oomph::Legendre_functions_helper Namespace Reference

Helper namespace for functions required for Helmholtz computations. More...

Functions
double	factorial (const unsigned &l)
	Factorial. More...
double	plgndr1 (const unsigned &n, const double &x)
	Legendre polynomials depending on one parameter. More...
double	plgndr2 (const unsigned &l, const unsigned &m, const double &x)
	Legendre polynomials depending on two parameters. More...

Detailed Description

Helper namespace for functions required for Helmholtz computations.

Function Documentation

factorial()

double oomph::Legendre_functions_helper::factorial

(

const unsigned &

l

)

Factorial.

    {
      if (l == 0) return 1.0;
      return double(l * factorial(l - 1));
    }

Referenced by oomph::FourierDecomposedHelmholtzDtNMesh< ELEMENT >::setup_gamma().

plgndr1()

double oomph::Legendre_functions_helper::plgndr1	(	const unsigned &	n,
		const double &	x
	)

Legendre polynomials depending on one parameter.

    {
      unsigned i;
      double pmm, pmm1;
      double pmm2 = 0;
 
#ifdef PARANOID
      // Shout if things went wrong
      if (std::fabs(x) > 1.0)
      {
        std::ostringstream error_stream;
        error_stream << "Bad arguments in routine plgndr1: x=" << x
                     << " but should be less than 1 in absolute value.\n";
        throw OomphLibError(
          error_stream.str(), OOMPH_CURRENT_FUNCTION, OOMPH_EXCEPTION_LOCATION);
      }
#endif
 
      // Compute pmm : if l=m it's finished
      pmm = 1.0;
      if (n == 0)
      {
        return pmm;
      }
 
      pmm1 = x * 1.0;
      if (n == 1)
      {
        return pmm1;
      }
      else
      {
        for (i = 2; i <= n; i++)
        {
          pmm2 = (x * (2 * i - 1) * pmm1 - (i - 1) * pmm) / i;
          pmm = pmm1;
          pmm1 = pmm2;
        }
        return pmm2;
      }
 
    } // end of plgndr1

References boost::multiprecision::fabs(), i, n, OOMPH_CURRENT_FUNCTION, OOMPH_EXCEPTION_LOCATION, and plotDoE::x.

plgndr2()

double oomph::Legendre_functions_helper::plgndr2	(	const unsigned &	l,
		const unsigned &	m,
		const double &	x
	)

Legendre polynomials depending on two parameters.

    {
      unsigned i, ll;
      double fact, pmm, pmmp1, somx2;
      double pll = 0.0;
 
#ifdef PARANOID
      // Shout if things went wrong
      if (std::fabs(x) > 1.0)
      {
        std::ostringstream error_stream;
        error_stream << "Bad arguments in routine plgndr2: x=" << x
                     << " but should be less than 1 in absolute value.\n";
        throw OomphLibError(
          error_stream.str(), OOMPH_CURRENT_FUNCTION, OOMPH_EXCEPTION_LOCATION);
      }
#endif
 
      // This one is easy...
      if (m > l)
      {
        return 0.0;
      }
 
      // Compute pmm : if l=m it's finished
      pmm = 1.0;
      if (m > 0)
      {
        somx2 = sqrt((1.0 - x) * (1.0 + x));
        fact = 1.0;
        for (i = 1; i <= m; i++)
        {
          pmm *= -fact * somx2;
          fact += 2.0;
        }
      }
      if (l == m) return pmm;
 
      // Compute pmmp1 : if l=m+1 it's finished
      else
      {
        pmmp1 = x * (2 * m + 1) * pmm;
        if (l == (m + 1))
        {
          return pmmp1;
        }
        // Compute pll : if l>m+1 it's finished
        else
        {
          for (ll = m + 2; ll <= l; ll++)
          {
            pll = (x * (2 * ll - 1) * pmmp1 - (ll + m - 1) * pmm) / (ll - m);
            pmm = pmmp1;
            pmmp1 = pll;
          }
          return pll;
        }
      }
    } // end of plgndr2

References boost::multiprecision::fabs(), i, m, OOMPH_CURRENT_FUNCTION, OOMPH_EXCEPTION_LOCATION, sqrt(), and plotDoE::x.

Referenced by oomph::FourierDecomposedHelmholtzDtNBoundaryElement< ELEMENT >::compute_gamma_contribution(), ProblemParameters::exact_minus_dudr(), PlanarWave::get_exact_u(), ProblemParameters::get_exact_u(), and main().