Request for Assistance in Matlab code

[Moin Uddin]

 Dear All,

I have written a code using the Manopt toolbox for matrix optimization, but unfortunately, I encountered an error while running it (please see the attached error message).

I would greatly appreciate any guidance or suggestions you might have to help resolve these issues. If you could provide insights on the possible causes or direct me to relevant resources, it would be incredibly helpful.

Thank you in advance for your assistance! I look forward to hearing from you.

function low_rank_matrix_completion_barrier

% Matrix dimensions and rank

m = 50; % Number of rows

n = 40; % Number of columns

r = 5; % Target rank

% Generate a random low-rank matrix A of rank r

U = randn(m,r);

V = randn(n,r);

A = U * V'; % A is a rank-r matrix

% Set of known entries S

S = rand(m,n) > 0.5; % Random mask for observed entries

% Manifold of m x n matrices of fixed rank r

manifold = fixedrankembeddedfactory(m, n, r);

% Objective function: Frobenius norm on the known entries

function F = frob_objective(X)

X_full = X.U * X.V'; % Reconstruct full matrix from factored form

P_X = S .* (X_full - A); % Projection onto known entries

F = 0.5 * norm(P_X, 'fro')^2;

end

% Barrier function to enforce non-negativity constraint

function B = barrier_function(X, mu)

X_full = X.U * X.V'; % Reconstruct full matrix from factored form

P_X = S .* (X_full - A); % Projection onto known entries

% Add log barrier for non-negative constraint

barrier_term = -mu * sum(log(X_full(X_full > 0)), 'all'); % Log barrier

B = 0.5 * norm(P_X, 'fro')^2 + barrier_term; % Objective + barrier

end

% Initial guess on the manifold

X0 = randn(m,r) * randn(n,r)';

% Set up the options for the Manopt solver

options.maxiter = 100; % Maximum number of iterations

options.tolgradnorm = 1e-6; % Tolerance for stopping

% Initial barrier parameter

mu_k = 1;

tol_mu = 1e-6; % Stopping condition for the barrier parameter

% Solve iteratively, reducing the barrier parameter

Xk = X0; % Initial guess

while mu_k > tol_mu

% Solve the unconstrained problem with the barrier term

problem.M = manifold;

problem.cost = @(X) barrier_function(X, mu_k);

problem.egrad = @(X) manifold.egrad(frob_objective(X)); % Gradient

[Xk, xcost, info] = trustregions(problem, Xk, options);

% Print information about the iteration

fprintf('mu = %f, cost = %f\n', mu_k, xcost);

% Decrease barrier parameter

mu_k = mu_k / 2;

end

% Final solution

disp('Final solution found:');

disp(Xk.U * Xk.V'); % Reconstruct final low-rank matrix

end

Error Mesage: > In trustregions (line 327)

In low_rank_matrix_completion_barrier (line 53)
Dot indexing is not supported for variables of this type.

Error in low_rank_matrix_completion_barrier/barrier_function (line 27)
        X_full = X.U * X.V'; % Reconstruct full matrix from factored form
                 ^^^
Error in low_rank_matrix_completion_barrier>@(X)barrier_function(X,mu_k) (line 50)
        problem.cost = @(X) barrier_function(X, mu_k);
                            ^^^^^^^^^^^^^^^^^^^^^^^^^
Error in getCost (line 59)
                cost = problem.cost(x);
                       ^^^^^^^^^^^^^^^
Error in getCostGrad (line 89)
        cost = getCost(problem, x, storedb, key);
               ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Error in trustregions (line 401)
[fx, fgradx] = getCostGrad(problem, x, storedb, key);
               ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Error in low_rank_matrix_completion_barrier (line 53)
        [Xk, xcost, info] = trustregions(problem, Xk, options);

[Nicolas Boumal]

Hello,

The issue is X0:  your code constructs X0 as a matrix. But points on the fixedrankembeddedfactory manifold should be encoded as structures with three fields: U, S, V.

Typing 'help fixedrankembeddedfactory' in the Matlab command prompt will provide more info.