In MATLAB, I have a defined cell array C of
size(C) = 1 by 150
Each matrix T of this cell C is of size
size(C{i}) = 8 by 16
I am wondering if there is a way to define a new multidimension (3D) matrix M that is of size 8 by 16 by 150
That is when I write the command size(M) I get 8 by 16 by 150
Thank you! Looking forward for your answers
If I'm understanding your problem correctly, you have a cell array of 150 cells, and each cell element is 8 x 16, and you wish to stack all of these matrices together in the third dimension so you have a 3D matrix of size 8 x 16 x 150.
It's a simple as:
M = cat(3, C{:});
This syntax may look strange, but it's very valid. The command cat performs concatenation of matrices where the first parameter is the dimension you want to concatenate to... so in your case, that's the third dimension, and the parameters after are the matrices you want to concatenate to make the final matrix.
Doing C{:} creates what is known as a comma-separated list. This is equivalent to typing out the following syntax in MATLAB:
C{1}, C{2}, C{3}, ..., C{150}
Therefore, by doing cat(3, C{:});, what you're really doing is:
cat(3, C{1}, C{2}, C{3}, ..., C{150});
As such, you're taking all of the 150 cells and concatenating them all together in the third dimension. However, instead of having to type out 150 individual cell entries, that is encapsulated by creating a comma-separated list via C{:}.
Related
If I have a square matrix of arrays such as:
[1,2], [2,3]
[5,9], [1,4]
And I want to get the mean of the first values in the arrays of each row such:
1.5
3
Is this possible in Matlab?
I've used the mean(matrix, 2) command to do this with a matrix of single values, but I'm not sure how to extend this to deal with the arrays.
Get the first elements in all arrays of matrix, then call mean function
mean(matrix(:,:,1))
maybe you need to reshape before call mean
a = matrix(:,:,1);
mean(a(:))
You can apply mean function inside mean function to get the total mean value of the 2D array at index 1. You can do similary with array at index 2. Consider the following snapshot.
After staring at your problem for a long time, it looks like your input is a 3D matrix where each row of your formatting corresponds to a 2D matrix slice. Therefore, in proper MATLAB syntax, your matrix is actually:
M = cat(3, [1,2; 2,3], [5,9; 1,4]);
We thus get:
>> M = cat(3, [1,2; 2,3], [5,9; 1,4])
M(:,:,1) =
1 2
2 3
M(:,:,2) =
5 9
1 4
The first slice is the matrix [1,2; 2,3] and the second slice is [5,9; 1,4]. From what it looks like, you would like the mean of only the first column of every slice and return this as a single vector of values. Therefore, use the mean function and index into the first column for all rows and slices. This will unfortunately become a singleton 3D array so you'll need to squeeze out the singleton dimensions.
Without further ado:
O = squeeze(mean(M(:,1,:)))
We thus get:
>> O = squeeze(mean(M(:,1,:)))
O =
1.5000
3.0000
I have a cell array A Mx3 in size where each entry contains a further cell-array Nx1 in size, for example when M=9 and N=5:
All data contained within in any given cell array is in vector format and of equal length. For example, A{1,1} contains 5 vectors 1x93 in size whilst A{1,2} contains 5 vectors 1x100 in size:
I wish to carry out this procedure on each of the 27 cells:
B = transpose(cell2mat(A{1,1}));
B = sort(B);
C = std(B,0,2); %Calculate standard deviation
Ultimately, the desired outcome would be, for the above example, 27 columns (9x3) containing the standard deviation results (padded with 0 or NaNs to handle differing lengths) printed in the order A{1,1}, A{1,2}, A{1,3}, A{2,1}, A{2,2}, A{2,3} and so forth.
I can do this by wrapping the above code into a loop to iterate over each one of the 27 cells in the correct order however, I was wondering if there was a clever cellfun or more succinct method to accomplish this particularly without the use of a loop?
You should probably realize that cellfun is essentially a glorified for loop over cells. There's simply extra error checking and all that to ensure that the whole thing works. In any case, yes it's possible to do what you're asking in a single cellfun call. Note that I am simply going to apply the same logic as you would have in a for loop with cellfun. Also note that because you're using cell arrays, you have no choice but to iterate over the entire master cell array. However, what you'll want to do is pad each resulting column vector in each output in the final cell array so that they all share the same length. We can do that with another two cellfun calls - one to determine the largest vector length and another to perform the padding operation.
Something like this could work:
% Step #1 - Sort the vectors in each cell array, then find row-wise std
B = cellfun(#(x) std(sort(cell2mat(x).'), 0, 2), A, 'un', 0);
% Step #2 - Determine the largest length vector and pad
sizes = cellfun(#numel, B);
B = cellfun(#(x) [x; nan(max(sizes(:)) - numel(x), 1)], B, 'un', 0);
The first line of code takes each element in A, converts each cell element into a N x 5 column matrix (i.e. cell2mat(x).'), we then sort each column individually with sort, then take the standard deviation row-wise. Because the output is ultimately a vector, we must make sure that the 'UniformOutput' flag is 0, or 'un=0'. Once we complete the standard deviation calculation, we determine the total number of elements for each resulting column vector for all cell elements, determine the largest size then use another cellfun call to pad these vectors so they all match the same size.
