Finding Minimum value of an anonymous function using fminbnd

Hi,

I am trying to find the minimum value of my anonyus function G, which depends on the variable na. I am getting the error "User supplied obective function mus return a scalar value" when I try to run my code. From some debugging, I can see that if I type G(0) in the command line, I get a 1X1000 double that is just the correct value for G(na=0), but repeated 1000 times. Can anyone help me fix this? Thanks for any advice, I've never posted on here before.

clear all
% Given :                   
R = 1.987;  %[cal/mol*K]
T = 500;    %[K]
G0 = -1000;  %[cal/mol]

%% Find values to plot G vs. E


% Calulate na for a  bunch of E:
    % E: [0,1]
E = linspace(0,1,1000);  % get 1000 evenly spaced values of E between 0 and 1
na = (.5.*(1-E));           % CHANGE THIS FOR THE EQUATION IN THE PROBLEM

% Calculate G-(ua/2)-(ub/2)

A = (1-(2.*na));  % define this bc it gets used a lot below
G = @(na) ((A.*G0)+((R*T).*((2.*na.*log(na))+(A.*log(A)))));

% plot it
figure();
plot(E, G(na))
title('Free Energy of System, G');
ylabel('G [cal/mol]'); xlabel('E');

% find minimum G value (equilbrium)
[na_min, Gmin] = fminbnd(G,na(end), na(2))

Answer 1

[Bruno Luong]

You should not mix between discrete sampling of your function G and continuous evaluation required by FMINBND

% Given :                   
R = 1.987;  %[cal/mol*K]
T = 500;    %[K]
G0 = -1000;  %[cal/mol]

%% Find values to plot G vs. E


% Calulate na for a  bunch of E:
    % E: [0,1]
E = linspace(0,1,1000);  % get 1000 evenly spaced values of E between 0 and 1
na = (.5.*(1-E));           % CHANGE THIS FOR THE EQUATION IN THE PROBLEM

% Calculate G-(ua/2)-(ub/2)

A = @(na) (1-(2.*na));  % define this bc it gets used a lot below
G = @(na) ((A(na).*G0)+((R*T).*((2.*na.*log(na))+(A(na).*log(A(na))))));


% find minimum G value (equilbrium)
[na_min, Gmin] = fminbnd(G,na(end), na(2))
Emin = 1 - na_min/0.5 % recover corresponding energy

figure();
plot(E, G(na),'b',Emin,Gmin,'+r')
title('Free Energy of System, G');
ylabel('G [cal/mol]'); xlabel('E');

[Emily Davenport]

Hi Bruno,

Thank you for your help. That makes much more sense now, I had never encoutnered fminbnd before.

Answer 2

[Alan Stevens]

You don't need fminbnd to find the minimum of G. Just

min(G(na))

will do it (or am I missing something?).