## Saturday, October 22, 2011

### Octave cheat sheet

I'm mucking about with Octave, MATLAB's open source cousin, as part of Stanford's Machine Learning class. Here are a few crib notes to keep me right side up.

The docs for Octave must be served from a Commodore 64 in Siberia judging by the speed, but Matlab's Function Reference is convenient. The Octave WikiBook covers a lot of the basics.

#### Matrices

Try some matrix operations. Create a 2x3 matrix, and a 3x2 matrix. Multiply them to get a 2x2 matrix. Try indexing.

>> A = [1 2 3; 4 5 6]
A =
1   2   3
4   5   6

>> B = 2 * ones(3,2)
B =
2   2
2   2
2   2

>> size(B)
ans =
3   2

>> A * B  % matrix multiplication
ans =
12   12
30   30

>> who    % list variables
A    B    ans

>> A(2,3) % get row 2, column 3
ans =  6

>> A(2,:) % get 2nd row
ans =
4   5   6

>> A'     % A transpose
ans =
1   4
2   5
3   6

>> A' .* B  % element-wise multiply
ans =
2    8
4   10
6   12

#### Sum

sum(A,dim) is a little bass-ackwards in that the columns are dimension 1, rows are dimension 2, contrary to R and common sense.

>> sum(A,2)
ans =
6
15

#### Max

The max function operates strangely. There are at least 3 forms of max.

[C,I] = max(A)
C = max(A,B)
[C,I] = max(A,[],dim)

For max(v), if v is a vector, returns the largest element of v. If A is an m x n matrix, max(A) returns a row vector of length n holding the largest element from each column of A. You can also get the indices of the largest values in the I return value.

To get the row maximums, use the third form, with an empty vector as the second parameter. Oddly, setting dim=1 gives you the max of the columns, while dim=2 gives the row maximums.

Perform file operations with Unix shell type commands: pwd, ls, cd. Import and export data, like this:

#### Printing output

The disp function is Octave's word for 'print'.

disp(sprintf('pi to 5 decimal places: %0.5f', pi))

#### Histogram

Plot a histogram for some normally distributed random numbers

>> w = -6 + sqrt(10)*(randn(1,10000))  % (mean = 1, var = 2)
>> hist(w,40)

#### Plotting

Plotting

t = [0:0.01:0.99];
y1 = sin(2*pi*4*t);
plot(t,y1);
y2 = cos(2*pi*2*t);
hold on;         % "hold off" to turn off
plot(t,y2,'r');
xlabel('time');
ylabel('value');
legend('sin','cos');
title('my plot');
print -dpng 'myPlot.png'
close;           % or,  "close all" to close all figs

Multiple plots in a grid.

figure(2), clf;  % select figure 2 and clear it
subplot(1,2,1);  % Divide plot into 1x2 grid, access 1st element
plot(t,y1);
subplot(1,2,2);  % Divide plot into 1x2 grid, access 2nd element
plot(t,y2);
axis([0.5 1 -1 1]);  % change axis scale

heatmap

figure;
imagesc(magic(15)), colorbar

These crib notes are based on the Octave tutorial from the ml class by Andrew Ng. Also check out the nice and quick Introduction to GNU Octave. I'm also collecting a few notes on matrix arithmetic.

Defining a function

function ret = test(a)
ret = a + 1;
end