Rheolef  7.2
an efficient C++ finite element environment
phi.h
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1 struct phi {
26  phi (Float n1=2, Float c1=1, Float r1=0) : n(n1), c(c1), r(r1) {}
27  Float operator() (const Float& x) const {
28  if (x <= 0) return 0;
29  if (n == 1) return x/(c+r);
30  if (r == 0) return pow(x/c,1/n);
31  Float y = x/(c+r);
33  for (size_t i = 0; true; ++i) {
34  Float ry = f(y)-x;
35  Float dy = -ry/df_dy(y);
36  if (fabs(ry) <= tol && fabs(dy) <= tol) break;
37  if (i >= max_iter) break;
38  if (y+dy > 0) {
39  y += dy;
40  } else {
41  y /= 2;
42  check_macro (1+y != y, "phi: machine precision problem");
43  }
44  }
45  return y;
46  }
47  Float derivative (const Float& x) const {
48  Float phi_x = operator()(x);
49  return 1/(r + n*c*pow(phi_x,-1+n));
50  }
51 protected:
52  Float f(Float y) const { return c*pow(y,n) + r*y; }
53  Float df_dy(Float y) const { return n*c*pow(y,-1+n) + r; }
55  static const size_t max_iter = 100;
56 };
see the Float page for the full documentation
check_macro(expr1.have_homogeneous_space(Xh1), "dual(expr1,expr2); expr1 should have homogeneous space. HINT: use dual(interpolate(Xh, expr1),expr2)")
space_mult_list< T, M > pow(const space_basic< T, M > &X, size_t n)
Definition: space_mult.h:120
Definition: phi.h:25
phi(Float n1=2, Float c1=1, Float r1=0)
Definition: phi.h:26
Float c
Definition: phi.h:54
Float derivative(const Float &x) const
Definition: phi.h:47
static const size_t max_iter
Definition: phi.h:55
Float n
Definition: phi.h:54
Float r
Definition: phi.h:54
Float f(Float y) const
Definition: phi.h:52
Float df_dy(Float y) const
Definition: phi.h:53
Float operator()(const Float &x) const
Definition: phi.h:27
Float epsilon