Difficulty in fitting two lines with polynomials

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Deepesh upadrashta
Deepesh upadrashta 2014-12-1
编辑： dpb 2014-12-3
Hi, I want to fit data which resembles two piecewise linear functions using polynomials.
Y=30000X for X<=0.001;
Y=27+3000X for 0.001<X<0.003.
When I use polyfit or cftool, the fitted curve has ups and downs (change of sign in curvature) which I don't want. I'm getting smooth curve when I use polynomials of the order 20 which is really high.
I would prefer a fitted curve without change in sign of curvature even at the expense of some accuracy (with lower orders of polynomials).
How can I do it?
Thanks, Deepesh.
  1 个评论
Image Analyst
Image Analyst 2014-12-3
Attach your data (so we can try things with it) and attach a screenshot so we can see what you're seeing.

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回答（2 个）

dpb
dpb 2014-12-3
编辑：dpb 2014-12-3
Piecewise linear regression is fairly easy to code anyway...the algebra to add the condition to match the two at the breakpoint is
y = a1 + b1 x, x<=c,
y = a2 + b2 x, x>c.
Match breakpoint, or a1 + b1 c = a2 + b2 c. Rearrange this to isolate (say) a2 as
a2 = a1 + b1 c - b2 c --> a1 + c(b1-b2) = aprime
Now have
y = a1 + b1 x, x<=c,
y = aprime + b2 x, x>c.
This is easy-peasy to code in Matlab and use as target for nlinfit --
function y=piecewise(coef,x)
% return piecewise linear fit given a1,b1,c,b2 as coefficient array and vector x
% c is breakpoint, a1 is intercept of first section, b1,b2 are two segment slopes
a1=coef(1); b1=coef(2); % reduce parentheses clutter....
c=coef(3); b2=coef(4);
ix=x>c; % location > breakpoint
y(ix)=[a1+c*(b1-b2)+b2*x(ix)];
y(~ix)=[a1+b1*x(~ix)];
y=y(:);
Use this as
coeff=nlinfit(X,Y,@piecewise,coeff0);
Example: for Hayden dataset
www.fs.usda.gov/rds/fedora/objects/RDS:RDS-2007-0004/datastreams/RDS-2007-0004/content
>> coeff=nlinfit(X,Y,@piecewise,[0 .01 1.5 0.1])
coeff =
-0.0077 0.0155 1.6804 0.1067
>>
dpb
dpb 2014-12-1
  2 个评论
Deepesh upadrashta
Deepesh upadrashta 2014-12-3
HI,
My problem is approximating two piecewise lines with polynomial.
After reading SLM help, I don't think it can do that. It is able to fit the data with polynomials upto 3 degree between knots. Thanks.
dpb
dpb 2014-12-3
A cubic spline is a polynomial, just a particular form of one... :)
It would appear that the other link is a linear piecewise polynomial w/ specified knot location.
Do you want/need continuous first/second derivatives or simply only two slopes?

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