recoverData.m

function X_rec = recoverData(Z, U, K)

% initialize recovered values
X_rec = zeros(size(Z, 1), size(U, 1));

for i = 1:size(X_rec,1)
    % projected_x is (1, K)
    projected_x = Z(i, :);

    % initialize x
    x = zeros(1, size(U,1));

    % iterate through dimensions to recover value
    for j = 1:size(x, 2)
        % Ufor_dimension = (1, K)
        Ufor_dimension = U(j, 1:K);

        % set the value for this dimension
        % (1, K) * (1, K)'
        % (1, K) * (K, 1) = (1, 1)
        recovered_for_dimension = projected_x * Ufor_dimension';
        x(j) = recovered_for_dimension;
    end 

    X_rec(i,:) = x;
end

end