Rheolef  7.2
an efficient C++ finite element environment
 
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gauss_radau_jacobi.icc
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1
21#include "rheolef/compiler.h"
22#include "rheolef/gamma.h"
23#include "rheolef/jacobi.h"
24#include "rheolef/jacobi_roots.h"
25#include <iterator>
26namespace rheolef {
27template <class Size, class OutputIterator1, class OutputIterator2>
28void gauss_radau_jacobi (Size R,
29 typename std::iterator_traits<OutputIterator1>::value_type alpha,
30 typename std::iterator_traits<OutputIterator1>::value_type beta,
31 OutputIterator1 zeta, OutputIterator2 omega)
32{
33 typedef typename std::iterator_traits<OutputIterator1>::value_type T;
34 check_macro (R >= 1, "gauss_radau_jacobi: node number " << R << " may be >= 1");
35 T num = pow(T(2), alpha+beta)/(beta+T(1.*R));
36 T w0 = pow(T(2), alpha+beta+1)*(beta+1);
37 if (alpha == floor(alpha) && beta == floor(beta)) {
38 num *= T(1.*R)/((alpha+T(1.*R))*(beta+T(1.*R)));
39 w0 *= 1/(T(1.*R)*(alpha+T(1.*R)));
40 for (Size k = 1; k <= size_t(static_cast<int>(beta)); k++) {
41 num *= T(1.*R+k)/(alpha+T(1.*R+k));
42 w0 *= T(sqr(T(int(k))))/(T(1.*R+k)*(alpha+R+k));
43 }
44 } else {
45 num *= (my_gamma(alpha+R)/my_gamma(alpha+beta+R+1))
46 *(my_gamma(beta+R)/my_gamma(T(1.*R)));
47 w0 *= sqr(my_gamma(beta+1))
48 *(my_gamma(T(1.*R))/my_gamma(beta+R+1))
49 *(my_gamma(alpha+R)/my_gamma(alpha+beta+R+1));
50 }
51 zeta [0] = -1;
52 omega[0] = w0;
53 jacobi_roots (R-1, alpha, beta+1, zeta+1);
54 jacobi<T> P1 (R-1, alpha, beta);
55 for (Size r = 1; r < R; ++r)
56 omega[r] = num*(1-zeta[r])/sqr(P1(zeta[r]));
57}
58} // namespace rheolef
Expr1::float_type T
Definition field_expr.h:230
check_macro(expr1.have_homogeneous_space(Xh1), "dual(expr1,expr2); expr1 should have homogeneous space. HINT: use dual(interpolate(Xh, expr1),expr2)")
This file is part of Rheolef.
void gauss_radau_jacobi(Size R, typename std::iterator_traits< OutputIterator1 >::value_type alpha, typename std::iterator_traits< OutputIterator1 >::value_type beta, OutputIterator1 zeta, OutputIterator2 omega)
space_mult_list< T, M > pow(const space_basic< T, M > &X, size_t n)
Definition space_mult.h:120
void jacobi_roots(Size R, T alpha, T beta, OutputIterator zeta)
T my_gamma(const T &x)
Definition gamma.icc:25