def plot_matrix_hybrid(A, **kwargs):
"""Provides a plot of a hybrid-mixed matrix."""
fig, ax = plt.subplots(1, 1)
petsc_mat = A.M.handle
total_size = petsc_mat.getSize()
f0_size = A.M[0, 0].handle.getSize()
f1_size = A.M[1, 1].handle.getSize()
Mij = PETSc.Mat()
petsc_mat.convert("aij", Mij)
n, m = total_size
Mnp = np.array(Mij.getValues(range(n), range(m)))
Am = np.ma.masked_values(Mnp, 0, rtol=1e-13)
my_cmap = plt.cm.magma
my_cmap.set_bad(color="lightgray")
# Plot the matrix
plot = ax.matshow(Am, cmap=my_cmap, **kwargs)
# plot = plt.spy(Am, **kwargs)
# Remove axis ticks and values
ax.tick_params(length=0)
ax.set_xticklabels([])
ax.set_yticklabels([])
ax.axhline(y=f0_size[0] - 0.5, color="k")
ax.axvline(x=f0_size[0] - 0.5, color="k")
ax.axhline(y=f0_size[0] + f1_size[0] - 0.5, color="k")
ax.axvline(x=f0_size[0] + f1_size[0] - 0.5, color="k")
return plot
def create_injection(self, dmc, dmf):
prefix = dmc.getOptionsPrefix()
mat_type = PETSc.Options(prefix).getString(
"mg_levels_transfer_mat_type", default="matfree")
I = self.create_transfer(get_appctx(dmf), get_appctx(dmc), mat_type,
False, False)
return PETSc.Mat().createTranspose(I)
def construct_kronecker_matrix(self, interp_1d):
"""
Construct the tensorized interpolation matrix.
Do this by computing the kron product of the rows of
the 1d univariate interpolation matrices.
In the future, this may be done matrix-free.
"""
# this is awfully slow in 3D!!!!!!!!!!! (FW: it might not be anymore)
IFW = PETSc.Mat().create(self.comm)
IFW.setType(PETSc.Mat.Type.AIJ)
comm = self.comm
# owned part of global problem
local_N = self.N // comm.size + int(comm.rank < (self.N % comm.size))
(lsize, gsize) = interp_1d[0].getSizes()[0]
IFW.setSizes(((lsize, gsize), (local_N, self.N)))
IFW.setUp()
for row in range(lsize):
row = self.lg_map_fe.apply([row])[0]
denserows = [A[row, :] for A in interp_1d]
values = reduce(np.kron, denserows)
columns = np.where(values != 0)[0].astype(np.int32)
values = values[columns]
IFW.setValues([row], columns, values)
IFW.assemble()
return IFW
def plot_matrix(A, **kwargs):
"""Provides a plot of a matrix."""
fig, ax = plt.subplots(1, 1)
petsc_mat = A.M.handle
size = petsc_mat.getSize()
Mij = PETSc.Mat()
petsc_mat.convert("aij", Mij)
n, m = size
Mnp = np.array(Mij.getValues(range(n), range(m)))
Am = np.ma.masked_values(Mnp, 0, rtol=1e-13)
my_cmap = plt.cm.magma
my_cmap.set_bad(color="lightgray")
# Plot the matrix
plot = ax.matshow(Am, cmap=my_cmap, **kwargs)
# Remove axis ticks and values
ax.tick_params(length=0)
ax.set_xticklabels([])
ax.set_yticklabels([])
return plot
def assemble(self):
"""
Compute values of G and assemble the sparse matrix
This method creates the underlying sparse covariance matrix based on the pre-computed entries,
allocates memory, sets the values, and finalizes assembly. No inputs, no return value. If this
method is called and the matrix has already been assembled, it will return with no effect.
"""
if self.is_assembled:
return
G_dict, nnz = self._compute_G_vals()
self.G = PETSc.Mat().create(comm=self.comm)
self.G.setType('aij')
self.G.setSizes(((self.nx_local, -1), (self.nx_local, -1)))
self.G.setPreallocationNNZ(nnz)
self.G.setFromOptions()
self.G.setUp()
for key, val in G_dict.items():
self.G.setValues(np.array(key, dtype=PETSc.IntType), val[1],
val[0])
self.G.assemble()
self.is_assembled = True
def construct_full_interpolation_matrix(self, IFW):
"""
Assemble interpolation matrix for vectorial tensorized spline space.
"""
# this is THE MOST awfully slow in 3D!!!!!!!!!!!
FullIFW = PETSc.Mat().create(self.comm)
FullIFW.setType(PETSc.Mat.Type.AIJ)
d = self.dim
free_dims = list(set(range(self.dim)) - set(self.fixed_dims))
dfree = len(free_dims)
((lsize, gsize), (lsize_spline, gsize_spline)) = IFW.getSizes()
FullIFW.setSizes(((d * lsize, d * gsize),
(dfree * lsize_spline, dfree * gsize_spline)))
# BIG TODO: figure out the sparsity pattern
FullIFW.setUp()
# this blows up the matrix to do the right thing
# on vector fields. It's not just a block matrix,
# but the values are interleaved as this is how
# firedrake handles vector fields
for row in range(lsize):
row = self.lg_map_fe.apply([row])[0]
(cols, vals) = IFW.getRow(row)
for j, dim in enumerate(free_dims):
FullIFW.setValues([d * row + dim],
[dfree * col + j for col in cols],
vals)
FullIFW.assemble()
return FullIFW
def createSubMatrix(self, mat, row_is, col_is, target=None):
if target is not None:
