How to take submatrix in matlab - matlab

Hello i have a matrix whose rows and columns are multiple of 8 let's say 256x160 and i need to have as output all the possible submatrix of 8x8 elements. Fore few elements i can write
bloc = 8;
imm = imread('cameraman.tif');
[rows, columns, dimension] = size(imm); % dimension if the image is RGB
nr = rows/bloc; % numeber of blocks of rows
nc = columns/bloc; % number of blocks of columns
cell_row = repmat(bloc,1,nr);
cell_columns = repmat(bloc,1,nc);
N = mat2cell(imm, [cell_row,[cell_columns]);
I think that now it works quite good but if there is a better way just tell me thanks

Related

What is the fastest way to compare vectors from 3D array in matlab?

Here's my example data.
Ycoordinate = 10;
Xcoordinate = 12;
Zdata = 4;
my3Darray = zeros(Ycoordinate, Xcoordinate, Zdata);
for i = 1:Ycoordinate
for j = 1:Xcoordinate
my3Darray(i,j,:) = uint8(rand(Zdata,1)*64);
end
end
my3Darray = uint8(my3Darray);
As you can see, there're 120 locations (Y:10 * X:12) and each location has 4 of uint8 value.
And here're my questions.
I want to find if there're any two or more locations have same vector of Zdata (4 of uint8 value). How can I do this?
My actual data will be Ycoordinate=7000, Xcoordinate=7000, Zdata = 500.
So it will be around 24GB array (7000*7000*500 = 24,500,000,000 byte)
Is it possible to find same Zdata with this huge size of array?
Additionally, my data is actually boolean so it is just 0 or 1 but I don't know how to allocate only "1 bit(not 1 byte)" to my data.
The code below will tell you how many locations have duplicate z-data vectors. The idea is to reshape your data in to a 2D matrix where each row represents a single column of z-data from the original matrix. The reshaped matrix will have Xcoordinate*Ycoordinate rows and Zdata columns. Then you can use the unique function to get the unique rows of this reshaped matrix, which essentially removes any duplicate z-data vectors.
You can also replace the nested loop in your code with the following line to directly generate a 3D random matrix:
my3Darray = uint8(rand(Ycoordinate, Xcoordinate, Zdata)*64);
If you want to store boolean data, use logical arrays in MATLAB.
Edit: Follow beaker's comment above to reduce the memory footprint.
Here's the code:
clear
clc
Ycoordinate = 4000;
Xcoordinate = 4000;
Zdata = 63;
my3Darray = uint8(rand(Ycoordinate,Xcoordinate,Zdata)*64);
%reshape data so that each z-column becomes a row
A = reshape(my3Darray,Ycoordinate*Xcoordinate,Zdata);
[A_unique, I, J] = unique(A,'rows'); %get the unique rows of A
duplicate_count = size(A,1) - size(A_unique,1)

