How do I change the list of value to all 1? I need the top right to bottom left also end up with 1.
rc = input('Please enter a value for rc: ');
mat = ones(rc,rc);
for i = 1:rc
for j = 1:rc
mat(i,j) = (i-1)+(j-1);
end
end
final = mat
final(diag(final)) = 1 % this won't work?
Code for the original problem -
final(1:size(final,1)+1:end)=1
Explanation: As an example consider a 5x5 final matrix, the diagonal elements would have indices as (1,1), (2,2) .. (5,5). Convert these to linear indices - 1, 7 and so on till the very last element, which is exactly what 1:size(final,1)+1:end gets us.
Edit : If you would like to set the diagonal(from top right to bottom left elements) as 1, one approach would be -
final(fliplr(eye(size(final)))==1)=1
Explanation: In this case as well we can use linear indexing, but just for more readability and maybe a little fun, we can use logical indexing with a proper mask, which is being created with fliplr(eye(size(final)))==1.
But, if you care about performance, you can use linear indexing here as well, like this -
final(sub2ind(size(final),1:size(final,1),size(final,2):-1:1))=1
Explanation: Here we are creating the linear indices with the rows and columns indices of the elements to be set. The rows here would be - 1:size(final,1) and columns are size(final,2):-1:1. We feed these two to sub2ind to get us the linear indices that we can use to index into final and set them to 1.
If you would to squeeze out the max performance here, go with this raw version of sub2ind -
final([size(final,2)-1:-1:0]*size(final,1) + [1:size(final,1)])=1
All of the approaches specified so far are great methods for doing what you're asking.
However, I'd like to provide another viewpoint and something that I've noticed in your code, as well as an interesting property of this matrix that may or may not have been noticed. All of the anti-diagonal values in your matrix have values equal to rc - 1.
As such, if you want to set all of the anti-diagonal values to 1, you can cheat and simply find those values equal to rc-1 and set these to 1. In other words:
final(final == rc-1) = 1;
Minor note on efficiency
As a means of efficiency, you can do the same thing your two for loops are doing when constructing mat by using the hankel command:
mat = hankel(0:rc-1,rc-1:2*(rc-1))
How hankel works in this case is that the first row of the matrix is specified by the vector of 0:rc-1. After, each row that follows incrementally shifts values to the left and adds an increasing value of 1 to the right. This keeps going until you encounter the vector seen in the second argument, and at this point we stop. In other words, if we did:
mat = hankel(0:3,3:6)
This is what we get:
mat =
0 1 2 3
1 2 3 4
2 3 4 5
3 4 5 6
Therefore, by specifying rc = 5, this is the matrix I get with hankel, which is identical to what your code produces (before setting the anti-diagonal to 1):
mat =
0 1 2 3 4
1 2 3 4 5
2 3 4 5 6
3 4 5 6 7
4 5 6 7 8
Tying it all together
With hankel and the cheat that I mentioned, we can compute what you are asking in three lines of code - with the first line of code asking for the dimensions of the matrix:
rc = input('Please enter a value for rc: ');
mat = hankel(0:rc-1, rc-1:2*(rc-1));
mat(mat == rc-1) = 1;
mat contains your final matrix. Therefore, with rc = 5, this is the matrix I get:
mat =
0 1 2 3 1
1 2 3 1 5
2 3 1 5 6
3 1 5 6 7
1 5 6 7 8
Here's a simple method where I just add/subtract the appropriate matrices to end up with the right thing:
final=mat-diag(diag(mat-1))+fliplr(diag([2-rc zeros(1,rc-2) 2-rc]))
Here is one way to do it:
Say we have a the square matrix:
a = ones(5, 5)*5
a =
5 5 5 5 5
5 5 5 5 5
5 5 5 5 5
5 5 5 5 5
5 5 5 5 5
You can remove the diagonal, then create a diagonal list of ones to replace it:
a = a - fliplr(diag(diag(fliplr(a)))) + fliplr(diag(ones(length(a), 1)))
a =
5 5 5 5 1
5 5 5 1 5
5 5 1 5 5
5 1 5 5 5
1 5 5 5 5
The diag(ones(length(a), 1)) can be any vector, ie. 1->5:
a = a - fliplr(diag(diag(fliplr(a)))) + fliplr(diag(1:length(a)))
a =
5 5 5 5 1
5 5 5 2 5
5 5 3 5 5
5 4 5 5 5
5 5 5 5 5
Related
I have been given this problem in a MATLAB course I am doing. The instructor's solution provided there is wrong, and I have been struggling with the same problem for hours as I am a beginner who has just started coding (a science student here).
Consider a one-dimensional matrix A such as A = \[5 8 8 8 9 9 6 6 5 5 4 1 2 3 5 3 3 \]. Show the percentage frequencies of unique
elements in the matrix A in descending order.
