def dx(u, FST, axis=0):
"""Compute integral of u over domain for channel solvers"""
sx = list(range(3))
sx.pop(axis)
uu = np.sum(u, axis=tuple(sx))
sl = FST.local_slice(False)[axis]
M = FST.shape()[axis]
c = np.zeros(M)
cc = np.zeros(M)
cc[sl] = uu
FST.comm.Reduce(cc, c, op=MPI.SUM, root=0)
quad = FST.bases[axis].quad
if FST.comm.Get_rank() == 0:
if quad == 'GL':
ak = np.zeros_like(c)
ak = dct(c, ak, 1, axis=0)
ak /= (M-1)
w = np.arange(0, M, 1, dtype=float)
w[2:] = 2./(1-w[2:]**2)
w[0] = 1
w[1::2] = 0
return sum(ak*w)*np.prod(np.take(config.params.L/config.params.N, sx))
assert quad == 'GC'
d = np.zeros(M)
k = 2*(1 + np.arange((M-1)//2))
d[::2] = (2./M)/np.hstack((1., 1.-k*k))
w = np.zeros_like(d)
w = dct(d, w, type=3, axis=0)
return np.sum(c*w)*np.prod(np.take(config.params.L/config.params.N, sx))
return 0
def dx(u, FST):
"""Compute integral of u over domain"""
uu = sum(u, axis=(1, 2))
sl = FST.local_slice(False)[0]
M = FST.shape()[0]
c = zeros(M)
cc = zeros(M)
cc[sl] = uu
FST.comm.Reduce(cc, c, op=MPI.SUM, root=0)
quad = FST.bases[0].quad
if FST.comm.Get_rank() == 0:
if quad == 'GL':
ak = zeros_like(c)
ak = dct(c, ak, 1, axis=0)
ak /= (M - 1)
w = arange(0, M, 1, dtype=float)
w[2:] = 2. / (1 - w[2:]**2)
w[0] = 1
w[1::2] = 0
return sum(ak * w) * config.params.L[1] * config.params.L[
2] / config.params.N[1] / config.params.N[2]
assert quad == 'GC'
d = zeros(M)
k = 2 * (1 + arange((M - 1) // 2))
d[::2] = (2. / M) / hstack((1., 1. - k * k))
w = zeros_like(d)
w = dct(d, w, type=3, axis=0)
return sum(c * w) * config.params.L[1] * config.params.L[
2] / config.params.N[1] / config.params.N[2]
return 0
def dx(self, u, quad):
"""Compute integral of u over domain"""
uu = sum(u, axis=(1, 2))
c = zeros(self.N[0])
self.comm.Gather(uu, c)
if self.rank == 0:
if quad == 'GL':
ak = zeros_like(c)
ak = dct(c, ak, 1, axis=0)
ak /= (self.N[0] - 1)
w = arange(0, self.N[0], 1, dtype=self.float)
w[2:] = 2. / (1 - w[2:]**2)
w[0] = 1
w[1::2] = 0
return sum(
ak * w) * self.L[1] * self.L[2] / self.N[1] / self.N[2]
assert quad == 'GC'
d = zeros(self.N[0])
k = 2 * (1 + arange((self.N[0] - 1) // 2))
d[::2] = (2. / self.N[0]) / hstack((1., 1. - k * k))
w = zeros_like(d)
w = dct(d, w, type=3, axis=0)
return sum(c * w) * self.L[1] * self.L[2] / self.N[1] / self.N[2]
return 0
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 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 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 ifct(self, fk, cj):
"""Inverse fast Chebyshev transform."""
if self.quad == "GC":
cj = dct(fk, cj, type=3, axis=0)
cj *= 0.5
cj += fk[0]/2
elif self.quad == "GL":
cj = dct(fk, cj, type=1, axis=0)
cj *= 0.5
cj += fk[0]/2
cj[::2] += fk[-1]/2
cj[1::2] -= fk[-1]/2
return cj
def fastChebScalar(self, fj, fk):
"""Fast Chebyshev scalar product."""
N = fj.shape[0]
if self.fast_transform:
if self.quad == "GC":
fk = dct(fj, fk, type=2, axis=0)
fk *= (pi/(2*N))
elif self.quad == "GL":
fk = dct(fj, fk, type=1, axis=0)
fk *= (pi/(2*(N-1)))
else:
if not self.points.shape == (N,): self.init(N)
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
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
def Q(u, rank, comm, N):
"""Integrate u over entire computational domain
"""
L = config.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
def Q(u, rank, comm, N):
"""Integrate u over entire computational domain
"""
L = config.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
