class SchoofSSA1dExact:
  """
  schoof_ssa_exact
  Returns certain exact solutions of the ssa equation found in 
  Schoof, A Variational Approach to Ice Stream Flow, 2006, pp 237-238.

  The PDE is:

  -d/dy ( Bh/2 |1/2 du/dy|^(-2/3) du/dy) = f (1-|y/L|^m)

  on the domain -3L <= y <= 3L with periodic boundary conditions.  The resulting $u$
  is the downstream velocity on an infinite slab.

  """

  def __init__(self,L,m,B=1,h=1,f=1):
    self.L = float(L)
    self.m = float(m)
    self.f = float(f)
    self.h = float(h)
    self.B = float(B)
    self.scale = 2*(f/(B*h))**3.

  def eval(self,x):
    L = self.L; m=self.m;
    W = (m+1.)**(1./m);
    u=abs(x/self.L)
    if u>W:
      v=0
    else:
      v = -L**4*(  (u**4-(m+1)**(4./m))/4 -
                      3*(u**(m+4)-(m+1)**(1+4./m))/( (m+1)*(m+4)) + 
                      3*(u**(2*m+4)-(m+1)**(2+4./m))/((m+1)**2*(2*m+4.)) -
                      (u**(3*m+4)-(m+1)**(3+4./m))/( (m+1)**3*(3*m+4) ) )

    v *= self.scale
    return v