How to create a sequence of matrices that depend on parameters whose values change?

Hi,

I have the following problem I'm trying to solve on Matlab: some matrices that depend on a set of parameters; I attribute values to the parameters and use the matrices to calculate law of motions for some variables.

I would like to make one of the parameters to change in a given interval and see how the law of motions vary. The way I see it, that would require creating a sequence of matrices, one for each value of the given parameter, and then solving the problem for each combination of matrices.

Any help on how to do it?

To make matters more clear, here goes an example. What I would like is to get a set of values for C1, C2 and M (at the end of the code) as delta changes.

%parameter values:

alpha = 3; beta = 0.99; chi = 1.55; eta = 0; rho = 0.5; sigma = 1; omega = 0.5; theta = 2.064;

%There is also a parameter “delta”, which I'd like to be:

delta = 0:0.1:2;

%calculate kappa:

kappa = (1-omega)*(1-beta*omega)/(alpha*omega);

%define the following matrices:

A0 = zeros(3,3); A0(1,1) = 1; A0(2,2) = 1; A0(2,1) = sigma^(-1); A0(3,3) = beta;

B0 = zeros(3,1); B0(1,1) = 1;

A1 = zeros(3,3); A1(1,1) = rho; A1(2,1) = sigma^(-1); A1(2,2) = 1; A1(3,2) = -kappa; A1(3,3) = 1;

%Element A1(2,3) is the only one that depends on delta:

A1(2,3) = sigma^(-1)*delta;

%calculate alternative state-space matrices:

A = inv(A0)*A1;

B = inv(A0)*B0;

%Jordan decomposition of A:

[p,lambda] = eig(A);

%rearrangement of Jordan form:

pstar = inv(p);

%sort eigenvectors and eigenvalues in ascending order:

val = abs(diag(lambda));

t = sortrows([val p'],1);

lambda = diag(t(:,1)); p = t(:,2:4)'; pstar = inv(p);

%partition the lambda, pstar and R = pstar*B matrices:

LAMBDA1=lambda(1,1); LAMBDA2=lambda(2:3,2:3);

P11=pstar(1,1); P12=pstar(1,2:3); P21=pstar(2:3,1); P22=pstar(2:3,2:3);

R=pstar*B;

% Matrices of solution of model:

C1=real(inv(P11-P12*inv(P22)*P21)*LAMBDA1*(P11-P12*inv(P22)*P21));

C2=real(inv(P11-P12*inv(P22)*P21)*R(1));

M=real(-inv(P22)*P21);

Answer 1

[Nihar Deodhar]

%Seems like you could use a simple for loop to run the code.

%The delta could be set as vector:

delta = 0:0.1:2;

%use a variable say 'd' to substitute delta in the matrix at location A1(2,3)

for i = 1:length(delta)

d = delta(i);

%% than execute the rest of the code above and put d at A1(2,3). % If C1, C2 and M are scalars and you wish to have all of them at once, % index them as C1(i) and C2(i) and M(i).

end

[Ana Neves]

Thanks for your help! Just one more question: your suggestion is that I run the whole code inside the loop, right? And then store only the final values of C1, C2 and M?

[Nihar Deodhar]

Exactly! That is what I meant. You could store the values of C1, C2 and M for each case of delta if you index it like C1(i), C2(i) and M(i).

[Ana Neves]

Great, it works! Many thanks! :)

[Nihar Deodhar]

You are welcome, indeed!