How can I use fmisearch() to evaluate the parameters in a matrix?
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I have the following equation:
f(t)=integral(g(t,x)*h(x) dx)
I discretized the problems because the symbolic expression can't be evaluate (too complicated), so:
where:
f(t) is a vector length=n;
g(t,x) is a matrix n rows and m columns;
h(x) should be a vector length=m. However it depends on 3 parameters.
I want to determine those 3 parameters such that f(t)-integral()=0.
If the 3 parameters are known I use trapz or Simpson method to evaluate the integral.
Do you know a method to apply fminsearch() to evaluate the 3 parameters?
Thank you in advance
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Star Strider
2021-4-30
If the objective is to determine the parameter at a zero-crossing (root), use fsolve or fzero, not fminsearch.
Try something like this —
g = @(t,x) sin(2*pi*x.*t); % Create Function
h = @(x) exp(x); % Create Function
a = -5; % Define Lower Integration Limit
b = +5; % Define Upper Integration Limit
f = @(t) integral(@(x)g(t,x).*h(x), a, b) % Integral Funciton Call (Objective Fucntion)
[T,Fval] = fsolve(f, 42) % Estimate Parameter
.
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Star Strider
2021-5-1
As always, my pleasure!
Even with the revisions, I cannot get it to even come remotely close to fitting ‘G’. If the code is correct, there could be a problems with the constant values or magnitudes.
For the record, the current code is —
G0N=2E5;
Me=18500;
M_star=160000;
k_tdd=1.05E-15;
k_rouse=2E-12;
beta=2.3;
% syms I t mw M0 a b
digits(5)
x = @(t,mw) t./(M_star*k_tdd*(mw.^2));
gx = @(t,mw) -x(t,mw)+sqrt(x(t,mw)).*sqrt(x(t,mw)+(sqrt(pi*x(t,mw)))+pi);
U = @(t,mw) ((1./k_tdd).*(1./(mw.^3)).*t)+(M_star.*gx(t,mw)./mw);
F_sr = @(t,mw) (8/pi^2)*integral(@(I) 1./((2*I-1).^2) .* exp(-(2*I-1).^2 .* U(t,mw)), 1, inf, 'ArrayValued',1);
wGEX = @(mw,M0,a,b) 1.9*(((mw./M0).^(a+1)).*exp(-(mw/M0).^b));
w = @(mw,M0,a,b) wGEX(mw,M0,a,b)./mw;
F_w = @(t,mw,M0,a,b) F_sr(t,mw).*w(mw,M0,a,b);
G = @(t,M0,a,b) integral(@(mw)F_w(t,mw,M0,a,b), 0, inf, 'ArrayValued',1);
G_fcn = @(t,M0,a,b) G0N.*(G(t,M0,a,b)).^beta;
t = [100 50 25 10 5 2.63 1.03 0.526 0.244 0.0991 0.0516 0.0251 0.00996 0.00495 0.00252 0.001 ];
G = [124 879 6110 31900 64000 94400 131000 151000 169000 184000 193000 201000 209000 215000 235000 303000 ];
G_fcnp = @(p,t) G_fcn(t,p(1),p(2),p(3));
ObjFcn = @(p) norm(G - G_fcnp(p,t))
% n_exp = numel(t);
% ObjFcn = @(p) (1./n_exp).*sum(((G -G_fcnp(p,t)).^2)./(G.^2));
P0=[10 3 200000];
ms = MultiStart;
problem = createOptimProblem('fmincon', 'x0',P0, 'objective',ObjFcn);
P = run(ms,problem,250)
% [P,resnorm] = lsqcurvefit(G_fcnp, randn(3,1), t, G)
G_out = G_fcnp(P,t)
figure
plot(t, G, 'p')
hold on
plot(t, G_fcnp(P,t), '-r')
hold off
grid
The estimates for the parameters are —
P =
336.9743 48.8744 369.3595
It does not converge to a successful result with either version of ‘ObjFcn’.
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