Curve fitting multiple parameters function

Hello,

I have a set of data that fits a defined curve fitting function model as

I = a*exp(-bx)+c;

the parameters a, b and c depends on a function r, say (a,b,c) = f(r)

My defined function I also depends on another parameter k , say (a,b,c) = f(k)

How can I define single function that that depends on both k and r, say

I = f(a,b,c)
I = a*exp(-bx)+c
(a,b,c) = f(k,r)

Thank you

[Sambit Supriya Dash]

Could you elaborate more the question with funs. or with some similar examples ?

[Kabir Shariff]

I want to develop an analytical modelfor turbulence from numerical sumulation data. I know the turbulence depends on three different parameters, the thrust const (r) , the ambient const (k) and the position (x).

I use an exponential function model to fit the numerical data as shown in the figure

The model equation is of the form

I = a*exp(-bx)+c;

where a, b and c are linear functions that depend on the ambinent const (k),

I maintain a value of r and simulate for different values of k to have different values of (a,b and c) to develop a relation. e.g

The same model is also used to obtain a similar parameters a, b, and c that depends on the thrust coeffcient (r) ( keeping k constant)

I want to to have an expression that combines both r and k in a, b and c parameters something like

Answer 1

[Sulaymon Eshkabilov]

You can write a function file or function handle, e.g.:

F=@(k, r, x)(2*r*k*exp(0.576*k*x)+c); % etc.
% OR

function F = MyFun(k,r, x)
F = (2*r*k*exp(0.576*k*x)+c);
end

[Kabir Shariff]

I think the function handle will not do the job.

I dont have the model with variation of both r and k, but I have a model for each separate variable (i.e model eqn for r and model eqn for k)

I want to have a single model that account for both variables

NB: the equations given are for example purpose

[Kabir Shariff]

Hello,

I would like to give more calrification on my case please.

1. My objective is to develop analytical model from a measured data for range of k and r

My measured data is dependent on both thrust const (r) and ambient constant (k) and varies along x

r =  [0.64 0.89 0.98];
k = [0.08 0.15 0.2 0.23];

I use a defined model equation to fit the data; my model equation of the form;

I = a*exp(-bx)+c;

2. with cftool, I fix r say 0.64, and find the parameters a, b, and c in the model equation for all values of k ( meaning i have 4 different values of a,b, and c correspoding to k)

3. I repeat the same step for r = 0.89 and r = 0.98 (each case obtaining a different coefficent of the model equation)

4. Then, I ploted k Vs a, k vs b and k vs c. to obtain the relationship between k and (a,b,c) which is linear relation

5. I did a similar plot this time with r, say r vs a, r vs b and r vs c ( also obtaining a linear dependance)

6. I have two different models, one with variable r (k constanrt) and the other with variable k (r constant)

Is there any way to optimize the model to be in the form?

I = a*r*kexp(-b*kx)+c*r;

for 0.064 < r < 0.98;

0.08 < k < 0.23

a, b,c constant

Thank you in advance