Indeed, my problem is a succession of my previous problem:
1) Extract submatrices, 2) vectorize and then 3) put back
Thanks to Dan and his ideas works perfectly for the purpose.
My new problem is this:
If I have a 3D matrix, 8 by 8 by 12, e.g. A = randn(8,8,12).
Let's see the linear index of the first slice:
From Dan's solution, I understand that A[4:6, 4:6, :] can extract the corresponding parts of all slices.
However, going back to my real situations, extracting parts by actually counting rows and columns seem not suit my purpose because my matrix size is huge and I do have many sub-matrices to be extracted.
So, I prefer to work on linear index and want to ask if there are any ways to work with this possibility.
Here is my trial:
By defining sub_group = [28 29 30 36 37 38 44 45 46], then A(sub_group) can extract sub-matrix from the first slice of the 3D matrix, A.
I understand that A(sub_group + 8*8*(n-1)) can extract the sub-matrix from the nth slice.
I aim to only work with my sub_group and then extract the same part of every slice.
Most importantly, I have to put back the sub-matrices after updating their values.
So, is there are any quick syntax for matlab to work for my purpose?
I appreciate for your help.
Approach #1
For cases like this when you need to calculate linear indices, you can use bsxfun as shown here -
%// Store number of rows in A as a variable
M = size(A,1)
%// Get start and offset linear indices for the first slice and thus sub_group
start_idx = (colstart-1)*M + rowstart
offset_idx = bsxfun(#plus,[0:rowstop - rowstart]', [0:colstop-colstart]*M) %//'
sub_group = reshape(start_idx + offset_idx,1,[])
%// Calculate sub_groups for all 3D slices
all_sub_groups = bsxfun(#plus,sub_group',[0:size(A,3)-1]*numel(A(:,:,1)))
Sample run -
A(:,:,1) =
0.096594 0.52368 0.76285 0.83984 0.27019
0.84588 0.65035 0.57569 0.42683 0.4008
0.9094 0.38515 0.63192 0.63162 0.55425
0.011341 0.6493 0.2782 0.83347 0.44387
A(:,:,2) =
0.090384 0.037262 0.38325 0.89456 0.89451
0.74438 0.9758 0.88445 0.39852 0.21417
0.032615 0.52234 0.25502 0.62502 0.0038592
0.42974 0.90963 0.90905 0.5676 0.88058
rowstart =
2
rowstop =
4
colstart =
3
colstop =
5
sub_group =
10 11 12 14 15 16 18 19 20
all_sub_groups =
10 30
11 31
12 32
14 34
15 35
16 36
18 38
19 39
20 40
Approach #2
For a quick syntax based solution, sub2ind could be suggested here. The implementation would look something like this -
[X,Y] = ndgrid(rowstart:rowstop,colstart:colstop);
sub_group = sub2ind(size(A(:,:,1)),X,Y);
[X,Y,Z] = ndgrid(rowstart:rowstop,colstart:colstop,1:size(A,3));
all_sub_groups = sub2ind(size(A),X,Y,Z);
Related
I would like to create a column vector from the elements of a matrix A of size (3,3) that are not on the diagonal. Thus, I would have 6 elements in that output vector. How can I do this?
Use eye and logical negation, although this is no better than Divakar's original answer, and possibly significantly slower for very large matrices.
>> A = magic(4)
A =
16 2 3 13
5 11 10 8
9 7 6 12
4 14 15 1
>> A(~eye(size(A)))
ans =
5
9
4
2
7
14
3
10
15
13
8
12
Use this to get such a column vector, assuming A is the input matrix -
column_vector = A(eye(size(A))==0)
If you don't care about the order of the elements in the output, you can also use a combination of setdiff and diag -
column_vector = setdiff(A,diag(A))
You can also use linear indexing to access the diagonal elements and null them. This will automatically reshape itself to a single vector:
A(1:size(A,1)+1:end) = [];
Bear in mind that this will mutate the original matrix A. If you don't want this to happen, make a copy of your matrix then perform the above operation on that copy. In other words:
Acopy = A;
Acopy(1:size(A,1)+1:end) = [];
Acopy will contain the final result. You need to create a vector starting from 1 and going to the end in increments of the rows of the matrix A added with 1 due to the fact that linear indices are column-major, so the linear indices used to access a matrix progress down each row first for a particular column. size(A,1) will allow us to offset by each column and we add 1 each time to ensure we get the diagonal coefficient for each column in the matrix.