# Repeat call, just return the matrix, since we don't
# actually assemble in here.
target.assemble()
return target
# These are the sets of ISes of which the the row and column
# space consist.
row_ises = self._y.function_space().dof_dset.field_ises
col_ises = self._x.function_space().dof_dset.field_ises
row_inds = find_sub_block(row_is, row_ises)
if row_is == col_is and row_ises == col_ises:
col_inds = row_inds
else:
col_inds = find_sub_block(col_is, col_ises)
splitter = ExtractSubBlock()
asub = splitter.split(self.a,
argument_indices=(row_inds, col_inds))
Wrow = asub.arguments()[0].function_space()
Wcol = asub.arguments()[1].function_space()
row_bcs = []
col_bcs = []
for bc in self.bcs:
if isinstance(bc, DirichletBC):
bc_temp = bc.reconstruct(field=row_inds, V=Wrow, g=bc.function_arg, sub_domain=bc.sub_domain, method=bc.method, use_split=True)
elif isinstance(bc, EquationBCSplit):
bc_temp = bc.reconstruct(field=row_inds, V=Wrow, row_field=row_inds, col_field=col_inds, use_split=True)
if bc_temp is not None:
row_bcs.append(bc_temp)
if Wrow == Wcol and row_inds == col_inds and self.bcs == self.bcs_col:
col_bcs = row_bcs
else:
for bc in self.bcs_col:
if isinstance(bc, DirichletBC):
bc_temp = bc.reconstruct(field=col_inds, V=Wcol, g=bc.function_arg, sub_domain=bc.sub_domain, method=bc.method, use_split=True)
elif isinstance(bc, EquationBCSplit):
bc_temp = bc.reconstruct(field=col_inds, V=Wcol, row_field=row_inds, col_field=col_inds, use_split=True)
if bc_temp is not None:
col_bcs.append(bc_temp)
submat_ctx = ImplicitMatrixContext(asub,
row_bcs=row_bcs,
col_bcs=col_bcs,
fc_params=self.fc_params,
appctx=self.appctx)
submat_ctx.on_diag = self.on_diag and row_inds == col_inds
submat = PETSc.Mat().create(comm=mat.comm)
submat.setType("python")
submat.setSizes((submat_ctx.row_sizes, submat_ctx.col_sizes),
bsize=submat_ctx.block_size)
submat.setPythonContext(submat_ctx)
submat.setUp()
return submat
def plot_matrix_mixed(a_form, bcs=[], **kwargs):
"""Provides a plot of a mixed matrix."""
fig, ax = plt.subplots(1, 1)
A = assemble(a_form, bcs=bcs, mat_type="aij")
petsc_mat = A.M.handle
total_size = petsc_mat.getSize()
f0_size = A.M[0, 0].handle.getSize()
Mij = PETSc.Mat()
petsc_mat.convert("aij", Mij)
n, m = total_size
Mnp = np.array(Mij.getValues(range(n), range(m)))
Am = np.ma.masked_values(Mnp, 0, rtol=1e-13)
# Plot the matrix
plot = ax.matshow(Am, cmap=my_cmap, **kwargs)
# Remove axis ticks and values
ax.tick_params(length=0)
ax.set_xticklabels([])
ax.set_yticklabels([])
ax.axhline(y=f0_size[0] - 0.5, color="k")
ax.axvline(x=f0_size[0] - 0.5, color="k")
return plot
def plot_matrix_hybrid_multiplier_spp(a_form, bcs=[], **kwargs):
"""Provides a plot of a condensed hybrid-mixed matrix for single scale problems."""
fig, ax = plt.subplots(1, 1)
_A = Tensor(a_form)
A = _A.blocks
S = A[2, 2] - A[2, :2] * A[:2, :2].inv * A[:2, 2]
Smat = assemble(S, bcs=bcs)
petsc_mat = Smat.M.handle
total_size = petsc_mat.getSize()
Mij = PETSc.Mat()
petsc_mat.convert("aij", Mij)
n, m = total_size
Mnp = np.array(Mij.getValues(range(n), range(m)))
Am = np.ma.masked_values(Mnp, 0, rtol=1e-13)
# Plot the matrix
plot = ax.matshow(Am, cmap=my_cmap, **kwargs)
# Below there is the spy alternative
# plot = plt.spy(Am, **kwargs)
# Remove axis ticks and values
ax.tick_params(length=0)
ax.set_xticklabels([])
ax.set_yticklabels([])
return plot
def create_interpolation(dmc, dmf):
cctx = firedrake.dmhooks.get_appctx(dmc)
fctx = firedrake.dmhooks.get_appctx(dmf)
manager = firedrake.dmhooks.get_transfer_manager(dmf)
V_c = cctx._problem.u.function_space()
V_f = fctx._problem.u.function_space()
row_size = V_f.dof_dset.layout_vec.getSizes()
col_size = V_c.dof_dset.layout_vec.getSizes()
cfn = firedrake.Function(V_c)
ffn = firedrake.Function(V_f)
cbcs = cctx._problem.bcs
fbcs = fctx._problem.bcs
ctx = Interpolation(cfn, ffn, manager, cbcs, fbcs)
mat = PETSc.Mat().create(comm=dmc.comm)
mat.setSizes((row_size, col_size))
mat.setType(mat.Type.PYTHON)
mat.setPythonContext(ctx)
mat.setUp()
return mat, None
def test_ForcingCovariance_init(fs):
"test init method of ForcingCovariance"
# note: tests only handle case of a single process
# need to think about testing more complicated cases
# simple example in 1D
sigma = np.log(1.)
