Weights of QGaussLogR

[simonsticko]

If I use QGaussLogR with the factor_out_singular_weights=true flag, the quadrature weights does not sum to one. From the documentation, it looks like they should.

Is this a bug? Or should the sum of the weights only converge to 1 when we increase the order? Do you know @luca-heltai ?

#include <deal.II/base/quadrature_lib.h>

using namespace dealii;

int
main()
{
  const int dim = 1;

  const Point<dim> ref_space_singularity;
  const double     singularity_scaling        = 1;
  const bool       factor_out_singular_weight = true;

  const unsigned int max_order = 12;
  for (unsigned int order = 1; order <= max_order; order++)
    {
      QGaussLogR<dim> quadrature(order,
                                 ref_space_singularity,
                                 singularity_scaling,
                                 factor_out_singular_weight);

      double sum_of_weights = 0;
      for (unsigned int i = 0; i < quadrature.size(); ++i)
        sum_of_weights += quadrature.weight(i);
     
      std::cout <<"order = "<<order <<", sum_of_weights = " << sum_of_weights << std::endl;
    }
}

order = 1, sum_of_weights = 0.910239
order = 2, sum_of_weights = 0.883331
order = 3, sum_of_weights = 0.936294
order = 4, sum_of_weights = 0.95993
order = 5, sum_of_weights = 0.972484
order = 6, sum_of_weights = 0.979941
order = 7, sum_of_weights = 0.984729
order = 8, sum_of_weights = 0.987986
order = 9, sum_of_weights = 0.990301
order = 10, sum_of_weights = 0.992005
order = 11, sum_of_weights = 0.993296
order = 12, sum_of_weights = 0.994298

[simonsticko]

Okey, never mind. I have convinced myself that there is no reason that they should sum to 1.

[masterleinad]

For factor_out_singular_weight=false, the weights should sum up to -1 and they do.

[luca-heltai]

Sorry, I'm late to the party. Summing the weights with factor_out_singular_weight=true does not make any sense, since you are not supposed to integrate smooth functions with it (and the constant is such a function). The documentation states

Notice that this quadrature rule is worthless if you try to use it for regular functions once you factored out the singularity.

I hope this is clear enough, but you are welcome to suggest any changes you think are appropriate in the documentation. I must admit it does not read well (I think I wrote this some 10 to 15 years ago, and I would have probably written it differently today).