def test_helmholtz2D(family, axis):
la = lla
if family == 'chebyshev':
la = cla
N = (8, 9)
SD = shenfun.Basis(N[axis], family=family, bc=(0, 0))
K1 = shenfun.Basis(N[(axis + 1) % 2], family='F', dtype='d')
subcomms = mpi4py_fft.pencil.Subcomm(MPI.COMM_WORLD, allaxes2D[axis])
bases = [K1]
bases.insert(axis, SD)
T = shenfun.TensorProductSpace(subcomms, bases, axes=allaxes2D[axis])
u = shenfun.TrialFunction(T)
v = shenfun.TestFunction(T)
if family == 'chebyshev':
mat = shenfun.inner(v, shenfun.div(shenfun.grad(u)))
else:
mat = shenfun.inner(shenfun.grad(v), shenfun.grad(u))
H = la.Helmholtz(*mat)
H = la.Helmholtz(*mat)
u = shenfun.Function(T)
u[:] = np.random.random(u.shape) + 1j * np.random.random(u.shape)
f = shenfun.Function(T)
f = H.matvec(u, f)
f = H.matvec(u, f)
g0 = shenfun.Function(T)
g1 = shenfun.Function(T)
M = {d.get_key(): d for d in mat}
g0 = M['ADDmat'].matvec(u, g0)
g1 = M['BDDmat'].matvec(u, g1)
assert np.linalg.norm(f - (g0 + g1)) < 1e-12, np.linalg.norm(f - (g0 + g1))
def test_biharmonic3D(family, axis):
la = lla
if family == 'chebyshev':
la = cla
N = (16, 16, 16)
SD = shenfun.Basis(N[allaxes3D[axis][0]], family=family, bc='Biharmonic')
K1 = shenfun.Basis(N[allaxes3D[axis][1]], family='F', dtype='D')
K2 = shenfun.Basis(N[allaxes3D[axis][2]], family='F', dtype='d')
subcomms = mpi4py_fft.pencil.Subcomm(MPI.COMM_WORLD, [0, 1, 1])
bases = [0] * 3
bases[allaxes3D[axis][0]] = SD
bases[allaxes3D[axis][1]] = K1
bases[allaxes3D[axis][2]] = K2
T = shenfun.TensorProductSpace(subcomms, bases, axes=allaxes3D[axis])
u = shenfun.TrialFunction(T)
v = shenfun.TestFunction(T)
if family == 'chebyshev':
mat = shenfun.inner(
v, shenfun.div(shenfun.grad(shenfun.div(shenfun.grad(u)))))
else:
mat = shenfun.inner(shenfun.div(shenfun.grad(v)),
shenfun.div(shenfun.grad(u)))
H = la.Biharmonic(*mat)
H = la.Biharmonic(*mat)
u = shenfun.Function(T)
u[:] = np.random.random(u.shape) + 1j * np.random.random(u.shape)
f = shenfun.Function(T)
f = H.matvec(u, f)
f = H.matvec(u, f)
g0 = shenfun.Function(T)
g1 = shenfun.Function(T)
g2 = shenfun.Function(T)
M = {d.get_key(): d for d in mat}
amat = 'ABBmat' if family == 'chebyshev' else 'PBBmat'
g0 = M['SBBmat'].matvec(u, g0)
g1 = M[amat].matvec(u, g1)
g2 = M['BBBmat'].matvec(u, g2)
assert np.linalg.norm(f - (g0 + g1 + g2)) < 1e-8, np.linalg.norm(f -
(g0 + g1 +
g2))
def test_mul2():
mat = shenfun.SparseMatrix({0: 1}, (3, 3))
v = np.ones(3)
c = mat * v
assert np.allclose(c, 1)
mat = shenfun.SparseMatrix({-2:1, -1:1, 0: 1, 1:1, 2:1}, (3, 3))
c = mat * v
assert np.allclose(c, 3)
SD = shenfun.Basis(8, "L", bc=(0, 0), plan=True, scaled=True)
u = shenfun.TrialFunction(SD)
v = shenfun.TestFunction(SD)
mat = shenfun.inner(shenfun.grad(u), shenfun.grad(v))
z = shenfun.Function(SD, val=1)
c = mat * z
assert np.allclose(c[:6], 1)
def test_to_ortho(basis, quad):
N = 10
if basis.family() == 'legendre':
B1 = lBasis[0](N, quad)
B3 = lBasis[0](N, quad)
elif basis.family() == 'chebyshev':
B1 = cBasis[0](N, quad)
B3 = cBasis[0](N, quad)
elif basis.family() == 'laguerre':
B1 = laBasis[0](N, quad)
B3 = laBasis[0](N, quad)
B0 = basis(N, quad=quad)
a = shenfun.Array(B0)
a_hat = shenfun.Function(B0)
b0_hat = shenfun.Function(B1)
b1_hat = shenfun.Function(B1)
a[:] = np.random.random(a.shape)
a_hat = a.forward(a_hat)
b0_hat = shenfun.project(a_hat, B1, output_array=b0_hat, fill=False, use_to_ortho=True)
b1_hat = shenfun.project(a_hat, B1, output_array=b1_hat, fill=False, use_to_ortho=False)
assert np.linalg.norm(b0_hat-b1_hat) < 1e-10
B2 = basis(N, quad=quad)
TD = shenfun.TensorProductSpace(shenfun.comm, (B0, B2))
TC = shenfun.TensorProductSpace(shenfun.comm, (B1, B3))
a = shenfun.Array(TD)
a_hat = shenfun.Function(TD)
b0_hat = shenfun.Function(TC)
b1_hat = shenfun.Function(TC)
a[:] = np.random.random(a.shape)
a_hat = a.forward(a_hat)
b0_hat = shenfun.project(a_hat, TC, output_array=b0_hat, fill=False, use_to_ortho=True)
b1_hat = shenfun.project(a_hat, TC, output_array=b1_hat, fill=False, use_to_ortho=False)
assert np.linalg.norm(b0_hat-b1_hat) < 1e-10
F0 = shenfun.Basis(N, 'F')
TD = shenfun.TensorProductSpace(shenfun.comm, (B0, F0))
TC = shenfun.TensorProductSpace(shenfun.comm, (B1, F0))
a = shenfun.Array(TD)
a_hat = shenfun.Function(TD)
b0_hat = shenfun.Function(TC)
b1_hat = shenfun.Function(TC)
a[:] = np.random.random(a.shape)
a_hat = a.forward(a_hat)
b0_hat = shenfun.project(a_hat, TC, output_array=b0_hat, fill=False, use_to_ortho=True)
b1_hat = shenfun.project(a_hat, TC, output_array=b1_hat, fill=False, use_to_ortho=False)
assert np.linalg.norm(b0_hat-b1_hat) < 1e-10
import pytest
import numpy as np
from mpi4py import MPI
import shenfun
N = 8
comm = MPI.COMM_WORLD
V = shenfun.Basis(N, 'C')
u0 = shenfun.TrialFunction(V)
T = shenfun.TensorProductSpace(comm, (V, V))
u1 = shenfun.TrialFunction(V)
TT = shenfun.VectorTensorProductSpace(T)
u2 = shenfun.TrialFunction(TT)
@pytest.mark.parametrize('basis', (u0, u1, u2))
def test_mul(basis):
e = shenfun.Expr(basis)
e2 = 2 * e
assert np.allclose(e2.scales(), 2.)
e2 = e * 2
assert np.allclose(e2.scales(), 2.)
if e.expr_rank() == 1:
a = tuple(range(e.dimensions))
e2 = a * e
assert np.allclose(e2.scales()[:, 0], (0, 1))