vectorization of symmetrical matrix with off-diagonal vectors multiplied with 2

Hi all,

I want to vectorize a matrix H. However the matrix H is symetric in the off-diagonal entries. The off diagonal entries on the to disired vector have the value of 2*H(ij).

imagine H as:

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

than, the to desired vector has the following form. if H is nxn matrix. the vector should have dimensions n(n+1)/2 with the off-diagonal vectors 2*H(ij) like

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

What is the best way to solve this problem?

Answer 1

[Andrei Bobrov]

k = 2;

o = ones(size(H));
Hl = H.*(tril(o,-1)*(k-1) + 1);
out = Hl(tril(o)>0);

or

e = H.*((k-1)*(1-eye(size(H))) + 1);
out = e(tril(e) > 0);

Answer 2

[Tim Elbers]

Thank you,

i have an aditional question,

which is like the same problem but than reversed.

if i have obtained the vector .

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

how could i obtain the same symatrical matrix of underneath form if only this vector is given.

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