matrix of circulating vectors without loop
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hi all , I want to built a matrix of circulating vectors without using loops
for example
input:
1 2 3 4
4 5 6 7
3 8 4 6
output :
1 2 3 4
4 1 2 3
3 4 1 2
2 3 4 1
4 5 6 7
7 4 5 6
6 7 4 5
5 6 7 4
3 8 4 6
6 3 8 4
4 6 3 8
8 4 6 3
I use the code
v =[1,2,3,4;4,5,6,7;3,8,4,6]
%notice the length of each vector in v is equal
len_rows=length(v(:,1));
len_cols=length(v(1,:));
mat_shifted=zeros(len_rows*len_cols,len_cols);
j=1;
for i=1:len_rows
vec=v(i,:);
mat=toeplitz([vec(1) fliplr(vec(2:end))], vec)
mat_shifted(j:j+len_cols-1,:)=mat
j=j+len_cols;
end
is there a smart way to do it without using loops , thanks in advance
采纳的回答
Honglei Chen
2018-5-4
Not necessarily better in performance, but if you really want to avoid explicitly calling a loop, try
y = arrayfun(@(r)gallery('circul',x(r,:)),1:size(x,1),'UniformOutput',false);
cat(1,y{:})
HTH
4 个评论
fatema hamodi
2018-5-4
Stephen23
2018-5-4
"do you think that the way you suggested would be better ?"
Using arrayfun will be slower than using a for loop. The main advantage of arrayfun / cellfun is more compact code. For a large array you probably would not want to swap a fast loop for slow arrayfun.
Honglei Chen
2018-5-4
Here is another way which should be more efficient and without explicit loop usage. But overall you want to find a tradeoff between time and memory when you deal with large data set.
x = [1 2 3 4;4 5 6 7;3 8 4 6];
[M,N] = size(x);
r = kron((1:M)',ones(N));
c = repmat(gallery('circul',1:N),M,1);
x(sub2ind([M,N],r,c))
HTH
fatema hamodi
2018-5-4
更多回答（2 个）
I think your concept is quite reasonable You could simplify the code a bit by using a cell array for the output, rather than keeping track of the rows:
M = [1,2,3,4;4,5,6,7;3,8,4,6];
N = size(M,1);
C = cell(N,1);
for k = 1:N
V = M(k,:);
C{k} = toeplitz([V(1),V(end:-1:2)],V);
end
Z = vertcat(C{:})
Carlos Sanchis
2018-5-4
Still with a for loop, but somewhat more readable...
input = [1 2 3 4; ...
4 5 6 7; ...
3 8 4 6];
[m, n] = size(input);
output = zeros(m * n, n);
for s = 0:n-1
output((0:m-1) * n + s + 1, :) = circshift(input, s, 2);
end
expected = [1 2 3 4; 4 1 2 3; 3 4 1 2; 2 3 4 1; ...
4 5 6 7; 7 4 5 6; 6 7 4 5; 5 6 7 4; ...
3 8 4 6; 6 3 8 4; 4 6 3 8; 8 4 6 3];
assert(isequal(output, expected));
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