%
% A few Matlab examples that can be cut and pasted directly into matlab
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% (c) Markus Weber
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%
% Starting matlab
%

matlab			% Type this in Unix



%
% Entering matrices
%

A = [ 1, 2, 3, ];	% produces a row vector

B = [ 1; 2; 3 ];	% produces a column vector

C = [ 1 2 3 ]';		% commas are redundant, "'" - operator gives transpose

D = [ 1 2; 3 4; 5 6]	% if you drop the ; at the end of a statement, the result is printed

D'


1:10			% a:b is a short form for [ a, a + 1, ..., b ]

[1:0.1:3]'		% a:i:b allows to specify an increment


% Some special building functions:

zeros(2, 3)		% Zeros
ones(4, 2)		% Ones
eye(5)			% Unit matrix
diag([1 5 2])		% Diagonal matrix
rand(10,2)		% Random numbers



%
% Indexing matrix elements
%
			
D(3, 2)			% single elements are obtained in the obvious way

D(:, 2)			% colon gives an entire column...
D(1, :)			% or row

D = magic(10)		% magic() just produces some data (a magic square actually...)

D(2:4, 6:9)		% vectors can be used to index sub-matrices

D([1 3 5], :)		% they do not need to specify continuous elements


A = [0 0 0; 0 0 0; 0 0 0]	

A([1 3], :) = [5 6 7; 8 9 10]	% You can select elements on the left hand side of an
				% assignment. Beware: the shape on the right hand side
				% has to fit!


A([1 3], :) = [5 6 7; 8 9 10]'  % This will not work!



%
% Matrix operations
%

% The intuitive things will work for scalars as well as for matrices

A = [1 2 3]; B = [1 0 -1];

A + B
A - B

A + 100			% Scalars are sometimes expanded to the right size matrix

a = 20; b = 1.5;

a * b			% Scalar multiplication

C = magic(3)

C * A'			% For vector multiplication, the sizes obviously should match

C * A			% Bad...

[1 2 3]' * [4 5 6]	% Of course we can do outer products.

[1 2 3] .* [10 100 1000] % Use the "." to specify pointwise operations

[1:10] .^ 2		% It works...



%
% Elementary Math Functions
%

help elfun		% Your favourite is there

X = [-6:0.1:6]';

Y = [sin(X), 2 * cos(X), 3 * abs(cos(X))];

plot(Y);



%
% Plotting and Printing
%

figure;	figure;		% You can use many "figures" at a time...
figure(2)		% ... and select any one for output

X = 1:10;
Y = X .^ 2;

plot(X, Y);		% "plot" can plot 2-D data in many convenient ways
plot(X, Y, 'y+');	% Uses yellow "+"s as markers

help plot		% Should give you a good idea

hold on;		% This way, your plot will not be erased...
plot(X, 100 * rand(10, 1))	% ...and you can superimpose things...
plot(X, 100 * rand(10, 1))	% ...and you can superimpose things
plot(X, 100 * rand(10, 1))	% ...and you can superimpose things
hold off;		% enough

% Some professors like to understand your plots:

title('L''art pour l''art!!');
xlabel('Age');
ylabel('Activity in V1');

print -deps filename.eps % Creates a PostScript file that can then be printed
			% like this (under Unix): "lpr filenam.eps"

clf;			% Clears the plot



%
% Loading and Saving
%

A = magic(20);		% Create important data
B = magic(3);

save huge_magic_square A 	% Save it as *.mat file.
save -ascii tiny_magic_square B	% Save it as ASCII file.

clear;

load huge_magic_square		% Load it...
whos				% yes, it's back!

load tiny_magic_square
whos


%
% Images
%

more on;		% For slow readers
help images		% Gives an overview of the image toolbox

A = rand(100, 100);	% Images are matrices

imagesc(A);		% Use imagesc() to display an image
colormap gray;		% You will mostly work on graylevel images

help imread		% See help pages for file handling of different image formats

imread(clown)



%
% Filtering
%

Gauss1D = [1 4 6 4 1];			% An approximation of a 1D Gaussian
Gauss1D = Gauss1D / sum(Gauss1D);	% Normalizes it

Gauss2D = Gauss1D' * Gauss1D;		% Makes a two-dimensional version
Gauss2D = Gauss2D / sum(sum(Gauss2D));

imagesc(conv2(A, Gauss2D, 'same'));	% 2D convolution, make sure the result has same size
					% as input

size(conv2(A, Gauss2D))			% See how it grows?



%
% Writing Progams (M-Files)
%




%
% Some useful functions (you might have to get them from the website)
%


downsample2()		% Implements a smart way to create lower resolution images

[Xg Yg] = meshgrid(1:5, 1:5)		% Generates X-Y grid