Assuming that the matrix is square,
v = A(mod(0:numel(A)-1, size(A,1)+1) > 0).';
I have two matrices like this:
gt = [30 40 20 40] and
de = [32 42 20 40; 34 12 20 40; 36 84 20 40]
I want to calculate the overlap area between gt and 3 rows of de respectively and the overlap is calculated by a function I write myself. Then I want to store the result in a new column vector like
result = [result1; result2; result3].
Could you tell me how to write a vectorization codes to achieve this?
Thanks!
The vectorization can only happen inside the overlap function. The only thing you can do outside it is replicate the vector gt, using repmat or bsxfun. You don't explain how the overlap function works. I suppose it has to do with co-ordinates, so I give an example for euclidean distance which works in a similar logic.
If you had to calculate the distance between point gt = [1 2] and points de = [5 6; 10 12; 0 -1] you would define
function result = dist(x, y)
result = sum(sqrt((x(:,1) - y(:,1)).^2 + (x(:,2) - y(:,2)).^2), 2)
and you would call it replicating the gt vector
dist(de, repmat(gt, 3, 1))
Alternatively, you could use bsxfun instead of repmat, which might have better performance (depending on various factors)
The key to vectorizing is performing operations column-wise (in this specific case it could be vectorized even further, however I am writing it this way to emphasize the column-wise operations)
Is there a function in MATLAB which allows to aggregate (or we can say sum) columns in a matrix per defined number of columns?
For example I have:
A =
1 2 3 4 5 6
9 10 11 12 13 14
17 18 19 20 21 22
I wish to aggregate every 2 columns, like this: col1+col2, and then col3+col4, and then col5+col6, so my output is:
A_agg =
3 7 11
19 23 27
35 39 43
I couldn't find a built-in function and was trying to write a for loop but I couldn't manage to do it since I am quite new to programming. Do you have any suggestions/solutions how this could be solved with a for loop, or maybe there is a built-in function?
Since sum operates down columns in a matrix, I first reshape A so that it has 2 rows and 9 columns, then sum down each column. Then reshape back to the desired output matrix A_agg.
A=[1 2 3 4 5 6
9 10 11 12 13 14
17 18 19 20 21 22]
[m,n]=size(A);
A_agg=reshape(sum(reshape(A',2,[])),m,[])'
You can use a combination of mat2cell and cellfun. You can use mat2cell to split up your matrices into individual 2 column chunks. Each chunk would be stored as a cell in a cell array. You can then use cellfun to take each cell and sum row-wise. After you're done, you can use cell2mat to convert back.
Using your example:
A = [1:6;9:14;17:22];
B = mat2cell(A, 3, [2 2 2]);
C = cellfun(#(x) sum(x,2), B, 'UniformOutput', false);
A_agg = cell2mat(C);
A_agg should thus give you:
A_agg =
3 7 11
19 23 27
35 39 43
Let's walk through the code slowly:
A is defined as we had before. B will be a cell array, and will segment your matrix into matrices of 2 columns per cell. The first parameter is the matrix you want to decompose (in our case A). The second parameter tells you how many rows each segment should have. Because we want all of the matrices to have the same number of rows, we thus supply one number which is 3. After, you specify the number of columns you want per matrix. Because there are 6 columns, we need 3 matrices, and so you'd specify a vector of [2 2 2].
C is the output of cellfun, where cellfun applies a function to every single element in a cell matrix. What you want to do here is for each cell (essentially each matrix), you want to sum row-wise. The first parameter is an anonymous function that takes in a matrix from each cell, and sums row-wise. The second parameter is the cell array we just created. You'll notice that we have an additional flag to set: UniformOutput. The reason why you have to set UniformOutput = false is because if you apply cellfun without that flag, the expected result at the end of the function you apply to each cell is scalar. Because we are outputting a column vector instead, we have to set this flag to false.
A_agg will thus aggregate all of your cells back to matrix form.
If you want to do this for any size matrix, bear in mind that there has to be an even amount of columns for this work. What I mean by even is that the number of columns has to be evenly divisible by 2. You would thus re-run the code like so:
B = mat2cell(A, size(A,1), 2*ones(1, size(A,2)/2));
C = cellfun(#(x) sum(x,2), B, 'UniformOutput', false);
A_agg = cell2mat(C);
Another possibility, if you have the Image Processing Toolbox, is to use blockproc. Let n denote the number of columns to be aggregated (2 in your example). Then:
A_agg = blockproc(A, [size(A,1) n], #(x) sum(x.data, 2));
I am trying to find the Extremum of a 3-dim matrix along the 2nd dimension.