l = np.log(0.1)
fc = ForcingCovariance(fs, sigma, l)
n = Function(fs).vector().size()
n_local = Function(fs).vector().local_size()
M = PETSc.Mat().create()
M.setSizes(((n_local, -1), (n_local, -1)))
M.setFromOptions()
M.setUp()
start, end = M.getOwnershipRange()
assert fc.nx == n
assert fc.nx_local == n_local
assert fc.function_space == fs
assert_allclose(fc.sigma, sigma)
assert_allclose(fc.l, l)
assert_allclose(fc.cutoff, 1.e-3)
assert_allclose(fc.regularization, 1.e-8)
assert fc.local_startind == start
assert fc.local_endind == end
assert not fc.is_assembled
def createSubMatrix(self, mat, row_is, col_is, target=None):
if target is not None:
# Repeat call, just return the matrix, since we don't
# actually assemble in here.
target.assemble()
return target
from firedrake import DirichletBC
# These are the sets of ISes of which the the row and column
# space consist.
row_ises = self._y.function_space().dof_dset.field_ises
col_ises = self._x.function_space().dof_dset.field_ises
row_inds = find_sub_block(row_is, row_ises)
if row_is == col_is and row_ises == col_ises:
col_inds = row_inds
else:
col_inds = find_sub_block(col_is, col_ises)
asub = ExtractSubBlock().split(self.a,
argument_indices=(row_inds, col_inds))
Wrow = asub.arguments()[0].function_space()
Wcol = asub.arguments()[1].function_space()
row_bcs = []
col_bcs = []
for bc in self.row_bcs:
for i, r in enumerate(row_inds):
if bc.function_space().index == r:
row_bcs.append(DirichletBC(Wrow.split()[i],
bc.function_arg,
bc.sub_domain,
method=bc.method))
if Wrow == Wcol and row_inds == col_inds and self.row_bcs == self.col_bcs:
col_bcs = row_bcs
else:
for bc in self.col_bcs:
for i, c in enumerate(col_inds):
if bc.function_space().index == c:
col_bcs.append(DirichletBC(Wcol.split()[i],
bc.function_arg,
bc.sub_domain,
method=bc.method))
submat_ctx = ImplicitMatrixContext(asub,
row_bcs=row_bcs,
col_bcs=col_bcs,
fc_params=self.fc_params,
appctx=self.appctx)
submat_ctx.on_diag = self.on_diag and row_inds == col_inds
submat = PETSc.Mat().create(comm=mat.comm)
submat.setType("python")
submat.setSizes((submat_ctx.row_sizes, submat_ctx.col_sizes),
bsize=submat_ctx.block_size)
submat.setPythonContext(submat_ctx)
submat.setUp()
return submat
def get_np_matrix(form, **kwargs):
L = get_PETSC_matrix(form, **kwargs)
size = L.getSize()
Lij = PETSc.Mat()
L.convert('aij', Lij)
Lnp = np.array(Lij.getValues(range(size[0]), range(size[1])))
return Lnp
def getNestSubMatrix(self, i, j):
if i == j:
s = self.standalones[i]
sizes = (s.Vf.dof_dset.layout_vec.getSizes(),
s.Vc.dof_dset.layout_vec.getSizes())
M_shll = PETSc.Mat().createPython(sizes, s, comm=s.Vf.mesh().comm)
M_shll.setUp()
return M_shll
else:
return None
def prolongation_matrix_matfree(Vf, Vc, Vf_bcs, Vc_bcs):
fele = Vf.ufl_element()
if isinstance(fele, MixedElement) and not isinstance(fele, (VectorElement, TensorElement)):
ctx = MixedInterpolationMatrix(Vf, Vc, Vf_bcs, Vc_bcs)
else:
ctx = StandaloneInterpolationMatrix(Vf, Vc, Vf_bcs, Vc_bcs)
sizes = (Vc.dof_dset.layout_vec.getSizes(), Vf.dof_dset.layout_vec.getSizes())
M_shll = PETSc.Mat().createPython(sizes, ctx)
M_shll.setUp()
return M_shll
def GetPETScBFBTApproximateToSchurInverse():
Fass = assemble(lhs(F))
Gass = assemble(inner(u, v) * dx)
# bcin.apply(Fass)
# bcnoslip.apply(Fass)
# bcin.apply(Gass)
# bcnoslip.apply(Gass)
A = Fass.M[0,0].handle
BT = Fass.M[0,1].handle
B = Fass.M[1,0].handle
D = Fass.M[1,1].handle
VM = Gass.M[0, 0].handle
# Adiag = A.getDiagonal()
Adiag = VM.getRowSum()
invAdiag = Adiag.duplicate()
Adiag.copy(invAdiag)
invAdiag.reciprocal()
Einv = A.duplicate()
Einv.setDiagonal(invAdiag)
# Einv.convert(PETSc.Mat.Type.SEQAIJ)
BEBT = B.matMult(Einv.matMult(BT))
BEBT_ksp = PETSc.KSP().create()
BEBT_ksp.setOperators(BEBT)
opts = PETSc.Options()
BEBT_ksp.setOptionsPrefix("bebt_")
opts['bebt_ksp_type'] = 'richardson'
opts['bebt_pc_type'] = 'hypre'
opts['bebt_ksp_max_it'] = 1
