Solving a system of equations using a specific initial guess in Matlab

1
votes

I have a question about solving a system of equations and initial guesses of the solution. I want to solve a system of equations where "x", a Tx1 vector, are my unknowns, "a" a Tx1 vector and "B" a TxT matrix. "f" is the function I want to solve for. I want to solve for "x" such that "f==0":

x = sym('x', [T,1]);

f = -x+1-(1+erf((a - B*x)./sqrt(2)))/2; % -x+1-normcdf(a-B*x)
Spp = solve(f==0, x);

I use Matlab's solve (or vpasolve) functions to obtain values. If the entries of "B" are above a certain value I should observe a jump for changing values of "a" (which I do). However, depending on the initial guess of the solution, i.e. for example either the initial guess is 1 or 0, the position of the jump occurs at different values for "a", a hysteresis cycle occurs.

I solved the equation using fzero for T=1. I specified the initial guess and indeed was able to observe the hysteresis cycle. For T>1, fzero does not work anymore and I tried solve as well as vpasolve. solve does not allow initial guesses and for vpasolve I even get with examples from Matlab's help site an error whenever I include more than the system of equations and the unknown variables, i.e. vpasolve(eqn,var) works fine but for vpasolve(eqn,var,init_guess) I get the following error:

Error using getEqnsVars (line 50) Expecting two arguments: a vector of equations and a vector of variables.

Error in sym/vpasolve (line 91) [eqns,vars] = getEqnsVars(varargin{1:end-1});

What am I doing wrong? Is there another function I could try?

Edit: I didn't use 'fsolve' but 'fzero' to find the roots.

1
matlabnumerical-methods

1 Answers

0
votes

You can use slightly different definition of function f and try fsolve. Here you don't have to explicitly define x as symbolic variables. 

f = @(x) -x+1-(1+erf((a - B*x)./sqrt(2)))/2; % -x+1-normcdf(a-B*x)
initial_guess = zeros(T,1);
Spp = fsolve(f,initial_guess);