I have many array (n*1 dimension), how can I do something like
matrix = [];
for i = 1:5
for j =1:5
matrix (i,j) = zeros(n,1); % store a given array to a cell of a matrix
end
end
I find Array of Matrices in MATLAB
But this is store matrices into array, not the otherwise.
Ying Xiong's suggestion is what you want if the vectors are of different lengths. But assuming the number of elements is constant (which they seem to be) you may also use a 3-dimensional array, where each (i,j) element contains a vector in the third dimension, like this:
rows = 5; cols = 5; n = 10; %// Dimensions
matrix = zeros(rows, cols, n); %// Initialize matrix
vector = 1:n; %// Just an example
for ii = 1:rows %// Bad practice to use i as a variable name
for jj = 1:cols %// Bad practice to use j as a variable name
matrix(ii,jj,:) = vector; %// Assignment
end
end
Now each index (i,j) contains the vectors you want, for instance:
squeeze(matrix(1,1,:))
ans =
1
2
3
4
5
6
7
8
9
10
Having all values in a single matrix can be a good thing if you want to do similar operations on all elements, as vectorized approaches are usually very fast in MATLAB. You might want to check out permute, reshape and functions like bsxfun.
Note that you might be able to vectorize the loops, but without knowing the specifics, that's impossible to know.
You need to use cell array.
n = 10;
matrix = cell(5,5);
for i = 1:5
for j = 1:5
matrix{i,j} = zeros(n,1);
end
end
Related
In Matlab I am trying to create a cell of size 16 x1 where each entry of this cell is a matrix. I have the following equation
$$W_g = exp^{\frac{j{2\pi m}{N}(n+\frac{g}{G}))} \,\,\,\,\,\,\, m,n=0,1,.....(N-1)$$
for this work assume $N=4$ and the index $g$ is the index that refers to the cell element i.e g=0:1:15
W=cell(16,1);
for g=1:16
for m=1:3
for n=1:3
W{g,m,n}= exp((2*pi*j*m/4)* n+(g-1)/16));
end
end
end
How can I make this work? I have two problems with this, you see g starts from 0 and MATLAB doesnt accept index of zero and how to actually define the matrices within the cell.
Thanks
So if I understand you have this equation:
And you just want the following code:
W=cell(16,1);
n = 1:3;
m = 1:3;
N = 4;
for g=1:16
W{g}= exp((2*pi*j.*m/4*N).*n+(g-1)/16);
end
%or the 1 line version:
W = cellfun(#(g) exp((2*pi*j.*m/4*N).*n+(g-1)/16),num2cell([1:16]),'UniformOutput',0);
With matlab you can use the Element-wise multiplication symbol .*
For example:
%A matrix multiplication
A = [2,3]
B = [1,3]';
result = A * B %result = 11
%An element wise multiplication
A = [2,3]
B = [1,3];
result = A .* B %result = [2,9]
First of all, i is the complex number in matlab (sqrt(-1)) not j, and you are correct, matlab is indexed in 1, so simply start counting g at 1, until 16.
Next, create a zero matrix, and calculate all indices accordingly. Something like this should work just fine :
clc
clear all
W=cell(16,1);
for g=1:16;
temp = zeros(3,3);
for m=1:3
for n=1:3
temp (m,n) = exp((2*pi*1i*m/4)* n+g/16);
end
end
W{g} = temp;
end
if you are considering doing much larger operations, consider using linspace to create your m and n indices and using matrix operations
Let's say I have a 3-dimensional matrix and have computed the max along the second dimension, and want to get the linear indices of the max values. However, the max-function only returns the subscripts along one dimension.
A = randn([5,5,5]); % Generate random matrix
[M, Ind] = max(A,[],2); % Take the max along dimension 2
How do I transfer the index to linear indexing, such that
M == A(Ind)
becomes true?
My intention for this problem is that I have two multi-dimensional matrices and need to compute the max in the first one. Then, I want to access the values in the second matrix at exactly those positions where I found a max in the first one.
One way is to use sub2ind:
A = randn([5,5,5]);
[M, col] = max(A,[],2);
[m,n,o] = size(A);
dim1 = mod((0:m*o-1)', m)+1;
dim2 = col(:);
dim3 = ceil((1:m*o)/m)';
ind = sub2ind(size(A), dim1, dim2, dim3)
verify it works with
isequal(M(:), A(ind))
to get them to have the same shape as M:
reshape(ind, m, 1, o)
Create the indices for the other dimensions.
In dim 1 the index needs to change fastest: [1,2,...,size(A,1)] and this size(A,3) times:
idx1 = repmat((1:size(A,1))',size(A,3),1);
In dim 2 the index is given by Ind.
In dim 3 the index need to change slowest: [1,1,...,1] for size(A,1) times and then [2,2,...,2] and so on until size(A,3).
idx3 = ones(size(A,1),1)*(1:size(A,3));
Access single values:
M_ = A(sub2ind(size(A),idx1(:),Ind(:),idx3(:)));
Compare:
M(:) == M_
3-dimensional case:
[m, n, p] = size(A);
[M, Ind] = max(A,[],2);
LinInd = bsxfun(#plus, (1:m).', (0:p-1)*m*n); %'//
LinInd = LinInd(:) + (Ind(:)-1)*m;
The desired linear index is LinInd. This produces
A(LinInd) == M(:)
with all true entries (note you need (:) on the right-hand side so that the comparison makes sense).