opts['bebt_ksp_atol'] = 1.0e-9
opts['bebt_ksp_rtol'] = 1.0e-9
BEBT_ksp.setUp()
BEBT_ksp.setFromOptions()
MIDDLE = B.matMult(Einv.matMult(A.matMult(Einv.matMult(BT))))
MIDDLE.scale(-1)
class SchurInvApprox(object):
def mult(self, mat, x, y):
y1 = y.duplicate()
BEBT_ksp.solve(x, y1)
y2 = y.duplicate()
MIDDLE.mult(y1, y2)
BEBT_ksp.solve(y2, y)
schur = PETSc.Mat()
schur.createPython(D.getSizes(), SchurInvApprox())
schur.setUp()
return schur
def create_transfer(cctx, fctx, mat_type, cbcs, fbcs):
cV = cctx.J.arguments()[0].function_space()
fV = fctx.J.arguments()[0].function_space()
cbcs = cctx._problem.bcs if cbcs else []
fbcs = fctx._problem.bcs if fbcs else []
if mat_type == "matfree":
I = prolongation_matrix_matfree(fV, cV, fbcs, cbcs)
elif mat_type == "aij":
I = PETSc.Mat().createTranspose(prolongation_matrix_aij(fV, cV, fbcs, cbcs))
else:
raise ValueError("Unknown matrix type")
return I
def GetPETScInverseMassApproximateToSchurInverse():
mass = assemble( p*q*dx).M[1,1].handle
mass_diag = mass.createVecLeft()
mass.getDiagonal(mass_diag)
mass_diag.reciprocal()
mass_diag.scale(-1)
class InvMassSchurInvApprox(object):
def mult(self, mat, x, y):
y.pointwiseMult(mass_diag, x)
schur = PETSc.Mat()
schur.createPython(mass.getSizes(), InvMassSchurInvApprox())
schur.setUp()
return schur
def duplicate(self, mat, copy):
if copy == 0:
raise NotImplementedError("We do now know how to duplicate a matrix-free MAT when copy=0")
newmat_ctx = ImplicitMatrixContext(self.a,
row_bcs=self.bcs,
col_bcs=self.bcs_col,
fc_params=self.fc_params,
appctx=self.appctx)
newmat = PETSc.Mat().create(comm=mat.comm)
newmat.setType("python")
newmat.setSizes((newmat_ctx.row_sizes, newmat_ctx.col_sizes),
bsize=newmat_ctx.block_size)
newmat.setPythonContext(newmat_ctx)
newmat.setUp()
return newmat
def create_interpolation(self, dmc, dmf):
# This should be generalised to work for arbitrary function
# spaces. Currently I think it only works for CG/DG on simplices.
# I used the same code as firedrake.P1PC.
cctx = get_appctx(dmc)
fctx = get_appctx(dmf)
cV = cctx.J.arguments()[0].function_space()
fV = fctx.J.arguments()[0].function_space()
cbcs = cctx._problem.bcs
fbcs = fctx._problem.bcs
I = prolongation_matrix(fV, cV, fbcs, cbcs)
R = PETSc.Mat().createTranspose(I)
return R, None
def __init__(self, function_space, coords):
"create and assemble interpolation matrix"
if not isinstance(function_space, WithGeometry):
raise TypeError(
"bad input type for function_space: must be a FunctionSpace")
self.coords = np.copy(coords)
self.function_space = function_space
self.comm = function_space.comm
self.n_data = coords.shape[0]
assert (coords.shape[1] == self.function_space.mesh().cell_dimension()
), "shape of coordinates does not match mesh dimension"
# allocate working vectors to handle parallel matrix operations and data transfer
# dataspace_vector is a distributed PETSc vector in the data space
self.dataspace_distrib = PETSc.Vec().create(comm=self.comm)
self.dataspace_distrib.setSizes((-1, self.n_data))
self.dataspace_distrib.setFromOptions()
self.n_data_local = self.dataspace_distrib.getSizes()[0]
# all data computations are done on root process, so create gather method to
# facilitate this data transfer
self.petsc_scatter, self.dataspace_gathered = PETSc.Scatter.toZero(
self.dataspace_distrib)
self.meshspace_vector = Function(self.function_space).vector()
self.n_mesh_local = self.meshspace_vector.local_size()
self.n_mesh = self.meshspace_vector.size()
nnz = len(self.function_space.cell_node_list[0])
self.interp = PETSc.Mat().create(comm=self.comm)
self.interp.setSizes(
((self.n_mesh_local, -1), (self.n_data_local, -1)))
self.interp.setPreallocationNNZ(nnz)
self.interp.setFromOptions()
self.interp.setUp()
self.is_assembled = False
def construct_full_interpolation_matrix(self, IFW):
"""
Assemble interpolation matrix for vectorial tensorized spline space.
