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.
Related
I'm facing a problem. I have a zeros matrix 600x600. I need to fill this matrix with 1080 1s randomly. Any suggestions?
Or, use the intrinsic routine randperm thusly:
A = zeros(600);
A(randperm(600^2,1080)) = 1;
A = sparse(600,600); %// set up your matrix
N=1080; %// number of desired ones
randindex = randi(600^2,N,1); %// get random locations for the ones
while numel(unique(randindex)) ~= numel(randindex)
randindex = randi(600^2,N,1); %// get new random locations for the ones
end
A(randindex) = 1; %// set the random locations to 1
This utilises randi to generate 1080 numbers randomly between 1 and 600^2, i.e. all possible locations in your vectors. The while loop is there in case it happens that one of the locations occurs twice, thus ending up with less than 1080 1.
The reason you can use a single index in this case for a matrix is because of linear indexing.
The big performance difference with respect to the other answers is that this initialises a sparse matrix, since 1080/600^2 = 0.3% is very sparse and will thus be faster. (Thanks to #Dev-iL)
This is one way to do it,
N = 1080; % Number of ones
M = zeros(600); % Create your matrix
a = rand(600^2,1); % generate a vector of randoms with the same length as the matrix
[~,asort] = sort(a); % Sorting will do uniform scrambling since uniform distribution is used
M(asort(1:N)) = 1; % Replace first N numbers with ones.
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,[]);
So my question refers to the regress() function in matlab. Click here for the Matlab documentation
If I want to run multiple regressions using this function and output both the coefficients and the confidence intervals, what's the best way to do this in a For loop?
Matlab's own syntax for this is [b,bint] = regress(y,X). But when I try to implement this in a for loop it tells me that the dimension mismatch. My code is the following:
for i=1:6
[a, b]=regress(Dataset(:,i),capm_factors);
capm_coefs(i,:)=a;
capm_ci(i,:)=b;
end
Please help, thanks!
regress outputs a column vector of coefficients that minimize the least squared error between your input data (capm_factors) and your predicted values (Dataset(:,i)). However, in your for loop, you are assuming that a and b are row vectors.
Also, the first output of regress is the solution to your system, but the second output contains a matrix of confidence values where the first column denotes the lower end of the confidence interval for each variable and the second column denotes the upper end of the confidence interval.
Specifically, your input capm_factors should be a M x N matrix where M is the total number of input samples and N is the total number of features. In your code, a would thus give you a N x 1 vector and b would give you a N x 2 matrix.
If you'd like use a loop, make sure capm_coefs is a N x l matrix where l is the total number of times you want to loop and capm_ci should either be a N x 2 x l 3D matrix or perhaps a l element cell array. Either way is acceptable.... but I'll show you how to do both.
Something like this comes to mind:
Confidences as a 3D matrix
l = 6; %// Define # of trials
[M,N] = size(capm_factors); %// Get dimensions of data
capm_coefs = zeros(N, l);
capm_ci = zeros(N, 2, l);
for ii = 1 : l
[a,b] = regress(Dataset(:,i), capm_factors);
capm_coefs(:,ii) = a;
capm_ci(:,:,ii) = b;
end
You'd then access the coefficients for a trial via capm_coefs(:,ii) where ii is the iteration you want. Similarly, the confidence matrix can be accessed via capm_ci(:,:,ii)
Confidences as a cell array
l = 6; %// Define # of trials
[M,N] = size(capm_factors); %// Get dimensions of data
capm_coefs = zeros(N, l);
capm_ci = cell(l); %// Cell array declaration
for ii = 1 : l
[a,b] = regress(Dataset(:,i), capm_factors);
capm_coefs(:,ii) = a;
capm_ci{ii} = b; %// Assign confidences to cell array
end
Like above, you'd access the coefficients for a trial via capm_coefs(:,ii) where ii is the iteration you want. However, the confidence matrix can be accessed via capm_ci{ii} as we are now dealing with cell arrays.
I want to concatenate 100 column vectors into one matrix. The code is the following:
for i = 1:100
X = mean(TMP(i).SonarReturnData.BeamsOutput(1:200, 25:35), 2);
end
What I want is to concatenate all 100 column vectors (each 200x1 length vectors) into one matrix (which should become a 200x100 matrix). I tried to use C = cat(2,X(:)), but it didn't work. Does anyone have an idea? Thank you.
Just pre-allocate X with your desired 200x100 size and then index into columns of X appropriately in your loop. I.e.,
X = zeros(200, 100);
for i = 1:100
X(:,i) = mean(TMP(i).SonarReturnData.BeamsOutput(1:200, 25:35), 2);
end
Is there an easy way to simulate a random permutation matrix (say of size 1000 by 1000) in Matlab? I would like to study the eigenvalue distribution of independent sum of such matrices.
Thanks in advance!
You can generate a random permutation matrix like so:
Create a unity matrix:
A = eye( N ); %// N is the size of your matrix
For large values of N it is better to use sparse matrices:
A = speye( N ); % create sparse identity matrix
Generate a random permutation:
idx = randperm(1:N);
Use vector indexing to rearrange the rows accordingly
A = A(idx, :);
Voila!
In Matlab (used R2012a) idx = randperm(1:N) gives a warning that input should be scalar. So: idx = randperm(N); .