Fitting an integral

I'm going to explain my problem with a sample. Assume that i have a function (f(x)=a.*x^2) and i need to calculate its integral indefinitely, lets assume this function doesn't have an indefinite integral. At the end i need to fit this integral to a data set. So I thought this could be achieved by quad function.

ftyp1 = fittype('quad(@(x) a.*x.^2,0,x)','options',ops1,'independent',{'x'},'coefficients',{'a'})

But in this example Matlab gives error. If i create another function to calculate quad function, like this :

function [c ] = myfunction( b ,a)

if length(a)==1, a = a(ones(size(b))); end

if length(b)==1, b = b(ones(size(a))); end

c=NaN(length(b),1);

parfor i=1:length(b)

c(i)=quad(@(x) a(i).*x.^2,0,b(i));

end

end

ftyp1 = fittype('myfunction(x,a)','options',ops1,'independent',{'x'},'coefficients',{'a'})

With using the sample code above, Matlab could find the coefficients. The trick is making it calculate quad function in another function as you can see.So my question is this : how could i implement quad function directly to fittype function without creating extra functions?

Answer 1

[Andrew Newell]

If your expression is a linear function of the coefficients, as in your example, you could do something like this:

ftyp1 = fittype('@(x) a.*quad(x.^2,0,x)','independent',{'x'},'coefficients',{'a'})

[deniz]

Thanks for the answer but it didn't work. It started as it would work as it states that 'Warning: Start point not provided, choosing random start point'. But after that it gave me this: ??? Undefined function or method 'isnan' for input arguments of type 'function_handle'.

I also tried this : char(inline('@(x) quad( a.*x^2,0,x)')) and it gave me same error. I also remind you that if there is another way or another function to fit (fitting quad), i would be happy to try that.

[Andrew Newell]

I confess I only went as far as creating a fittype object and did not try to fit anything.

Answer 2

[Andrew Newell]

I think the heart of the problem is that quad only accepts scalars for the lower and upper bounds, so it cannot deal with the vector x. I tried using arrayfun, but it does not accept function handles. Also, fittype does not accept function handles, so solutions involving nested functions are out. Your myfunction is probably the best approach.

[deniz]

Thanks anyway

Answer 3

[Giovanni Ughi]

Useful topic. In case I have to fit a model like this: model = b.*x .* quad(a.*x.^2) with a,b parameters and x independent variable?

apparently is not possible to write something like this

for i:1:length(b)

c(i) = @(x) b(i).*x .* quad(@(x) a(i).*x^2,0,d(i))

end

any suggestion?

[Walter Roberson]

c{i} = @(x) b(i).*x .* quad(@(x) a(i).*x^2,0,d(i));

Function handles can not be stored as elements of regular arrays, but can be stored as elements of cell arrays.

What you are going to _do_ with those stored function handles, I do not know.