"""
# this is one of the two bottlenecks that slow down initiating Bsplines
FullIFW = PETSc.Mat().create(self.comm)
FullIFW.setType(PETSc.Mat.Type.AIJ)
# set proper matrix sizes
d = self.dim
free_dims = list(set(range(self.dim)) - set(self.fixed_dims))
dfree = len(free_dims)
((lsize, gsize), (lsize_spline, gsize_spline)) = IFW.getSizes()
FullIFW.setSizes(((d * lsize, d * gsize), (dfree * lsize_spline,
dfree * gsize_spline)))
# (over)estimate sparsity pattern using row with most nonzeros
# possible memory improvement: allocate precise sparsity pattern
# row by row (but this needs nnzdiagonal and nnzoffidagonal;
# not straightforward to do)
global_rows = self.lg_map_fe.apply([range(lsize)])
for ii, row in enumerate(range(lsize)):
row = global_rows[row]
self.FullIFWnnz = max(self.FullIFWnnz, len(IFW.getRow(row)[1]))
FullIFW.setPreallocationNNZ(self.FullIFWnnz)
# preallocate matrix
FullIFW.setUp()
# fill matrix by blowing up entries from IFW to do the right thing
# on vector fields (it's not just a block matrix: values are
# interleaved as this is how firedrake handles vector fields)
innerloop_idx = [[i, free_dims[i]] for i in range(dfree)]
for row in range(lsize): # for every FE dof
row = self.lg_map_fe.apply([row])[0]
# extract value of all tensorize Bsplines at this dof
(cols, vals) = IFW.getRow(row)
expandedcols = dfree * cols
for j, dim in innerloop_idx:
FullIFW.setValues(
[d * row + dim], # global row
expandedcols + j, # global column
vals)
FullIFW.assemble()
return FullIFW
def solve(ctx, state):
out_file = File(solution_out) if solution_out else None
mass = state["mass"]
hats = state["hats"]
u = ctx[2]["u"]
u0 = ctx[2]["u0"]
solver = ctx[1]
from firedrake.petsc import PETSc
ksp_hats = PETSc.KSP()
ksp_hats.create()
ksp_hats.setOperators(hats)
opts = PETSc.Options()
opts['ksp_type'] = inner_ksp
opts['ksp_max_it'] = max_iterations
opts['pc_type'] = 'hypre'
ksp_hats.setFromOptions()
class SchurInv(object):
def mult(self, mat, x, y):
tmp1 = y.duplicate()
tmp2 = y.duplicate()
ksp_hats.solve(x, tmp1)
mass.mult(tmp1, tmp2)
ksp_hats.solve(tmp2, y)
pc_schur = PETSc.Mat()
pc_schur.createPython(mass.getSizes(), SchurInv())
pc_schur.setUp()
pc = solver.snes.ksp.pc
pc.setFieldSplitSchurPreType(PETSc.PC.SchurPreType.USER, pc_schur)
for step in range(steps):
casper.invoke_task(ctx, "assign", state)
solver.solve()
if out_file is not None:
out_file.write(u.split()[0], time=step)
if compute_norms:
nu = norm(u)
if comm.rank == 0:
print(step, 'L2(u):', nu)
def __init__(self, a, bcs, *args, **kwargs):
# sets self._a and self._bcs
super(ImplicitMatrix, self).__init__(a, bcs)
appctx = kwargs.get("appctx", {})
from firedrake.matrix_free.operators import ImplicitMatrixContext
ctx = ImplicitMatrixContext(a,
row_bcs=self.bcs,
col_bcs=self.bcs,
fc_params=kwargs["fc_params"],
appctx=appctx)
self.petscmat = PETSc.Mat().create(comm=self.comm)
self.petscmat.setType("python")
self.petscmat.setSizes((ctx.row_sizes, ctx.col_sizes),
bsize=ctx.block_size)
self.petscmat.setPythonContext(ctx)
self.petscmat.setUp()
self.petscmat.assemble()
def create_interpolation(self, dmc, dmf):
cctx = get_appctx(dmc)
fctx = get_appctx(dmf)
cV = cctx.J.arguments()[0].function_space()
fV = fctx.J.arguments()[0].function_space()
cbcs = cctx._problem.bcs
fbcs = fctx._problem.bcs
prefix = dmc.getOptionsPrefix()
mattype = PETSc.Options(prefix).getString("mg_levels_transfer_mat_type", default="matfree")
if mattype == "matfree":
I = prolongation_matrix_matfree(fV, cV, fbcs, cbcs)
elif mattype == "aij":
I = prolongation_matrix_aij(fV, cV, fbcs, cbcs)
else:
raise ValueError("Unknown matrix type")
R = PETSc.Mat().createTranspose(I)
return R, None
def create_injection(dmc, dmf):
_, clvl = utils.get_level(dmc)
_, flvl = utils.get_level(dmf)
cctx = dmc.getAppCtx()
V_c = dmc.getAttr("__fs__")()
V_f = dmf.getAttr("__fs__")()
nrow = sum(x.dof_dset.size * x.dof_dset.cdim for x in V_f)
ncol = sum(x.dof_dset.size * x.dof_dset.cdim for x in V_c)
cfn = firedrake.Function(V_c)
ffn = firedrake.Function(V_f)
cbcs = cctx._problems[clvl].bcs
class Injection(object):
def __init__(self, cfn, ffn, cbcs=None):
self.cfn = cfn
self.ffn = ffn
self.cbcs = cbcs or []
def multTranspose(self, mat, x, y):
with self.ffn.dat.vec as v:
x.copy(v)
firedrake.inject(self.ffn, self.cfn)
for bc in self.cbcs:
bc.apply(self.cfn)
with self.cfn.dat.vec_ro as v:
v.copy(y)
ctx = Injection(cfn, ffn, cbcs)
mat = PETSc.Mat().create()
mat.setSizes(((nrow, None), (ncol, None)))
mat.setType(mat.Type.PYTHON)
mat.setPythonContext(ctx)
mat.setUp()
return mat
def construct_kronecker_matrix(self, interp_1d):
"""
Construct the tensorized interpolation matrix.