Create a submatrix using random columns and loop

I have a 102-by-102 matrix. I want to select square sub-matrices of orders from 2 up to 8 using random column numbers. Here is what I have done so far.
matt is the the original matrix of size 102-by-102.
ittr = 30
cols = 3;
for i = 1:ittr
rr = randi([2,102], cols,1);
mattsub = matt([rr(1) rr(2) rr(3)], [rr(1) rr(2) rr(3)]);
end
I have to extract matrices of different orders from 2 to 8. Using the above code I would have to change the mattsub line every time I change cols. I believe it is possible to do with another loop inside but cannot figure out how. How can I do this?
There is no need to extract elements of a vector and concatenate them, just use the vector to index a matrix.
Instead of :
mattsub = matt([rr(1) rr(2) rr(3)], [rr(1) rr(2) rr(3)]);
Use this:
mattsub = matt(rr, rr);
Defining a set of random sizes is pretty easy using the randi function. Once this is done, they can be projected along your iterations number N using arrayfun. Within the iterations, the randperm and sort functions can be used in order to build the random indexers to the original matrix M.
Here is the full code:
% Define the starting parameters...
M = rand(102);
N = 30;
% Retrieve the matrix rows and columns...
M_rows = size(M,1);
M_cols = size(M,2);
% Create a vector of random sizes between 2 and 8...
sizes = randi(7,N,1) + 1;
% Generate the random submatrices and insert them into a vector of cells...
subs = arrayfun(#(x)M(sort(randperm(M_rows,x)),sort(randperm(M_cols,x))),sizes,'UniformOutput',false);
This can work on any type of matrix, even non-squared ones.
You don't need another loop, one is enough. If you use randi to get a random integer as size of your submatrix, and then use those to get random column and row indices you can easily get a random submatrix. Do note that the ouput is a cell, as the submatrices won't all be of the same size.
N=102; % Or substitute with some size function
matt = rand(N); % Initial matrix, use your own
itr = 30; % Number of iterations
mattsub = cell(itr,1); % Cell for non-uniform output
for ii = 1:itr
X = randi(7)+1; % Get random integer between 2 and 7
colr = randi(N-X); % Random column
rowr = randi(N-X); % random row
mattsub{ii} = matt(rowr:(rowr+X-1),colr:(colr+X-1));
end

Select an element of a Sub matrix

I have a Matrix of 100 sub matrix . Each of this sub matrix have 6 elements (1*6),
I need to compute the mean of the first element of each sub matrix then the
second, etc
Example:
B=[4,**3**,2,1,1,2]
C=[4,**3**,5,1,1,2]
D=[6,**3**,2,1,1,2]
A={B,C,D}
...etc
So I want the mean of the surlined numbers, then the next etc
How can I do that ???
Thanks by advance,
i think what you need here is the command cell2mat. here a small script of how to compute means automatically without knowing the size of the data. let me know if that was what you were looking for.
% Problem
vec1 = [4,3,2,1,1,2];
vec2 = [4,3,5,1,1,2];
vec3 = [6,3,2,1,1,2];
A = {vec1,vec2,vec3};
% get dimensions
cols = numel(cell2mat(A(1)));
rows = numel(A);
% convert list of vectors to matrix
M = cell2mat(A);
M = reshape(M,[cols,rows]);
M = M';
means = mean(M)

How can I build a Scilab / MATLAB program that averages a 3D matrix?

I need to make a scilab / MATLAB program that averages the values of a 3D matrix in cubes of a given size(N x N x N).I am eternally grateful to anyone who can help me.
Thanks in advance
In MATLAB, mat2cell and cellfun make a great team for working on N-dimensional non-overlapping blocks, as I think is the case in the question. An example scenario:
[IN]: A = [30x30x30] array
[IN]: bd = [5 5 5], size of cube
[OUT]: B = [6x6x6] array of block means
To accomplish the above, the solution is:
dims = [30 30 30]; bd = [5 5 5];
A = rand(dims);
f = floor(dims./bd);
remDims = mod(dims,bd); % handle dims that are not a multiple of block size
Ac = mat2cell(A,...
[bd(1)*ones(f(1),1); remDims(1)*ones(remDims(1)>0)], ....
[bd(2)*ones(f(2),1); remDims(2)*ones(remDims(2)>0)], ....
[bd(3)*ones(f(3),1); remDims(3)*ones(remDims(3)>0)] );
B = cellfun(#(x) mean(x(:)),Ac);
If you need a full size output with the mean values replicated, there is a straightforward solution involving the 'UniformOutput' option of cellfun followed by cell2mat.
If you want overlapping cubes and the same size output as input, you can simply do convn(A,ones(blockDims)/prod(blockDims),'same').
EDIT: Simplifications, clarity, generality and fixes.
N = 10; %Same as OP's parameter
M = 10*N;%The input matrix's size in each dimensiona, assumes M is an integer multiple of N
Mat = rand(M,M,M); % A random input matrix
avgs = zeros((M/N)^3,1); %Initializing output vector
l=1; %indexing
for i=1:M/N %indexing 1st coord
for j=1:M/N %indexing 2nd coord
for k=1:M/N % indexing third coord
temp = Mat((i-1)*N+1:i*N,(j-1)*N+1:j*N,(k-1)*N+1:k*N); %temporary copy
avg(l) = mean(temp(:)); %averaging operation on the N*N*N copy
l = l+1; %increment indexing
end
end
end
The for loops and copying can be eliminated once you get the gist of indexing.

