How to create a symmetrical matrix?

Question

ric1321 2017-2-3

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编辑： Stephen23 2023-1-27

Hi, I have to fill a matrix with some data that come from a subroutine. The matrix is symmetrical over the two diagonals, so I have to build just a quarter of it and then to copy one the other parts. How can I do?

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Stephen23 2017-2-3

编辑：Stephen23 2017-2-3

@ric1321: what happens along the diagonals? Are the diagonal values constant?

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Answer 1

Stephen23 2017-2-3

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编辑：Stephen23 2017-2-3

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I looked at this task, and tried several possibilities to convert this:

>> M = [1,2,3,4,5;0,6,7,8,0;0,0,9,0,0;0,0,0,0,0;0,0,0,0,0]
M =
   2     3     4     5
   6     7     8     0
   0     9     0     0
   0     0     0     0
   0     0     0     0

But then it occurred to me: the question states "I have to fill a matrix with some data that come from a subroutine", so perhaps the simplest way is to avoid it all together: if you have to fill the matrix with these values (presumably in a loop and using some indexing), then instead of just filling one value, fill in all four values at once. This is likely going to be simpler than any method of taking that quarter matrix, rotating, and merging again...

So the simplest way for your situation might be to not "copy and rotate", but to allocate each new value to four locations when you put it into the matrix:

S = size(M);
[R,C] = find(M);
Z = nan(S);
for k = 1:numel(R) % for each subroutine value
    x = [R(k),1+S(1)-R(k),C(k),1+S(2)-C(k)]; % index
    m = M(R(k),C(k)); % new subroutine value here
    Z(x,x) = m;
end

which gives this:

 Z =
   4     3     4     5
   8     7     8     4
   7     9     7     3
   8     7     8     4
   4     3     4     5

Or you can use the method exactly as I did here: to copy the elements of that quarter to the other quarters.

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Answer 2

Guillaume 2017-2-3

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编辑：Guillaume 2017-2-3

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One of the many ways to do this:

v = [1 2 3 4; 0 5 6 7; 0 0 8 9; 0 0 0 10];
tv = v';
v(tril(true(size(v)))) = tv(tril(true(size(v))))

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Answer 3

Benjamin Klassen 2023-1-26

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https://ww2.mathworks.cn/matlabcentral/answers/323231-how-to-create-a-symmetrical-matrix#answer_1157230

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Symmetric Matrix Generator

% Rows
r1=[1,2,3,4,5,6,7,8];
r2=[5,2,6,7,9,8,5];
r3=[1,4,6,2,8,6];
r4=[1,6,2,9,4];
r5=[1,3,2,7];
r6=[1,7,9];
r7=[6,2];
r8=[9];
nr=length(r1); % Number of rows
K=zeros(nr,nr);
% Symmetric Matrix Assembly
for i=1:nr
    d=join(['r',num2str(i)])
    rowvalues=eval(d);
    K(i,i:end)=rowvalues;
    K(i:end,i)=rowvalues;
end

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Stephen23 2023-1-27

编辑：Stephen23 2023-1-27

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This would be much better without the evil EVAL call and anti-pattern numbered variable names:

C = {[1,2,3,4,5,6,7,8];[5,2,6,7,9,8,5];[1,4,6,2,8,6];[1,6,2,9,4];[1,3,2,7];[1,7,9];[6,2];9}
C = 8×1 cell array
    {[1 2 3 4 5 6 7 8]}
    {[  5 2 6 7 9 8 5]}
    {[    1 4 6 2 8 6]}
    {[      1 6 2 9 4]}
    {[        1 3 2 7]}
    {[          1 7 9]}
    {[            6 2]}
    {[              9]}
N = numel(C);
M = zeros(N,N);
for k = 1:N
    V = C{k};
    M(k,k:end) = V;
    M(k:end,k) = V;
end
display(M)
M = 8×8
     1     2     3     4     5     6     7     8
     2     5     2     6     7     9     8     5
     3     2     1     4     6     2     8     6
     4     6     4     1     6     2     9     4
     5     7     6     6     1     3     2     7
     6     9     2     2     3     1     7     9
     7     8     8     9     2     7     6     2
     8     5     6     4     7     9     2     9