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From: Alex Berkovich on 6 May 2008 09:03
Hello,

Is there a function like 'polyfit' but one that can make
sure that the resulting curve passes through certain
points or points?

Thank you very much
Alex
From: John D'Errico on 6 May 2008 09:52
"Alex Berkovich" <alexber(a)tx.technion> wrote in message
<fvpku7$11a$1(a)fred.mathworks.com>...
> Is there a function like 'polyfit' but one that can make
> sure that the resulting curve passes through certain
> points or points?

Its trivial to do with lsqlin, so if you have
the optimization toolbox, then no problem.

If not, then its is as trivial to use my lse code,
as found on the file exchange.

http://www.mathworks.com/matlabcentral/fileexchange/loadFile.do?
objectId=13835&objectType=FILE

For example:

x = randn(20,1);
err = randn(size(x))/10;
y = 1 - x + x.^2 + err;

% simple polyfit, unconstrained
p0 = polyfit(x,y,2)
p0 =
0.97807 -1.0345 0.98762

% Note that at x = 0.5, we know this curve
% must pass through y = 0.75. polyfit was
% close, but not exact.
polyval(p0,0.5)
ans =
0.71487

xf = 0.5;
Aeq = [xf.^2,xf,1];
Beq = 0.75;

% using lse, we get
pf = lse([x.^2,x,ones(size(x))],y,Aeq,Beq)
pf =
0.9844
-1.0087
1.0083

polyval(pf,0.5)
ans =
0.75

HTH,
John
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