Maxima of a function using fminbnd

I want to find the maximum of lambda for a function M(lambda,T), describing the radiation, for fixed values of T using the method fminbnd. Basically it is a well-known formula for radiation and I want to know if there is some obvious things that are wrong. So, I red through the help section and came up with this:

 %
T1=3000; %Define parameter
T2=4000;
T3=5000;
fminbnd(@(lambda)planck(lambda,T1),0,1e-5)%Second bound is chosen arbitrary
fminbnd(@(lambda)planck(lambda,T1),0,1e-5)
fminbnd(@(lambda)planck(lambda,T1),0,1e-5)

All gives the same output..which is clearly wrong.

The function is defined by

%
function M=planck(lambda,T)
h=6.6256e-34; 
c=2.9979e8;   
k=1.3805e-23; 
a=2*pi*h*c^2;
b=h*c/k./lambda./T;
M=-a./lambda.^5./(exp(b)-1); %I put a minus sign since I want to minimize the negative function

Answer 1

[Alan Weiss]

The problem is you are running into some scaling issues. Try scaling your problem so that the value of lambda is between 0 and 1.

 scaledplanck = @(x,lambda)planck(x*1e-5,lambda);
 fminbnd(@(lambda)scaledplanck(lambda,T1),0,1)
 fminbnd(@(lambda)scaledplanck(lambda,T2),0,1)
 fminbnd(@(lambda)scaledplanck(lambda,T3),0,1)

Alan Weiss

MATLAB mathematical toolbox documentation

[Snirisa Gödel]

Thank you. How did you see that? And when do they occur? (In case I'll run into it again in the future)

[Alan Weiss]

I suspected it from the start, but I saw it by plotting the functions for various values of T, and saw that fminbnd was not giving a correct answer.

There are various stopping criteria for optimization solvers, and one is called TolX, which stops the solver when steps are too small. This tolerance applies to fminbnd, and I believe that is why fminbnd stopped too soon.

Alan Weiss

MATLAB mathematical toolbox documentation