Hint: Use the functions tabulate and sort.
How do I solve this problem using only tabulate, sort, and find functions (find is for eliminating zero frequency elements in tabulate table, which my instructor did not do)?
I tried first extracting the indices of non-zero elements in the percentage column of tabulating table using the find function, which I succeeded in doing using the following:
A = [5 8 8 8 9 9 6 6 5 5 4 1 2 3 5 3 3 ];
B = tabulate(A);
C = find(B(:,3) > 0)
But I am now struggling to return the values corresponding to the 3rd column of B using indices in C. Please help. Also please give me some alternative syntax where one can easily make a vector out of non-zero elements of a row or column easily by omitting the zeroes in that vector if it exists. Rest of the problem I'll do by myself.
With your find command, you are just finding the indices of the matrix and not the values themselves.
So you either will do something like this:
A = [5 8 8 8 9 9 6 6 5 5 4 1 2 3 5 3 3 ];
B = tabulate(A);
for i = 1:size(B,1)-1
if B(i,3) == 0
B(i,:) = [];
end
end
sortrows(B,3,'descend')
where you remove the 0 value's row.
Or since you have all the numbers with none-zero frequency you can ask for their rows. Like this:
A = [5 8 8 8 9 9 6 6 5 5 4 1 2 3 5 3 3 ];
B = tabulate(A);
C = find(B(:,3) > 0);
sortrows(B(C(:),:),3,'descend')
in a bit more elegant way. B(C(:),:) calls all the rows with first indices the indices of matrix C. Which is exactly what you are asking for. While at the same time you sort your matrix based on row 3 at a descending order.
Suppose that I have a matrix , let's call it A, as follows:
1 2 3 4 5 1 2 3 4 5
0 2 4 6 8 1 3 5 7 9
And I want to reshape it into a matrix like this:
1 2 3 4 5
0 2 4 6 8
1 2 3 4 5
1 3 5 7 9
So, basically, what I want to be done is that MATLAB first reads a block of size (2,5) and then splits the remaining matrix to the next row and then repeats this so on so forth until we get something like in my example.
I tried to do this using MATLAB's reshape command in several ways but I failed. Any help is appreciated. In case that it matters, my original data is larger. It's (2,1080). Thanks.
I don't believe you can do this in a single command, but perhaps someone will correct me. If speed isn't a huge concern a for loop should work fine.
Alternatively you can get your results by reshaping each row of A and then placing the results into every other row of a new matrix. This will also work with your larger data.
A = [1 2 3 4 5 1 2 3 4 5
0 2 4 6 8 1 3 5 7 9];
An = zeros(numel(A)/5, 5); % Set up new, empty matrix
An(1:2:end,:) = reshape(A(1,:), 5, [])'; % Write the first row of A to every other row of An
An(2:2:end,:) = reshape(A(2,:), 5, [])' % Write second row of A to remaining rows
An =
1 2 3 4 5
0 2 4 6 8
1 2 3 4 5
1 3 5 7 9
You may need to read more about indexing in the Matlab's documentation.
For your example, it is easy to do the following
A=[1 2 3 4 5 1 2 3 4 5; 0 2 4 6 8 1 3 5 7 9]
a1=A(:,1:5); % extract all rows, and columns from 1 to 5
a2=A(:,6:end); % extract all rows, and columns from 6 to end
B=[a1;a2] % construct a new matrix.
It is not difficult to build some sort of loops to extract the rest.
Here's a way you can do it in one line using the reshape and permute commands:
B = reshape(permute(reshape(A,2,5,[]), [1,3,2]), [], 5);
The reshape(A,2,5,[]) command reshapes your A matrix into a three-dimensional tensor of dimension 2 x 5 x nblocks, where nblocks is the number of blocks in A in the horizontal direction. The permute command then swaps the 2nd and 3rd dimensions of this 3D tensor, so that it becomes a 2 x nblocks x 5 tensor. The final reshape command then transforms the 3D tensor into a matrix of dimension (2*nblocks) x 5.
Looking at the results at each stage may give you a better idea of what's happening.
I have a 4x8 matrix which I want to select two different columns of it then derive dot product of them and then divide to norm values of that selected columns, and then repeat this for all possible two different columns and save the vectors in a new matrix. can anyone provide me a matlab code for this purpose?
The code which I supposed to give me the output is:
A=[1 2 3 4 5 6 7 8;1 2 3 4 5 6 7 8;1 2 3 4 5 6 7 8;1 2 3 4 5 6 7 8;];
for i=1:8
for j=1:7
B(:,i)=(A(:,i).*A(:,j+1))/(norm(A(:,i))*norm(A(:,j+1)));
end
end
I would approach this a different way. First, create two matrices where the corresponding columns of each one correspond to a unique pair of columns from your matrix.
