constructing symatrical matrix out of vector

Hello all,

I have a question,

I have a vector that is previously vectorized out of a symatrical matrix and has the following form. (lengt 1 x L(L+1)/2 )

v = 1, 2*6, 2*7, 2*8, 2*9, 2, 2*10, 2*1,1 2*12, 3, 2*13, 2*14, 4, 2*15, 5

I now want to obtain the same matrix as before (Matrix H) of the underneath form (lengt L x L). How can I obtain this matrix out of above vector?

H =
     1     6     7     8     9
     6     2    10    11    12
     7    10     3    13    14
     8    11    13     4    15
     9    12    14    15     5

thanks in advance

Answer 1

[Jos (10584)]

v = [1, 2*6, 2*7, 2*8, 2*9, 2, 2*10, 2*11 2*12, 3, 2*13, 2*14, 4, 2*15, 5]
%                                       |
%   I assume the comma here in your example was a typo
m = tril(ones(5)) 
m(m==1) = v 
m = (m + m.')/2

Answer 2

[Josh]

I'm a little fuzzy on what v is supposed to be (are the off-diagonal elements of H stored in v all multiplied by 2?), so I'll solve the problem in two steps:

First, the indexing problem, how to reinflate v into H:

% Define inputs
v = [1, 6, 7, 8, 9, 2, 10, 11, 12, 3, 13, 14, 4, 15, 5];
L = (sqrt(1 + 8 * numel(v)) - 1)/2;

% Create an index matrix, I, such that v(I) give us H:

% Create a matrix of indices:
I = reshape(1:L*L, L, L);

% Duplicate the indices of the lower half into the upper half:
I = min(I, I');

% Re-index I to remove unused indices:
[~, ~, purged] = unique(I(:));
I = reshape(purged, size(I));

% Calculate the expanded matrix, H:
H = v(I);

If you do need to divide the off diagonal elements by 2:

H = v(I) ./ (2 - eye(L));