How to set up the Matrix variables to use Options = optimoptions('lsqcurvefit','algorithm','levenberg-marquardt')
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I have two sets of M1 and M2 vectors (1x20) of experimental values that correspond to two sets of K1 and K2 inputs (1x20) respectively. Theoretlcal values of M1 and M2 (call them M1T and M2T) have a relationship with K1 and K2 such that M1-T is a function of K1 and K2, and M2-T is also a function of K1 and K2 with a series of a1 to a6 coefficients.
I am trying to find those a1 to a6 coefficients by minimizing the error function Total Error = (M1 - M1T)^2 + (M2-M2T)^2 by the use of
options = optimoptions('lsqcurvefit','Algorithm','levenberg-marquardt'), however, I don't know how to set up my variables into these names/function (i.e. don't know the approriate coding syntax).
As an example;
the inputs are: M1 = [ i1 i2 i3 ............ i20], M2 = [ i1 i2 i3 .............i20], K1 = [ i1 i2 i3 ............ i20], K2 = [ i1 i2 i3 .............i20],
the relationship between theroretical values of M1, M2 and the K1 and K2 are:
M1T(i) = a1*K1(i) + a2*K1(i)*K2(i) + a3*K2(i) + a4*(K1(i))^2
M2T(i) = a2*K2(i) + a2*K1(i) + a5*(K2(i))^2 + a6*K1(i)*K2(i)
Accepted Answer
I am not certain how ‘M1T’ and ‘M2T’ enter into this, however witth the ‘K’ values as the independent variables, and the ‘M’ values as the dependent variables, this is how I would set this up. (I prefer column vectors and column-oriented matrices, so I transposed the original row vectors to column vectors here.)
Try this, with your actual data —
M1 = randn(1,20);
M2 = randn(1,20);
K1 = randn(1,20);
K2 = randn(1,20);
% M1T = randn(1,20);
% M2T = randn(1,20);
M = [M1; M2].';
K = [K1; K2].';
MT = [M1T; M2T].';
objfcn = @(a,K) [a(1).*K(:,1) + a(2).*K(:,1).*K(:,2) + a(3).*K(:,2) + a(4).*K(:,1).^2, a(2).*K(:,2) + a(2).*K(:,1) + a(5).*K(:,2).^2 + a(6).*K(:,1).*K(:,2)]
A0 = rand(6,1);
[A,Rsdnrm,Rsd,ExFlg,OptmInfo,Lmda,Jmat] = lsqcurvefit(objfcn, A0, K, M);
Estimated_Parameters = A
I did not include the options call or options structure here, for simplicity. I usually lett lsqcurvefit pick the approopriate algorthm.
.
23 Comments
Selim
on 28 Jul 2024
Star Strider
on 28 Jul 2024
Edited: Star Strider
on 28 Jul 2024
As always, my pleasure!
I believe that I understand how the ‘M’ and ‘K’ matrices are related, however I do not understand how a matching ‘MT’ matrix fits into it. Please describe that.
My guess is that it mightt go somethng like this —
M1 = randn(1,20);
M2 = randn(1,20);
K1 = randn(1,20);
K2 = randn(1,20);
M1T = randn(1,20);
M2T = randn(1,20);
M = [M1; M2].';
K = [K1; K2].';
MT = [M1T; M2T].';
objfcn = @(a,K) [a(1).*K(:,1) + a(2).*K(:,1).*K(:,2) + a(3).*K(:,2) + a(4).*K(:,1).^2, a(2).*K(:,2) + a(2).*K(:,1) + a(5).*K(:,2).^2 + a(6).*K(:,1).*K(:,2)];
A0 = rand(6,1);
options = optimoptions('lsqcurvefit','Algorithm','levenberg-marquardt');
[A,Rsdnrm,Rsd,ExFlg,OptmInfo,Lmda,Jmat] = lsqcurvefit(objfcn, A0, K, M, [], [], options);
Estimated_Parameters = A
Mest = objfcn(A,K) % Fitted Values of 'M' From Regression
Merr = MT - Mest % Matrix Of Differences
MerrRMS = sqrt(mean(Merr.^2)) % Root-Mean_Squared Error
[Ks, idx] = sort(K);
figure
col = 1;
plot(K(idx(:,col),col), M(idx(:,col),col), '.')
