I am trying to inverse a matrix in matlab however i am struggling.
It is essentially a 3x3 matrix however each position of the matrix has 801 points.
I assume i need to use a for loop somehow to get out a inversed 3x3 matrix each containing 801 points.
inv(A11(1) A12(1) A13(1);A21(1) A22(1) A23(1);A31(1) A32(1) A33(1))
For example this inverse would give me the first of 801 points of the matrix
Try this:
m = cell(801,1);
for i=1:801
m{i} = inv([A11(i),A12(i),A13(i); A21(i),A22(i),A23(i); A31(i),A32(i),A33(i)]);
end
Now m is a cell array, and you access the i-th result with m{i}.
I think you are not looking for the inverse of a matrix as it is some mathematically thing, but you are trying to flip its order. If you want to flip the 3x3 matrix try
A=fliplr(A) %for left-right flip
A=flipud(A) %for up down flip
if you want the matrix A to stay the same try and inverse each containing vektor try
cellfun(#(x) flipud(x),A,'Uniformoutput',false) %for up down flip in every cell
Related
I am trying to implement Principal Component Analysis (PCA) to extract the features from the image in MATLAB. I have implemented the following code.
[Rows, Columns] = size(x); % find size of input matrix
m=mean(x); % find mean of input matrix
y=x-ones(size(x,1),1)*m; % normalise by subtracting mean
c=cov(y); % find covariance matrix
[V,D]=eig(c); % find eigenvectors (V) and eigenvalues (D) of covariance matrix
[D,idx] = sort(diag(D)); % sort eigenvalues in descending order by first diagonalising eigenvalue matrix, idx stores order to use when ordering eigenvectors
D = D(end:-1:1)';
V = V(:,idx(end:-1:1)); % put eigenvectors in order to correspond with eigenvalues
V2d=V(:,1:200); % (significant Principal Components we use, OutputSize is input variable)
prefinal=V2d'*y';
final=prefinal'; % final is normalised data projected onto eigenspace
imshow(final);
I want to know that how can I check the 1st Eigen faces,2nd Eigen faces.. etc
EDIT:
Here is the Input Image and the Eigen Image is Eigen Image
The first eigenface is the first eigenvector!
My guess, is that with your code:
eigenface1=reshape(V(:,1),rows,cols);
as, if your code is right, each eigenvector should be the same size as your input images, but unrolled. I am assuming that rows and cols are the size of the image.
I'm trying to do a bunch of rolling sums over matrices in MATLAB. In order to avoid loops I've used repmat to layer my 2D matrices into a 3D structure. However, now the fast convolution function conv2 can no longer be used for the accumulator. However, the N-dimensional convolution function (convn) is not what I'm looking for either as it literally convolves all 3 dimensions. I want something that will do a 2D convolution on each slice and return a 3D matrix.
Tiling the matrices in 2D instead of layering them in 3D won't work because it will corrupt the convolution edge cases. I could pad with zeros in between but then it starts getting kind of messy.
In other words, without a for-loop, how can I perform the following:
A = ones(5,5,5);
B = zeros(size(A));
for i = 1 : size(A, 3)
B(:,:,i) = conv2(A(:,:,i), ones(2), 'same');
end
Thanks in advance for the help!
convn will work with an n-dimensional matrix and a 2-dimensional filter. Simply:
A = ones(5,5,5);
B = convn(A, ones(2), 'same');
You can use some padding with zeros and reshaping like so -
%// Store size parameters
[m,n,r] = size(A)
[m1,n1] = size(kernel)
%// Create a zeros padded version of the input array. We need to pad zeros at the end
%// rows and columns to replicate the convolutionoperation around those boundaries
Ap = zeros(m+m1-1,n+n1-1,r);
Ap(1:m,1:n,:) = A;
%// Reshape the padded version into a 3D array and apply conv2 on it and
%// reshape back to the original 3D array size
B_vect = reshape(conv2(reshape(Ap,size(Ap,1),[]),kernel,'same'),size(Ap))
%// Get rid of the padded rows and columns for the final output
B_vect = B_vect(1:m,1:n,:);
The basic idea is to reshape the input 3D array into a 2D array and then apply the 2D convolution on it. Extra step is needed with padding so as to have the same behavior as you would see with conv2 around the boundaries.
