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 Fitting with a distribution of parameters

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CStWue Posted - 10/23/2019 : 09:04:24 AM
Origin Ver. and Service Release (Select Help-->About Origin): OriginPro 2019b (64-bit)
Operating System: Windows 10

Hello,

I'm analyzing datasets of fluorescence lifetime experiments that contain discrete time channels in the X column and the signal and instrument response in two separate Y columns.

Currently, I'm fitting the data with a convolution of a single-exponential decay curve and the instrument response as shown in this tutorial for Origin C: https://www.originlab.com/doc/Tutorials/Fitting-Convolution

Now instead of the simple decay law f(x) = y0 + a * exp(-t*x) with individual parameters "a" and "t" I want to fit with a distribution of parameters such that my fitting function is:

f(x) = y0 + integral(0->tmax) P(t) * exp(-t*x) dt with P(t,A,tc,w) = A/(w*sqrt(pi/(4*ln(2)))) * exp(-4*ln(2)*(t-tc)^2/w^2)

"tmax", the upper limit of integration, will be a fixed value. The mean lifetime "tc", full width at half maximum "w" and area "A" of the distribution should be fitting parameters.

This function f(x) will then be convoluted with the instrument response as described in the link above.

How can I implement this idea with Origin?

Thank you!
3   L A T E S T    R E P L I E S    (Newest First)
YimingChen Posted - 10/28/2019 : 11:30:42 AM
Hi,

I thought you wanted to fit a convolution function same as that in the tutorial except replacing the Exponential Decay function with your defined f(x). Since you mentioned:
"This function f(x) will then be convoluted with the instrument response as described in the link above."

Please send email to <tech@originlab.com> and provide more details on the approach you were using.

Thank you

James
CStWue Posted - 10/28/2019 : 08:51:26 AM
Hello James,

thank you for your reply. I have looked at the tutorial you linked and this seems to be a good approach.

However, because the Origin C documentation is overall very limited, it is not clear to me how to combine the NAG integral function with the convolution that is linked in my initial post.

The NAG integral seems to take the x and values simply from the columns specified in the NLFit dialog. In the tutorial for the convolution fit these columns are accessed as datasets which are then passed to vectors, presumably for the fft convolution algorithm. These approaches seem fundamentally different two me, how could they be combined?
YimingChen Posted - 10/23/2019 : 12:12:31 PM
Hi,

To include integral into your fitting function, please refer to this page:
https://www.originlab.com/doc/Tutorials/Fitting-Integral-NAG

See if you can replace 
vSignal = A * exp( -t*vSample );
with an integral function.

James

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