Posted by
Michael Schmid on
Mar 23, 2018; 6:00pm
URL: http://imagej.273.s1.nabble.com/fitting-y-f-x-data-to-arbitrary-functions-in-ImageJ-tp5020273p5020324.html
Hi Herbie, Fred,
oops, yes, I missed the 'abs'!
So one can't use the built-in version, and fitting certainly becomes tricky!
One should probably rewrite the problem as
y = a * (1 + b*exp(-x/c))
or, if the c parameter is known to be always positive, the following may
be better:
y = a * (1 + b*exp(-x/(c*c)))
Then, the pre-exponential factor has to be calculated as a*b.
Like this, the ImageJ CurveFitter can eliminate the factor 'a' as a
'multiplyParameter' via linear regression, and it becomes a
two-parameter fit.
If the data typically look like the example data, with a minimum where
the argument of the 'abs' passes through zero,
0.1 1123.175
0.25 838.206
0.5 469.32
0.75 453.003
1 725.135
1.25 1094.36
1.5 1450.741
1.75 1787.361
2 2128.119
5 4670.12
then one should take the minimum and find initial b and c values where
the function becomes zero at the minimum (here named xOfMin):
1 + b*exp(-xOfMin/c) = 0
or
b = -exp(xOfMin/c)
If there is no prior knowledge for c, this parameter might be taken
equal to the difference between the highest and lowest x value.
(For the second fit function with c*c, replace 'c' with 'c*c' everywhere.)
Michael
________________________________________________________________
On 23/03/2018 18:30, Herbie wrote:
> Sorry to intrude,
>
> but the function in question is
>
> Math.abs( p[1] + p[2]*Math.exp(-x/p[0]) )
>
> where the absolute value may make the situation more complicated.
>
> Best regards
>
> Herbie
>
> ::::::::::::::::::::::::::::::::::::::::
> Am 23.03.18 um 17:21 schrieb Fred Damen:
>> Greetings Michael,
>>
>> Thanks for the reply.
>>
>> I must have missed the NaN trick in the documentation.
>>
>> The fit function (UserFunction), is:
>> public double userFunction(double[] p, double x) {
>> return Math.abs( p[1] + p[2]*Math.exp(-x/p[0]) );
>> }
>>
>> which was in the example plugin below my signature, which includes
sample data
>> and plot for the fit mentioned in 2 and can produce the exception if the
>> variable 'ipv' is replaced with the null value.
>>
>> Note that without the call to setOffsetMultiplySlopeParams the fits are
>> acceptable almost all of the time, i.e., only about 10-20
apparently valid
>> datum fail with obnoxious results out of 40%*64x64 fits.
>>
>> My main interest in using the method setOffsetMultiplySlopeParams is
>> efficiency. Right now on a fast computer it takes about 2-5 seconds to
>> process a slice.
>>
>> Thanks,
>>
>> Fred
>>
>> On Fri, March 23, 2018 9:00 am, Michael Schmid wrote:
>>> Hi Fred,
>>>
>>> concerning (1), restricting parameter ranges:
>>> You can have a function that returns NaN if the parameter enters an
>>> invalid range. Then the CurveFitter will avoid this range.
>>> Convergence will be rather bad if the best fit lies very close to a
'NaN
>>> boundary', however.
>>>
>>> > On fits to some data the parameters returned are obnoxiously bad.
>>> What is the fit function? maybe I have some idea how to improve the
>>> situation.
>>>
>>> Concering (2) setOffsetMultiplySlopeParams:
>>> Parameter numbers that are not set should be -1. Note that 0 refers to
>>> parameter 'a', 1 to 'b', etc. Since you can specify only two out of the
>>> three arguments, at least one of (multiplyParam or slopeParam) them has
>>> to be -1.
>>> If you let me know the fit function, I can tell you the
>>> setOffsetMultiplySlopeParams call should look like.
>>>
>>> Concerning (3), NullPointerException:
>>> I'll have a look at it.
>>> Anyhow, if you have problems with the fit not converging properly, I
>>> would strongly suggest setting initial parameter that give at least the
>>> order of magnitude of the initial parameters. Better, specify also the
>>> initialParamVariations (e.g. for each parameter 1/10 of the range that
>>> it may have).
>>>
>>>
>>> Michael
>>> ________________________________________________________________
>>> On 22/03/2018 22:07, Fred Damen wrote:
>>>> Greetings,
>>>>
>>>> First, thanks for expounding on CurveFitter.
>>>>
>>>> I have a few questions and a bug.