hold on
plot(K(idx(:,col),col), Mest(idx(:,col),col), '-r')
hold off
grid
xlabel("K(:,"+col+")")
ylabel("M(:,"+col+")")
figure
col = 2;
plot(K(idx(:,col),col), M(idx(:,col),col), '.')
hold on
plot(K(idx(:,col),col), Mest(idx(:,col),col), '-r')
hold off
grid
xlabel("K(:,"+col+")")
ylabel("M(:,"+col+")")
Micro$oft once again randomly crashed my computer, apparently because it is fun for them (since there is no obvious reason for it) while I was typing this. My apologies for the resulting delay.
EDIT — (28 Jui 2024 at 17:19)
Since the options structure is required, it is now added. Code otherwise unchanged.
.
Selim
on 28 Jul 2024
Moved: Star Strider
on 28 Jul 2024
As always, my pleasure!
That is relatively straightforward. I did not know how you wanted ot integrate the ‘M’ and ‘MT’ arrays into your code.
My code changes slightly to —
M1 = randn(1,20);
M2 = randn(1,20);
K1 = randn(1,20);
K2 = randn(1,20);
M1T = randn(1,20);
M2T = randn(1,20);
M = [M1; M2].';
K = [K1; K2].';
MT = [M1T; M2T].';
objfcn = @(a,K) [2*a(1).*K(:,1) + a(2).*K(:,2).*K(:,2) + 3*a(4).*K(:,1).^2 + a(5).*K(:,1).*K(:,2), a(2).*K(:,1) + 2*a(3).*K(:,2) + a(5).*K(:,2).^2 + a(6).*K(:,1).*K(:,2) + 3.*a(7).*K(:,1).^2];
A0 = rand(7,1);
options = optimoptions('lsqcurvefit','Algorithm','levenberg-marquardt');
[A1,Rsdnrm1,Rsd1,ExFlg1,OptmInfo1,Lmda1,Jmat1] = lsqcurvefit(objfcn, A0, K, M, [], [], options);
ParmNames = {'A','B','C','D','E','F','G'};
M_Parameters = table(A1, 'RowNames',ParmNames)
M_est = objfcn(A1,K) % Fitted Values of 'M' From Regression
[A2,Rsdnrm2,Rsd2,ExFlg2,OptmInfo2,Lmda2,Jmat2] = lsqcurvefit(objfcn, A0, K, MT, [], [], options);
MT_Parameters = table(A2, 'RowNames',ParmNames)
MT_est = objfcn(A2,K) % Fitted Values of 'M' From Regression
[Ks, idx] = sort(K);
figure
col = 1;
plot(K(idx(:,col),col), M(idx(:,col),col), '.')
hold on
plot(K(idx(:,col),col), M_est(idx(:,col),col), '-r')
hold off
grid
xlabel("K(:,"+col+")")
ylabel("M(:,"+col+")")
figure
col = 2;
plot(K(idx(:,col),col), M(idx(:,col),col), '.')
hold on
plot(K(idx(:,col),col), M_est(idx(:,col),col), '-r')
hold off
grid
xlabel("K(:,"+col+")")
ylabel("M(:,"+col+")")
figure
col = 1;
plot(K(idx(:,col),col), MT(idx(:,col),col), '.')
hold on
plot(K(idx(:,col),col), MT_est(idx(:,col),col), '-r')
hold off
grid
xlabel("K(:,"+col+")")
ylabel("MT(:,"+col+")")
figure
col = 2;
plot(K(idx(:,col),col), MT(idx(:,col),col), '.')
hold on
plot(K(idx(:,col),col), MT_est(idx(:,col),col), '-r')
hold off
grid
xlabel("K(:,"+col+")")
ylabel("MT(:,"+col+")")
This uses the new version of ‘objfcn’ however I suggest that you check it. Now, a(1)=A, ... a(7)=G.
