def fastChebScalar(self, fj, fk):
"""Fast Chebyshev scalar product."""
N = fj.shape[0]
if self.quad == "GC":
fk[:] = dct(fj, type=2, axis=0)*np.pi/(2*N)
elif self.quad == "GL":
fk[:] = dct(fj, type=1, axis=0)*np.pi/(2*(N-1))
return fk
def ifct(self, fk, cj):
"""Inverse fast Chebyshev transform."""
if self.quad == "GC":
cj[:] = 0.5*dct(fk, type=3, axis=0)
cj += 0.5*fk[0]
elif self.quad == "GL":
cj[:] = 0.5*dct(fk, type=1, axis=0)
cj += 0.5*fk[0]
cj[::2] += 0.5*fk[-1]
cj[1::2] -= 0.5*fk[-1]
return cj
def fct(self, fj, cj):
"""Fast Chebyshev transform."""
N = fj.shape[0]
if self.quad == "GC":
cj[:] = dct(fj, type=2, axis=0)
cj /= N
cj[0] /= 2
elif self.quad == "GL":
cj[:] = dct(fj, type=1, axis=0)/(N-1)
cj[0] /= 2
cj[-1] /= 2
return cj
def fastChebScalar(self, fj, fk):
"""Fast Chebyshev scalar product."""
if self.fast_transform:
N = fj.shape[0]
if self.quad == "GC":
fk[:] = dct(fj, type=2, axis=0)*pi/(2*N)
elif self.quad == "GL":
fk[:] = dct(fj, type=1, axis=0)*pi/(2*(N-1))
else:
if self.points is None: self.init(fj.shape[0])
fk[:] = np.dot(self.V, fj*self.weights)
return fk
def energy(u, N, comm, rank, L):
uu = sum(u, axis=(1,2))
c = zeros(N[0])
comm.Gather(uu, c)
if rank == 0:
ak = 1./(N[0]-1)*dct(c, 1, axis=0)
w = arange(0, N[0], 1, dtype=float)
w[2:] = 2./(1-w[2:]**2)
w[0] = 1
w[1::2] = 0
return sum(ak*w)*L[1]*L[2]/N[1]/N[2]
else:
return 0