Do this by computing the kron product of the rows of
the 1d univariate interpolation matrices.
In the future, this may be done matrix-free.
"""
# this is one of the two bottlenecks that slow down initiating Bsplines
IFW = PETSc.Mat().create(self.comm)
IFW.setType(PETSc.Mat.Type.AIJ)
comm = self.comm
# owned part of global problem
local_N = self.N // comm.size + int(comm.rank < (self.N % comm.size))
(lsize, gsize) = interp_1d[0].getSizes()[0]
IFW.setSizes(((lsize, gsize), (local_N, self.N)))
# guess sparsity pattern from interp_1d[0]
for row in range(lsize):
row = self.lg_map_fe.apply([row])[0]
nnz_ = len(interp_1d[0].getRow(row)[0]) # lenght of nnz-array
self.IFWnnz = max(self.IFWnnz, nnz_**self.dim)
IFW.setPreallocationNNZ(self.IFWnnz)
IFW.setUp()
for row in range(lsize):
row = self.lg_map_fe.apply([row])[0]
M = [[A.getRow(row)[0],
A.getRow(row)[1],
A.getSize()[1]] for A in interp_1d]
M = reduce(self.vectorkron, M)
columns, values, lenght = M
IFW.setValues([row], columns, values)
IFW.assemble()
return IFW
def nonlocal_integral_eq(
mesh,
scatterer_bdy_id,
outer_bdy_id,
wave_number,
options_prefix=None,
solver_parameters=None,
fspace=None,
vfspace=None,
true_sol_grad_expr=None,
actx=None,
dgfspace=None,
dgvfspace=None,
meshmode_src_connection=None,
qbx_kwargs=None,
):
r"""
see run_method for descriptions of unlisted args
args:
gamma and beta are used to precondition
with the following equation:
\Delta u - \kappa^2 \gamma u = 0
(\partial_n - i\kappa\beta) u |_\Sigma = 0
"""
# make sure we get outer bdy id as tuple in case it consists of multiple ids
if isinstance(outer_bdy_id, int):
outer_bdy_id = [outer_bdy_id]
outer_bdy_id = tuple(outer_bdy_id)
# away from the excluded region, but firedrake and meshmode point
# into
pyt_inner_normal_sign = -1
ambient_dim = mesh.geometric_dimension()
# {{{ Build src and tgt
# build connection meshmode near src boundary -> src boundary inside meshmode
from meshmode.discretization.poly_element import \
InterpolatoryQuadratureSimplexGroupFactory
from meshmode.discretization.connection import make_face_restriction
factory = InterpolatoryQuadratureSimplexGroupFactory(
dgfspace.finat_element.degree)
src_bdy_connection = make_face_restriction(actx,
meshmode_src_connection.discr,
factory, scatterer_bdy_id)
# source is a qbx layer potential
from pytential.qbx import QBXLayerPotentialSource
disable_refinement = (fspace.mesh().geometric_dimension() == 3)
qbx = QBXLayerPotentialSource(src_bdy_connection.to_discr,
**qbx_kwargs,
_disable_refinement=disable_refinement)
# get target indices and point-set
target_indices, target = get_target_points_and_indices(
fspace, outer_bdy_id)
# }}}
# build the operations
from pytential import bind, sym
r"""
..math:
x \in \Sigma
grad_op(x) =
\nabla(
\int_\Gamma(
u(y) \partial_n H_0^{(1)}(\kappa |x - y|)
)d\gamma(y)
)
"""
grad_op = pyt_inner_normal_sign * sym.grad(
ambient_dim,
sym.D(HelmholtzKernel(ambient_dim),
sym.var("u"),
k=sym.var("k"),
qbx_forced_limit=None))
r"""
..math:
x \in \Sigma
op(x) =
i \kappa \cdot
\int_\Gamma(
u(y) \partial_n H_0^{(1)}(\kappa |x - y|)
)d\gamma(y)
"""
op = pyt_inner_normal_sign * 1j * sym.var("k") * (sym.D(
HelmholtzKernel(ambient_dim),
sym.var("u"),
k=sym.var("k"),
qbx_forced_limit=None))
# bind the operations
pyt_grad_op = bind((qbx, target), grad_op)
pyt_op = bind((qbx, target), op)
# }}}
class MatrixFreeB(object):
def __init__(self, A, pyt_grad_op, pyt_op, actx, kappa):
"""
:arg kappa: The wave number
"""
self.actx = actx
self.k = kappa
self.pyt_op = pyt_op
self.pyt_grad_op = pyt_grad_op
self.A = A
self.meshmode_src_connection = meshmode_src_connection
# {{{ Create some functions needed for multing
self.x_fntn = Function(fspace)
# CG
self.potential_int = Function(fspace)
self.potential_int.dat.data[:] = 0.0
self.grad_potential_int = Function(vfspace)
self.grad_potential_int.dat.data[:] = 0.0
self.pyt_result = Function(fspace)
self.n = FacetNormal(mesh)
self.v = TestFunction(fspace)
# some meshmode ones
self.x_mm_fntn = self.meshmode_src_connection.discr.empty(
self.actx, dtype='c')
# }}}
def mult(self, mat, x, y):
# Copy function data into the fivredrake function
self.x_fntn.dat.data[:] = x[:]
# Transfer the function to meshmode
self.meshmode_src_connection.from_firedrake(project(
self.x_fntn, dgfspace),
out=self.x_mm_fntn)
# Restrict to boundary
x_mm_fntn_on_bdy = src_bdy_connection(self.x_mm_fntn)
# Apply the operation
potential_int_mm = self.pyt_op(self.actx,
u=x_mm_fntn_on_bdy,
k=self.k)
grad_potential_int_mm = self.pyt_grad_op(self.actx,
u=x_mm_fntn_on_bdy,
k=self.k)
# Store in firedrake
self.potential_int.dat.data[target_indices] = potential_int_mm.get(
)
for dim in range(grad_potential_int_mm.shape[0]):
self.grad_potential_int.dat.data[
target_indices, dim] = grad_potential_int_mm[dim].get()
# Integrate the potential
r"""
Compute the inner products using firedrake. Note this
will be subtracted later, hence appears off by a sign.