Use the correct values for the relevant vectors, and this should do what you want. (The plots are optional. I included them because I like to see how the regressions look.)
.
Star Strider
on 31 Jul 2024
Edited: Star Strider
on 31 Jul 2024
The best way to see if it makes sense is to run it.
I did my best to get this to run, and that required several significant changes. The problem is that ‘objfcn’ need to return a (9x2) matrix. Before my changes, your code would not run at all. After my changes, ‘objfcn’ returns a (9x18) matrix. I am not certain what you want to do, so I will leave tthis for the time being and check back when ‘objfcn’ works correctly, or at least that I understand what you want to do with it. I creeated a ‘Q’ variable to see what ‘objfcn’ returns. You can use it for that purpose, to get ‘objfcn’ to work correctly.
M1 = [5 11 18 25 32 39 46 52 60];
M2 = [9 10 11 12 13 15 16 18 21];
K1 = [0 0.2 0.36 0.44 0.49 0.51 0.52 0.54 0.55];
K2 = [0.75 0.77 0.8 0.84 0.88 0.94 0.98 1.0 1.02];
%Theoritical Calculation of M1 and M2 in terms of the coefficients and K1 and K2
%M1_Theory = 2*Cff(1)*K1 + Cff(2)*K2 + 3*Cff(4)*K1^2 + 2*Cff(5)*K1*K2 + Cff(6)*K2^2;
%M2_Theory = Cff(2)*K1 + 2*Cff(3)*K2 + Cff(5)*K1^2 + 2*Cff(6)*K1*K2 + 3*Cff(7)*K2^2;
K = [K1; K2].'
M = [M1; M2].'
M1_Theory = @(Cff,K) 2*Cff(1).*K(:,1) + Cff(2).*K(:,2) + 3*Cff(4).*K(:,1) + 2*Cff(5).*K(:,1).*K(:,2) + Cff(6).*K(:,2).^2;
M2_Theory = @(Cff,K) Cff(2).*K(:,1) + 2*Cff(3).*K(:,2) + Cff(5).*K(:,1).^2 + 2*Cff(6).*K(:,1).*K(:,2) + 3*Cff(7).*K(:,2).^2;
M_Theory = @(Cff,K) [M1_Theory(Cff,K); M2_THeory(Cff,K)].';
objfcn = @(Cff,K) [(M1-M1_Theory(Cff,K)).^2 -(M2-M2_Theory(Cff,K)).^2];
Cff0 = ones(7,1);
Q = objfcn(Cff0,K) % Check: 'objfcn'
options = optimoptions('lsqcurvefit','Algorithm','levenberg-marquardt');
[A1,Rsdnrm,Rsd,ExFlg,OptmInfo,Lmda,Jmat] = lsqcurvefit(objfcn, Cff0, K, M, [], [], options);
ParmNames = {'A','B','C','D','E','F','G'};
M_Parameters = table(A1,'RowNames',ParmNames)
M_Theory = objfcn(A1,M_Theory)
.
Selim
on 1 Aug 2024
As always, my pleasure!
Note that ‘objfcn’ does not need to consider ‘[M1; M2].'’ so they do not belong in it. The lsqcurvefit function will calculate the values of ‘M1_Theory’ and ‘M2_Theory’ using the ‘Cff’ coefficients (that it estimates) and the ‘K’ matrix, so ‘M1’ and ‘M2’ should not be present in it, since they the dependent variables. The lsqcurvefit function calculates ‘objfcn’ using ‘K’ and estimates the values of ‘Cff’ to minimise the least-squares error between it and the ‘M’ matrix.