Easiest way I can think of is to create all possible combinations of pairs, and eliminate the duplicates. You can do this by creating a meshgrid of values where the outputs X and Y give you a pairing of each pair of vectors and only selecting out the lower triangular part of each matrix offsetting by 1 to get the main diagonal just one below the diagonal.... so do this:
num_columns = size(A,2);
[X,Y] = meshgrid(1:num_columns);
X = X(tril(ones(num_columns),-1)==1); Y = Y(tril(ones(num_columns),-1)==1);
In your case, here's what the grid of coordinates looks like:
>> [X,Y] = meshgrid(1:num_columns)
X =
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
Y =
1 1 1 1 1 1 1 1
2 2 2 2 2 2 2 2
3 3 3 3 3 3 3 3
4 4 4 4 4 4 4 4
5 5 5 5 5 5 5 5
6 6 6 6 6 6 6 6
7 7 7 7 7 7 7 7
8 8 8 8 8 8 8 8
As you can see, if we select out the lower triangular part of each matrix excluding the diagonal, you will get all combinations of pairs that are unique, which is what I did in the last parts of the code. Selecting the lower-part is important because by doing this, MATLAB selects out values column-wise, and traversing the columns of the lower-triangular part of each matrix gives you the exact orderings of each pair of columns in the right order (i.e. 1-2, 1-3, ..., 1-7, 2-3, 2-4, ..., etc.)
The point of all of this is that can then use X and Y to create two new matrices that contain the columns located at each pair of X and Y, then use dot to apply the dot product to each matrix column-wise. We also need to divide the dot product by the multiplication of the magnitudes of the two vectors respectively. You can't use MATLAB's built-in function norm for this because it will compute the matrix norm for matrices. As such, you have to sum over all of the rows for each column respectively for each of the two matrices then multiply both of the results element-wise then take the square root - this is the last step of the process:
matrix1 = A(:,X);
matrix2 = A(:,Y);
B = dot(matrix1, matrix2, 1) ./ sqrt(sum(matrix1.^2,1).*sum(matrix2.^2,1));
I get this for B:
>> B
B =
Columns 1 through 11
1 1 1 1 1 1 1 1 1 1 1
Columns 12 through 22
1 1 1 1 1 1 1 1 1 1 1
Columns 23 through 28
1 1 1 1 1 1
Well.. this isn't useful at all. Why is that? What you are actually doing is finding the cosine angle between two vectors, and since each vector is a scalar multiple of another, the angle that separates each vector is in fact 0, and the cosine of 0 is 1.
You should try this with different values of A so you can see for yourself that it works.
To make this code compatible for copying and pasting, here it is:
%// Define A here:
A = repmat(1:8, 4, 1);
%// Code to produce dot products here
num_columns = size(A,2);
[X,Y] = meshgrid(1:num_columns);
X = X(tril(ones(num_columns),-1)==1); Y = Y(tril(ones(num_columns),-1)==1);
matrix1 = A(:,X);
matrix2 = A(:,Y);
B = dot(matrix1, matrix2, 1) ./ sqrt(sum(matrix1.^2,1).*sum(matrix2.^2,1));
Minor Note
If you have a lot of columns in A, this may be very memory intensive. You can get your original code to work with loops, but you need to change what you're doing at each column.
You can do something like this:
num_columns = nchoosek(size(A,2),2);
B = zeros(1, num_columns);
counter = 1;
for ii = 1 : size(A,2)
for jj = ii+1 : size(A,2)
B(counter) = dot(A(:,ii), A(:,jj), 1) / (norm(A(:,ii))*norm(A(:,jj)));
counter = counter + 1;
end
end
Note that we can use norm because we're specifying vectors for each of the inputs into the function. We first preallocate a matrix B that will contain the dot products of all possible combinations. Then, we go through each pair of combinations - take note that the inner for loop starts from the outer most for loop index added with 1 so you don't look at any duplicates. We take the dot product of the corresponding columns referenced by positions ii and jj and store the results in B. I need an external counter so we can properly access the right slot to place our result in for each pair of columns.
I was given the following Question:
Write a function call zigzag that takes in a 2-dimensional array A and return a 1- dimensional array created by traverse through A in zigzag way starting at position (1,1).
Example:
A =[1 2 3 4 5 6
7 8 9 1 3 4
3 4 5 6 3 1
3 4 5 6 7 8]
zigzag(A) should return:
[1 2 3 4 5 6 4 3 1 9 8 7 3 4 5 6 3 1 8 7 6 5 4 3]
The way I solved it, I am not sure if this is a correct method to do it. I would be glad to know if this is perfect and how I could improve my answer:
function B=zigzag(A)
[r,c]=size(A);
B= reshape(A’,1,:);
m=0
n=0
For r>m+2
m=m+2;
n=n+1;
For i=1:c
B(nc+i)=B(2cn-i+1);
End
End
disp(B)
If it gives you the right output, then you're certainly doing something right. However, what I would have done was access the even rows of your matrix, reverse the directions so that they're displayed in reverse order, transpose your matrix then unravel it.
