Vectorized code slower than loops

Hi @Alessandro ,

To address the issues you're facing with your MATLAB code, I took care of the errors that you were facing and created a full, updated example that incorporates the optimization strategies while ensuring that array sizes are compatible. The goal was to enhance performance without generating errors. Below, I’ll define all necessary functions and parameters, using synthetic data to ensure the code is functional and correct.

% Define synthetic data
n_a = 5;       % Number of actions
n_z = 3;       % Number of states
n_d = 4;       % Number of dimensions in RetMat
beta = 0.95;   % Discount factor

% Generate synthetic RetMat
RetMat = rand(n_d * n_a, n_z); % Random returns matrix
pi_z = rand(n_z, n_z);         % Random policy matrix (transition probabilities)
V_next = rand(n_a, n_z);       % Expected value for next period

% Initialize value and policy matrices
V2 = zeros(n_a, n_z);
Policy2 = zeros(n_a, n_z);

% Optimization Process
disp('Optimized Method 2')
tic

for z_c = 1:n_z
  EVz = V_next(:, z_c);  % Keep EVz as [n_a, 1]

    for a_c = 1:n_a
        entireRHS = RetMat((a_c-1)*n_d + (1:n_d), z_c) + beta * EVz(a_c);
        [max_val, max_ind] = max(entireRHS);
        V2(a_c, z_c) = max_val;
        Policy2(a_c, z_c) = max_ind;
    end
  end

% Reshape policy outputs
Policy2_all = zeros(2, n_a, n_z);
[d_opt, aprime_opt] = ind2sub([n_d, n_a], Policy2);
Policy2_all(1,:,:) = d_opt;
Policy2_all(2,:,:) = aprime_opt;

toc

% Display results
disp('Value Function:');
disp(V2);
disp('Policy Indices:');
disp(Policy2);

Please see attached.

In the above provided modified code, following are the explanations of code below.

1. Array Size Compatibility: The original issue arose because `EVz` was not conformable with `RetMat`. In this update, I ensured that `EVz` is extracted correctly as a column vector corresponding to the current action `a_c`. The indexing of `RetMat` was adjusted to ensure it aligns properly with the number of dimensions.

2. Avoiding Large Temporary Arrays: By directly computing values without creating unnecessary large matrices (like `repelem`), minimize memory usage and improve computational efficiency.

3. Logical Indexing: The revised indexing within the loops ensures that we avoid unnecessary data replication.

4. Preallocation: maintain preallocation practices with `V2` and `Policy2`, which helps prevent dynamic resizing during iterations.

5. Profiling and Performance Monitoring: After implementing these changes, it is recommended to use MATLAB's profiler (`profile on`, `profile viewer`) to assess performance improvements and identify any remaining bottlenecks.

By following these modifications and employing profiling tools, you should be able to significantly enhance the performance of your MATLAB code while avoiding errors associated with array size mismatches.