def eval(self, x, output_array=None):
"""Return expression evaluated on x
Parameters
----------
x : float or array of floats
Array must be of shape (D, N), for N points in D dimensions
"""
from shenfun import MixedTensorProductSpace
from shenfun.fourier.bases import R2CBasis
V = self.function_space()
basis = self.basis()
if output_array is None:
output_array = np.zeros(x.shape[1], dtype=V.forward.input_array.dtype)
else:
output_array[:] = 0
work = np.zeros_like(output_array)
assert V.dimensions == len(x)
for vec, (base, ind) in enumerate(zip(self.terms(), self.indices())):
for base_j, b0 in enumerate(base):
M = []
sc = self.scales()[vec, base_j]
test_sp = V
if isinstance(V, MixedTensorProductSpace):
test_sp = V.flatten()[ind[base_j]]
r2c = -1
last_conj_index = -1
sl = -1
for axis, k in enumerate(b0):
xx = test_sp[axis].map_reference_domain(np.squeeze(x[axis]))
P = test_sp[axis].evaluate_basis_derivative_all(xx, k=k)
M.append(P[..., V.local_slice()[axis]])
if isinstance(test_sp[axis], R2CBasis):
r2c = axis
m = test_sp[axis].N//2+1
if test_sp[axis].N % 2 == 0:
last_conj_index = m-1
else:
last_conj_index = m
sl = V.local_slice()[axis].start
bv = basis if basis.rank == 0 else basis[ind[base_j]]
work.fill(0)
if len(x) == 2:
work = evaluate.evaluate_2D(work, bv, M, r2c, last_conj_index, sl)
elif len(x) == 3:
work = evaluate.evaluate_3D(work, bv, M, r2c, last_conj_index, sl)
output_array += sc*work
return output_array
def _eval_cython(self, points, coefficients, output_array):
"""Evaluate Function at points, given expansion coefficients
Parameters
----------
points : float or array of floats
coefficients : array
Expansion coefficients
output_array : array
Return array, function values at points
"""
P = []
r2c = -1
last_conj_index = -1
sl = -1
for base in self:
axis = base.axis
x = base.map_reference_domain(points[axis])
D = base.evaluate_basis_all(x=x)
P.append(D[..., self.local_slice()[axis]])
if isinstance(base, R2CBasis):
r2c = axis
M = base.N // 2 + 1
if base.N % 2 == 0:
last_conj_index = M - 1
else:
last_conj_index = M
sl = self.local_slice()[axis].start
if len(self) == 2:
output_array = evaluate.evaluate_2D(output_array, coefficients, P,
r2c, last_conj_index, sl)
elif len(self) == 3:
output_array = evaluate.evaluate_3D(output_array, coefficients, P,
r2c, last_conj_index, sl)
output_array = np.atleast_1d(output_array)
output_array = self.comm.allreduce(output_array)
return output_array
def eval(self, x, output_array=None):
"""Return expression evaluated on x
Parameters
----------
x : float or array of floats
Array must be of shape (D, N), for N points in D dimensions
"""
from shenfun import MixedTensorProductSpace
from shenfun.fourier.bases import R2CBasis
if len(x.shape) == 1: # 1D case
x = x[None, :]
V = self.function_space()
basis = self.basis()
if output_array is None:
output_array = np.zeros(x.shape[1],
dtype=V.forward.input_array.dtype)
else:
output_array[:] = 0
work = np.zeros_like(output_array)
assert V.dimensions == len(x)
for vec, (base, ind) in enumerate(zip(self.terms(), self.indices())):
for base_j, b0 in enumerate(base):
M = []
test_sp = V
if isinstance(V, MixedTensorProductSpace):
test_sp = V.flatten()[ind[base_j]]
r2c = -1
last_conj_index = -1
sl = -1
for axis, k in enumerate(b0):
xx = test_sp[axis].map_reference_domain(np.squeeze(
x[axis]))
P = test_sp[axis].evaluate_basis_derivative_all(xx, k=k)
if not test_sp[axis].domain_factor() == 1:
P *= test_sp[axis].domain_factor()**(k)
if len(x) > 1:
M.append(P[..., V.local_slice()[axis]])
if isinstance(test_sp[axis], R2CBasis) and len(x) > 1:
r2c = axis
m = test_sp[axis].N // 2 + 1
if test_sp[axis].N % 2 == 0:
last_conj_index = m - 1
else:
last_conj_index = m
sl = V.local_slice()[axis].start
bv = basis if basis.rank == 0 else basis[ind[base_j]]
work.fill(0)
if len(x) == 1:
work = np.dot(P, bv)
elif len(x) == 2:
work = evaluate.evaluate_2D(work, bv, M, r2c,
last_conj_index, sl)
elif len(x) == 3:
work = evaluate.evaluate_3D(work, bv, M, r2c,
last_conj_index, sl)
sc = self.scales()[vec, base_j]
if not hasattr(sc, 'free_symbols'):
sc = float(sc)
else:
sym0 = sc.free_symbols
m = []
for sym in sym0:
j = 'xyzrs'.index(str(sym))
m.append(x[j])
sc = sp.lambdify(sym0, sc)(*m)
output_array += sc * work
return output_array