Try this —
M1 = [5 11 18 25 32 39 46 52 60];
M2 = [9 10 11 12 13 15 16 18 21];
K1 = [0 0.2 0.36 0.44 0.49 0.51 0.52 0.54 0.55];
K2 = [0.75 0.77 0.8 0.84 0.88 0.94 0.98 1.0 1.02];
K = [K1; K2].';
M = [M1; M2].';
M1_Theory = @(Cff,K) 2*Cff(1).*K(:,1) + Cff(2).*K(:,2) + 3*Cff(4).*K(:,1) + 2*Cff(5).*K(:,1).*K(:,2) + Cff(6).*K(:,2).^2;
M2_Theory = @(Cff,K) Cff(2).*K(:,1) + 2*Cff(3).*K(:,2) + Cff(5).*K(:,1).^2 + 2*Cff(6).*K(:,1).*K(:,2) + 3*Cff(7).*K(:,2).^2;
M_Theory = @(Cff,K) [M1_Theory(Cff,K); M2_THeory(Cff,K)].';
objfcn = @(Cff,K) [M1_Theory(Cff,K).^2 M2_Theory(Cff,K).^2];
Cff0 = rand(7,1);
Q = objfcn(Cff0,K)
options = optimoptions('lsqcurvefit','Algorithm','levenberg-marquardt');
[A1,Rsdnrm,Rsd,ExFlg,OptmInfo,Lmda,Jmat] = lsqcurvefit(objfcn, Cff0, K, M, [], [], options);
% options = optimoptions('lsqcurvefit','Algorithm','levenberg-marquardt');
% [A1,Rsdnrm,Rsd,ExFlg,OptmInfo,Lmda,Jmat] = lsqcurvefit(objfcn, Cff0, K, M, [], [], options);
ParmNames = {'A','B','C','D','E','F','G'};
M_Parameters = table(A1,'RowNames',ParmNames)
M_Theory = objfcn(A1,K)
Err = M - M_Theory
RMS_Err = sqrt(mean(Err.^2))
figure
col = 1;
plot(K(:,col), M(:,col), '.', 'DisplayName','Data')
hold on
plot(K(:,col), M_Theory(:,col), '-r', 'DisplayName','Regression')
hold off
grid
xlabel('K')
ylabel('M')
title("Column "+col)
legend('Location','best')
figure
col = 2;
plot(K(:,col), M(:,col), '.', 'DisplayName','Data')
hold on
plot(K(:,col), M_Theory(:,col), '-r', 'DisplayName','Regression')
hold off
grid
xlabel('K')
ylabel('M')
title("Column "+col)
legend('Location','best')
Now I understand how this is supposed to work!
The ‘M1_Theory’ regression fits quite well, however ‘M2_Theory’ does not, so you need to check it and make any necessary changes only to it (the code will adapt automatically, so no other changes are necessary), then run this code again.
.
EDIT — (01 Aug 2024 at 13:05)
objfcn = @(Cff,K) [M1_Theory(Cff,K).^2 -M2_Theory(Cff,K).^2];
to:
objfcn = @(Cff,K) [M1_Theory(Cff,K).^2 M2_Theory(Cff,K).^2];
and then re-ran the code to get the current result.
Code otherwise unchanged.
.
Selim
on 1 Aug 2024
Moved: Star Strider
on 1 Aug 2024
This works! I noticed in the objfcn the minus sign needed to plus between M1_Theory and M2_Theory (since we are adding up the errors). I ran it afterwords, got the second graph as; 
I think this is it - you did it :-) Thank you again,
On a side note, when I ran the code, it gives the yellow warnings of " Value assigned to variable might be unsued.Considr replacing the variable with ~ instead.". But obviously, this is just FYI.
Star Strider
on 1 Aug 2024
As always, my pleasure!
I am plesed that all this is now sorted!
I got no warnings, even after updating the code to remove the unary minus sign (see EDIT in my previoous Comment) and re-running it. I suspect that you got the warning because you are using the code inside a function.
