def test_krylov_reuse_pc_lu():
"""Test that LU re-factorisation is only performed after
set_operator(A) is called"""
# Test requires PETSc version 3.5 or later. Use petsc4py to check
# version number.
try:
from petsc4py import PETSc
except ImportError:
pytest.skip("petsc4py required to check PETSc version")
else:
if not PETSc.Sys.getVersion() >= (3, 5, 0):
pytest.skip("PETSc version must be 3.5 of higher")
mesh = UnitSquareMesh(MPI.comm_world, 12, 12)
V = FunctionSpace(mesh, ("Lagrange", 1))
u, v = TrialFunction(V), TestFunction(V)
a = Constant(1.0) * u * v * dx
L = Constant(1.0) * v * dx
assembler = fem.Assembler(a, L)
A = assembler.assemble_matrix()
b = assembler.assemble_vector()
norm = 13.0
solver = PETScKrylovSolver(mesh.mpi_comm())
solver.set_options_prefix("test_lu_")
PETScOptions.set("test_lu_ksp_type", "preonly")
PETScOptions.set("test_lu_pc_type", "lu")
solver.set_from_options()
solver.set_operator(A)
x = PETScVector(mesh.mpi_comm())
solver.solve(x, b)
assert round(x.norm(cpp.la.Norm.l2) - norm, 10) == 0
assembler = fem.assemble.Assembler(Constant(0.5) * u * v * dx, L)
assembler.assemble(A)
x = PETScVector(mesh.mpi_comm())
solver.solve(x, b)
assert round(x.norm(cpp.la.Norm.l2) - 2.0 * norm, 10) == 0
solver.set_operator(A)
solver.solve(x, b)
assert round(x.norm(cpp.la.Norm.l2) - 2.0 * norm, 10) == 0
def assembly():
# Whether to use custom kernels instead of FFC
useCustomKernels = False
mesh = UnitSquareMesh(MPI.comm_world, 13, 13)
Q = FunctionSpace(mesh, "Lagrange", 1)
u = TrialFunction(Q)
v = TestFunction(Q)
a = dolfin.cpp.fem.Form([Q._cpp_object, Q._cpp_object])
L = dolfin.cpp.fem.Form([Q._cpp_object])
# Compile the Poisson kernel using CFFI
kernel_name = "_poisson_kernel"
compile_kernels(kernel_name, verbose=True)
# Import the compiled kernel
kernel_mod = importlib.import_module(kernel_name)
ffi, lib = kernel_mod.ffi, kernel_mod.lib
# Get pointers to the CFFI functions
fnA_ptr = ffi.cast("uintptr_t", ffi.addressof(lib, "tabulate_tensor_A"))
fnB_ptr = ffi.cast("uintptr_t", ffi.addressof(lib, "tabulate_tensor_b"))
if useCustomKernels:
# Configure Forms to use own tabulate functions
a.set_cell_tabulate(0, fnA_ptr)
L.set_cell_tabulate(0, fnB_ptr)
else:
# Use FFC
ufc_form = ffc_jit(dot(grad(u), grad(v)) * dx)
ufc_form = cpp.fem.make_ufc_form(ufc_form[0])
a = cpp.fem.Form(ufc_form, [Q._cpp_object, Q._cpp_object])
ufc_form = ffc_jit(v * dx)
ufc_form = cpp.fem.make_ufc_form(ufc_form[0])
L = cpp.fem.Form(ufc_form, [Q._cpp_object])
start = time.time()
assembler = cpp.fem.Assembler([[a]], [L], [])
A = PETScMatrix()
b = PETScVector()
assembler.assemble(A, cpp.fem.Assembler.BlockType.monolithic)
assembler.assemble(b, cpp.fem.Assembler.BlockType.monolithic)
end = time.time()
print(f"Time for assembly: {(end-start)*1000.0}ms")
Anorm = A.norm(cpp.la.Norm.frobenius)
bnorm = b.norm(cpp.la.Norm.l2)
print(Anorm, bnorm)
#A_np = scipy2numpy(A.mat())
