def project_onto(self, mesh, proj_type="Fekete"):
"""
Projects 'self' onto the 'mesh' using the 'proj_type' projection.
proj_type == "Fekete"/"L2"/"H1"
"""
if mesh == self._mesh:
return self
if proj_type == "Fekete":
return Function(self, mesh)
elif proj_type in ["L2", "H1"]:
from hermes1d.h1d_wrapper.h1d_wrapper import \
(assemble_projection_matrix_rhs, Mesh, FESolution)
from hermes_common._hermes_common import CooMatrix
pts, orders = mesh.get_mesh_data()
m = Mesh(pts, orders)
n_dof = m.assign_dofs()
A = CooMatrix(n_dof)
rhs = empty(n_dof)
assemble_projection_matrix_rhs(m, A, rhs, self,
projection_type=proj_type)
coeffs = solve(A.to_scipy_coo().todense(), rhs)
return FESolution(m, coeffs).to_discrete_function()
else:
raise ValueError("Unknown projection type")
def calculate_FE_coeffs(self):
if self._fe_sol is None:
from hermes1d.h1d_wrapper.h1d_wrapper import \
(assemble_projection_matrix_rhs, Mesh, FESolution)
from hermes_common._hermes_common import CooMatrix
pts, orders = self._mesh.get_mesh_data()
m = Mesh(pts, orders)
n_dof = m.assign_dofs()
A = CooMatrix(n_dof)
rhs = empty(n_dof)
assemble_projection_matrix_rhs(m, A, rhs, self,
projection_type="L2")
coeffs = solve(A.to_scipy_coo().todense(), rhs)
self._fe_sol = FESolution(m, coeffs)
def solve_dirac(mesh, kappa=1, Z=1, eig_num=4):
"""
Solves the Dirac equation on the given mesh.
Returns the energies and eigenfunctions.
"""
mesh.set_bc_left_dirichlet(0, 0);
mesh.set_bc_right_dirichlet(0, 0);
N_dof = mesh.assign_dofs()
A = CooMatrix(N_dof)
B = CooMatrix(N_dof)
assemble_dirac(mesh, A, B, kappa=kappa, Z=Z)
eigs = solve_eig_scipy(A.to_scipy_coo(), B.to_scipy_coo())
c = 137.03599911
eigs = [(E, eig) for E, eig in eigs if E > -2*c**2 and E < 0]
eigs = eigs[:eig_num]
#assert len(eigs) == eig_num
energies = [E for E, eig in eigs]
eigs = [eig for E, eig in eigs]
return N_dof, array(energies), eigs
def test_matrix2():
m = CooMatrix(5)
m.add(1, 3, 3.5)
m.add(2, 3, 4.5)
m.add(3, 4, 1.5)
m.add(0, 2, 1.5)
m.add(2, 3, 1)
d2 = array([
[0, 0, 1.5, 0, 0],
[0, 0, 0, 3.5, 0],
[0, 0, 0, 5.5, 0],
[0, 0, 0, 0, 1.5],
[0, 0, 0, 0, 0],
])
_coo_conversions_test(m, d2)
def test_matrix7():
m = CooMatrix(5, is_complex=True)
m.add(1, 3, 3.5 + 1j)
m.add(2, 3, 4.5 + 2j)
m.add(3, 4, 1.5 + 3j)
m.add(1, 3, 1.5 + 4j)
m.add(2, 3, 1 + 4j)
d2 = array([
[0, 0, 0, 0, 0],
[0, 0, 0, 5 + 5j, 0],
[0, 0, 0, 5.5 + 6j, 0],
[0, 0, 0, 0, 1.5 + 3j],
[0, 0, 0, 0, 0],
])
_coo_conversions_test(m, d2)
def test_matrix4():
m = CooMatrix(5, is_complex=True)
m.add(1, 3, 3.5)
m.add(2, 3, 4.5)
m.add(3, 4, 1.5)
m.add(4, 2, 1.5)
m.add(2, 3, 1)
d2 = array([
[0, 0, 0, 0, 0],
[0, 0, 0, 3.5, 0],
[0, 0, 0, 5.5, 0],
[0, 0, 0, 0, 1.5],
[0, 0, 1.5, 0, 0],
])
_coo_conversions_test(m, d2)
def test_matrix2():
