Vector to lower-triangular matrix

Hello.

Im trying to estimate multivariate normal distribution. Correlation matrix is one of the parameters, and I need to have all parameters in a vector for fmincon.

I can vectorize a lower-triangular of correlation matrix, indeed, but how do I do an opposite?

I mean, I have a matrix C - a correlation matrix:

       1  c12 c13
  C = c12  1  c23
      c13 c23  1

Then I do:

a = tril(C,-1);
a = a(:);
b = a(a(:)>0);
b = [c12; c13; c23];

I get b - a vectorized lower-triangular matrix. How can I do an opposite (for matrices of any dimensions)? To get a lower-triangular matrix from a vector? Thanks!

Answer 1

[Matt J]

b=rand(1,10)

b = 1×10

0.5909 0.3646 0.0131 0.7843 0.1867 0.2957 0.2750 0.2019 0.1148 0.6168

n=roots([1,1,-2*numel(b)]);
n=n(n>0)+1;
validateattributes(n,{'numeric'},{'positive', 'integer'}) %numel(b) must be a pyramidal number

C=tril(ones(n),-1);
C(logical(C))=b;
C=C+C.'+eye(n)

C = 5×5

1.0000 0.5909 0.3646 0.0131 0.7843 0.5909 1.0000 0.1867 0.2957 0.2750 0.3646 0.1867 1.0000 0.2019 0.1148 0.0131 0.2957 0.2019 1.0000 0.6168 0.7843 0.2750 0.1148 0.6168 1.0000