>>>>
>>>> a) Is there any way to keep the fitting within a given range for each
>>>> parameter? On fits to some data the parameters returned are
obnoxiously
>>>> bad.
>>>> The input data resembles data that fits reasonably, i.e., I do not
suspect
>>>> that the initial parameters are outside the local minimum. This
is not
>>>> using
>>>> setOffsetMultiplySlopeParams.
>>>>
>>>> b) When using the method setOffsetMultiplySlopeParams and passing
a value to
>>>> doCustionFit's initialParamVariations parameter, set to what is
documented
>>>> as
>>>> the default value that would be used if null is passed, the fitting is
>>>> effectively a linear fit; see example below. A reasonable fit is
had if the
>>>> call to setOffsetMultiplySlopeParams is commented out. If this
worked what
>>>> kind of improvement would I expect to see in efficiency or
goodnees-of-fit?
>>>>
>>>> b) When using the method setOffsetMultiplySlopeParams and passing
a null
>>>> value
>>>> to doCustionFit's initialParamVariations parameter, a null pointer
exception
>>>> is thrown:
>>>> ImageJ 1.50h; Java 1.8.0_91 [64-bit]; Linux 4.5.5-300.fc24.x86_64;
287MB of
>>>> 1820MB (15%)
>>>>
>>>> java.lang.NullPointerException
>>>> at
>>>>
ij.measure.CurveFitter.modifyInitialParamsAndVariations(CurveFitter.java:835)
>>>> at ij.measure.CurveFitter.doFit(CurveFitter.java:178)
>>>> at ij.measure.CurveFitter.doCustomFit(CurveFitter.java:283)
>>>> at My_Plugin2.nonlinearFit(My_Plugin2.java:38)
>>>> at My_Plugin2.run(My_Plugin2.java:14)
>>>> at ij.plugin.PlugInExecuter.runCompiledPlugin(Compiler.java:318)
>>>> at ij.plugin.PlugInExecuter.run(Compiler.java:307)
>>>> at java.lang.Thread.run(Thread.java:745)
>>>>
>>>> Thanks in advance,
>>>>
>>>> Fred
>>>>
>>>> ----------------------------
>>>> import ij.*;
>>>> import ij.process.*;
>>>> import ij.gui.*;
>>>> import java.awt.*;
>>>> import ij.plugin.*;
>>>> import ij.plugin.frame.*;
>>>> import ij.measure.*;
>>>>
>>>> public class My_Plugin2 implements PlugIn {
>>>>
>>>> public void run(String arg) {
>>>> double[] x =
{0.10,0.25,0.50,0.75,1.00,1.25,1.50,1.75,2.00,5.00};
>>>> double[] y =
>>>>
{1123.175,838.206,469.320,453.003,725.135,1094.360,1450.741,1787.361,2128.119,4670.120};
>>>> double[] p = nonlinearFit(x,y);
>>>> Plot plot = new Plot("","x","y");
>>>> plot.setLineWidth(2);
>>>> plot.setColor(Color.black);
>>>> plot.addPoints(x,y,PlotWindow.X);
>>>> double[] y2 = new double[y.length];
>>>> for(int i=0; i<y.length; i++)
>>>> y2[i] = Math.abs( p[1] + p[2]*Math.exp(-x[i]/p[0]) );
>>>> plot.setColor(Color.blue);
>>>> plot.addPoints(x,y2,PlotWindow.LINE);
>>>> plot.show();
>>>>
>>>> }
>>>>
>>>> private double[] nonlinearFit(double[] x, double[] y) {
>>>>
>>>> CurveFitter cf = new CurveFitter(x, y);
>>>> double[] params = {1, 2*y[0], -(y[0]+y[y.length-1])};
>>>> double[] ipv = new double[params.length];
>>>> for(int i=0; i<ipv.length; i++)
>>>> ipv[i] = Math.abs(params[i]*0.1);
>>>>
>>>> cf.setMaxIterations(200);
>>>> cf.setOffsetMultiplySlopeParams(1, 2, -1);
>>>> cf.doCustomFit(new UserFunction() {
>>>> @Override
>>>> public double userFunction(double[] p, double x) {
>>>> return Math.abs( p[1] + p[2]*Math.exp(-x/p[0]) );
>>>> }
>>>> }, params.length, "", params, ipv, false);
>>>> //IJ.log(cf.getResultString());
>>>>
>>>> return cf.getParams();
>>>> }
>>>> }
--
ImageJ mailing list:
http://imagej.nih.gov/ij/list.html