# Parallelize nested loops with parfor

6 views (last 30 days)

Show older comments

I'm trying to speed up the simulation of some panel data. I have to simulate first over individuals (for ii from 1 to N) and then for each individual over age from 1 to JJ. The code is slow because inside the two loops there is a bilinear interpolation to do. Since the iterations in the outer loop are independent, I tried to use parfor in the outer loop, but I get the error message "the parfor cannot run due to the way the variable hsim is used".

Could someone explain why and how to solve the problem if possible? Any help is greatly appreciated!

%% Generate fake data for MWE

clear;clc

Nsim = 500;

JJ = 66;

na = 50;

nh = 30;

nz = 7;

a_grid = linspace(-15,100,na)'; % NOT necessarily equispaced!

h_grid = linspace(0,20,nh)'; % NOT necessarily equispaced!

apol = rand(na,nh,nz,JJ);

hpol = rand(na,nh,nz,JJ);

z_sim_ind = unidrnd(nz,Nsim,JJ);

%---------- START REAL CODE

tic

% a_grid and h_grid are column vectors with 50 and 35 elements,

% respectively

% z_sim_ind is a matrix of integers with size [Nsim,JJ]

a_sim = zeros(Nsim,JJ);

h_sim = zeros(Nsim,JJ);

% Find point on a_grid corresponding to zero assets

aa0 = 8;%find_loc(a_grid,0.0);

% Zero housing

hh0 = 1;

a_sim(:,1) = a_grid(aa0);

h_sim(:,1) = h_grid(hh0);

for ii=1:Nsim %with for loop it works but is very slow. parfor is illegal

for jj=1:JJ-1

z_c = z_sim_ind(ii,jj);

apol_interp = griddedInterpolant({a_grid,h_grid},apol(:,:,z_c,jj));

hpol_interp = griddedInterpolant({a_grid,h_grid},hpol(:,:,z_c,jj));

a_sim(ii,jj+1) = apol_interp(a_sim(ii,jj),h_sim(ii,jj));

h_sim(ii,jj+1) = hpol_interp(a_sim(ii,jj),h_sim(ii,jj));

end

end

toc

##### 0 Comments

### Answers (2)

Matt J
on 27 Jan 2023

Edited: Matt J
on 27 Jan 2023

I don't think it makes sense to use any loops here at all. Just make vectorized calls to your griddedInterpolant objects.

[~,~,m,n]=size(apol);

[~,Jcol]=ndgrid(1:Nsim,1:JJ);

F=griddedInterpolant({a_grid,h_grid,1:m,1:n},apol);

a_sim=F(a_sim(:),h_sim(:), z_sim_ind(:),Jcol(:));

F.Values=hpol;

h_sim=F(a_sim(:),h_sim(:), z_sim_ind(:),Jcol(:));

a_sim=circshift( reshape(a_sim, Nsim,JJ) ,[0,1]);

h_sim=circshift( reshape(h_sim, Nsim,JJ ,[0,1]);

a_sim(:,1) = a_grid(aa0);

h_sim(:,1) = h_grid(hh0);

##### 2 Comments

Matt J
on 27 Jan 2023

Matt J
on 27 Jan 2023

Edited: Matt J
on 27 Jan 2023

Never mind my other answer. I didn't notice that a_sim and h_sim were recursively defined. You can't avoid a loop, but you only need the loop over jj. It cannot be parallelized.

Nsim = 50000;

JJ = 66;

% a_grid and h_grid are column vectors with 50 and 35 elements,

% respectively

% z_sim_ind is a matrix of integers with size [Nsim,JJ]

a_sim = zeros(Nsim,JJ);

h_sim = zeros(Nsim,JJ);

% Find point on a_grid corresponding to zero assets

aa0 = 8;%find_loc(a_grid,0.0);

% Zero housing

hh0 = 1;

a_sim(:,1) = a_grid(aa0);

h_sim(:,1) = h_grid(hh0);

%%%%%%%%%%%%%%%%%%%%%%%

k=(1:Nsim)';

apol_interp = griddedInterpolant({a_grid,h_grid,k},apol(:,:,k,1));

hpol_interp = griddedInterpolant({a_grid,h_grid,k},hpol(:,:,k,1));

for jj=1:JJ-1

z_c = z_sim_ind(:,jj);

I=sub2ind( [Nsim,JJ], zc, repelem(jj,Nsim,1) );

apol_interp.Values = apol(:,:,I);

hpol_interp.Values = hpol(:,:,I);

a_sim(:,jj+1) = apol_interp(a_sim(:,jj),h_sim(:,jj),k);

h_sim(:,jj+1) = hpol_interp(a_sim(:,jj),h_sim(:,jj),k);

end

### See Also

### Categories

### Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!