I have a 2x2 matrix that I want to multiply by itself 10 times while storing the result after each multiplication. This can easily be done with a for loop but I would like to vectorize it an eliminate the for loop. My approach was to have my 2x2 matrix a and raise it to a vector b with elements 1:10. The answer should be a 2x2x10 matrix that replicates typing
a^b(1)
a^b(2)
.
.
.
a^b(10)
To clarify I'm not doing this element wise I need actual matrix multiplication, and prefer not to use a for loop. Thanks for any help you can give me.
here is the code for you. I use the cellfun to do this and I have comments after each line of the code. It can compute and store from fisrt - nth order of the self-multiplication of an arbitrary matrix m. If you have any question, feel free to ask.
function m_powerCell = power_store(m, n) %m is your input matrix, n is the highest power you want to reach
n_mat = [1:n]; %set a vector for indexing each power result in cell
n_cell = mat2cell(n_mat,1,ones(1,n)); %set a cell for each of the power
m_powerCell = cellfun(#(x)power(m, x), n_cell, 'uni', 0); %compute the power of the matrix
end
%this code will return a cell to you, each element is a matrix, you can
%read each of the matrix by m_powerCell{x}, x represents the xth order
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 have a vector created from linspace between specific numbers and have dimensions of 1*150. Now i want to multiply each element of the above created vector with another vector whose dimension is 1*25. The detail of my code is given below
c_p = linspace(1,.3*pi,150);
c = c_p';
C = zeros([150,25]);
for i= 1:1:size(C,1)
wp= c(i);
for n= 1:25
c_wp(n) = cos(n*wp);
end
C(i,25)= c_wp;
end
The vector is actually a multiple of cosine of length 25 and here wp is the elements of first vector of dimension 1*150. SO by the logic, I must have an output of 150*25 but instead giving me "subscripted assignment dimension mismatch". Any help would be appreciated, as i am new to matlab.
To multiply each element of a row vector a with each element of another row vector b, we can use linear algebra. We transpose a to make it a column vector and then use matrix multiplication:
a.' * b
That way you don't even need a for loop.
I have a 3D array M(d*d,m,n). For each d*d vector of M (i.e. vectors of the first dimension), I split it into d parts and take the sum of each part to form a new vector (of size d).
For example, if u is a vector along the first dimension of M, then it will be replaced by the vector v, computed by:
v = sum(reshape(u,d,d))';
For the moment I use a loop as following, but I think there should be a much faster way to do it.
N = zeros(d,m,n)
for i=1:m
for j=1:n
N(:,i,j) = sum(reshape(M(:,i,j),d,d))'; %//'
end
end
Thank you so much for any suggestions!
Try this -
N = reshape(sum(reshape(M,d,[])),d,m,n)
I may not be understanding the question correctly but is this what you are looking for?
N=squeeze(sum(reshape(M,[d,d,size(M,2),size(M,3)])))
Say I have 3 matrix data files in a folder..
I have a function (clustering_coef_bu) which calculates the clustering coefficient of a 2D matrix (data; has the dimensions 512x512) file. The output vector of the function creates a 512x1 Matrix (Clustering Coefficient), in double format.
With the for loop below, for each matrix (data) I'm calculating the clustering coefficient. However, I am having difficulties being able to store the output clustering coefficient for each run of the for loop. It would be ideal to output the clustering coefficient of each matrix into one singular structure. I.e a cell array, which has the dimensions 512x3.
for k = 1:3
ClusteringCoefficient=clustering_coef_bu(data)
end
Any help would be great. Thanks.
Something like this would probably help you:
widthArray = 3;
ClustingeringCoefficient = zeros(size(data, 1), widthArray);
for k = 1:widthArray
ClusteringCoefficient(:, k) = clustering_coef_bu(data); % a 512x3 double matrix
end
I have a M x N matrix. I want to multiply each of the N columns by a M x M matrix. The following does this in a loop, but I have no idea how to vectorize it.
u=repmat(sin(2*pi*f*t),[n 1]);
W = rand(n);
answer = size(u);
for i=1:size(u,2)
answer(:,i) = W*u(:,i);
end
You simply need to multiply the two matrices:
answer = W*u;
Think about it: in every iteration of your loop you multiply a matrix by a vector. The result of that operation is a vector, which you save into your answer in column i. Matrix multiplication is a similar thing: you can understand it as multiplication of a matrix (W) by a set of vectors, which form your matrix u.
So your code is good, just remove the loop :)