IntGen¶

To give a full example, let’s take numerical integration. If a code uses an integral with discrete and symbolic parts, there are huge gains if the code evaluates the symbolic parts before they are run. For example take the following integral, where comes from a discrete function in the code:

A quick optimization would be to evaluate and at the quadrature points, assuming two quadrature points, the new code would be:

But that code is meaningless with out the formula above! What’s more the user has to evaluate the symbolic parts by hand which becomes yet another source of error. It would be better to have a high level code that generates the low level code when a new integral (or even better precision) is required.

u = DiscFunc("u")
x = Symbol("x")
dx = Dom(x, 0, 1)

integral = (Func(cos(x), x)*u + Func(sin(x), x))*dx
select_quad_rule(num_pts=2, name="Gauss")
gen_file("ex1", [integral],  ["eval_gen"], ['u'])

const unsigned int NUM_QUAD_PTS = 2;
const double QUAD_PTS[2] = {-0.57735026919, 0.57735026919};
const double QUAD_WTS[2] = {1.0, 1.0};

inline double eval_gen(double* u)
{
  double ret_val = 0.0;
  ret_val += 0.459697694131860;

  ret_val += 0.488876937571022*(u[0])
          + 0.352392910067197*(u[1]);
  return ret_val;
  }