How do I make a fitting function with the fitting coefficient for x-data?
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Hi.
I am trying to fit the experimental data to the mastercurve we have.
I have set of "xdata".
Let's say I have [0,1,2,3,4,5].
Then, the master curve is the function of xdata.
Let's say master = (xdata)^2.
Here, I also have ydata that corresponds to the xdata from the experiment.
My whole set of data are
xdata = [0,1,2,3,4,5]
ydata = [0,1,2,3,4,5]
Here, I want to have a fitting coefficient multiplied on "xdata" to fit the ydata into mastercurve.
Which means, I will have new plot of ydata vs C*xdata and mastercurve as a function of C*xdata.
I tried to write out a fitting function but confused about the setting since the input parameter is changing for both raw data set and mastercurve. (I tried to use lsqcurvefit but xdata is changing so I am confused.)
Can anyone help me on this?
I also want to obtain a R-squared value out of it.
Thank you very much!
- Sean
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Joe Goddard
2018-6-25
I can provide a recently written Matlab program to estimate a master curve using fmincon. Joe Goddard jgoddard@ucsd.edu
采纳的回答
For a single coefficient, it's as simple as,
C=((xdata(:)).^2)\ydata(:);
5 个评论
Joe Goddard
2018-6-25
I believe a derivation is in order. This does not seem to agree with a rigorously derived formula for finding shift factors for a master curve of y vs x.
John D'Errico
2018-6-25
@Joe - actually, it does. This is the correct answer. There is no need to use fmincon either.
@Joe- I'm not sure how I could "derive" it when my answer consists only of a function call. A\b is a Matlab command which invokes a least squares solver for linear equations A*x=b. I have simply applied it here with the substitutions,
A=xdata(:).^2
b=ydata(:)
x=C
Joe Goddard
2018-6-26
You have provided a numerical formula without a mathematical derivation to back it up. To obtain a "best fit" to the scale factors necessary to reduce a set of curves to a master curve is not a trivial matter. If this is not what you are trying to do, then we are talking past one another. JG
My best interpretation of what the OP was trying to do is to find the scalar C that minimizes
f(C) = norm( C*xdata(:).^2 -ydata(:) )^2
If that much is true, then the solution is trivially given by what I posted.
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