To solve a problem of this type using Optimization Toolbox 3.0 (R14), you must create a function that takes as its input the value of "x", and then numerically computes the value of "y" by calling the FSOLVE function.
For the example:
y = A*(x0-x) - B*log(y/y0) + y0;
Your function could resemble the following:
function yout = myImplicitF(x, AB)
x0 = 0.01;
y0 = 0.01;
A=AB(1);
B=AB(2);
yout = zeros(size(x));
opt = optimset('display','off');
for i=1:length(x)
yout(i) = fsolve(@(y) x(i)- (x0-(y+B*log(y/y0)+y0)/A), .1, opt);
end
The FOR loop is used to allow the function to handle vector inputs for "x". For more information about FSOLVE, type the following at the MATLAB command prompt:
doc fsolve
This function can now be treated as an explicit function of "x". For example, it can be plotted as follows:
ezplot(@(x)myImplicitF(x,[1 1]),[-5 1])
The above statement plots the curve over the range [-5, 1], for "A" and "B" parameters equal to 1.
Suppose you have some measured data, for example:
x = -5:.1:1;
y = myImplicitF(x,[1 1]) + randn(size(x))/100;
The function can be used in curve fitting functions such as LSQCURVEFIT as follows:
lsqcurvefit(@(params, xdata) myImplicitF(xdata,params),[0.1 0.1], x, y)