Sorry to bother you but for some strange reason, now my code is not working. Anything that stands out for you? ( I am getting the error below)
My code is:
M1 = [5 11 18 25 32 39 46 52 60];
M2 = [9 10 11 12 13 15 16 18 21];
K1 = [0 0.2 0.36 0.44 0.49 0.51 0.52 0.54 0.55];
K2 = [0.75 0.77 0.8 0.84 0.88 0.94 0.98 1.0 1.02];
K = [K1; K2].';
M = [M1; M2].';
M1_Theory = @(Cff,K) 2*Cff(1).*K(:,1) + Cff(2).*K(:,2) + 3*Cff(4).*K(:,1) + 2*Cff(5).*K(:,1).*K(:,2) + Cff(6).*K(:,2).^2;
M2_Theory = @(Cff,K) Cff(2).*K(:,1) + 2*Cff(3).*K(:,2) + Cff(5).*K(:,1).^2 + 2*Cff(6).*K(:,1).*K(:,2) + 3*Cff(7).*K(:,2).^2;
M_Theory = @(Cff,K) [M1_Theory(Cff,K); M2_Theory(Cff,K)].';
objfcn = @(Cff,K) [(M1-M1_Theory(Cff,K)).^2 +(M2-M2_Theory(Cff,K)).^2];
Cff0 = rand(7,1);
options = optimoptions('lsqcurvefit','Algorithm','levenberg-marquardt');
[A1,Rsdnrm,Rsd,ExFlg,OptmInfo,Lmda,Jmat] = lsqcurvefit(objfcn, Cff0, K, M, [], [], options);
options = optimoptions('lsqcurvefit','Algorithm','levenberg-marquardt');
[A1,Rsdnrm,Rsd,ExFlg,OptmInfo,Lmda,Jmat] = lsqcurvefit(objfcn, Cff0, K, M, [], [], options);
ParmNames = {'A','B','C','D','E','F','G'};
M_Parameters = table(A1,'RowNames',ParmNames)
M_Theory = objfcn(A1,K)
Err = M - M_Theory
RMS_Err = sqrt(mean(Err.^2))
figure
col = 1;
plot(K(:,col), M(:,col), '.', 'DisplayName','Data')
hold on
plot(K(:,col), M_Theory(:,col), '-r', 'DisplayName','Regression')
hold off
grid
xlabel('K')
ylabel('M')
title("Column "+col)
legend('Location','best')
figure
col = 2;
plot(K(:,col), M(:,col), '.', 'DisplayName','Data')
hold on
plot(K(:,col), M_Theory(:,col), '-r', 'DisplayName','Regression')
hold off
grid
xlabel('K')
ylabel('M')
title("Column "+col)
legend('Location','best')
Torsten
on 5 Aug 2024
Use
M_Theory = @(Cff,K) [M1_Theory(Cff,K), M2_Theory(Cff,K)];
objfcn = @(Cff,K) M_Theory(Cff,K);
instead of
M_Theory = @(Cff,K) [M1_Theory(Cff,K); M2_Theory(Cff,K)].';
objfcn = @(Cff,K) [(M1-M1_Theory(Cff,K)).^2 +(M2-M2_Theory(Cff,K)).^2];
Selim
on 5 Aug 2024
Torsten
on 5 Aug 2024
Read again how to change the two lines.
‘Anything that stands out for you?’
Yes! When in doubt, see what ‘objfcn’ returns with the default parameter vector and an appropriate independent variable. Here, ‘objfcn’ is returning a (9x18) matrix instead of the (9x2) matriux that it should. This is because ‘M1’ and ‘M2’ are(1x9) row vectors, and the subtracting them uses ‘iimplicit expansion’ to do that, rather than throwing an error. (Automatic implicit expansion was introduced in R2014b and has caused these sort of problems ever since.) That is the reason the the ‘M’ matrix transposes ‘M1’ and ‘M2’ to column vectors before concatenating them into a matrix.
The solution is to revert to the original code for this that I wrote, because it does not consider ‘M1’ and ‘M2’ at all in ‘objfcn’ since lsqcurvefit does that comparison internally to fit ‘objfcn’ to ‘M’, so doing it in ‘objfcn’ will produce inaccurate results for the parameter vector ‘Cff’.
