Working with 3D matrix in Matlab

To visualize the 3D matrix just consider that them as stack of images or layers.

{There is one more very important way,  that is third dimension representing the feature vector’s length}

So a(:, :, i) = all elements in the layer i, so changing i will give you next image.

where a(r,c, i) will move in the image.

a = [];
a(:,1,:) = [111 112 113 114 ; 121 122 123 124 ; 131 132 133 134];
a(:,2,:) = [211 212 213 214 ; 221 222 223 224 ; 231 232 233 234];
a(:,3,:) = [311 312 113 114 ; 321 322 323 324 ; 331 332 333 334];
a(:,4,:) = [411 412 113 114 ; 421 422 423 424 ; 431 432 433 434];
a(:,5,:)= [511 512 513 514 ; 521 522 523 524 ; 531 532 533 534];

Will make the 3D matrix ‘a’

size(a)

ans =

     3     5     4

That is there are 4 images and each image is of 3 rows and 5 cols.

But let’s Say you want to represent 3rd dimension as the feature vector  so each a(r,c, : ) represents a feature vector.

Now let’s say you want to make a 3D matrix from one feature vector.

vt = squeeze([a( 2,1, : ) ] );
vt = vt(:)';
%//make it into 2 by 3 by length(feature) matrix
%//repmat will repeat this matrix and make a 6 row matrix
%//the reshape picks the elements from the 1st col, 1st row and start moving downward in the row and so on
%//therefore each time it will meet same element as it moves down the row and fills our first image
tempT = (reshape(repmat(vt, 2*3,1), 2, 3, length(vt)));
size(tempT)
ans =
     2     3     4

Matlab Memory management

Oh it turns out that the matlab does not copy the data while passing it to the function if the function is not changing the values.
Which is big saving.
http://blogs.mathworks.com/loren/2006/05/10/memory-management-for-functions-and-variables/#1

Running Variance

Just in mid of the code wanted to find the Running Variance, just as habit typed and found not so good links.

1/N*[sum(i=1:N-1, Xi*Xi') + X*X'] – (1/N^2)*[ sum(i=1:(N-1), Xi) + X][ sum(i=1:(N-1), Xi) + X]‘

Matlab code for calculating the running Variance is as follow

%updating Mean

newMean = (newMean*(N-1) + X)/N;

sumOfSq = sumOfSq*(N-1)  + X*X';

covMat =  (1/N)*sumOfSQ - newMean*newMean'

Externally there are few links that are worth reading

• Accurately computing running variance
• From Google Answers, someone gave even the posted Java Code ; Simple and clear that could be easily read by any one knowing any programming language

Using Many Colors in the Matlab

While using the ‘plot’ function you end up using only small number of colors. I searched online to see if there are any solutions

One is given by http://blogs.mathworks.com/pick/2008/08/15/colors-for-your-multi-line-plots/

It discusses “varycolor” file. Which is very nice for generating many colors on the run.

However I found that for plotting of the poitns and data following is much distinguishable.

It is 72 element array.

clr = [ '.r';'.b'; '.g'; '.c';'.m'; '.y';...
        '*r';'*b'; '*g'; '*c';'*m'; '*y';...
        'xr';'xb'; 'xg'; 'xc';'xm'; 'xy';...
        '+r';'+b'; '+g'; '+c';'+m'; '+y';...
        'or';'ob'; 'og'; 'oc';'om'; 'oy';...
        'dr';'db'; 'dg'; 'dc';'dm'; 'dy';...
        'sr';'sb'; 'sg'; 'sc';'sm'; 'sy';...
        'pr';'pb'; 'pg'; 'pc';'pm'; 'py';...
        'hr';'hb'; 'hg'; 'hc';'hm'; 'hy';...
        'vr';'vb'; 'vg'; 'vc';'vm'; 'vy';...
        '>r';'>b'; '>g'; '>c';'>m'; '>y';...
        '.k';'xk'; '*k'; '+k';'ok'; 'dk';...
        ];

Hi, Everyone

This blog is just my “Zambeel” of programming codes, Zambeel is the Urdu word for a leather container that a traveler carries with himself.

But to me these words are more related to the Umar-o-Ayar,  a spy character in urdu literature. His magical “Zambeel” carried everything he ever placed  in it and when he needed something that thing magically came to his hand.

I will try to make this my Zambeel of codes.