MATLAB expriment for correlation matrix compleition

ncm_compare.m

%NCM_COMPARE
% M-file to carry out experiment in "Explicit Solutions to Correlation
% Matrix Completion Problems, with an Application to Risk Management and
% Insurance" by Dan I. Georgescu, Nicholas J. Higham and Gareth W. Peters.

C = [%
1     0.25  0.6   0.55  0.65  0     0.4  0.6  0.2    0.3
0.25  1     0     0     0     0    NaN   NaN  NaN    NaN 
0.6   0     1     0.75  0.75  0    NaN   NaN  NaN    NaN 
0.55  0     0.75  1     0.5   0    NaN   NaN  NaN    NaN 
0.65  0     0.75  0.5   1     0    NaN   NaN  NaN    NaN 
0     0     0     0     0     1    NaN   NaN  NaN    NaN 
0.4   NaN   NaN   NaN   NaN   NaN  1     0.25  0.25  0.5 
0.6   NaN   NaN   NaN   NaN   NaN  0.25  1     0.25  0 
0.2   NaN   NaN   NaN   NaN   NaN  0.25  0.25  1     0 
0.3   NaN   NaN   NaN   NaN   NaN  0.5   0     0     1];

format short

pattern = ~isnan(C);
A = C; A(isnan(A)) = 0
eigA = eig(A)

% Max det completion.
A11 = C(1,1);
B = C(1,2:6); CC = C(1,7:end); 
A22 = C(2:6,2:6);
E  = C(2:6,7:end);
A33 = C(7:end,7:end);

E_maxdet = B'*(A11\CC)
normF_Emaxdet = norm(E_maxdet,'fro')
dist_maxdet = norm(E_maxdet)
Y = A;
Y(2:6,7:end) = E_maxdet;
Y(7:end,2:6) = E_maxdet';
format short e
eig_maxdet = eig(Y)'
det_maxdet = det(Y)

% Use code from https://github.com/higham/anderson-accel-ncm
% Adjust next line as necessary.
addpath d:\tex\anderson\matlab -end
[X,iter] = nearcorr_aa(A,pattern);

format short
E_ncm = X(2:6,7:end)
normF_Encm = norm(E_ncm,'fro')
format short e
eig_ncm = eig(X)'
dist_ncm = norm(A-X,'fro')
det_ncm = det(X)

% Use code from https://github.com/higham/shrinking
% Adjust next line as necessary.
addpath d:\tex\shrinking\matlab -end

M0 = A;
M1 = Y;
alpha = shrink_bisect(M0,M1,1e-14)
Z = alpha*M1 + (1-alpha)*M0
format short 
E_shrink = Z(2:6,7:end)
normF_Eshrink = norm(E_shrink,'fro')
dist_shrink = norm(A-Z,'fro')
det_shrink = det(Z)
format short e
eig_shrink = eig(Z)'

Z = inv(Y);
norm_inv_unspec = norm(Z(2:6,7:end))