How can I create a 22x22 Matrix from 231 values of the triangular matrix?

I have 231 doubles which represent the values of one triangular of the complete matrix. I want to add the diagonal (all 1s) and the complementary triangular to get the full 22x22 matrix (which I need for the next task).

This is the closest I've got so far:

test = horzcat(tri,tri)
reshape(test,22,22,[])
Error using reshape
Product of known dimensions, 484, not divisible into total number of elements, 462.

The error is due to the fact that the diagonal (22x1) is missing, but I don't know how to add that...

Answer 1

[Matt J]

load(websave('Tri.mat','https://www.mathworks.com/matlabcentral/answers/uploaded_files/493054/Tri.mat'));

N=roots([1,1,-2*numel(tri)])+1; %deduce the matrix dimensions
N(N<=0)=[];


idx=triu(true(N),1);

result=double(idx)+eye(N);

result(idx)=tri

result = 22×22

1.0000 0.2208 0.4880 0.4947 0.2733 0.3649 0.0302 0.2423 0.2521 -0.0407 0.3021 0.1282 -0.1977 0.4136 0.2318 0.0752 0.0599 0.4877 0.2686 -0.1919 0.0251 0.0543 0 1.0000 0.7913 0.4877 0.1072 0.1893 0.2650 0.3895 -0.0477 0.1563 0.5627 0.0351 0.3776 0.1872 0.4656 0.1598 0.0450 0.5441 -0.0250 -0.2780 -0.1442 -0.0107 0 0 1.0000 0.1311 0.3054 0.2138 0.4619 0.3481 -0.1696 0.2788 0.2901 0.3879 0.1732 0.4028 0.5422 0.6153 0.0933 0.5289 -0.3991 0.0534 -0.0662 0.5230 0 0 0 1.0000 -0.0548 -0.0903 0.7944 0.1480 -0.0469 0.2187 -0.0151 0.5569 0.2483 0.3056 0.0899 0.6903 0.1973 -0.2567 0.4054 0.3837 -0.0314 0.5232 0 0 0 0 1.0000 0.3347 0.3109 0.6274 0.1273 -0.2127 0.0853 0.1171 -0.2536 0.4088 0.1076 0.5081 0.1207 -0.2646 -0.5002 0.0302 0.1260 0.4296 0 0 0 0 0 1.0000 0.0140 0.4290 -0.1978 0.3986 0.3021 0.5588 0.3812 0.1024 0.6478 -0.1360 0.0285 0.0335 0.6610 0.2112 -0.2129 -0.1944 0 0 0 0 0 0 1.0000 0.0329 0.2104 0.6568 0.1223 0.4741 0.0456 0.0759 -0.2626 0.2613 -0.2659 -0.0490 0.2160 0.1493 0.2505 -0.3117 0 0 0 0 0 0 0 1.0000 0.0476 0.3159 -0.2352 0.2346 0.0961 0.2040 0.6898 -0.0124 0.7119 0.5553 -0.0067 -0.0415 0.4431 -0.1951 0 0 0 0 0 0 0 0 1.0000 0.1573 0.3977 0.3480 0.4854 0.2864 0.0616 0.0998 0.0775 -0.2745 0.3565 -0.0333 -0.2181 0.0910 0 0 0 0 0 0 0 0 0 1.0000 0.1360 -0.0104 0.6928 -0.3302 0.0644 0.0466 -0.0979 0.2668 0.5872 -0.1525 0.1251 0.3016

[Jean Kröll]

Thank you so much!