How to use polynomial as an input for an integral function?

I am building a code where I need to find a polynomial using values given from an interation, and then use the polynomial in a Gauss-Kronrod integral. In order to calculate this integral I need to build a function that gets the polynomial as an input (along with many other arguments) and uses that polynomial in the Gauss-Kronrod function. My problem is that Matlab does not accept the Poly2sym function as an input for the integral. I really need to use this function because I get the polynomial values from the Polyfit function and then I use the Poly2sym to transform that vector into a polynomial. My program is large so I have made a shorter sample of my problem:

function o = func(Bt,r,q,sigma,t)

o = Bt + ola(Bt,poly2sym([1 3 2]),r,q,sigma,t);

end

function F = ola(Bt,Bx,r,q,sigma,t)

F = quadgk(integral1(Bt,Bx,r,q,sigma,t),0,t);

end

function i1 = integral1(Bt,Bx,r,q,sigma,t)

i1 = @(x)(t-x).*d1(Bt,t-x,Bx,r,q,sigma);

end

function u = d1(S,t,B,r,q,sigma)

u =log(S./B)+(r-q+0.5*(sigma^2))*t;

    end

My main question is: How do I use the poly2sym function here without an error, in a way that the function calculates the integral using poly2sym polynomial correctly?

This short sample is part of a much larger problem that I would be happy to provide to you if you can't understand my problem.

Thank you very much for your time.

Answer 1

[Walter Roberson]

integral1() is for numeric integration. When you want to do symbolic integration (poly2sym generates symbolic) then use the symbolic routine int().

You would probably want to use matlabFunction() on the result of int() if you are going to put it into a quadgk call. Or you could just int() it again symbolically and double() the rssult. Or you could use the symbolic toolbox numeric integration routines.

Answer 2

[Filipe Pereira]

integral1 in my program is just a name I am using to define that function. I am not sure I know where to include the int() function there. Do you mind rewrite my program with the changes you suggested in order to make it run correctly with the polynomial?

Thank you for your time.

[Walter Roberson]

When you get down to the d1 level, where you divide by the B which has been passed down from the poly2sym() result, then what is your expectation of what should happen there? Are you wanting the resulting "u" to be a function handle used by one of the layers above and upwards into the quadgk()? Or are you wanting to evaluate the polynomial at x at the place it shows B ?

[Filipe Pereira]

The resulting "u" is supposed to be a function handle with the polynomial resulting from the poly2sym function that will be used on the quadgk().