error message using polyfit (nonlinear regression)
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hi,
I get the following error meesage using the polyfit function:
Warning: Polynomial is badly conditioned. Add points with distinct X
values, reduce the degree of the polynomial, or try centering
and scaling as described in HELP POLYFIT.
Has anybody see that before and has an idea what I need to do? I tried it with the help function, but I didn't understand what excatly could be false
the code I am using if the following, in case it helps:
if length(dataT(:,1))==1
SlopeSkew(number)=0;
elseif length(dataT(:,1))==2
SlopeSkew(number)=0;
else
% x is the Strike
x= dataT(:,2);
%is the implied volatility
y=dataT(:,10);
p = polyfit(x,y,2);
f = polyval(p,x);
thanks!
a=p(3);
b=p(2);
c=p(1);
SlopeSkew(number)=b+2*c.*x;
Slope=SlopeSkew';
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채택된 답변
Image Analyst
2013년 4월 21일
So what is the length of x and y, and do you have any repeated x values?
댓글 수: 4
Image Analyst
2013년 4월 21일
If you have two Y values for the same x value, then it doesn't like that and will complain. All your x values have to be unique. You can use
uniqueX = unique(x)
and see if length(uniqueX) is the same length as length(x). If they're the same then there are no repeats. If unique() returns a shorter vector, then at least one x value is repeated and you need to decide how to handle that. You might be able to just add a very small amount to one of the x's, like 0.000001, just to make sure they are not the same anymore.
추가 답변 (2개)
Tom Lane
2013년 4월 22일
There was a time when this function issued an error asking you not to have repeated X values. But the new error message is more accurate. You don't need unique X values. It's just that repeated X values won't allow you to estimate higher-order polynomials. So for instance:
x = [1;2;3;3;4];
y = (1:5)';
polyfit(x,y,2)
polyfit(x,y,4)
The first call to polyfit works. The second would work if we had 5 points with distinct X values, but it doesn't work here because the 4 distinct X values allow polynomials only up to an exponent of 3.
In your example of fitting up to power 2, it seems like you either don't have 3 distinct points, or you have very ill-conditioned data.
댓글 수: 2
Tom Lane
2013년 4월 23일
I don't know exactly. Of the following three, the first one works. The second does not because there are only two distinct x values. The third does not because it is very ill-conditioned.
polyfit([0;1;2],[10;20;30],2);
polyfit([0;1;1],[10;20;30],2);
polyfit([0;eps;1],[10;20;30],2);
I don't know what the issue is in your case. Try to boil this down to a specific call to polyfit, then examine the x and y values in that call and see how they look.
Jan
2013년 4월 23일
Instead of repeated values, did you test the condition of the problem already? The docs suggest to use
[p, S, mu] = polyfit(x,y,n)
for a proper scaling. The matrix for the least-squares fit is ill-conditioned, when the values of x have a wide range and are far away from zero. Therefore the scaling does:
xx = (x - mean(x)) / std(x)
to get all data near to zero. The conversion back to the original values in POLIVAL is trivial.
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