assert (np.isclose(Anorm, 56.124860801609124))
assert (np.isclose(bnorm, 0.0739710713711999))
def test_save_and_read_vector(tempdir):
filename = os.path.join(tempdir, "vector.h5")
# Write to file
local_range = MPI.local_range(MPI.comm_world, 305)
x = PETScVector(MPI.comm_world, local_range, [], 1)
x[:] = 1.2
with HDF5File(MPI.comm_world, filename, "w") as vector_file:
vector_file.write(x, "/my_vector")
# Read from file
with HDF5File(MPI.comm_world, filename, "r") as vector_file:
y = vector_file.read_vector(MPI.comm_world, "/my_vector", False)
assert y.size() == x.size()
x.axpy(-1.0, y)
assert x.norm(dolfin.cpp.la.Norm.l2) == 0.0
def test_numba_assembly():
mesh = UnitSquareMesh(MPI.comm_world, 13, 13)
Q = FunctionSpace(mesh, "Lagrange", 1)
u = TrialFunction(Q)
v = TestFunction(Q)
a = cpp.fem.Form([Q._cpp_object, Q._cpp_object])
L = cpp.fem.Form([Q._cpp_object])
sig = types.void(types.CPointer(typeof(ScalarType())),
types.CPointer(types.CPointer(typeof(ScalarType()))),
types.CPointer(types.double), types.intc)
fnA = cfunc(sig, cache=True)(tabulate_tensor_A)
a.set_cell_tabulate(0, fnA.address)
fnb = cfunc(sig, cache=True)(tabulate_tensor_b)
L.set_cell_tabulate(0, fnb.address)
if (False):
ufc_form = ffc_jit(dot(grad(u), grad(v)) * dx)
ufc_form = cpp.fem.make_ufc_form(ufc_form[0])
a = cpp.fem.Form(ufc_form, [Q._cpp_object, Q._cpp_object])
ufc_form = ffc_jit(v * dx)
ufc_form = cpp.fem.make_ufc_form(ufc_form[0])
L = cpp.fem.Form(ufc_form, [Q._cpp_object])
assembler = cpp.fem.Assembler([[a]], [L], [])
A = PETScMatrix()
b = PETScVector()
assembler.assemble(A, cpp.fem.Assembler.BlockType.monolithic)
assembler.assemble(b, cpp.fem.Assembler.BlockType.monolithic)
Anorm = A.norm(cpp.la.Norm.frobenius)
bnorm = b.norm(cpp.la.Norm.l2)
print(Anorm, bnorm)
assert (np.isclose(Anorm, 56.124860801609124))
assert (np.isclose(bnorm, 0.0739710713711999))
list_timings([TimingType.wall])
def test_krylov_solver_lu():
mesh = UnitSquareMesh(MPI.comm_world, 12, 12)
V = FunctionSpace(mesh, ("Lagrange", 1))
u, v = TrialFunction(V), TestFunction(V)
a = Constant(1.0) * inner(u, v) * dx
L = inner(Constant(1.0), v) * dx
A = assemble(a)
b = assemble(L)
norm = 13.0
solver = PETScKrylovSolver(mesh.mpi_comm())
solver.set_options_prefix("test_lu_")
PETScOptions.set("test_lu_ksp_type", "preonly")
PETScOptions.set("test_lu_pc_type", "lu")
solver.set_from_options()
x = PETScVector()
solver.set_operator(A)
solver.solve(x, b)
# *Tight* tolerance for LU solves
assert round(x.norm(cpp.la.Norm.l2) - norm, 12) == 0
def assembly():
# Whether to use custom kernels instead of FFC
useCustomKernel = True
# Whether to use CFFI kernels instead of Numba kernels
useCffiKernel = False
mesh = UnitSquareMesh(MPI.comm_world, 13, 13)
Q = FunctionSpace(mesh, "Lagrange", 1)
u = TrialFunction(Q)
v = TestFunction(Q)
a = dolfin.cpp.fem.Form([Q._cpp_object, Q._cpp_object])
L = dolfin.cpp.fem.Form([Q._cpp_object])
