Nonlinear least squares through a point

nonlinlstsq.m

function [p,yhat] = lsq_fit_nonlin_force_thru_point(x,y,x0,y0,n);  

 x = x(:); %reshape the data into a column vector  
 y = y(:);  
 % 'C' is the Vandermonde matrix for 'x'  
 V(:,n+1) = ones(length(x),1,class(x));  
 for j = n:-1:1  
 V(:,j) = x.*V(:,j+1);  
 end  
 C = V;  
 % 'd' is the vector of target values, 'y'.  
 d = y;  
 %%  
 % There are no inequality constraints in this case, i.e.,  
 A = [];  
 b = [];  
 %%  
 % We use linear equality constraints to force the curve to hit the required point. In  
 % this case, 'Aeq' is the Vandermoonde matrix for 'x0'  
 Aeq = x0.^(n:-1:0);  
 % and 'beq' is the value the curve should take at that point  
 beq = y0;  
 %%  
 p = lsqlin( C, d, A, b, Aeq, beq );  
 %%  
 % We can then use POLYVAL to evaluate the fitted curve  
 yhat = polyval( p, linspace(0,max(x),100) );