MATLAB: I want plot these three function but…

plot

    xb = linspace(0,1);
    ub =- 1.654e-9*xb^24 - 3.277e-9*xb^23 - 8.551e-9*xb^22 - 1.629e-8*xb^21 - 4.667e-8*xb^20 - 8.351e-8*xb^19 - 2.739e-7*xb^18 - 4.503e-7*xb^17 - 1.774e-6*xb^16 - 2.997e-6*xb^15 - 1.047e-5*xb^14 - 3.428e-5*xb^13 + 0.0005502*xb^12 + 0.006917*xb^11 - 0.02256*xb^10 - 0.1796*xb^9 + 0.1328*xb^8 + 1.242*xb^7 - 0.2103*xb^6 - 3.288*xb^5 - 0.03086*xb^4 + 2.845*xb^3 + 0.1762*xb^2 + xb
h =1.084e-10*xb^24 + 2.913e-10*xb^23 + 5.82e-10*xb^22 + 1.702e-9*xb^21 + 3.313e-9*xb^20 + 1.067e-8*xb^19 + 2.383e-8*xb^18 + 6.368e-8*xb^17 + 4.368e-7*xb^16 - 4.523e-6*xb^15 - 4.935e-5*xb^14 + 3.007e-5*xb^13 + 0.00044*xb^12 + 0.001541*xb^11 + 0.007978*xb^10 - 0.01332*xb^9 - 0.1013*xb^8 + 0.03164*xb^7 + 0.3714*xb^6 - 0.01464*xb^5 - 0.3494*xb^4 + 0.06627*xb^3 - 0.4087*xb^2 + 0.4678*xb
p =- 2.291e-9*xb^24 - 4.735e-9*xb^23 - 1.5e-8*xb^22 - 2.869e-8*xb^21 - 1.056e-7*xb^20 - 1.678e-7*xb^19 - 7.968e-7*xb^18 - 5.587e-7*xb^17 - 6.405e-6*xb^16 + 1.66e-5*xb^15 - 8.231e-5*xb^14 + 0.001329*xb^13 - 0.01798*xb^12 - 0.1518*xb^11 + 0.1903*xb^10 + 1.909*xb^9 - 0.5747*xb^8 - 9.41*xb^7 + 0.2686*xb^6 + 22.1*xb^5 + 0.5245*xb^4 - 36.49*xb^3 + 0.5638*xb^2 + 47.27*xb
  figure
  plot(xb,ub,'-b',xb,h,'--r',xb, p,'-..k')

Best Answer

Ali, you need to use dot-operations...

 ub = - 1.654e-9*xb.^24 - 3.277e-9*xb.^23

since xb is a vector (notice the dots in front of the ^ ) and so on and so forth.

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MATLAB: Failure of do loop after first step when applying globalsearch to a nonlinear least squares problem

Dear All,

There was a simple solution.

I replaced:

for i = 1:100
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for i = 1:100
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MATLAB: Fitting Monod Equation with ODE45 to data using lsqcurvefit function

Here's my solution.

First set up the measured data, plot it, and look to see that it is all OK.

t = [0 3 5 8 9.5 11.5 14 16 18 20 25 27]' 
x = [0.0904 0.1503 0.2407 0.3864 0.5201 0.6667 0.8159 0.9979 1.0673 1.1224 1.1512 1.2093]'; 
s = [9.0115 8.8088 7.9229 7.2668 5.3347 4.911 3.5354 1.4041 0 0 0 0]';
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No problems there. Note that the measured data is in columns.

Now, we need a function to export the predicted measurements as a function of the unknown parameters and initial conditions. My function is:

function ypred = paramfun1(p,t)
umax = p(1); ks = p(2); Yxs = p(3); Yps = p(4); % use disperse here ...
xt0 = p(5:7); % initial conditions 
f = @(t,a) [umax*a(1)*a(2)/(ks + a(2)); ... 
            -(1/Yxs)*umax*a(1)*a(2)/(ks + a(2)); ...
            (1/Yps)*umax*a(1)*a(2)/(ks + a(2))];
[~,ypred] = ode45(f,t,xt0);
end

May I suggest that you think about naming your functions sensible names. Also it is more elegant to use disperse (from the user's group) here.

Now we are ready to test it, and make sure our output is the same shape as the actual data.

xt0 = [0.1;9;0.1]; % read off from data plot [x0 ,S0, p0]';   
p0 = [umax; ks; Yxs; Yps; xt0] 
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Now we are ready for the fit. I'm using your initial conditions, and we can get reasonable start values from the data.

pfit = lsqcurvefit(@paramfun1,p0,t,[x,s,p])

Now plot the fitted curve and the actual data. They should line up.

umax = pfit(1);  ks = pfit(2);Yxs = pfit(3); Yps = pfit(4);
f = @(t,a) [umax*a(1)*a(2)/(ks + a(2)); -(1/Yxs)*umax*a(1)*a(2)/(ks + a(2)); (1/Yps)*umax*a(1)*a(2)/(ks + a(2))];
xt0 = pfit(5:7); 
[tspan,a] = ode45(f,[0 25],xt0);    
plot(tspan,a(:,1),tspan,a(:,2),tspan,a(:,3), '-', ...
     t,x,'o',t,s,'+',t,p,'s')

Plot shows the regressed fit is not too bad:

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