The result of solving a polynom equation is a 1x2 vector or a 1x1 in some instances. I am trying to store all solutions for equations with different coefficients. so some solutions are just 1x1 vectors. how can i store these efficiently?
n = 1;
%sol = zeros(size(coef)); %create solution matrix in memory
sol = {};
while n < size(coef,2)
sol(n) = roots(coef(:,n));
end
"Conversion to cell from double is not possible."
error.
coef is coefficient matrix
You're almost there!
In order to store the vectors as cells in the cell array, use curly braces {} during their assignment:
sol(n) = {roots(coef(:,n))};
or alternatively:
sol{n} = roots(coef(:,n));
That way, the vectors/arrays can be of any size. Check this link for more info about accessing data in cell arrays.
Also, don't forget to increment n otherwise you will get an infinite loop.
Whole code:
n = 1;
%sol = zeros(size(coef)); %create solution matrix in memory
sol = {};
while n <= size(coef,2)
sol(n) = {roots(coef(:,n))};
n = n+1
end
Related
My code needs to in a loop modify the elements of a sparse matrix. Doing this matlab warns me that This sparse indexing expression is likely to be slow. I am preallocating the sparse arrays using the Spalloc function but am still getting this warning. What is the optimal approach for assembling of sparse matrices? This is what I am currently doing.
K=spalloc(n,n,100); f=spalloc(n,1,100);
for i = 1:Nel
[Ke,fe] = myFunction(Ex(i),Ey(i));
inds = data(i,2:end);
K(inds,inds) = K(inds,inds) + Ke;
f(inds) = f(inds)+fe;
end
the indices in inds may be appear several times in the loop, meaning an element in K or f may receive multiple contributions. The last two lines within the loop are where I'm getting warnings.
A common approach is to use the triplet form of the sparse constructor:
S = sparse(i,j,v,m,n)
i and j are row and column index vectors and v is the corresponding data vector. Values corresponding to repeated indices are summed like your code does. So you could instead build up row and column index vectors along with a data vector and then just call sparse with those.
For example something like:
nout = Nel*(size(data,2)-1);
% Data vector for K
Kdata = zeros(1,nout);
% Data vector for f
fdata = zeros(1,nout);
% Index vector for K and f
sparseIdxvec = ones(1,nout);
outIdx = 1;
for i = 1:Nel
[Ke,fe] = myFunction(Ex(i),Ey(i));
inds = data(i,2:end);
nidx = numel(inds);
outIdxvec = outIdx:outIdx+nidx-1;
sparseIdxvec(outIdxvec) = inds;
Kdata(outIdxvec) = Ke;
fdata(outIdxvec) = fe;
outIdx = outIdx + nidx;
end
K = sparse(sparseIdxvec,sparseIdxvec,Kdata,n,n);
f = sparse(sparseIdxvec,1,fdata,n,1);
Depending on your application, that may or may not actually be faster.
I've written a function that generates a sparse matrix of size nxd
and puts in each column 2 non-zero values.
function [M] = generateSparse(n,d)
M = sparse(d,n);
sz = size(M);
nnzs = 2;
val = ceil(rand(nnzs,n));
inds = zeros(nnzs,d);
for i=1:n
ind = randperm(d,nnzs);
inds(:,i) = ind;
end
points = (1:n);
nnzInds = zeros(nnzs,d);
for i=1:nnzs
nnzInd = sub2ind(sz, inds(i,:), points);
nnzInds(i,:) = nnzInd;
end
M(nnzInds) = val;
end
However, I'd like to be able to give the function another parameter num-nnz which will make it choose randomly num-nnz cells and put there 1.
I can't use sprand as it requires density and I need the number of non-zero entries to be in-dependable from the matrix size. And giving a density is basically dependable of the matrix size.
I am a bit confused on how to pick the indices and fill them... I did with a loop which is extremely costly and would appreciate help.
EDIT:
Everything has to be sparse. A big enough matrix will crash in memory if I don't do it in a sparse way.
You seem close!
You could pick num_nnz random (unique) integers between 1 and the number of elements in the matrix, then assign the value 1 to the indices in those elements.
To pick the random unique integers, use randperm. To get the number of elements in the matrix use numel.
M = sparse(d, n); % create dxn sparse matrix
num_nnz = 10; % number of non-zero elements
idx = randperm(numel(M), num_nnz); % get unique random indices
M(idx) = 1; % Assign 1 to those indices
I have a matrix:
1|2|3|4
4|5|6|7
7|8|9|10
10|11|12|13
I want to multiply the indices of this matrix with indices of another matrix of different size:
7|8|9
9|10|10
10|11|11
for these two matrices I have used the following for loops:
for x=1:4
for y=1:4
for m=1:3
for n=1:3
c=(m*x+n*y);
end
end
end
end
Is there any way to rewrite the above code without using loops? If the indices of each element can be generated in the above matrices, I think it can be done. Please help
mx = m'*x;
mx = mx(:);
ny = n'*y;
ny = ny(:);
mxe = repmat(mx, [length(ny), 1]);
nye = repmat(ny, [length(mx), 1]);
c = mxe+nye;
This will result in c containing all the values that get put in during that loop you have there (note that in your loop, value gets assigned and overwritten).
