Error using sum, interpn and ndgrid: Arrays have incompatible sizes for this operation

I am using MATLAB R2021b. I have a stochastic dynamic programming problem that I'm trying to solve by value function iteration (VFI). I want to solve for V in:

My endogenous state variable is , my exogenous state variables are P and ϵ and my choice variable is s (ϵ is random). have defined a grid of values for the states. I am interpolating the value function through ndgrid but when I try to find the expected value of the value function I get the following error. This is my code:

% state space
p_vec=linspace(0.5,5,50)';
epsilon_vec = linspace(0.5,2.5,3)'; % epsilon has 3 states
s_vec = linspace(sbar,15,100)';
% a finer state space for interpolation
pp = linspace(0.5,5,100)';
epep = linspace(0.5,2.5,20)';
ss = linspace(sbar,15,200)';
% grids for interpolation
[p_grid,epsilon_grid,s_grid] = ndgrid(p_vec,epsilon_vec,s_vec);
[pp_grid,epep_grid, ss_grid] = ndgrid(pp,epep,ss);
% transition matrix for epsilon
pi=[0.3,0.4,0.3;0.25,0.25,0.5;0.7,0.22,0.08]; % pi(i,j) = Pr(next period state is j|today's state is i).
% so each row sums to 1
% initial guess for V
V0=zeros(length(p_vec),length(epsilon_vec),length(s_vec));
% other parameters
beta=0.95;
r=0.05;

% interpolate and calculating expected value of V
sum(pi(state_ep,:)*interpn(p_grid,epsilon_grid,s_grid,V0,pp_grid,epep_grid,ss_grid));

I am getting two errors. The first one is:

'Error using *

Arguments must be 2-D, or at least one argument must be scalar. Use TIMES (.*) for elementwise multiplication"

So I changed the code to:

sum(pi(state_ep,:).*interpn(p_grid,epsilon_grid,s_grid,V0,pp_grid,epep_grid,ss_grid));

This produced the following error:

"Arrays have incompatible sizes for this operation."

Where am I going wrong?

Answer 1

[Jan]

It is a bad idea to redefine "pi" as variable, because this conflicts with the constant pi.

Use the debugger to examine the problem. Type this in the command window:

dbstop if error

Then run the code again. When Matlab stops at the error, check the sizes of the used variables:

size(sum(pi(state_ep,:)))
size(interpn(p_grid, epsilon_grid, s_grid, V0, pp_grid, epep_grid, ss_grid))

Now decide, which kind of multiplication you want. Just trying * or .* because an error occurs is "gunshot programming". Prefer to convert your intentions to the correct operator instead of changing the code until no error occurs.

[Saunok Chakrabarty]

Thanks for the answer. I apologize for the syntax, I'm new to Matlab. I used the debugger, and the error was was that the grid sizes were not compatible. I have not yet solved the issue, and I am working on a simpler problem with two state variables, one endogenous and one exogenous. That does not require me to form a grid for the interpolation.

[Jan]

@Saunok Chakrabarty: There is no need to apologize. Your questions about Matlab are welcome and they are the purpose of this forum. I'm glad if I could assist you a little bit to find the source of the problem.