Non-linear least squares fit forced through a point

Sometimes you want a least-squares polynomial fit to data but to constrain it so it passes through a certain point. Well ... Inputs: x, y (data); x0 and y0 are the coordinates of the point you want it to pass through, and n is the degree of polynomial

	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) );

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