I have a 1-by-4 cell array, D. Each of the cell elements contains 2-by-2 double matrices. I want to do random permutation over each matrix independently which in result I will have the same size cell array as D but its matrices' elements will be permuted and then the inverse in order to obtain the original D again.
for a single matrix case I have the code and it works well as follows:
A=rand(3,3)
p=randperm(numel(A));
A(:)=A(p)
[p1,ind]=sort(p);
A(:)=A(ind)
but it doesn't work for a cell array.
The simplest solution for you is to use a loop:
nd = numel(D);
D_permuted{1,nd} = [];
D_ind{1,nd} = [];
for d = 1:nd)
A=D{d};
p=randperm(numel(A));
A(:)=A(p)
[~,ind]=sort(p);
D_permuted{d} = A;
D_ind{d} = ind;
end
Assuming your D matrix is just a list of identically sized (e.g. 2-by-2) matrices, then you could avoid the loop by using a 3D double matrix instead of the cell-array.
For example if you hade a D like this:
n = 5;
D = repmat([1,3;2,4],1,1,n)*10 %// Example data
Then you can do the permutation like this
m = 2*2; %// Here m is the product of the dimensions of each matrix you want to shuffle
[~,I] = sort(rand(m,n)); %// This is just a trick to get the equivalent of a vectorized form of randperm as unfortunately randperm only accepts scalars
idx = reshape(I,2,2,n);
D_shuffled = D(idx);
I've got 2 different files, one of them is an input matrix (X) which has 3823*63 elements (3823 input and 63 features), the other one is a class vector (R) which has 3823*1 elements; those elements have values from 0 to 9 (there are 10 classes).
I have to compute covariance matrices for every classes. So far, i could only compute mean vectors for every classes with so many nested loops. However, it leads me to brain dead.
Is there any other easy way?
There is the code for my purpose (thanks to Sam Roberts):
xTra = importdata('optdigits.tra');
xTra = xTra(:,2:64); % first column's inputs are all zero
rTra = importdata('optdigits.tra');
rTra = rTra(:,65); % classes of the data
c = numel(unique(rTra));
for i = 1:c
rTrai = (rTra==i-1); % Get indices of the elements from the ith class
meanvect{i} = mean(xTra(rTrai,:)); % Calculate their mean
covmat{i} = cov(xTra(rTrai,:)); % Calculate their covariance
end
Does this do what you need?
X = rand(3263,63);
R = randi(10,3263,1)-1;
numClasses = numel(unique(R));
for i = 1:numClasses
Ri = (R==i); % Get indices of the elements from the ith class
meanvect{i} = mean(X(Ri,:)); % Calculate their mean
covmat{i} = cov(X(Ri,:)); % Calculate their covariance
end
This code loops through each of the classes, selects the rows of R that correspond to observations from that class, and then gets the same rows from X and calculates their mean and covariance. It stores them in a cell array, so you can access the results like this:
% Display the mean vector of class 1
meanvect{1}
% Display the covariance matrix of class 2
covmat{2}
Hope that helps!
Don't use mean and sum as a variable names because they are names of useful Matlab built-in functions. (Type doc mean or doc sum for usage help)
Also cov will calculate the covariance matrix for you.
You can use logical indexing to pull out the examples.
covarianceMatrices = cell(m,1);
for k=0:m-1
covarianceMatrices{k} = cov(xTra(rTra==k,:));
end
One-liner
covarianceMatrices = arrayfun(#(k) cov(xTra(rTra==k,:)), 0:m-1, 'UniformOutput', false);
First construct the data matrix for each class.
Second compute the covariance for each data matrix.
The code below does this.
% assume allData contains all the data you've read in, each row is one data point
% assume classVector contains the class of each data point
numClasses = 10;
data = cell(10,1); %use cells to store each of the data matrices
covariance = cell(10,1); %store each of the class covariance matrices
[numData dummy] = size(allData);
%get the data out of allData and into each class' data matrix
%there is probably a nice matrix way to do this, but this is hopefully clearer
for i = 1:numData
currentClass = classVector(i) + 1; %Matlab indexes from 1
currentData = allData(i,:);
data{currentClass} = [data{currentClass}; currentData];
end
%calculate the covariance matrix for each class
for i = 1:numClasses
covariance{i} = cov(data{i});
end