m = CooMatrix(5)
m.add(1, 3, 3.5)
m.add(2, 3, 4.5)
m.add(3, 4, 1.5)
m.add(0, 2, 1.5)
m.add(2, 3, 1)
d2 = array([
[0, 0, 1.5, 0, 0],
[0, 0, 0, 3.5, 0],
[0, 0, 0, 5.5, 0],
[0, 0, 0, 0, 1.5],
[0, 0, 0, 0, 0],
])
_coo_conversions_test(m, d2)
def test_matrix7():
m = CooMatrix(5, is_complex=True)
m.add(1, 3, 3.5+1j)
m.add(2, 3, 4.5+2j)
m.add(3, 4, 1.5+3j)
m.add(1, 3, 1.5+4j)
m.add(2, 3, 1+4j)
d2 = array([
[0, 0, 0, 0, 0],
[0, 0, 0, 5+5j, 0],
[0, 0, 0, 5.5+6j, 0],
[0, 0, 0, 0, 1.5+3j],
[0, 0, 0, 0, 0],
])
_coo_conversions_test(m, d2)
def test_matrix4():
m = CooMatrix(5, is_complex=True)
m.add(1, 3, 3.5)
m.add(2, 3, 4.5)
m.add(3, 4, 1.5)
m.add(4, 2, 1.5)
m.add(2, 3, 1)
d2 = array([
[0, 0, 0, 0, 0],
[0, 0, 0, 3.5, 0],
[0, 0, 0, 5.5, 0],
[0, 0, 0, 0, 1.5],
[0, 0, 1.5, 0, 0],
])
_coo_conversions_test(m, d2)
def solve_dirac(mesh, kappa=1, Z=1, eig_num=4):
"""
Solves the Dirac equation on the given mesh.
Returns the energies and eigenfunctions.
"""
mesh.set_bc_left_dirichlet(0, 0)
mesh.set_bc_right_dirichlet(0, 0)
N_dof = mesh.assign_dofs()
A = CooMatrix(N_dof)
B = CooMatrix(N_dof)
assemble_dirac(mesh, A, B, kappa=kappa, Z=Z)
eigs = solve_eig_scipy(A.to_scipy_coo(), B.to_scipy_coo())
c = 137.03599911
eigs = [(E, eig) for E, eig in eigs if E > -2 * c**2 and E < 0]
eigs = eigs[:eig_num]
#assert len(eigs) == eig_num
energies = [E for E, eig in eigs]
eigs = [eig for E, eig in eigs]
return N_dof, array(energies), eigs
def test_l2_h1_proj_run():
"""
Test that the projections run.
It doesn't test if it's correct.
"""
pts = arange(0, 2*pi, 1)
orders = [3]*(len(pts)-1)
m = Mesh(pts, orders)
n_dof = m.assign_dofs()
A = CooMatrix(n_dof)
rhs = empty(n_dof)
assemble_projection_matrix_rhs(m, A, rhs, f_sin, projection_type="L2")
x = solve(A.to_scipy_coo().todense(), rhs)
sol_l2 = FESolution(m, x).to_discrete_function()
A = CooMatrix(n_dof)
assemble_projection_matrix_rhs(m, A, rhs, f_sin, projection_type="H1")
x = solve(A.to_scipy_coo().todense(), rhs)
sol_h1 = FESolution(m, x).to_discrete_function()
sol_l2.plot(False)
sol_h1.plot(False)
def test_l2_h1_proj3():
"""
Tests conversion to FE basis.
"""
pts = arange(0, 2*pi, 0.1)
orders = [2]*(len(pts)-1)
m = Mesh(pts, orders)
f = Function(lambda x: sin(x), Mesh1D(pts, orders))
n_dof = m.assign_dofs()
A = CooMatrix(n_dof)
rhs = empty(n_dof)
assemble_projection_matrix_rhs(m, A, rhs, f, projection_type="L2")
x = solve(A.to_scipy_coo().todense(), rhs)
sol_l2 = FESolution(m, x).to_discrete_function()
A = CooMatrix(n_dof)
assemble_projection_matrix_rhs(m, A, rhs, f, projection_type="H1")
x = solve(A.to_scipy_coo().todense(), rhs)
sol_h1 = FESolution(m, x).to_discrete_function()
assert sol_l2 == f
assert sol_h1 == f
def test_l2_h1_proj2():
"""
Tests the correctness of the projections.
