How to curve fit following summation equation in MATLAB with given experimental data.

Asked by abxz on 12 Nov 2019

Latest activity Edited by abxz on 15 Nov 2019 at 15:31

Accepted Answer by Alex Sha

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and

a,k,c,b, and g are constants to be determined.

4 Comments

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abxz on 12 Nov 2019

Not able to write code.. will you please help with the code

abxz on 12 Nov 2019

@ Kalyan Acharjya, will you please help out with code

KALYAN ACHARJYA on 13 Nov 2019

For assignments or homework, we help only after looking at your efforts to solve the question.

3 Answers

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Answer by Alex Sha on 13 Nov 2019

Accepted Answer

d(K/ (1+exp(c-b*t)))/dt=k*exp(c-b*t)*b/sqr(1+exp(c-b*t)),so your fitting function become:

is the above correct? if yes, you may see the function is over-fit, that means the parameters will not be unique， one solution likes below:

Root of Mean Square Error (RMSE): 11257.9862380487
Sum of Squared Residual: 1647649303.76923
Correlation Coef. (R): 0.891727403408187
R-Square: 0.795177761989108
Adjusted R-Square: 0.726903682652144
Determination Coef. (DC): 0.795103266693536
F-Statistic: 7.64708134900884
Parameter          	Best Estimate
--------------------	-------------
a	67082.9685482823
k	2.55264230357405E16
c	39.1820152654189
b	0.0511178327965598
g	1.74671169710137E-249

2 Comments

KALYAN ACHARJYA on 13 Nov 2019

@Alex

Why you are providing the two answers?

You can add the modified answer as a comments in the first answer.

abxz on 13 Nov 2019

@ Alex Sha, Thanks a lot for your help.

will you please provide the code also.

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Answer by Alex Sha on 12 Nov 2019

Hi, Yadav, in your function "a*d/dt(k/1+exp(c-b*t))", what is "d/dt"? does "k/1" equal to "k"? Please describe clearly.

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abxz on 12 Nov 2019

@Alex Sha , will you please help out with code.

abxz on 13 Nov 2019

@Alex Sha , will you please help out with code.

abxz on 13 Nov 2019

@ Alex Sha , Please send code . I need code so if i have to do similar kind of fitting , i can take the help from the code.

Thank you.

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Answer by Alex Sha on 14 Nov 2019

Hi， Yadav, I actually use a software package other than Matlab, named 1stOpt, it is much easy for using without guessing initial start-values, since it adopts global optimization algorithm. The code looks like below:

Parameter a,k,c,b,g;
ConstStr f=a*(k*exp(c-b*t(i))*b)/(1+exp(c-b*t(i)))^2;
Variable t,z[OutPut],y;
StartProgram [Basic];
Sub MainModel
Dim as integer i, j, n
Dim as double temd1, temd2
   for i = 0 to DataLength - 1
        n = t(i)
        temd1 = 0
        for j = 0 to n
            temd1 = temd1 + f
        next
        temd2 = 0
        for j = 0 to n
            temd2 = temd2 + g*y(j)
        next
        z(i) = temd1 + temd2
    Next
End Sub
EndProgram;
Data;
t=[0,2,4,6,8,10,12,14,16,18,20,22,24];
z=[0,0,666.6,5333.33,10666.6,21333,42666.6,4666.6,42666.6,42666.6,42666.6,42666.6,85333.3];
y=[1.25*10^8,1.*10^8,1.25*10^8,2.2*10^10,1.3*10^11,1.4*10^11,1.25*10^11,4.7*10^10,7.9*10^10,9.5*10^10,9.4*10^10,8.8*10^10,9.4*10^10];

a much better result:

Root of Mean Square Error (RMSE): 9901.69220512954
Sum of Squared Residual: 1274565610.8266
Correlation Coef. (R): 0.918681151445272
R-Square: 0.84397505802081
Adjusted R-Square: 0.791966744027747
Determination Coef. (DC): 0.841498837497943
F-Statistic: 9.7840155772957
Parameter          	Best Estimate
--------------------	-------------
a	-277156.527610417
k	-10698197.9029827
c	28.5533367811484
b	0.35649699061682
g	3.06293808255498E-8

3 Comments

KALYAN ACHARJYA on 14 Nov 2019

@Alex Is this package supports by Matlab? You are giving multiple answers for same question. you can add extentions answer in the comment section of respective answer.

Alex Sha on 14 Nov 2019

Sorry for giving multi-answers.

1stOpt is an independent software package I think, not the add-in or toolbox of Matlab.

abxz on 15 Nov 2019 at 15:22

@ Alex Sha , Thank you so much.

You are now following this question

abxz (view profile)