M1 = [5 11 18 25 32 39 46 52 60];
M2 = [9 10 11 12 13 15 16 18 21];
K1 = [0 0.2 0.36 0.44 0.49 0.51 0.52 0.54 0.55];
K2 = [0.75 0.77 0.8 0.84 0.88 0.94 0.98 1.0 1.02];
K = [K1; K2].';
M = [M1; M2].';
M1_Theory = @(Cff,K) 2*Cff(1).*K(:,1) + Cff(2).*K(:,2) + 3*Cff(4).*K(:,1) + 2*Cff(5).*K(:,1).*K(:,2) + Cff(6).*K(:,2).^2;
M2_Theory = @(Cff,K) Cff(2).*K(:,1) + 2*Cff(3).*K(:,2) + Cff(5).*K(:,1).^2 + 2*Cff(6).*K(:,1).*K(:,2) + 3*Cff(7).*K(:,2).^2;
M_Theory = @(Cff,K) [M1_Theory(Cff,K); M2_Theory(Cff,K)].';
% objfcn = @(Cff,K) [(M1-M1_Theory(Cff,K)).^2 +(M2-M2_Theory(Cff,K)).^2];% % Inaccurate
objfcn = @(Cff,K) [(M1_Theory(Cff,K)).^2 +(M2_Theory(Cff,K)).^2]; % Corrected
Cff0 = rand(7,1);
Check_objfcn = objfcn(Cff0,K)
M
% return
options = optimoptions('lsqcurvefit','Algorithm','levenberg-marquardt');
[A1,Rsdnrm,Rsd,ExFlg,OptmInfo,Lmda,Jmat] = lsqcurvefit(objfcn, Cff0, K, M, [], [], options);
options = optimoptions('lsqcurvefit','Algorithm','levenberg-marquardt');
[A1,Rsdnrm,Rsd,ExFlg,OptmInfo,Lmda,Jmat] = lsqcurvefit(objfcn, Cff0, K, M, [], [], options);
ParmNames = {'A','B','C','D','E','F','G'};
M_Parameters = table(A1,'RowNames',ParmNames)
M_Theory = objfcn(A1,K)
Err = M - M_Theory
RMS_Err = sqrt(mean(Err.^2))
figure
col = 1;
plot(K(:,col), M(:,col), '.', 'DisplayName','Data')
hold on
plot(K(:,col), M_Theory(:,col), '-r', 'DisplayName','Regression')
hold off
grid
xlabel('K')
ylabel('M')
title("Column "+col)
legend('Location','best')
figure
col = 2;
plot(K(:,col), M(:,col), '.', 'DisplayName','Data')
hold on
plot(K(:,col), M_Theory(:,col), '-r', 'DisplayName','Regression')
hold off
grid
xlabel('K')
ylabel('M')
title("Column "+col)
legend('Location','best')
You can certainly change ‘objfcn’ to a new version with different expressions (that might be a better match to ‘M2’), however it is not appropriate to include ‘M1’ and ‘M2’ in it at all.
.
Selim
on 5 Aug 2024
If you square M1_theory and M2_theory in
objfcn = @(Cff,K) [(M1_Theory(Cff,K)).^2 +(M2_Theory(Cff,K)).^2];
don't you also have to square M1 and M2 ?
In the case above, I think lsqcurvefit will try to minimize
sum_i ((M1_Theory(i)^2 - M1(i))^2 + (M2_theory(i)^2 - M2(i))^2)
I think
M_Theory = @(Cff,K) [M1_Theory(Cff,K), M2_Theory(Cff,K)];
objfcn = @(Cff,K) M_Theory(Cff,K);
is the correct choice.
Selim
on 5 Aug 2024
As always, my pleasure!
Thank you!
I did not initially pick up on the squaring, since I was concentrating on a different problem.
i believe that they shoud not be squared in any event, at least not in ‘objfcn’. Let lsqcurvefit take care of those details.
