Hi Matlab experts,
I am trying to solve a system of highly nonlinear equations below: f(x) = .01*(2*(1.04+x).^(-4.8).*(.1+x).^(-1.9)+(1.04+x).^(-3.8).*(.1+x).^(-2.9)).*A-3*B; where both A and B are vectors, say of size 100 by 1.
I tried to solve this nonlinear equation by fsolve and I run into 3 issues: 1) the results from using fsolve in vector form (solve all equations in one go) are different from in scalar form (each time solve one equation) 2) I got complex results, no matter what starting values I tried, particularly in vector form (almost all x estimated are complex). Results from the 3 procedures are different too! 3) when I try to solve the nonlinear problem equation by equation, I get exitflag = 2 for some equations, is the result with exitflag = 2 correct? In this case I also try different starting values and it does not work.
I add in 'JacobPattern' in options as suggested by one of your colleague but it does not seem to help much.
Thank you so much for your help!
Below is my matlab codes:
////////////////////////////////////////////////////////////////////////////////////////////
function main()
% assign values for B and A (skipped here)
........
% Solve nonlinear equations one by one%
options=optimset('Display','off');
sb = length(B);
for i = 1:sb
fmiu = @(x)miu(B(i),A(i),x);
[xs(i,1),fval(i,1),exitflag(i,1)] = fsolve(@(x)fmiu(x),.05,options);
while exitflag(i,1) <= 0
[xs(i,1),fval(i,1),exitflag(i,1)] = fsolve(@(x)fmiu(x),rand(1)*.1,options);
end
end
if sum(xs ~= real(xs)) disp('!!!Warning: xs is complex!!!'); mu end
[xs mu]
% solve nonlinear equations in one go - vector form%
options = optimset('Display', 'notify', 'JacobPattern', speye(sb));
fx = @(x)miu(B,A,x);
[xz, fval, exitflag] = fsolve(@(x)fx(x),rand(sb,1), options);
function fun = miu(B,A,x)
fun = .01*(2*(1.04+x).^(-4.8).*(.1+x).^(-1.9)+(1.04+x).^(-3.8).*(.1+x).^(-2.9)).*A-3*B;
end
end
