks :-)

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