MATLAB: Parameter estimation of predefined function

predefine function paramater estimation

Hi everyone, I have a function defined as following:

I'd would like to know if there is a Matlab function that can estimate these two parameters given a set of values of (x,y).

With kind regards,

Winn

Best Answer

There is lsqcurvefit in the Optimization Toolbox and nlinfit in the Statistics Toolbox. If you have neither, there is fminspleas ( Download ). The latter could be useful, because your model is loglinear in beta

   log(E)-log(1-y) = beta*f(x,alpha)

which fminspleas can advantage of. In particular, fitting log(E)-log(1-y) with fminspleas only requires a good initial guess for alpha. The solution fminspleas gives you for both alpha and beta can then be used as initial guesses in a more refined fit.

Related Solutions

MATLAB: How to do non-linear fitting on a model defined implicitly

1. Using "nlinfit"

The "nlinfit" function expects a response vector "Y" and a function of unknown parameters. Simply encapsulate the implicit model in a function of the form:

       0 = y - model(x,y,beta)

The response vector to be passed to "nlinfit" becomes

       Y = zeros(size(y));

The new predictor array now contains both the old predictor variables and the old responses packed together in one array:

       X = [x,y];

and the new model is specified by the anonymous function

       modelfun = @(beta,X) ( X(:,2) - model(X(:,1),X(:,2),beta) );

where "model" is the implicit model with inputs "x" and "y", output "y", and parameterized by the (unknown) parameter vector "beta".

Finally, use "nlinfit" with an initial guess "beta0" as follows:

       beta = nlinfit(X,Y,modelfun,beta0)

2. Using "lsqnonlin"

Alternatively, you could achieve the same results with the "lsqnonlin" function of the Optimization Toolbox.

The "lsqnonlin" function tries to solve a least-squares equation of the form

       min_x { f_1(x)^2 + f_2(x)^2 + ... + f_n(x)^2 }

for an unknown vector "x".

In the case of fitting an implicit model, the vector "x" would be the vector of unknown parameters "beta" of the implicit model and f_i(x) would be:

       f_i(beta) = y_i - model(x_i,y_i,beta)

where "X=[x_i]" are the predictors and "Y=[y_i]" are the responses used to fit the model.

However, "lsqnonlin" takes as input argument a handle to a function of only 1 argument (the parameters). You would have to pass extra parameters (in this case, the predictors and responses) by using an anonymous function. Assume your implicit model is defined in a function file called "model". Then, "modelfun" is a handle to an anonymous function defined as:

       modelfun = @(beta) ( Y - model(X,Y,beta) );

where "Y" is the vector of responses, "X" is the vector of predictors, and "beta" is the vector of unknown parameters.

With an initial guess "beta0", call "lsqnonlin" as follows:

       beta = lsqnonlin(modelfun,beta0)

MATLAB: How to plot this implicit function

Try symbolic expression

clc,clear
alpha=1.5; A=0.0207; gamma=0.25;
syms beta eps
x = (beta-alpha*(beta-gamma)+sqrt((beta-alpha*(beta-gamma)).^2+4*alpha*beta*gamma*A))./(2*beta);
y =  x.*(1-x).*beta/gamma;
t =  -x+x.*y.*(alpha-eps*beta)./((A+x+y).^2);
d =  eps*beta.*x.*y.*(x.^2+(A+x).*x+A*alpha)./((A+x+y).^3);
    % convert symbolic expression to function handle
F = matlabFunction(t.^2 - d,'vars',[beta eps]);
ezplot(F,[0,1,0,1]);

Best Answer

Related Solutions

MATLAB: How to do non-linear fitting on a model defined implicitly

MATLAB: How to plot this implicit function

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