Solving a system of 5 nonlinear equations in Matlab - matlab

Question

I'm having difficulty using the fsolve function to solve a set of 5 equations in Matlab.
Here are the 5 equations:
y = a + d + e
y + x = c + d + 2e
2x = 4a + 2b + 2c
k1 = (d * b^3 / (a * c) ) * ((P/Pref)/(a+b+c+d+e))^2
k2 = be/(dc)
y,x,k1,k2,P,Pref are all parameters that I set, but would like to leave them in the function so that I can change them quickly in my code to find new answers. a,b,c,d,e are the variables that I'd like to solve for (they are compositions of a reaction equilibrium equation)
I tried to hard code the parameters in the function, but that didn't work. I'm just not sure what to do. Every thing I change creates a new error. The most common is that the data type has to be "double".
Edit: adding code
first the function:
function F = myfun(Q,I)
a = Q(1);
b = Q(2);
c = Q(3);
d = Q(4);
e = Q(5);
x = I(1);
y = I(2);
k1 = I(3);
k2 = I(4);
P = I(5);
Pref = I(6);
F(1) = a + d + e - y;
F(2) = c + d + 2*e - y - x;
F(3) = 4*a + 2*b + 2*c - 2*x;
F(4) = ((d * b^3)/(a*c))*((P/Pref)/(a+b+c+d+e))^2 - k1;
F(5) = (b*e)/(c*d);
next is the program:
%Q = [a,b,c,d,e]
%I = [x,y,k1,k2,P,Pref]
%The values for the inputs will be changed to vary the output
%Inputs:
x=5;
y=1;
k1=5;
Pref=1;
P=1;
k2=-0.01;
syms K
k1 = solve(log10(k1) - k1);
syms L
k2 = solve(log10(k2) - k2);
x = double(x);
y = double(y);
Pref = double(Pref);
P = double(P);
k1 = double(k1);
k2 = double(k2);
%Solving:
I = [x,y,k1,k2,P,Pref];
q = [0,0,0,0,0]; %initial guess
Q = fsolve(#myfun,[q,I])
when I run this, these errors comes up:
Error using myfun (line 7)
Not enough input arguments.
Error in fsolve (line 218)
fuser = feval(funfcn{3},x,varargin{:});
Error in Coal (line 27)
Q = fsolve(#myfun,[q,I])
Caused by:
Failure in initial user-supplied objective function evaluation. FSOLVE cannot continue.
Edit 2: changed the fsolve line, but still got errors:
Error using trustnleqn (line 28)
Objective function is returning undefined values at initial point. FSOLVE cannot continue.
Error in fsolve (line 376)
[x,FVAL,JACOB,EXITFLAG,OUTPUT,msgData]=...
Error in Coal (line 27)
fsolve(#(q) myfun(q,I),q)
Edit3: changed a couple parameters and the initial guess, I am now getting an answer, but it also comes up with this:
Solver stopped prematurely.
fsolve stopped because it exceeded the function evaluation limit,
options.MaxFunEvals = 500 (the default value).
ans =
0.0000 2.2174 3.7473 1.4401 3.8845
how can I get it to not stop prematurely?

Answer 1

Re: how can I get it to not stop prematurely?
Pass non-default options in your call to fsolve.
Refer to the signature, fsolve(myfun,q,options) here,
http://www.mathworks.com/help/optim/ug/fsolve.html
And read about creating the options using optimoptions here,
http://www.mathworks.com/help/optim/ug/optimoptions.html
You should be able to get it to "not stop prematurely" by increasing the values of convergence criteria such as TolFun and TolX.
However, it's advisable to read up on the underlying algorithms you're relying upon to perform this numerical solution here,
(EDIT: I tried to fix non-linky links, but I'm not allowed to provide more than two ... Boo) www.mathworks.com/help/optim/ug/fsolve.html#moreabout
The error you received simply indicates that after 500 function evaluations the algorithm has not yet converged on an acceptable solution conforming to the default solver options. Just increasing MaxFunEvals may allow the algorithm extra iterations needed to converge within default tolerances. For example,
options = optimoptions('MaxFunEvals',1000); % try something bigger than 500
fsolve(#(q) myfun(q,I),q,options);