Fsolve for different values of a parameter

Hello all,

I use fsolve to find the solutions of a system of 5 nonlinear equations. I get the solutions with a value set for each parameter of the model.

However, I would like to calculate the system's solutions for several values of one of the parameter (from 0 to 1 with an increment of 0.01), without having to change it manually each time. I would also like to keep the set of solutions (for each value of the parameter in question), and then make a graph that shows the evolution of each of the variables when the value of the parameter changes.

Is there a simple way to do this?

More precisely:

It is the parameter 'rho' that I want to pass from 0 to 1 with an incrementation of 0.01, then represent the evolution of the variables (theta, eseuil, u ..) according to the value of rho.

Here is my code :

clear all
diary calibration_firmlevel
close all

 %%VALUES OF PARAMETERS %%

ebarh=1;
delta=0.3919;
kappa=0.6578;
z=0.2510;
r=0.012;
alpha=0.5;
A=0.7;
gamma=0.2345;
rho=0;
c=0.5;

%%EQUILIBRIUM %%

% Parameters

P=[ebarh,delta,kappa,z,r,alpha,A,gamma,rho,c];

% Initial conditions 

theta0=0.72;
eseuil0=0.2;
u0=0.047;
tau0=0.06;
phi0=0;

% Fsolve: find the solutions of non linear system of equations

[X,fval,exitflag,output]=fsolve('equilibrePissarides_expost_firmlevelv4',[theta0,eseuil0,u0,tau0,phi0],optimset('fsolve'),P);

theta=X(1);
eseuil=X(2);
u=X(3);
tau=X(4);
phi=X(5);

% Values of Job destruction and job creation
JD=delta*unifcdf(eseuil);
JC=theta*(A*theta^(-alpha));

%%RESULTS %%

disp('RESULTS')
disp('')
disp('PARAMETERS VALUES')
disp('')
disp('    ebarh     delta      kappa     z           r      alpha      A        gamma        rho      c ')
disp([ebarh,delta,kappa,z,r,alpha,A,gamma,rho,c]);
disp('')
disp('VARIABLES VALUES')
disp('')
disp('     u       theta     eseuil       tau       phi');
disp([u,theta,eseuil,tau,phi]);
disp('     JC       JD');
disp('')
disp([JC,JD]);

Thank you, Yann

Answer 1

[Torsten]

Call fsolve in a loop and change the value of rho in this loop according to your needs. Save the results for (theta, eseuil, u ..) in arrays depending on the loop index. As soon as the loop is done, plot the results.

Best wishes

Torsten.