The reason why we transpose it is because when we unravel a matrix in MATLAB, this means that the columns of the matrix are stacked on top of each other so that one single vector is produced. We want the rows to be stacked on top of each other and making the even rows in reverse order will allow you to do the zigzag that you expect. If you want the rows to be stacked on top of each other, you need to transpose the matrix first so that rows become columns, and when you unravel this matrix, you'll stack the rows on top of each other instead to create a single vector.
Something like this:
B = A; %// Make a copy
B(2:2:end,:) = fliplr(B(2:2:end,:)); %// Flip even rows
B = reshape(B.', 1, []); %// Unravel
With your example, I get:
B =
Columns 1 through 13
1 2 3 4 5 6 4 3 1 9 8 7 3
Columns 14 through 24
4 5 6 3 1 8 7 6 5 4 3
The Mean Square Error(MSE), is a method used to define the difference in between two blocks, and can be calculated as follow: a and b two blocks equal size
MSE = sqrt(sum(sum((a-b).^2)))/size(a or b)
If the MSE is less than a given threshold, than the two blocks are not different.
Given a matrix A, already reshaped to be contain blocks all in the same raw,
the purpose is to extract all blocks where the MSE is less than a given threshold (based on the first block), then return the mean of those blocks. again, extract the second group of blocks which the MSE is less than the given threshold where the blocks that already assigned to be a part of other group of blocks must not be extracted again. Better than that, it must be deleted to reduce the search time. and so on till all blocks of the matrix A are assigned to be part of a group. And here is an example :
Given matrix A where the size of A is 2 by 14:
A= [1 1 2 2 9 9 4 4 6 6 5 5 3 3
1 1 2 2 9 9 4 4 6 6 5 5 3 3];
PS: its not necessary the blocks contain the same numbers, it is just to make the example clear.
blocks size is : 2 by 2
the threshold is 2
now we extract all blocks where the MSE is less than the threshold starting from the first block in the matrix A. so the blocks are:
1 1 2 2 3 3
1 1 2 2 3 3
the mean of those blocks is
Result= [ 2 2
2 2];
again. we extract all blocks where the MSE is less than the threshold, but we need to avoid the blocks that already extracted, so the second group of blocks is :
9 9
9 9
the mean of this block is it self, so:
Result= [2 2 9 9
2 2 9 9];
again. we extract all blocks where the MSE is less than the threshold, but we need to avoid the blocks that already extracted, so the third group of blocks is :
4 4 6 6 5 5
4 4 6 6 5 5
the block
3 3
3 3
is not a part of this group even if the MSE is less then the threshold because is already extracted to be part of the first group.
the mean of those blocks is:
5 5
5 5
therefore the result should be:
Result= [2 2 9 9 5 5
2 2 9 9 5 5];
there are any fast way to apply that ?
Here's my solution:
A = [1 1 2 2 9 9 4 4 6 6 5 5 3 3
1 1 2 2 9 9 4 4 6 6 5 5 3 3];
blockLen = 2;
MSEthresh = 1;
nBlocks = size(A,2) / blockLen;
meanBlocks = [];
bSelectRefBlock = true;
while(~isempty(A))
if(bSelectRefBlock)
%// Select new reference block
refBlock = A(:, 1:blockLen);
bSelectRefBlock = false;
A = A(:, blockLen+1:end);
iBlock = 1;
selectedBlocks = refBlock;
else
if(iBlock > size(A,2))
%// End of A reached. Compute mean of selected blocks
blockCols = reshape(selectedBlocks, [numel(refBlock) numel(selectedBlocks)/numel(refBlock)]);
meanBlockCols = mean(blockCols, 2);
meanBlocks(:, end+1:end+blockLen) = reshape(meanBlockCols, [size(refBlock, 1) blockLen]);
bSelectRefBlock = true;
else
%// Test next block with MSE and select if below threshold
MSE = sqrt(sum(sum((A(:, iBlock:(iBlock+blockLen-1)) - refBlock).^2))) / numel(refBlock);
if(MSE <= MSEthresh)
selectedBlocks(:, end+1:end+blockLen) = A(:, iBlock:(iBlock+blockLen-1));
A(:, iBlock:(iBlock+blockLen-1)) = [];
else
iBlock = iBlock + blockLen;
end
end
end
end
%// Compute mean of selected blocks for last group
blockCols = reshape(selectedBlocks, [numel(refBlock) numel(selectedBlocks)/numel(refBlock)]);
meanBlockCols = mean(blockCols, 2);
meanBlocks(:, end+1:end+blockLen) = reshape(meanBlockCols, [size(refBlock, 1) blockLen]);