How do I perform regression and impose a constraint on the regression function using the Statistics toolbox in MATLAB 7.13 (R2011b)?

I want to perform regression on a set of X and Y data, but I want to constrain the function f in some way; for instance, to insure that the regression satisfies y0=f(x0) for a specified point (x0,y0). How do I do this in MATLAB 7.13 (R2011b)?

Answer 1

[MathWorks Support Team]

You can do this using the FMINCON function in the Optimization Toolbox. As an example, you can try to fit the curve f(x)=m*x+b with the constraint that f(1)=2. The steps you will need to use are:

1) Write a function which computes the error in the fit given vectors of coefficients and the X-Y data. A small example of such a function is:

function error=myfun(coeff,x,y)

m=coeff(1);b=coeff(2);

error=sum((m*x+b-y).^2);

% Taking the sum of the squares of the residuals to minimize

2) Write a constraint function, such as:

function [ineq,eq]=mycon(coeff,x,y)

m=coeff(1);b=coeff(2);

x0=1;y0=2;

% We want the curve to pass through (1,2)

ineq=0;

% Nonlinear inequality constraint

eq=abs(m*x0+b-y0);

% Linear inequality constraint

The EQ value is the difference between the function value at x0 (m*x0+b) and the value you want the function to have at x0.

3) Choose initial guesses for the coefficients and generate the data:

ic=[1 1];

% Initial coefficient guesses

xdata=1:10;

ydata=5*xdata-3+rand(size(xdata));

% Generate slightly noisy x and y data

4) Call FMINCON.

MyCoeffs=fmincon(@myfun,ic,[],[],[],[],[],[],@mycon,[],xdata,ydata);