General multi-dimensonal case:
d = 3; %// dimension along which max will be computed
s = size(A);
sLow = prod(s(1:d-1));
sHigh = prod(s(d+1:end));
[M, Ind] = max(A,[],d);
LinInd = bsxfun(#plus, (1:sLow).', (0:sHigh-1)*sLow*s(d)); %'//
LinInd = LinInd(:) + (Ind(:)-1)*sLow;
Let's suppose A and B are the two matrices you have and you need to get max indices from A and use those indices to index into B for the desired output. One approach to achieve the same could be like this -
%// Your code to get Ind
A = randn([5,5,5]); % Generate random matrix
[M, Ind] = max(A,[],2); % Take the max along dimension 2
%// ------- Solution code -------------
%// Get the size of A
[n1,n2,n3] = size(A)
%// Linear indices corresponding to column and third dimension indices
col_dim3_lin_idx = bsxfun(#plus,(Ind-1)*n1,permute([0:n3-1]*n1*n2,[1 3 2]))
%// Finally get the overall linear indices
linear_index = bsxfun(#plus,col_dim3_lin_idx,[1:n1]') %//'
%// Get the corresponding elements from B
out = B(linear_index)
Slightly different way to have the desired linear indices as a 2D array would be like this -
[n1,n2,n3] = size(A) %// Get the size of A
idx = bsxfun(#plus,bsxfun(#plus,squeeze((Ind-1)*n1),[0:n3-1]*n1*n2),[1:n1]')
idx(:) would be the column vector of linear indices with this new approach, which you can index into B i.e. B(idx(:)) to have the desired output as a column vector.
A= [1 1
2 2
3 3
. .
. .
. .
N N]
I have an [N,2] matrix and I need to split it row-wise into some number of [N/4,2] submatrices. Then for each submatrix I need to find linear regression where the first column of each submatrix is my x data and the second column is my y data. The output should be a struct with fields a,b,c,d.... and values of linear regression for each submatrix
First I tried splitting the matrix with mat2cell where k = length(N)/4 and mat = mat2cell(A, [k k k k], [1 1]).
Next I tried converting mat into struct with out = cell2struct(mat,fields,1) where fields = {'col1','col2'} and use
new = structfun(#(x)polyfit(x.col1, x.col2,1), out,'UniformOutput', false)
But I get the error:
Inputs to STRUCTFUN must be scalar structures.
Does anyone know how to do it? Many thanks
The most straightforawrd way (and probably the fastest) to do this is with a good old for loop:
A = [1:64;1:64]'; % Demo data
m = 4;
N = size(A,1);
k = N/m; % Assumes that length is evenly divisible by 4
c = zeros(m,2); % Coefficients
for i = 1:m
c(i,:) = polyfit(A((i-1)*k+1:i*k,1),A(i-1)*k+1:i*k,2),1);
end
Or rather than using cell2struct and structfun you can use cellfun:
A = [1:64;1:64]'; % Demo data
m = 4;
N = size(A,1);
k = N/m; % Assumes that length is evenly divisible by 4
c = cellfun(#(x)polyfit(x(:,1),x(:,2),1).',mat2cell(A,k+zeros(1,m),2),'UniformOutput',false)
or alternatively
Ac = mat2cell(A,k+zeros(1,m),[1 1])
c = cellfun(#(x1,x2)polyfit(x1,x2,1).',Ac(:,1),Ac(:,2),'UniformOutput',false)
You can convert the output of cellfun to a matrix with:
c = [c{:}].'
As for why you're getting the error, your variable out is a 4-by-1 struct array (array of structures) rather than a simple (scalar) structure of arrays. The documentation for structfun points out this requirement in the description of the short function: "Apply function to each field of scalar structure." This video from The MathWorks tries to explain the difference.
I have these 10 vectors in MATLAB, mean(alltmws{l}'), where l is from 1 to 10. The size of each of these vectors is 1X10001. Now I want to store all these values in one vector, one after the other, so that I can calculate and plot the overall mean. How can I do this concatenation? Any help will be greatly appreciated.
If you have, for example,
a{1} = rand(10,1);
a{2} = rand(10,1);
a{3} = rand(10,1);
You can do
A = [a{:}];
A = A(:)
EDIT: The question is ambiguous, but if it is the means that one wants to concatenate and plot, you can do:
% Create example data
data = {};
for k = 1:10
data{k} = rand(100,1);
end
% Compute and plot array of means
mu = []
for k = 1:length(data)
mu(k) = mean(data{k});
end
plot(mu)
If you have a 1x10 cell array, then you can directly do:
concatnatedArray=cell2mat(yourCellArray);
If you have a 10x1 cell array, first transpose it and then apply above technique. This will only work if all the vectors in each cell are of the same length, which the case for you.
I need to create a list (of size n) of random, non-repeating set of coordinates on a matrix of predefined size.
Is there a fast way to generate this in Matlab?
My initial idea was to create a list of size n with permutations the size of (width x length) and to translate them back to Row and Col values, but it seems to me too much.
Thanks,
Guy
You can use randperm to generate a linear index, and convert it to [row,col] if needed using ind2sub.
x = rand(7,9);
n = 20;
ndx = randperm(numel(x), n);
[row,col] = ind2sub(size(x), ndx);
As long as n is less than the number of elements in the matrix this is simple:
% A is the matrix to be sampled
% N is the number of coordinate pairs you want
numInMat = numel(A);
% sample from 1:N without replacement
ind = randperm(numInMat, N);
% convert ind to Row,Col pairs
[r, c] = ind2sub( size(A), ind )
Your idea is a good one, although you don't even have to convert your linear indices back to row and col indices, you can do linear indexing directly into a 2D array.
idx = randperm(prod(size(data)))
where data is your matrix. This will generate a vector of random integers between 1 and prod(size(data)), i.e. one index for each element.
e.g.
n = 3;
data = magic(n);
idx = randperm(prod(size(data)));
reshape(data(idx), size(data)) %this gives you your randomly indexed data matrix back