Sum every n rows of matrix

Is there any way that I can sum up columns values for each group of three rows in a matrix?
I can sum three rows up in a manual way.
For example
% matrix is the one I wanna store the new data.
% data is the original dataset.
matrix(1,1:end) = sum(data(1:3, 1:end))
matrix(2,1:end) = sum(data(4:6, 1:end))
...
But if the dataset is huge, this wouldn't work.
Is there any way to do this automatically without loops?
Here are four other ways:
The obligatory for-loop:
% for-loop over each three rows
matrix = zeros(size(data,1)/3, size(data,2));
counter = 1;
for i=1:3:size(data,1)
matrix(counter,:) = sum(data(i:i+3-1,:));
counter = counter + 1;
end
Using mat2cell for tiling:
% divide each three rows into a cell
matrix = mat2cell(data, ones(1,size(data,1)/3)*3);
% compute the sum of rows in each cell
matrix = cell2mat(cellfun(#sum, matrix, 'UniformOutput',false));
Using third dimension (based on this):
% put each three row into a separate 3rd dimension slice
matrix = permute(reshape(data', [], 3, size(data,1)/3), [2 1 3]);
% sum rows, and put back together
matrix = permute(sum(matrix), [3 2 1]);
Using accumarray:
% build array of group indices [1,1,1,2,2,2,3,3,3,...]
idx = floor(((1:size(data,1))' - 1)/3) + 1;
% use it to accumulate rows (appliead to each column separately)
matrix = cell2mat(arrayfun(#(i)accumarray(idx,data(:,i)), 1:size(data,2), ...
'UniformOutput',false));
Of course all the solution so far assume that the number of rows is evenly divisble by 3.
This one-liner reshapes so that all the values needed for a particular cell are in a column, does the sum, and then reshapes the back to the expected shape.
reshape(sum(reshape(data, 3, [])), [], size(data, 2))
The naked 3 could be changed if you want to sum a different number of rows together. It's on you to make sure the number of rows in each group divides evenly.
Slice the matrix into three pieces and add them together:
matrix = data(1:3:end, :) + data(2:3:end, :) + data(3:3:end, :);
This will give an error if size(data,1) is not a multiple of three, since the three pieces wouldn't be the same size. If appropriate to your data, you might work around that by truncating data, or appending some zeros to the end.
You could also do something fancy with reshape and 3D arrays. But I would prefer the above (unless you need to replace 3 with a variable...)
Prashant answered nicely before but I would have a simple amendment:
fl = filterLength;
A = yourVector (where mod(A,fl)==0)
sum(reshape(A,fl,[]),1).'/fl;
There is the ",1" that makes the line run even when fl==1 (original values).
I discovered this while running it in a for loop like so:
... read A ...
% Plot data
hold on;
averageFactors = [1 3 10 30 100 300 1000];
colors = hsv(length(averageFactors));
clear legendTxt;
for i=1:length(averageFactors)
% ------ FILTERING ----------
clear Atrunc;
clear ttrunc;
clear B;
fl = averageFactors(i); % filter length
Atrunc = A(1:L-mod(L,fl),:);
ttrunc = t(1:L-mod(L,fl),:);
B = sum(reshape(Atrunc,fl,[]),1).'/fl;
tB = sum(reshape(ttrunc,fl,[]),1).'/fl;
length(B)
plot(tB,B,'color',colors(i,:) )
%kbhit ()
endfor