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radoslavb
USA
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 Posted - 08/25/2008 : 5:24:42 PM
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This question is for OriginPro 8.0 SP2
I have data in 3 columns:
col(omega) = (x-axis)
col(y_Re) = real part
col(y_Im) = imaginary part
I need to fit simultaneously the real and imaginary part to the complex Debye equation
A/(1+i*omega*tau),
where "A" and "tau" are fitting parameters (both are real).
The Debye equation can be separated in Re and Im parts analytically (and I have already done independent fits to the Re and Im parts), however I need the fit to satisfy both parts simultaneously with one set of parameters. In addition, there are generalizations of the Debye eqn. which cannot be separated analytically in Re and Im parts. Is there a way to define a complex fitting function?
Thanks,
rb
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Echo_Chu
China
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Posted - 08/26/2008 : 05:15:27 AM
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Hi,
Your function is
y1 + i * y2 = A/(1+i*omega*tau),
Then it can be write as
y1 + i * y2 = A/(1+(omega*tau)^2) - i * (A*tao)/(1+(omega*tau)^2)
That is,
y1 = A/(1+(omega*tau)^2);
y2 = -(A*tao)/(1+(omega*tau)^2)
So it can be solved by defining a function with multiple independents. You can refer to this page to see how to fit with multiple independent variable.
Echo
OriginLab Corp
quote:
Originally posted by radoslavb
This question is for OriginPro 8.0 SP2
I have data in 3 columns:
col(omega) = (x-axis)
col(y_Re) = real part
col(y_Im) = imaginary part
I need to fit simultaneously the real and imaginary part to the complex Debye equation
A/(1+i*omega*tau),
where "A" and "tau" are fitting parameters (both are real).
The Debye equation can be separated in Re and Im parts analytically (and I have already done independent fits to the Re and Im parts), however I need the fit to satisfy both parts simultaneously with one set of parameters. In addition, there are generalizations of the Debye eqn. which cannot be separated analytically in Re and Im parts. Is there a way to define a complex fitting function?
Thanks,
rb
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radoslavb
USA
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Posted - 08/26/2008 : 11:40:14 AM
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quote:
Originally posted by Echo_Chu
...
So it can be solved by defining a function with multiple independents. You can refer to this page to see how to fit with multiple independent variable.
Do you mean multiple Dependents (y1, y2)? |
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greg
USA
1378 Posts |
Posted - 08/26/2008 : 3:16:56 PM
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I tested the following which works in Origin8 (and should work in earlier versions as well). Note that the y2 formula is different than in Echo's post:
Indpendent Variable omega
Dependent Variables y1,y2
Parameter Names A,tau
Function
y1= A/(1+(omega*tau)^2);
y2=-(A*tau*omega)/(1+(omega*tau)^2);
and check Use OriginC.
For Parameter initialization, you can use:
A=1;
tau=1;
(unless you have a better idea of what you parameters are close to.)
When you use this function, you will need to assign omega, y1 and y2 to three datasets. |
Edited by - greg on 08/26/2008 5:31:10 PM |
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greg
USA
1378 Posts |
Posted - 08/26/2008 : 3:58:04 PM
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You can also use complex numbers within OriginC:
Independent Var omega
Dependent var y1,y2
Parameter names A,tau
Using OriginC our function definition becomes:
complex cc = A/(1+1i*omega*tau);
y1 = cc.m_re;
y2 = cc.m_im;
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Edited by - greg on 08/26/2008 5:29:55 PM |
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radoslavb
USA
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Posted - 08/27/2008 : 5:11:31 PM
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Thanks, Greg!
Your second comment is particularily useful, since it will work even if the complex function does not have a nice analytical separation of real and imaginary parts. I've tested both methods and they both work.
-Regards! |
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complex fit function in Origin 8?