How do I make a lower triangular matrix from a column vector?

I am trying to make a lower triangular matrix from a column vector to then produce a fully populated 24x24 symmetric matrix.

The column vector I'm using (A as a simple example) has 300 elements and I need to populate the triangular matrix (B as a simple example) as follows:

A = [i1 i2 i3 i4 i5 i6 i7 i8 i9 i10 ...]

B = [i1; i2 i3; i4 i5 i6; i7 i8 i9 i10; ....]

Any help would be appreciated. It may be that it's easier to make the symmetric matrix straight away, if so I'm open to suggestions. Thanks in advance.

Answer 1

[Jan]

Create the symmetric matrix directly:

n   = 24;
Ind = zeros(n, n);
Ind((1:n) >= (1:n).') = 1:300;
Ind = Ind + Ind.' - diag(diag(Ind));

B = A(Ind);

[Leo Cordery Smith]

Thanks for this Jan, really helpful.

[Leo Cordery Smith]

Hi Jan, do you know how to write the above code in Python? I've had to change my program from MATLAB to Python. Thanks.

[Jan]

Sorry, I have basic programming skills in Python only. Ask this in a python forum.

Answer 2

[Rik]

The functions you should be looking for are tril and triu. You should be using triu, because you seem to want to fill your array in row-major order, while the Matlab default is column-major.

A=1:21;%replace with your data

%sz will only be a positive integer if numel(A) is a triangle number
sz=-0.5+sqrt(0.25-4*0.5*-numel(A));
B=triu(ones(sz));
B(logical(B))=A;
B=B.';
disp(B)

     1     0     0     0     0     0
     2     3     0     0     0     0
     4     5     6     0     0     0
     7     8     9    10     0     0
    11    12    13    14    15     0
    16    17    18    19    20    21

[Leo Cordery Smith]

Hi Rik, do you know how to write the above code in Python? I've had to change my program from MATLAB to Python. Thanks.

[Rik]

Similar to Jan, my Python skill are only rudimentary. If you are an actual Python user, your success in googling documentation will probably be higher.