# Variant 1: Compile the Poisson kernel using CFFI
kernel_name = "_poisson_kernel"
compile_kernels(kernel_name)
# Import the compiled kernel
kernel_mod = importlib.import_module(kernel_name)
ffi, lib = kernel_mod.ffi, kernel_mod.lib
# Variant 2: Get pointers to the Numba kernels
sig = nb.types.void(nb.types.CPointer(nb.types.double),
nb.types.CPointer(nb.types.CPointer(nb.types.double)),
nb.types.CPointer(nb.types.double), nb.types.intc)
fnA = nb.cfunc(sig, cache=True, nopython=True)(tabulate_tensor_A)
fnb = nb.cfunc(sig, cache=True, nopython=True)(tabulate_tensor_b)
if useCustomKernel:
if useCffiKernel:
# Use the cffi kernel, compiled from raw C
fnA_ptr = ffi.cast("uintptr_t",
ffi.addressof(lib, "tabulate_tensor_A"))
fnB_ptr = ffi.cast("uintptr_t",
ffi.addressof(lib, "tabulate_tensor_b"))
else:
# Use the numba generated kernels
fnA_ptr = fnA.address
fnB_ptr = fnb.address
a.set_cell_tabulate(0, fnA_ptr)
L.set_cell_tabulate(0, fnB_ptr)
else:
# Use FFC
ufc_form = ffc_jit(dot(grad(u), grad(v)) * dx)
ufc_form = cpp.fem.make_ufc_form(ufc_form[0])
a = cpp.fem.Form(ufc_form, [Q._cpp_object, Q._cpp_object])
ufc_form = ffc_jit(v * dx)
ufc_form = cpp.fem.make_ufc_form(ufc_form[0])
L = cpp.fem.Form(ufc_form, [Q._cpp_object])
assembler = cpp.fem.Assembler([[a]], [L], [])
A = PETScMatrix()
b = PETScVector()
assembler.assemble(A, cpp.fem.Assembler.BlockType.monolithic)
assembler.assemble(b, cpp.fem.Assembler.BlockType.monolithic)
Anorm = A.norm(cpp.la.Norm.frobenius)
bnorm = b.norm(cpp.la.Norm.l2)
print(Anorm, bnorm)
assert (np.isclose(Anorm, 56.124860801609124))
assert (np.isclose(bnorm, 0.0739710713711999))
def solve():
# Whether to use custom Numba kernels instead of FFC
useCustomKernels = True
# Generate a unit cube with (n+1)^3 vertices
n = 22
mesh = UnitCubeMesh(MPI.comm_world, n, n, n)
Q = FunctionSpace(mesh, "Lagrange", 1)
u = TrialFunction(Q)
v = TestFunction(Q)
# Define the boundary: vertices where any component is in machine precision accuracy 0 or 1
def boundary(x):
return np.sum(np.logical_or(x < DOLFIN_EPS, x > 1.0 - DOLFIN_EPS),
axis=1) > 0
u0 = Constant(0.0)
bc = DirichletBC(Q, u0, boundary)
# Initialize bilinear form and rhs
a = dolfin.cpp.fem.Form([Q._cpp_object, Q._cpp_object])
L = dolfin.cpp.fem.Form([Q._cpp_object])
# Signature of tabulate_tensor functions
sig = nb.types.void(nb.types.CPointer(nb.types.double),
nb.types.CPointer(nb.types.CPointer(nb.types.double)),
nb.types.CPointer(nb.types.double), nb.types.intc)
# Compile the python functions using Numba
fnA = nb.cfunc(sig, cache=True, nopython=True)(tabulate_tensor_A)
fnL = nb.cfunc(sig, cache=True, nopython=True)(tabulate_tensor_L)
module_name = "_laplace_kernel"
# Build the kernel
ffi = cffi.FFI()
ffi.set_source(module_name, TABULATE_C)
ffi.cdef(TABULATE_H)
ffi.compile()
# Import the compiled kernel
kernel_mod = importlib.import_module(module_name)
ffi, lib = kernel_mod.ffi, kernel_mod.lib
