Fit of numerical expression

Hi all, i have my data which i want to be fitted consisting of the independent variable x and the dependent variable y. My function that should fit the data is something like f(x,a,b,c,d) = integral(g(x,y,a,b,c),y,0,d) where d is known and a, b and c are the fitting parameters. g can only be integrated numericaly. If i try to do the fit using ft = fittype('f(x,a,b,c,d)') i get an error like: Expression f(x,a,b,c,d) is not a valid MATLAB expression,

has non-scalar coefficients, or cannot be evaluated

Any ideas how i can solve this problem?

Edit: If i try to compute values for f for certain sets of variables i get: Warning: Reached the limit on the maximum number of intervals in use. Approximate bound on error is

4.0e-01. and a probably right value for f, but this value is much smaller than the suggested error. g is definitly finite over the range i integrate. How reliable could this value be and how could i manage to get an smaller error?

Answer 1

[Torsten]

Use an anonymous function to define your model equation.

For examples, see

https://de.mathworks.com/help/curvefit/fittype.html#btpaend-14

[Moritz Ruhwedel]

I don't know if i do it the wrong way, but this way i get the same error.

[Torsten]

Try with a simple function for f to check if the error message is due to an integration problem.

[Moritz Ruhwedel]

I tried something like ft = fittype(@(a,x) integral(@(y) a*x*y,0,1)) and this gave:

Expression integral(@(y)a*x*y,0,1) is not a valid MATLAB expression, has non-scalar coefficients, or

cannot be evaluated:

Error while trying to evaluate FITTYPE function :

Output of the function must be the same size as the input. If FUN is an array-valued integrand, set the

'ArrayValued' option to true.

[Torsten]

ft = fittype(@(a,x) integral(@(y) a*x*y,0,1,'ArrayValued',1))

[Moritz Ruhwedel]

Thank you, that works, but why array valued?

[Torsten]

x is the array of the independent variable, "integral" usually sends y as an array to your function to be integrated. Then x*y is undefined if they don't agree in size.

ArrayValued = 1 tells MATLAB to send y as a sequence of scalars so that x*y can be evaluated.

[Moritz Ruhwedel]

Okay thank you, but know that i tried to do this with my real model i get:

>> ft = fittype(@(d_Fe, r_bulk_Pt, r_Fe, mfp_Pt, h, k, x) ((x/((x)/(1e-2) * integral(@(t) (mfp_Pt.*r_bulk_Pt)./((x+ h.*sin(k.*t)).*(mfp_Pt./(x+ h.*sin(k.*t)) - (3.*mfp_Pt.^2)./(8.*(x+ h.*sin(k.*t)).^2) + (3.*mfp_Pt.^2.*(((x+ h.*sin(k.*t)).*etp(-(x+ h.*sin(k.*t))./mfp_Pt))./(12.*mfp_Pt) - etp(-(x+ h.*sin(k.*t))./mfp_Pt).*((x+ h.*sin(k.*t)).^2./(24.*mfp_Pt.^2) - 1./2) - etp(-(x+ h.*sin(k.*t))./mfp_Pt)./4 + ((x+ h.*sin(k.*t)).^2.*ei(-(x+ h.*sin(k.*t))./mfp_Pt).*((x+ h.*sin(k.*t)).^2 - 12.*mfp_Pt.^2))./(24.*mfp_Pt.^4) + ((x+ h.*sin(k.*t)).*etp(-(x+ h.*sin(k.*t))./mfp_Pt).*((x+ h.*sin(k.*t)).^2 - 12.*mfp_Pt.^2))./(24.*mfp_Pt.^3)))./(2.*(x+ h.*sin(k.*t)).^2)))./(x+ h.*sin(k.*t)), 0, 1e-2, 'ArrayValued', 1)) + d_Fe/r_Fe)*1/(x + d_Fe))^(-1))

Error using fittype/testCustomModelEvaluation (line 12)

Expression

((x/((x)/(1e-2)*integral(@(t)(mfp_Pt.*r_bulk_Pt)./((x+h.*sin(k.*t)).*(mfp_Pt./(x+h.*sin(k.*t))-(3.*mfp_Pt.^2)./(8.*(x+h.*sin(k.*t)).^2)+(3.*mfp_Pt.^2.*(((x+h.*sin(k.*t)).*etp(-(x+h.*sin(k.*t))./mfp_Pt))./(12.*mfp_Pt)-etp(-(x+h.*sin(k.*t))./mfp_Pt).*((x+h.*sin(k.*t)).^2./(24.*mfp_Pt.^2)-1./2)-etp(-(x+h.*sin(k.*t))./mfp_Pt)./4+((x+h.*sin(k.*t)).^2.*ei(-(x+h.*sin(k.*t))./mfp_Pt).*((x+h.*sin(k.*t)).^2-12.*mfp_Pt.^2))./(24.*mfp_Pt.^4)+((x+h.*sin(k.*t)).*etp(-(x+h.*sin(k.*t))./mfp_Pt).*((x+h.*sin(k.*t)).^2-12.*mfp_Pt.^2))./(24.*mfp_Pt.^3)))./(2.*(x+h.*sin(k.*t)).^2)))./(x+h.*sin(k.*t)),0,1e-2,'ArrayValued',1))+d_Fe/r_Fe)*1/(x+d_Fe))^(-1)

is not a valid MATLAB expression, has non-scalar coefficients, or cannot be evaluated:

Error while trying to evaluate FITTYPE function :

Undefined function 'etp' for input arguments of type 'double'.

Error in fittype>iCreateFittype (line 373)

testCustomModelEvaluation( obj );

Error in fittype (line 330)

obj = iCreateFittype( obj, varargin{:} );

Caused by:

Error using fittype/evaluate (line 88)

Error while trying to evaluate FITTYPE function :

Undefined function 'etp' for input arguments of type 'double'.

[Torsten]

Don't define your function in the call to "fittype", but use a separate function file:

ft = fittype(@(d_Fe, r_bulk_Pt, r_Fe, mfp_Pt, h, k, x) fun(d_Fe,r_bulk_Pt,r_Fe,mfp_Pt,h,k,x));

and write a function

function res = fun(d_Fe,r_bulk_Pt,r_Fe,mfp_Pt,h,k,x)
...
end

This way, you have the possibility to debug what is happening.

One obvious thing is that x/((x)... is wrong because x is a vector. Use elementwise division here.

[Moritz Ruhwedel]

Okay now i found the problem, when replacing a variable called x i replaced accidently the x in exp with a t. Now it works, thank you Torsten, you saved my Bachelorthesis :D