I have two vectors A & B of size 250x4. The first column in each vector has the X values and the second column has the Y values. I want to calculate the euclidean distance between each the X & Y of each row in the two vectors and save the result in a new vector C of size 250x1 which holds the result of the euclidean distance. For example, if the first row in A is A1x, A1y, A1n, A1m and the first row in B is B1x, B1y, B1n, B1m so I want to get the eucledian distance which will be [(A1x-B1x)^2 + (A1y-B1y)^2]^0.5 and the result will be saved in C1 and same will be done for the rest of the 250 rows. So if anyone could please advise how to do this in Matlab.
Like this:
%// First extract on x-y data from A and B
Axy = A(:,1:2);
Bxy = B(:,1:2);
%// Find all euclidean distances (row-wise)
C1 = sqrt(sum((Axy-Bxy).^2,2));
plus it handles higher dimension too
use pdist2:
C1=diag(pdist2(A(:,1:2),B(:,1:2)));
Actually, pdist2 will give you a 250x250 matrix, because it calculate all the distances. You need only the main diagonal, so calling diag on the result (as in the code above) will produce the wanted result.
I have a 512x512x3 matrix that stores 512x512 there-dimensional vectors. What is the best way to normalize all those vectors, so that my result are 512x512 vectors with length that equals 1?
At the moment I use for loops, but I don't think that is the best way in MATLAB.
If the vectors are Euclidean, the length of each is the square root of the sum of the squares of its coordinates. To normalize each vector individually so that it has unit length, you need to divide its coordinates by its norm. For that purpose you can use bsxfun:
norm_A = sqrt(sum(A .^ 2, 3)_; %// Calculate Euclidean length
norm_A(norm_A < eps) == 1; %// Avoid division by zero
B = bsxfun(#rdivide, A, norm_A); %// Normalize
where A is your original 3-D vector matrix.
EDIT: Following Shai's comment, added a fix to avoid possible division by zero for null vectors.
I have a 4-D matrix A of size NxNxPxQ. How can I easily change the diagonal values to 1 for each NxN 2-D submatrix in a vectorized way?
Incorporating gnovice's suggestion, an easy way to index the elements is:
[N,~,P,Q]=size(A);%# get dimensions of your matrix
diagIndex=repmat(logical(eye(N)),[1 1 P Q]);%# get logical indices of the diagonals
A(diagIndex)=1;%# now index your matrix and set the diagonals to 1.
You can actually do this very simply by directly computing the linear indices for every diagonal element, then setting them to 1:
[N,N,P,Q] = size(A);
diagIndex = cumsum([1:(N+1):N^2; N^2.*ones(P*Q-1,N)]);
A(diagIndex) = 1;
The above example finds the N diagonal indices for the first N-by-N matrix (1:(N+1):N^2). Each subsequent N-by-N matrix (P*Q-1 of them) is offset by N^2 elements from the last, so a matrix of size PQ-1-by-N containing only the value N^2 is appended to the linear indices for the diagonal of the first matrix. When a cumulative sum is performed over each column using the function CUMSUM, the resulting matrix contains the linear indices for all diagonal elements of the 4-D matrix.
You can use direct indexing, and some faffing about with repmat, to add the indexes for a single 50x50 diagonal to the offsets within the larger matrix of each 50x50 block:
Here's an example for a smaller problem:
A = NaN(10,10,5,3);
inner = repmat(sub2ind([10 10], [1:10],[1:10]), 5*3, 10); % diagonals
outer = repmat([10*10 * [0:5*3-1]]', 1, 10*10); % offsets to blocks
diags = inner + outer;
A(diags(:)) = 1;