# Get pointer to the compiled function
fnA_ptr = ffi.cast("uintptr_t", ffi.addressof(lib, "tabulate_tensor_A"))
# Get pointers to Numba functions
#fnA_ptr = fnA.address
fnL_ptr = fnL.address
if useCustomKernels:
# Configure Forms to use own tabulate functions
a.set_cell_tabulate(0, fnA_ptr)
L.set_cell_tabulate(0, fnL_ptr)
else:
# Use FFC
# Bilinear form
jit_result = ffc_jit(dot(grad(u), grad(v)) * dx)
ufc_form = dolfin.cpp.fem.make_ufc_form(jit_result[0])
a = dolfin.cpp.fem.Form(ufc_form, [Q._cpp_object, Q._cpp_object])
# Rhs
f = Expression("2.0", element=Q.ufl_element())
jit_result = ffc_jit(f * v * dx)
ufc_form = dolfin.cpp.fem.make_ufc_form(jit_result[0])
L = dolfin.cpp.fem.Form(ufc_form, [Q._cpp_object])
# Attach rhs expression as coefficient
L.set_coefficient(0, f._cpp_object)
assembler = dolfin.cpp.fem.Assembler([[a]], [L], [bc])
A = PETScMatrix()
b = PETScVector()
# Perform assembly
start = time.time()
assembler.assemble(A, dolfin.cpp.fem.Assembler.BlockType.monolithic)
end = time.time()
# We don't care about the RHS
assembler.assemble(b, dolfin.cpp.fem.Assembler.BlockType.monolithic)
print(f"Time for assembly: {(end-start)*1000.0}ms")
Anorm = A.norm(dolfin.cpp.la.Norm.frobenius)
bnorm = b.norm(dolfin.cpp.la.Norm.l2)
print(Anorm, bnorm)
# Norms obtained with FFC and n=13
assert (np.isclose(Anorm, 60.86192203436385))
assert (np.isclose(bnorm, 0.018075523965828778))
comm = L.mesh().mpi_comm()
solver = PETScKrylovSolver(comm)
u = Function(Q)
solver.set_operator(A)
solver.solve(u.vector(), b)
# Export result
file = XDMFFile(MPI.comm_world, "poisson_3d.xdmf")
file.write(u, XDMFFile.Encoding.HDF5)
def solve(n_runs: int, mesh_size: int, element: FiniteElement,
reference_tensor: ReferenceTensor, kernel_generator):
# Whether to use custom kernels instead of FFC
useCustomKernels = True
# Generate a unit cube with (n+1)^3 vertices
mesh = generate_mesh(mesh_size)
print("Mesh generated.")
A0 = reference_tensor
Q = FunctionSpace(mesh, element)
u = TrialFunction(Q)
v = TestFunction(Q)
# Define the boundary: vertices where any component is in machine precision accuracy 0 or 1
def boundary(x):
return np.sum(np.logical_or(x < DOLFIN_EPS, x > 1.0 - DOLFIN_EPS),
axis=1) > 0
u0 = Constant(0.0)
bc = DirichletBC(Q, u0, boundary)
if useCustomKernels:
# Initialize bilinear form and rhs
a = dolfin.cpp.fem.Form([Q._cpp_object, Q._cpp_object])
L = dolfin.cpp.fem.Form([Q._cpp_object])
# Signature of tabulate_tensor functions
sig = nb.types.void(
nb.types.CPointer(nb.types.double),
nb.types.CPointer(nb.types.CPointer(nb.types.double)),
nb.types.CPointer(nb.types.double), nb.types.intc)
# Compile the python functions using Numba
fnA = nb.cfunc(sig, cache=True,
nopython=True)(numba_kernels.tabulate_tensor_A)
fnL = nb.cfunc(sig, cache=True,
nopython=True)(numba_kernels.tabulate_tensor_L)
module_name = "_laplace_kernel"
compile_poisson_kernel(module_name,
kernel_generator,
A0,
verbose=False)
print("Finished compiling kernel.")
