Contraints of multiple variables.

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Thu, 06/18/2009 - 08:32 am

I am trying to curve fit my FCS data to a user defined formula Sum(Ai/((1+4*Di*t/w^2)*sqrt(1+4*Di*t/z^2)))

So basically Ai is 3 different variables A1,A2,A3 which represent the percentage of a specific component (Free dye, dye+enzyme, dye+enzyme+DNA) . Is there a way to set their initial guess and to also have A1+A2+A3=1?

Igor 6.04
OS X build

Thanks!
Michael Meadows
m.meadows wrote:
I am trying to curve fit my FCS data to a user defined formula Sum(Ai/((1+4*Di*t/w^2)*sqrt(1+4*Di*t/z^2)))

So basically Ai is 3 different variables A1,A2,A3 which represent the percentage of a specific component (Free dye, dye+enzyme, dye+enzyme+DNA) . Is there a way to set their initial guess and to also have A1+A2+A3=1?

Igor 6.04
OS X build

Thanks!
Michael Meadows


Rather than having A1, A2 and A3 all as fit coefficients, you should fit A1 and A2 and then use 1-(A1+A2) instead of A3.

The alternative would be to use two constraint expressions. Say K0 is A1, K1 is A2, and K3 is A3:
K0+K1+K2>0
K0+K1+K2<0

That involves making a text wave with those two lines and then selecting that text wave in the Curve Fitting dialog. But really my first answer is preferable- you don't have three coefficients, you really only have two because of the constraint on the sum. Fitting will work better if you do it that way.

John Weeks
WaveMetrics, Inc.
support@wavemetrics.com

June 18, 2009 at 02:32 pm - Permalink