I am trying to reshape a matrix, but not in the standard way. It is basically a "chunk" reshape. I have a column vector named matrix1 which is (T*N x 1) and a matrix named matrix2 which is TxN. I want the first N elements of the column vector matrix1 to be transposed into the first row of matrix2. Then the second chunk of N elements of vector matrix1 to be transposed into the second row of matrix2.
I know how to do it with a loop (see code below). Just wondering if there is a smarter way to do it.
T = 2;
N = 7;
matrix1 = rand(T*N,1);
matrix2 = NaN(T,N);
for t = 1:T
matrix2(t,:) = matrix1(t*N-N+1:t*N,1)';
end
Use reshape for reshaping... You literally describe a standard reshape in the text.
reshape(matrix1,N,T).'
Related
I have an njxnj matrix made up of nxn matrices. I want to extract the diagonal j blocks of nxn matrices. i.e. I want to extract the diagonal (for n = 2, j = 4):
What would be the most efficient way of doing this?
To index the elements you can use blkdiag to create a corresponding mask.
%your parameters
n=2
j=4
%some example matrix
M=magic(n*j);
%create the input for blkdiag, j matrices of size n
h=repmat({true(n)},j,1)
%use blkdiag to select the elements
M(logical(blkdiag(h{:})))
For large j, this answer of #Daniel becomes slow. I would instead recommend using linear indices of block diagonal.
n=2;
j=4;
%some example matrix
M=magic(n*j);
linIndices = (0:n*((n*j)+1):n*((n*j)+1)*(j-1))+reshape((1:n)'+n*j*(0:n-1),[],1);
newM = reshape(M(linIndices),n,n,[]);
I need to generate all square matrices of order n with given properties.
Matrices are symmetric.
Entries are 0 and 1.
Diagonal elements are zeros.
I am using Matlab2012b. Can you help me with the code?
I was trying to write it down. It needs a long sequences of for loops. Any simpler technique?
Try this:
N = 4; %// matrix size
M = (N^2-N)/2; %// number of values to fill in each matrix
P = 2^M; %// number of matrices
x = dec2bin(0:P-1)-'0'; %// each row contains the values of a matrix, "packed" in a vector
result = NaN(N,N,P); %// preallocate
for k = 1:P
result(:,:,k) = squareform(x(k,:)); %// unpack values
end
The matrices are result(:,:,1), result(:,:,2) etc.
I have a 512x512 image , which i made 4x4 block for entire image, then i want access the (3rd row , 3rd element) of the all indivial 4x4 matrices and add it to the index values, which i obtained. Please help me on below code.
[row col] = size(a);
m = zeros(row,col);
count = [(row-4)*(col-4)]/4;
outMat = zeros(4,4,count);
l = 0;
for i=2:4:row-4
for j=2:4:col-4
l = l + 1;
outMat(:,:,l) = double(a(i-1:i+2,j-1:j+2));% for each matrix i have to find(3rd row,3rd element of each matrix.
end;
end;
Adding the (3rd row,3rd element):
m(i,j) = sum(sum(a .* w)); %index value of each 4x4 matrix % w = 4x4 matrix.
LUT = m(i,j)+ outMat(3,3);%(3rd row,3rd element each matrix should be added to all m(i,j) values. In which i fail to add all(3rd row,3rd element) of all 4x4 matrices.
I am going to reword your question so that it's easier to understand, as well as allowing it to be easy for me to write an answer.
From your comments in Kostya's post, you have two images img1 and img2 where they are decomposed into 4 x 4 blocks. outMat would be a 3D matrix where each slice contains a 4 x 4 block extracted from img1. From this, you have a matrix m that stores a weighted sum of 4 x 4 blocks stored outMat.
Next, you'll have another matrix, let's call this outMat2, which also is a 3D matrix where each slice is a 4 x 4 block extracted from img2. From this 3D matrix, you wish to extract the third row and third column of each block, add this to the corresponding position of m and store the output into a variable called LUT.
All you have to do is extract a single vector that slices through all of the slices located at the third row and third column. You would then have to reshape this into a matrix that is the same size as m then add this on top of m and store it into a variable called LUT. Bear in mind that if we reshape this into a matrix, the reshaping will be done in column major format, and so you would stack the values by columns. Because your blocks were created row-wise, what we need to do reshape this matrix so that it has size(m,2) rows and size(m,1) columns then transpose it.
Therefore:
vec = outMat2(3,3,:);
vec = vec(:); %// Make sure it's a 1D vector
m2 = reshape(vec, size(m,2), size(m,1)).';
LUT = m + m2;
LUT will contain a 2D matrix where each element contains the weighted sum of the 4 x 4 blocks from img1 with the corresponding third row, third column of each block in img2.
Next time, please update your question so that you have all of the information. We shouldn't have to dig through your comments to figure out what you want.