Squaring the difference would be appropriate for some optimisation functions such as fminsearch or fmincon in which it would be:
objfcn = @(Cff) [(M1.'-M1_Theory(Cff,K)).^2 (M2.'-M2_Theory(Cff,K)).^2];
inheriting ‘K’ from the workspace, and that would probably work (note the simple transpose operations denoted by.'). I did not test it with any of those functions.
Not squaring produces —
M1 = [5 11 18 25 32 39 46 52 60];
M2 = [9 10 11 12 13 15 16 18 21];
K1 = [0 0.2 0.36 0.44 0.49 0.51 0.52 0.54 0.55];
K2 = [0.75 0.77 0.8 0.84 0.88 0.94 0.98 1.0 1.02];
K = [K1; K2].';
M = [M1; M2].';
M1_Theory = @(Cff,K) 2*Cff(1).*K(:,1) + Cff(2).*K(:,2) + 3*Cff(4).*K(:,1) + 2*Cff(5).*K(:,1).*K(:,2) + Cff(6).*K(:,2).^2;
M2_Theory = @(Cff,K) Cff(2).*K(:,1) + 2*Cff(3).*K(:,2) + Cff(5).*K(:,1).^2 + 2*Cff(6).*K(:,1).*K(:,2) + 3*Cff(7).*K(:,2).^2;
M_Theory = @(Cff,K) [M1_Theory(Cff,K); M2_Theory(Cff,K)].';
% objfcn = @(Cff,K) [(M1-M1_Theory(Cff,K)).^2 +(M2-M2_Theory(Cff,K)).^2];% % Inaccurate
objfcn = @(Cff,K) [(M1_Theory(Cff,K)) (M2_Theory(Cff,K))]; % Corrected
Cff0 = rand(7,1);
Check_objfcn = objfcn(Cff0,K)
M
% return
options = optimoptions('lsqcurvefit','Algorithm','levenberg-marquardt');
[A1,Rsdnrm,Rsd,ExFlg,OptmInfo,Lmda,Jmat] = lsqcurvefit(objfcn, Cff0, K, M, [], [], options);
% options = optimoptions('lsqcurvefit','Algorithm','levenberg-marquardt');
% [A1,Rsdnrm,Rsd,ExFlg,OptmInfo,Lmda,Jmat] = lsqcurvefit(objfcn, Cff0, K, M, [], [], options);
ParmNames = {'A','B','C','D','E','F','G'};
M_Parameters = table(A1,'RowNames',ParmNames)
M_Theory = objfcn(A1,K)
Err = M - M_Theory
RMS_Err = sqrt(mean(Err.^2))
figure
col = 1;
plot(K(:,col), M(:,col), '.', 'DisplayName','Data')
hold on
plot(K(:,col), M_Theory(:,col), '-r', 'DisplayName','Regression')
hold off
grid
xlabel('K')
ylabel('M')
title("Column "+col)
legend('Location','best')
figure
col = 2;
plot(K(:,col), M(:,col), '.', 'DisplayName','Data')
hold on
plot(K(:,col), M_Theory(:,col), '-r', 'DisplayName','Regression')
hold off
grid
xlabel('K')
ylabel('M')
title("Column "+col)
legend('Location','best')
So not squaring produces different parameter estimates, however the same essential fit.
.
Star Strider
on 5 Aug 2024
‘Thanks again. I have a feeling that this will not my last question :-)
As always, my plesure!
I will do my best to provide an appropriate respoinse!
Torsten
on 5 Aug 2024
Squaring the difference would be appropriate for some optimisation functions such as fminsearch or fmincon in which it would be:
objfcn = @(Cff) [(M1.'-M1_Theory(Cff,K)).^2 (M2.'-M2_Theory(Cff,K)).^2];
inheriting ‘K’ from the workspace, and that would probably work (note the simple transpose operations denoted by.'). I did not test it with any of those functions.
For "fminsearch" or "fmincon", you even had to sum over the squared differences.
Star Strider
on 5 Aug 2024
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