The vectorized code after eliminating the loop over d is the following. Choose either 'loops' or 'vec' at the beginning of the script to compare the running time of the two methods: loops vs vectorized. It turns out that loops are faster! I found this relatively surprising since loops are generally slow in Matlab.
clear
close all
clc
rng("default")
method = 'loops'; % 'loops','vec'
% Size of grids
n_b = 1000;
n_d = 40;
n_e = 5000;
% Parameters
delta = 0.2696037674949296;
%omega_0 = 0.0015534835229589;
%omega_1 = 0.0013023827114628;
% Generate fake data
cost_mat = rand(n_e,n_d);
prob_mat = rand(n_e,n_d);
option_nob = rand(n_b,1);
d_grid = linspace(0,2.3,n_d)';
%% Create a grid for "e". The non-standard feature is that the upper bound
% of the e_grid depends on "d"
e_grid_mat = zeros(n_e,n_d);
e_min = 0;
space = 1.5;
for d_c=1:n_d
d_val = d_grid(d_c);
e_max = 0.1+0.2*d_val; %silly example, don't take this literally
% e_grid is NOT equally spaced
e_grid_mat(:,d_c) = e_min+(e_max-e_min)*(linspace(0,1,n_e).^space)';
end
%% The code below is the part that I'd like to speed up
tic
switch method
case 'loops'
disp('loops')
e_opt = zeros(n_b,n_d);
for d_c = 1:n_d
% Effort grid depends on d (upper bound changes, but same no. of elements)
e_grid = e_grid_mat(:,d_c); %each column of e_grid_mat is different!
% V(e,b) has dim: (n_e,n_b) and I maximize with respect to the first dimension, e
V = -cost_mat(:,d_c)-delta*prob_mat(:,d_c).*option_nob';
[~,max_ind] = max(V,[],1); %maxind is (1,n_b) vector
e_opt(:,d_c) = e_grid(max_ind);
end %end d
case 'vec'
disp('vec')
% compute the full V, with dim (n_e,n_d,n_b)
V = -cost_mat-delta*prob_mat.*reshape(option_nob, 1, 1, n_b);
%V = -cost_mat-delta*prob_mat.*shiftdim(option_nob,-2);
[~, max_ind] = max(V, [], 1); % max_ind is (1,n_d,n_b)
max_ind = permute(max_ind, [2 3 1]); % % max_ind is now (n_d,n_b)
%max_ind = max_ind + (0:n_d-1).'*n_e; % apply linear indexing
% e_grid_mat is [n_e,n_d], but e_opt gives only "e" indices
max_ind = sub2ind([n_e,n_d],max_ind,repmat((1:n_d)',1,n_b));
e_opt = e_grid_mat(max_ind).'; % retrieve maximizing values
end
loops
toc
Elapsed time is 0.263274 seconds.
%To check results
disp(mean(mean(e_opt)))
0.1364
