I need help transforming data

Hello,

I have multiple sets of nx3 matrices, where n is varying between the matrices and the matrices consist of coordinate points. I am trying to transform the data to get a matrix where the first column of my nx3 matrices (the x-coordinates) are the row indices, the 2nd column of the nx3 matrices (y-coordinates) are the column indices, and the 3rd column of the nx3 matrices (z-coordinates) are the values of the new matrix where the value matches with it's corresponding x and y indices (so the z-coordinate corresponds with its appropriate x and y coordinates). This is all to use the functions surf(Z) and surface(Z) in order to try and recreate an object in MATLAB. So far, I have the code

 function Z = GetZmatrix(concatenatedmatrix)
Z=zeros(size(concatenatedmatrix,1));   %create matrix of zeroes
x = (1:size(concatenatedmatrix,1));
y = (1:size(concatenatedmatrix,2));
sorted = ceil(sortrows(concatenatedmatrix))  %sorts and gets rid of decimals
for i = sorted(:,1).' 
    for j = 1:size(concatenatedmatrix,1)
        for l = sorted(:,2).'
            for k = 1:size(concatenatedmatrix,2)
                if i == j
                    if l == k 
                        Z(k,j) = Z(k,j) + sorted(i,3);
                    end
                end
            end
        end
    end
end

However, this is not giving me the output I want for my test matrix. I created the matrix

in hopes of getting

However my code gave me

Can anyone help me understand why my code is giving the wrong output and maybe help me get what I'm trying to get? And I'm fairly new to MATLAB, so forgive my code if it is ugly or sloppy. Thanks! Michael

[Michael J]

Also, would it be possible to get a mathematical equation of this object? I'm not sure if using the Fourier series or doing an FFT would work or not.

[Star Strider]

What would you want to get in terms of a mathematical relation? It’s defined by Matrix ‘A’, so that’s about as good as it gets as a mathematical definition. You could certainly use fft2 to do the Fourier transform. What information do you want from it?

[Michael J]

I am trying to get some sort of mathematical formula for the object (and the process for other future objects) so that I can make inferences on it as certain parameters are advised or become interesting.

[Star Strider]

Is the ‘object’ you’re referring to ‘A’ or ‘B’?

The only process I see maps the third column of ‘A’ by the column and row indices (respectively) given in its first two columns. So long as that remains unique, you simply have a discrete mapping.

Answer 1

[Star Strider]

Alternatively, a very simple implementation with one loop is:

A = [1 2 4; 5 6 4; 3 2 1; 1 1 1; 2 3 4; 4 1 5];
B = zeros(6);
for k1 = 1:size(A,1)
    B(A(k1,2),A(k1,1)) = A(k1,3);
end

[Michael J]

I like this code a lot as it achieves the result I want and is much simpler, but unfortunately I am unable to create the zero matrix. The number of coordinate points I have is beyond the maximum variable size allowed by the program. Thanks for your help though, I at least learned a bit more about coding in MATLAB!

[Star Strider]

My pleasure!

The sparse functions (and its friends) may be worth considering.

I don’t have a lot of experience with sparse matrices, but using them could solve your maximum variable size problem.

[Guillaume]

If I was going for a handwritten loop, I would have written it like this:

A = [1 2 4; 5 6 4; 3 2 1; 1 1 1; 2 3 4; 4 1 5];
B = sparse(max(A(:, 1)), max(A(:, 2))); %don't hard code dimensions
for point = A'  %iterate directly over the rows of A, without using an index
   B(point(1), point(2)) = point(3);
end

[Star Strider]

Guillaume, chill !

Let each Answer succeed or fail on its own merits, according to what the OP wants.

[Guillaume]

I am chilled. I'm just pointing a slightly more efficient way (in my opinion) to write the loop (saves on a indexing operation).

Note that I did it as a comment to your answer, so Michael would still accept your answer if he wanted to go with the loop.

[Star Strider]

It seems indexing operations aren’t what Michael J wants anyway.

He’s looking for a mathematical relation that defines the indexing operation.

I don’t see it, and a linear regression (of columns 1:2 against column 3) is a poor fit. (We don’t have the data that created the ‘A’ matrix.) Until we learn more, I doubt any answer (thus far) is what he’s looking for.

Answer 2

[Guillaume]

accumarray is what you want:

A = [1 2 4
     5 6 4
     3 2 1
     1 1 1
     2 3 4
     4 1 5]
B = accumarray(A(:, [1 2]), A(:, 3))'

Note if you have identical x and y, the default behaviour of accumarray is to sum the z. You could use @min or @max or whatever you want if that were to happen and the sum doesn't suit you:

B = accumarray(A(:, [1 2]), A(:, 3), [], @min)'

[Michael J]

This works for my test matrix A that I made up, but when I try to use it on the matrix of coordinate points, I get the error "First input SUBS must contain positive integer subscripts". I'm not sure how to fix this issue as I used the ceil function to make it so that my data is all positive integers and my coordinate points exist in the first octant. When I look at the data, the smallest point is (17, 12, 60). Do you know how to get around this error? Thanks for you help!

[Guillaume]

What does

[r, c] = find(A(:, [1 2]) < 1 | mod(A(:, [1 2]), 1));

return?

If you get this error it's either because because some coordinates are not integer or are less than 1. Either way, you'll get the same error with Star Strider's answer.

You'll also get the same issue of creating a matrix big enough to hold all your points. The answer is also to create a sparse matrix, which accumarray allows you to do:

B = accumarray(A(:, [1 2]), A(:, 3), [], [], [], true);

Note that accumarray is probably faster than a handwritten loop.