To finally get your desired output, you need to transpose the cell array, then unroll the elements in column major order. Remember that MATLAB accesses things in column major, so a common trick to get things in row-major (what you want) as opposed to column major is to first transpose, then unroll in column-major fashion to perform a row-major readout. Doing this in one line is tricky, so you'll need to not only transpose the cell array, you must use reshape to ensure that the elements are read out in row major format, but then ensuring that the result is placed in a row of cells, then call cell2mat so you can piece these vectors together. The final result should be a 27 column matrix where we have pieced all of these vectors together in a single row-wise fashion:
C = cell2mat(reshape(B.', 1, []));
I first want to clarify if my logic in the following is correct:
In a 2 dimensional array, say A[x][y], x represents the number of braces and y the number of elements in each brace. So int A[2][3] is initialized as:
{
{1,2,3}, //from A[0][0] to A[0][2];
{4,5,6} //from A[1]{0] to A[1][2];
};
Second, I want to know what the similar correlations are in a 3 dimensional array, four dimensional, and so on, and how to know which dimension number correlates to what level for any multi-dimensional array.
For example, in A[3][4][2], does the 3 denote the number of 2d tables, or rows/columns in each table? And in A[2][3][4][5], does 2 represent the number of 2d tables, no. of 3d tables, no. of 1d tables, or no. of rows/columns per 1d table? Note:I'm getting my head around multi dimensional arrays for the first time, please explain as simplistically as possible.
Yes what you say it's correct. You can think that recursively.
Start from a 1D array (let's assume that it has 3 elements):
int 1darray[] = {0, 1, 2};
Now producing a 2D array simply says go inside every element of 1darray and put another 1D array, to produce a 2D one, like this:
int 2darray[] = {1darray_0, 1darray_1, 1darray_2};
where the 1darray_0, 1darray_1, 1darray_2 are 1D arrays, just like the 1darray we created in the start. So now this will form a 3x3 2D array.
Now the 3D array can be formed like this:
int 3darray[] = {2darray_0, 2darray_1, 2darray_2};
where the 2darray_0, 2darray_1, 2darray_2 are 2D arrays, just like the 2darray we created above. So now this will form a 3x3x3 3D array.
Your example:
A[3][4][2]
says that A has:
3 rows
4 columns
2 z-columns
In general however, I would advice you to have in mind the picture I have in my 2D dynamic array (C):
which describes in a nutshell what I tried to explain in the start.
As you increase your dimensions, you replace every element of the previous array with an array of the next dimension, while you reach the end.
I currently have a 3 dimensional matrix and I want to extract a single row (into the third dimension) from it by index (say matrix(2,1,:)). I initially anticipated that the result of this would be a 1 dimensional matrix however what I got was a 1 by 1 by n matrix. Usually this wouldn't be a problem but some of the functions I'm using don't like 3D matrices. For example see the problem replicated below:
threeDeeMatrix=rand(3,3,3);
oneDeeAttempt=threeDeeMatrix(1,1,:);
norm(oneDeeAttempt)
Which returns the error message:
Error using norm
Input must be 2-D.
This is because oneDeeAttempt is
oneDeeAttempt(:,:,1) =
0.8400
oneDeeAttempt(:,:,2) =
0.0700
oneDeeAttempt(:,:,3) =
0.7663
rather than [0.8400 0.0700 0.7663]
How can I strip these extra dimensions? The only solution I can come up with is to use a loop to manually copy the values but that seems a little excessive.
Using permute to rearrange the matrix
The solution (which I found in the final stages of asking this) is to use permute which rearranges the order of the dimensions (similar to a=a' for 2D matrices). Once the unit dimensions are last they are stripped from the matrix and it becomes 1 dimensional.
oneDee=permute(oneDeeAttempt,[3 1 2]) %rearrange so the previous third dimension is now the first
%the matrix is now 3 by 1 by 1 which becomes 3
Using squeeze to remove leading singleton dimensions
As pointed out by Luis Mendo squeeze will very simply remove these leading singleton dimensions without having to worry about which dimensions are non singleton
oneDee=squeeze(oneDeeAttempt);
I have a 4D matrix of size 300x200x3x20 where 300x200 is the size of one video frame, 3 is the number of channels (Red-Green-Blue channels) and 20 is the number of frames.
I want to extract all the color vectors from this matrix and store them in a 2D array of size 3x1,200,000 (300 x 200 x 20 = 1,200,000) where each row represents a component of the RGB color space and each column contain the RGB values of one pixel in the original matrix.
Besides, I want to carry out pixel-wise operations on this data such as extracting visual features but I cannot find a way to effectively access vectors along the third dimension.
How could I efficiently do these, possible without using loops?
Try this code -
IN = your_4D_data;
OUT = reshape(permute(IN,[3 1 2 4]),3,numel(IN)/3);
help reshape says:
B = reshape(A,m,n,p,...) or B = reshape(A,[m n p ...]) returns an n-dimensional array with the same elements as A but reshaped to have the size m-by-n-by-p-by-.... The product of the specified dimensions, m*n*p*..., must be the same as numel(A).
is this what you are looking for?
also, you can adress pixels like this: Matrix(i,j,:,k) which gives you the 3 colorchanels of pixel i,j in frame k.