"""
pts = arange(0, 2*pi, 3)
orders = [4]*(len(pts)-1)
m = Mesh(pts, orders)
pts = array(list(arange(0, pts[-1], 0.1)) + [pts[-1]])
orders = [6]*(len(pts)-1)
f_exact = Function(lambda x: sin(x), Mesh1D(pts, orders))
n_dof = m.assign_dofs()
A = CooMatrix(n_dof)
rhs = empty(n_dof)
assemble_projection_matrix_rhs(m, A, rhs, f_sin, projection_type="L2")
x = solve(A.to_scipy_coo().todense(), rhs)
sol_l2 = FESolution(m, x).to_discrete_function()
A = CooMatrix(n_dof)
assemble_projection_matrix_rhs(m, A, rhs, f_sin, projection_type="H1")
x = solve(A.to_scipy_coo().todense(), rhs)
sol_h1 = FESolution(m, x).to_discrete_function()
assert (sol_l2 - f_exact).l2_norm() < 0.002
assert (sol_h1 - f_exact).l2_norm() < 0.002
def test_matrix3():
m = CooMatrix(5)
m.add(0, 0, 2)
m.add(0, 1, 3)
m.add(1, 0, 3)
m.add(1, 2, 4)
m.add(1, 4, 6)
m.add(2, 1, -1)
m.add(2, 2, -3)
m.add(2, 3, 2)
m.add(3, 2, 1)
m.add(4, 1, 4)
m.add(4, 2, 2)
m.add(4, 4, 1)
d2 = array([
[2, 3, 0, 0, 0],
[3, 0, 4, 0, 6],
[0,-1,-3, 2, 0],
[0, 0, 1, 0, 0],
[0, 4, 2, 0, 1],
])
_coo_conversions_test(m, d2)
# CSR test:
m = CSRMatrix(m)
assert _eq(m.IA, [0, 2, 5, 8, 9, 12])
assert _eq(m.JA, [0, 1, 0, 2, 4, 1, 2, 3, 2, 1, 2, 4])
assert _eq(m.A, [2, 3, 3, 4, 6, -1, -3, 2, 1, 4, 2, 1])
# CSC test:
m = CSCMatrix(m)
assert _eq(m.JA, [0, 2, 5, 9, 10, 12])
assert _eq(m.IA, [0, 1, 0, 2, 4, 1, 2, 3, 4, 2, 1, 4])
assert _eq(m.A, [2, 3, 3, -1, 4, 4, -3, 1, 2, 2, 6, 1])
def test_matrix3():
m = CooMatrix(5)
m.add(0, 0, 2)
m.add(0, 1, 3)
m.add(1, 0, 3)
m.add(1, 2, 4)
m.add(1, 4, 6)
m.add(2, 1, -1)
m.add(2, 2, -3)
m.add(2, 3, 2)
m.add(3, 2, 1)
m.add(4, 1, 4)
m.add(4, 2, 2)
m.add(4, 4, 1)
d2 = array([
[2, 3, 0, 0, 0],
[3, 0, 4, 0, 6],
[0, -1, -3, 2, 0],
[0, 0, 1, 0, 0],
[0, 4, 2, 0, 1],
])
_coo_conversions_test(m, d2)
# CSR test:
m = CSRMatrix(m)
assert _eq(m.IA, [0, 2, 5, 8, 9, 12])
assert _eq(m.JA, [0, 1, 0, 2, 4, 1, 2, 3, 2, 1, 2, 4])
assert _eq(m.A, [2, 3, 3, 4, 6, -1, -3, 2, 1, 4, 2, 1])
# CSC test:
m = CSCMatrix(m)
assert _eq(m.JA, [0, 2, 5, 9, 10, 12])
assert _eq(m.IA, [0, 1, 0, 2, 4, 1, 2, 3, 4, 2, 1, 4])
assert _eq(m.A, [2, 3, 3, -1, 4, 4, -3, 1, 2, 2, 6, 1])