I think you can do just
LUT = sum( sum( a(3:4:row,3:4,col) * w(3,3) ) );
I have a 128 x 100 matrix in matlab, where each column should be treated as a separate element. Lets call this matrix M.
I have another 128 x 2000 matrix(called V) composed of columns from matrix M.
How would I make a histogram that maps the frequency of each column being used in the second matrix?
hist(double(V),double(M)) gives the error:
Error using histc
Edge vector must be monotonically
non-decreasing.
what should I be doing?
Here is an example. We start with data that resembles what you described
%# a matrix of 100 columns
M = rand(128,100);
sz = size(M);
%# a matrix composed of randomly selected columns of M (with replacement)
V = M(:,randi([1 sz(2)],[1 2000]));
Then:
%# map the columns to indices starting at 1
[~,~,idx] = unique([M,V]', 'rows', 'stable');
idx = idx(sz(2)+1:end);
%# count how many times each column occurs
count = histc(idx, 1:sz(2));
%# plot histogram
bar(1:sz(2), count, 'histc')
xlabel('column index'), ylabel('frequency')
set(gca, 'XLim',[1 sz(2)])
[Lia,Locb] = ismember(A,B,'rows') also returns a vector, Locb,
containing the highest index in B for each row in A that is also a row
in B. The output vector, Locb, contains 0 wherever A is not a row of
B.
ismember with the rows argument can identify which row of one matrix the rows of another matrix come from. Since it works on rows, and you are looking for columns, just transpose both matrices.
[~,Locb]=ismember(V',M');
histc(Locb)
Is there a way to combine 2 vectors in MATLAB such that:
mat = zeros(length(C),length(S));
for j=1:length(C)
mat(j,:)=C(j)*S;
end
Using normal MATLAB syntax similar to:
mat = C * S(1:length(S))
This gives a "Inner matrix dimensions must agree error" because it's trying to do normal matrix operations. This is not a standard Linear Algebra operation so I'm not sure how to correctly express it in MATLAB, but it seems like it should be possible without requiring a loop, which is excessively slow in MATLAB.
From your description, it sounds like a simple matrix operation. You just have to make sure you have the right dimensions for C and S. C should be a column vector (length(C)-by-1) and S should be a row vector (1-by-length(S)). Assuming they are the right dimensions, just do the following:
mat = C*S;
If you're not sure of their dimensions, this should work:
mat = (C(:))*(S(:)');
EDIT: Actually, I went a little crazy with the parentheses. Some of them are unnecessary, since there are no order-of-operation concerns. Here's a cleaner version:
mat = C(:)*S(:)';
EXPLANATION:
The matrix multiplication operator in MATLAB will produce either an inner product (resulting in a scalar value) or an outer product (resulting in a matrix) depending on the dimensions of the vectors it is applied to.
The last equation above produces an outer product because of the use of the colon operator to reshape the dimensions of the vector arguments. The syntax C(:) reshapes the contents of C into a single column vector. The syntax S(:)' reshapes the contents of S into a column vector, then transposes it into a row vector. When multiplied, this results in a matrix of size (length(C)-by-length(S)).
Note: This use of the colon operator is applicable to vectors and matrices of any dimension, allowing you to reshape their contents into a single column vector (which makes some operations easier, as shown by this other SO question).
Try executing this in MATLAB:
mat = C*S'
As In:
C = [1; 2; 3];
S = [2; 2; 9; 1];
mat = zeros(length(C),length(S));
for j=1:length(C)
mat(j,:)=C(j)*S;
end
% Equivalent code:
mat2 = C*S';
myDiff = mat - mat2
Do you mean the following?
mat = zeros(length(C),length(S));
for j=1:length(C)
mat(j,:)=C(j)*S;
end
If so, it's simply matrix multiplication:
C' * S % if C and S are row vectors
C * S' % if C and S are column vectors
If you don't know whether C and S are row vectors or column vectors, you can use a trick to turn them into column vectors, then transpose S before multiplying them:
C(:) * S(:)'
I'm not entirely clear on what you're doing - it looks like your resulting matrix will consist of length(C) rows, where the ith row is the vector S scaled by the ith entry of C (since subscripting a vector gives a scalar). In this case, you can do something like
mat = repmat(C,[1 length(S)]) .* repmat(S, [length(C) 1])
where you tile C across columns, and S down rows.
Try this:
C = 1:3
S = 1:5
mat1 = C'*S
mat2 = bsxfun(#times, C',S)
(esp. good when the function you need isn't simpler MATLAB notation)
--Loren
Try using meshgrid:
[Cm, Sm] = meshgrid(C, S);
mat = Cm .* Sm;
edit: nevermind, matrix multiplication will do too. You just need one column vector C and one row vector S. Then do C * S.