Symbolic library for C++

[Ryan Shrott]

Can anyone recommend a nice symbolic library for C++? I was trying to use SymbolicC++, but it very outdated and not well kept. Looking for suggestions, possibly from @Polter or @Daniel Duffy.

 

[Daniel Duffy]

What kinds of applications do you have in mind?

 

[Ryan Shrott]

I was working on a curve fitting exercise with my Binomial Lattice application. I used Neville's algorithm and used SymbolicC++ library, but it hasn't been well kept.

So something like this:

void neville(BinomialLattice<Symbolic> &lat, curve curve, Symbolic x)
{

    for (int i = 0; i < 5; ++i)
    {
        lat(4, i) = curve[i][0];
    }

    for (int i = 3; i != -1; --i)
    {
        for (int j = 0; j <= i; ++j)
        {
            lat(i, j) = ((lat(4, j) - x) * lat(i + 1, j) + (x - lat(4, j)) * lat(i + 2, j)) / (lat(4, j) - lat(4, i));
        }
    }
}

 

[Daniel Duffy]

I think Neville can be done in 'normal' C++?

The underlying BinomialLattice can be used but the backwards induction algo to update its node values uses the array of x_i and y_i values I = 0,...n. As in here

Neville's algorithm - Wikipedia, the free encyclopedia

You can create a class with x,y member data that has a function

double getValue(double x) const;

 

[Daniel Duffy]

A similar application is Romberg integration. The code presented can easily be ported to your framework.

It's structurally similar to Neville except that the starting point is a continuous function f:R -> R.

Romberg's method - Wikipedia, the free encyclopedia

 

[Ryan Shrott]

Yea I think it could be done without the symbolic library, but it's just so much easier that way.

 

[Daniel Duffy]

Yea I think it could be done without the symbolic library, but it's just so much easier that way.

I see. One idea is that Automatic Differentiation packages might worth a look. I have no experience here.

Automatic differentiation - Wikipedia, the free encyclopedia

[1107.1831] Adjoints and Automatic (Algorithmic) Differentiation in Computational Finance