.. math::
\langle
n(x) \cdot \nabla(
\int_\Gamma(
u(y) \partial_n H_0^{(1)}(\kappa |x - y|)
)d\gamma(y)
), v
\rangle_\Sigma
- \langle
i \kappa \cdot
\int_\Gamma(
u(y) \partial_n H_0^{(1)}(\kappa |x - y|)
)d\gamma(y), v
\rangle_\Sigma
"""
self.pyt_result = assemble(
inner(inner(self.grad_potential_int, self.n), self.v) *
ds(outer_bdy_id) -
inner(self.potential_int, self.v) * ds(outer_bdy_id))
# y <- Ax - evaluated potential
self.A.mult(x, y)
with self.pyt_result.dat.vec_ro as ep:
y.axpy(-1, ep)
# {{{ Compute normal helmholtz operator
u = TrialFunction(fspace)
v = TestFunction(fspace)
r"""
.. math::
\langle
\nabla u, \nabla v
\rangle
- \kappa^2 \cdot \langle
u, v
\rangle
- i \kappa \langle
u, v
\rangle_\Sigma
"""
a = inner(grad(u), grad(v)) * dx \
- Constant(wave_number**2) * inner(u, v) * dx \
- Constant(1j * wave_number) * inner(u, v) * ds(outer_bdy_id)
# get the concrete matrix from a general bilinear form
A = assemble(a).M.handle
# }}}
# {{{ Setup Python matrix
B = PETSc.Mat().create()
# build matrix context
Bctx = MatrixFreeB(A, pyt_grad_op, pyt_op, actx, wave_number)
# set up B as same size as A
B.setSizes(*A.getSizes())
B.setType(B.Type.PYTHON)
B.setPythonContext(Bctx)
B.setUp()
# }}}
# {{{ Create rhs
# Remember f is \partial_n(true_sol)|_\Gamma
# so we just need to compute \int_\Gamma\partial_n(true_sol) H(x-y)
sigma = sym.make_sym_vector("sigma", ambient_dim)
r"""
..math:
x \in \Sigma
grad_op(x) =
\nabla(
\int_\Gamma(
f(y) H_0^{(1)}(\kappa |x - y|)
)d\gamma(y)
)
"""
grad_op = pyt_inner_normal_sign * \
sym.grad(ambient_dim, sym.S(HelmholtzKernel(ambient_dim),
sym.n_dot(sigma),
k=sym.var("k"), qbx_forced_limit=None))
r"""
..math:
x \in \Sigma
op(x) =
i \kappa \cdot
\int_\Gamma(
f(y) H_0^{(1)}(\kappa |x - y|)
)d\gamma(y)
)
"""
op = 1j * sym.var("k") * pyt_inner_normal_sign * \
sym.S(HelmholtzKernel(ambient_dim),
sym.n_dot(sigma),
k=sym.var("k"),
qbx_forced_limit=None)
rhs_grad_op = bind((qbx, target), grad_op)
rhs_op = bind((qbx, target), op)
# Transfer to meshmode
metadata = {'quadrature_degree': 2 * fspace.ufl_element().degree()}
dg_true_sol_grad = project(true_sol_grad_expr,
dgvfspace,
form_compiler_parameters=metadata)
true_sol_grad_mm = meshmode_src_connection.from_firedrake(dg_true_sol_grad,
actx=actx)
true_sol_grad_mm = src_bdy_connection(true_sol_grad_mm)
# Apply the operations
f_grad_convoluted_mm = rhs_grad_op(actx,
sigma=true_sol_grad_mm,
k=wave_number)
f_convoluted_mm = rhs_op(actx, sigma=true_sol_grad_mm, k=wave_number)
# Transfer function back to firedrake
f_grad_convoluted = Function(vfspace)
f_convoluted = Function(fspace)
f_grad_convoluted.dat.data[:] = 0.0
f_convoluted.dat.data[:] = 0.0
for dim in range(f_grad_convoluted_mm.shape[0]):
f_grad_convoluted.dat.data[target_indices,
dim] = f_grad_convoluted_mm[dim].get()
f_convoluted.dat.data[target_indices] = f_convoluted_mm.get()
r"""
\langle
f, v
\rangle_\Gamma
+ \langle
i \kappa \cdot \int_\Gamma(
f(y) H_0^{(1)}(\kappa |x - y|)
)d\gamma(y), v
\rangle_\Sigma
- \langle
n(x) \cdot \nabla(
\int_\Gamma(
f(y) H_0^{(1)}(\kappa |x - y|)
)d\gamma(y)
), v
\rangle_\Sigma
"""
rhs_form = inner(inner(true_sol_grad_expr, FacetNormal(mesh)),
v) * ds(scatterer_bdy_id, metadata=metadata) \
+ inner(f_convoluted, v) * ds(outer_bdy_id) \
- inner(inner(f_grad_convoluted, FacetNormal(mesh)),
v) * ds(outer_bdy_id)