# Import the compiled kernel
kernel_mod = importlib.import_module(f"simd.tmp.{module_name}")
ffi, lib = kernel_mod.ffi, kernel_mod.lib
# Get pointer to the compiled function
fnA_ptr = ffi.cast("uintptr_t", ffi.addressof(lib,
"tabulate_tensor_A"))
# Get pointers to Numba functions
# fnA_ptr = fnA.address
fnL_ptr = fnL.address
# Configure Forms to use own tabulate functions
a.set_cell_tabulate(0, fnA_ptr)
L.set_cell_tabulate(0, fnL_ptr)
else:
# Use FFC
# Bilinear form
jit_result = ffc_jit(dot(grad(u), grad(v)) * dx)
ufc_form = dolfin.cpp.fem.make_ufc_form(jit_result[0])
a = dolfin.cpp.fem.Form(ufc_form, [Q._cpp_object, Q._cpp_object])
# Rhs
f = Expression("2.0", element=Q.ufl_element())
jit_result = ffc_jit(f * v * dx)
ufc_form = dolfin.cpp.fem.make_ufc_form(jit_result[0])
L = dolfin.cpp.fem.Form(ufc_form, [Q._cpp_object])
# Attach rhs expression as coefficient
L.set_coefficient(0, f._cpp_object)
print("Built form.")
assembler = dolfin.cpp.fem.Assembler([[a]], [L], [bc])
A = PETScMatrix()
b = PETScVector()
# Callable that performs assembly of matrix
assembly_callable = lambda: assembler.assemble(
A, dolfin.cpp.fem.Assembler.BlockType.monolithic)
# Get timings for assembly of matrix over several runs
time_avg, time_min, time_max = utils.timing(n_runs,
assembly_callable,
verbose=True)
print(
f"Timings for element matrix assembly (n={n_runs}) avg: {round(time_avg*1000, 2)}ms, min: {round(time_min*1000, 2)}ms, max: {round(time_max*1000, 2)}ms"
)
# Assemble again to get correct results
A = PETScMatrix()
assembler.assemble(A, dolfin.cpp.fem.Assembler.BlockType.monolithic)
assembler.assemble(b, dolfin.cpp.fem.Assembler.BlockType.monolithic)
Anorm = A.norm(dolfin.cpp.la.Norm.frobenius)
bnorm = b.norm(dolfin.cpp.la.Norm.l2)
print(Anorm, bnorm)
# Check norms of assembled system
if useCustomKernels:
# Norms obtained with FFC and n=22
assert (np.isclose(Anorm, 118.19435458024503))
#assert (np.isclose(bnorm, 0.009396467472097566))
return
# Solve the system
comm = L.mesh().mpi_comm()
solver = PETScKrylovSolver(comm)
u = Function(Q)
solver.set_operator(A)
solver.solve(u.vector(), b)
# Export result
file = XDMFFile(MPI.comm_world, "poisson_3d.xdmf")
file.write(u, XDMFFile.Encoding.HDF5)
ufc_form = dolfin.cpp.fem.make_ufc_form(jit_result[0])
L = dolfin.cpp.fem.Form(ufc_form, [Q._cpp_object])
# Attach rhs expression as coefficient
L.set_coefficient(0, f._cpp_object)
assembler = dolfin.cpp.fem.Assembler([[a]], [L], [bc])
A = PETScMatrix()
b = PETScVector()
print("Running assembly...")
assembler.assemble(A, dolfin.cpp.fem.Assembler.BlockType.monolithic)
assembler.assemble(b, dolfin.cpp.fem.Assembler.BlockType.monolithic)
Anorm = A.norm(dolfin.cpp.la.Norm.frobenius)
bnorm = b.norm(dolfin.cpp.la.Norm.l2)
print("A.norm(frobenius)={:.12e}\nb.norm(l2)={:.12e}".format(Anorm, bnorm))
# Norms obtained with n=22 and bcs
assert (np.isclose(Anorm, 60.86192203436385))
assert (np.isclose(bnorm, 0.018075523965828778))
# Norms obtained with n=22 and no bcs
#assert (np.isclose(Anorm, 29.416127208482518))
#assert (np.isclose(bnorm, 0.018726593629987284))
print("Running solver...")
