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Re: Fitting multiple datasets to "partially" the same model (global fit
From: |
JokerOne |
Subject: |
Re: Fitting multiple datasets to "partially" the same model (global fit with shared parameters) |
Date: |
Tue, 8 Dec 2015 03:51:13 -0800 (PST) |
Thanks everybody for your effort,
since I am not too common to the maths in these regression/optimization
routines it will take be a while to understand your advises.
Allen asks for some actual data. However, there is no "real" data, yet. For
my tests I just simulated some data in a simple way .
Here, I replaced the logaritmic term with a power term to underline that the
logaritmic term in indeed just an example function as Allen assumed
correctly. I do not know the function that will suit my final task, yet. I
am just checking the basic concept of the fitting routine with some example
functions.
# Create simulated data for fit using "shared" parameter
# Define Parameters to be fitted
a0 = 1; # offset poly 2nd order
a1 = -3; # linear term poly 2nd order
a2 = 0.5; # quadratic poly 2nd order
b1 = 1.5; # power term : base
b2_list = [1:0.2:2]; # list of exponential factors in power term
x = [1:10]; # Just some x-values
# Create simulation data
c1 = 0; # counter
for b2 = b2_list
c1++; # increment counter
# HERE: FOR SIMULATTION PURPOSE USE :
# f(x) = b1^(-1*b2*x) * (a0+a1*x+a2*x^2)
y(:,c1) = b1.^(-1.*b2.*x).*(a0 + a1.*x +a2.*x.^2);
# Data is sorted in a matrix, could be handled otherwise if
reasonable/required...
endfor
# left for now : Add some noise to the data
# y = y +0.25.* randn(size(y));
# Simulation data ready
# plot data
figure(1)
plot(x,y,'o');
# To solve:
# Find parameters a0, a1, a2 and all parameters of b2_list using
# a regression/fit routine that makes uses of fact, that a0,a1,a2 are
# equal for all colums in y
I am very happy for any further advises and help.
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