I started with
[~,index] = max(abs(mat),[],2), but I don't know how to advance from here. How is the index vector to be used together with the original matrix. Or is there a completely different solution to this problem?
To illustrate the task assume the following matrix:
mat(:,:,1) =
23 8 -4
-1 -26 46
mat(:,:,2) =
5 -27 12
2 -1 18
mat(:,:,3) =
-10 49 39
-13 -46 41
mat(:,:,4) =
30 -24 18
-40 -16 -36
The expected result would then be
ext(:,:,1) =
23
-46
ext(:,:,2) =
-27
18
ext(:,:,3) =
49
-46
ext(:,:,4) =
30
-40
I don't know how to use the index vector with mat to get the desired result ext.
1) If you want to find a maximum just along, let's say, 2d dimension, your variable index will be a matrix having dimensions (N,1,M), where N and M are number of elements of your matrix in the first and third dimensions respectively. In order to remove dummy dimensions, there is function squeeze() exist: index=squeeze(index) After that size(index) gives N,M
2) Depending on your problem, you probably need matlab function ind2sub(). First, you take a slice of your matrix, than find its maximum with linear indexing, and than you can restore your indicies with int2sub(). Here is an example for a 2D matrix:
M = randn(5,5);
[C,I] = max(M(:));
[index1,index2] = ind2sub(size(M),I);
Same method allows to find the absolute maximal element in whole 3D matrix.
Use ndgrid to generate the values along dimensions 1 and 3, and then sub2ind to combine the three indices into a linear index:
[~, jj] = max(abs(mat),[],2); %// jj: returned by max
[ii, ~, kk] = ndgrid(1:size(mat,1),1,1:size(mat,3)); %// ii, kk: all combinations
result = mat(sub2ind(size(mat), ii, jj, kk));
A fancier, one-line alternative:
result = max(complex(mat),[],2);
This works because, acccording to max documentation,
For complex input A, max returns the complex number with the largest complex modulus (magnitude), computed with max(abs(A)).
In matlab, after meeting a specific criterion, I used to return back the pixel itself and store it in the vector pixels as follows:
pixels(index) = y(i,j);
Now, I would like to return the location of those pixels. Should I do the following?
pixels(index) = i,j;
EDIT
If I want to then set those indexes to the value 1, I do the following, right?
for i=1:m
for j=1:n
y(i,j)=1
end
end
Thanks.
It is extremely inefficient to do so in a nested loop in Matlab.
Using sub2ind can help you do so much faster:
y( sub2ind( size(y), i, j ) ) = 1;
EDIT - sub2ind
What sub2ind does?
Suppose you have a matrix M of size [4 6]:
M = [ 1 5 9 13 17 21
2 6 10 14 18 22
3 7 11 15 19 23
4 8 12 16 20 24 ];
You wish to access two elements: the one at the first row and second column, and another at the fourth row and the fifth column.
In that case you have the rows you wish to access r = [ 1 4 ] and the columns you wish to access c = [ 2 5 ]. However, if you try and access
>> M( r, c )
This is a 2x2 matrix
ans =
5 17
8 20
And not the two elements you were looking for (which are 5 and 20).
What sub2ind does is convert the row/column indices you have into linear indices
>> sub2ind( size(M), r, c )
ans =
5 20
which happens to be the linear indices of the requested entries.
You can think of linear indices as the single index required to access an element in a matrix in the case that the matrix was converted to a vector stacking its columns one after the other.
A few comments:
Matlab has a few ways of indexing matrices: by row / column indices (like i and j in your question). By linear indices (like index in your question). However, the more efficient way is to use logical indexing: that is, using a matrix of the same size as y with true for the entries you wish to set / get.
So, in your example, if you could get such a logical matrix instead of index or i and j it would have been better.
Matlab has many advantages over other programing languages. One of them is its ability to perform vector/matrix operations extremely efficient. Resorting to loops, or worse, nested loops, is something that should be avoided in Matlab.
It is not a good practice to use i and j as variables in Matlab.
If you want to find the occurrence of a value y(i,j) simply evaluate
idx = (pixels == y(i,j));
Depending on your variables you can then probably do
index(idx) = 1;