comm = L.mesh().mpi_comm()
solver = PETScKrylovSolver(comm)
u = Function(Q)
def assembly():
# Whether to use custom kernels instead of FFC
useCustomKernels = True
# Generate a unit cube with (n+1)^3 vertices
n = 20
mesh = UnitCubeMesh(MPI.comm_world, n, n, n)
Q = FunctionSpace(mesh, "Lagrange", 1)
u = TrialFunction(Q)
v = TestFunction(Q)
def boundary0(x):
wrong = np.logical_or(x[:, 1] < DOLFIN_EPS, x[:, 1] > 1.0 - DOLFIN_EPS)
one = np.logical_or(x[:, 0] < DOLFIN_EPS, x[:, 0] > 1.0 - DOLFIN_EPS)
two = np.logical_or(x[:, 2] < DOLFIN_EPS, x[:, 2] > 1.0 - DOLFIN_EPS)
return np.logical_and(np.logical_or(one, two), np.logical_not(wrong))
def boundary1(x):
return np.logical_or(x[:, 1] < DOLFIN_EPS, x[:, 1] > 1.0 - DOLFIN_EPS)
u0 = Constant(0.0)
bc0 = DirichletBC(Q, u0, boundary0)
u1 = Constant(1.0)
bc1 = DirichletBC(Q, u1, boundary1)
# Initialize bilinear form and rhs
a = dolfin.cpp.fem.Form([Q._cpp_object, Q._cpp_object])
L = dolfin.cpp.fem.Form([Q._cpp_object])
# Signature of tabulate_tensor functions
sig = nb.types.void(nb.types.CPointer(nb.types.double),
nb.types.CPointer(nb.types.CPointer(nb.types.double)),
nb.types.CPointer(nb.types.double), nb.types.intc)
# Compile the numba functions
fnA = nb.cfunc(sig, cache=True, nopython=True)(tabulate_tensor_A)
fnb = nb.cfunc(sig, cache=True, nopython=True)(tabulate_tensor_b)
if useCustomKernels:
# Configure Forms to use own tabulate functions
a.set_cell_tabulate(0, fnA.address)
L.set_cell_tabulate(0, fnb.address)
else:
# Use FFC
jit_result = ffc_jit(dot(grad(u), grad(v)) * dx)
ufc_form = dolfin.cpp.fem.make_ufc_form(jit_result[0])
a = dolfin.cpp.fem.Form(ufc_form, [Q._cpp_object, Q._cpp_object])
f = Expression("20.0", element=Q.ufl_element())
jit_result = ffc_jit(f * v * dx)
ufc_form = dolfin.cpp.fem.make_ufc_form(jit_result[0])
L = dolfin.cpp.fem.Form(ufc_form, [Q._cpp_object])
L.set_coefficient(0, f._cpp_object)
start = time.time()
assembler = dolfin.cpp.fem.Assembler([[a]], [L], [bc0, bc1])
A = PETScMatrix()
b = PETScVector()
assembler.assemble(A, dolfin.cpp.fem.Assembler.BlockType.monolithic)
assembler.assemble(b, dolfin.cpp.fem.Assembler.BlockType.monolithic)
end = time.time()
print(f"Time for assembly: {(end-start)*1000.0}ms")
Anorm = A.norm(dolfin.cpp.la.Norm.frobenius)
bnorm = b.norm(dolfin.cpp.la.Norm.l2)
print(Anorm, bnorm)
# Norms obtained with FFC and n=20
#assert (np.isclose(Anorm, 55.82812911070811))
#assert (np.isclose(bnorm, 29.73261456296761))
comm = L.mesh().mpi_comm()
solver = PETScKrylovSolver(comm)
u = Function(Q)
solver.set_operator(A)
solver.solve(u.vector(), b)
file = XDMFFile(MPI.comm_world, "poisson_3d.xdmf")
file.write(u, XDMFFile.Encoding.HDF5)