rhs = assemble(rhs_form)
# {{{ set up a solver:
solution = Function(fspace, name="Computed Solution")
# {{{ Used for preconditioning
if 'gamma' in solver_parameters or 'beta' in solver_parameters:
gamma = complex(solver_parameters.pop('gamma', 1.0))
import cmath
beta = complex(solver_parameters.pop('beta', cmath.sqrt(gamma)))
p = inner(grad(u), grad(v)) * dx \
- Constant(wave_number**2 * gamma) * inner(u, v) * dx \
- Constant(1j * wave_number * beta) * inner(u, v) * ds(outer_bdy_id)
P = assemble(p).M.handle
else:
P = A
# }}}
# Set up options to contain solver parameters:
ksp = PETSc.KSP().create()
if solver_parameters['pc_type'] == 'pyamg':
del solver_parameters['pc_type'] # We are using the AMG preconditioner
pyamg_tol = solver_parameters.get('pyamg_tol', None)
if pyamg_tol is not None:
pyamg_tol = float(pyamg_tol)
pyamg_maxiter = solver_parameters.get('pyamg_maxiter', None)
if pyamg_maxiter is not None:
pyamg_maxiter = int(pyamg_maxiter)
ksp.setOperators(B)
ksp.setUp()
pc = ksp.pc
pc.setType(pc.Type.PYTHON)
pc.setPythonContext(
AMGTransmissionPreconditioner(wave_number,
fspace,
A,
tol=pyamg_tol,
maxiter=pyamg_maxiter,
use_plane_waves=True))
# Otherwise use regular preconditioner
else:
ksp.setOperators(B, P)
options_manager = OptionsManager(solver_parameters, options_prefix)
options_manager.set_from_options(ksp)
import petsc4py.PETSc
petsc4py.PETSc.Sys.popErrorHandler()
with rhs.dat.vec_ro as b:
with solution.dat.vec as x:
ksp.solve(b, x)
# }}}
return ksp, solution
def assemble_mixed_mass_matrix(V_A, V_B):
"""
Construct the mixed mass matrix of two function spaces,
using the TrialFunction from V_A and the TestFunction
from V_B.
"""
if len(V_A) > 1 or len(V_B) > 1:
raise NotImplementedError(
"Sorry, only implemented for non-mixed spaces")
if V_A.ufl_element().mapping() != "identity" or V_B.ufl_element().mapping(
) != "identity":
msg = """
Sorry, only implemented for affine maps for now. To do non-affine, we'd need to
import much more of the assembly engine of UFL/TSFC/etc to do the assembly on
each supermesh cell.
"""
raise NotImplementedError(msg)
mesh_A = V_A.mesh()
mesh_B = V_B.mesh()
dim = mesh_A.geometric_dimension()
assert dim == mesh_B.geometric_dimension()
assert dim == mesh_A.topological_dimension()
assert dim == mesh_B.topological_dimension()
(mh_A, level_A) = get_level(mesh_A)
(mh_B, level_B) = get_level(mesh_B)
if mesh_A is mesh_B:
def likely(cell_A):
return [cell_A]
else:
if (mh_A is None or mh_B is None) or (mh_A is not mh_B):
# No mesh hierarchy structure, call libsupermesh for
# intersection finding
intersections = intersection_finder(mesh_A, mesh_B)
likely = intersections.__getitem__
else:
# We do have a mesh hierarchy, use it
if abs(level_A - level_B) > 1:
raise NotImplementedError(
"Only works for transferring between adjacent levels for now."
)
# What are the cells of B that (probably) intersect with a given cell in A?
if level_A > level_B:
cell_map = mh_A.fine_to_coarse_cells[level_A]
def likely(cell_A):
return cell_map[cell_A]
elif level_A < level_B:
cell_map = mh_A.coarse_to_fine_cells[level_A]
def likely(cell_A):
return cell_map[cell_A]
assert V_A.value_size == V_B.value_size
orig_value_size = V_A.value_size
if V_A.value_size > 1:
V_A = firedrake.FunctionSpace(mesh_A,
V_A.ufl_element().sub_elements()[0])
if V_B.value_size > 1:
V_B = firedrake.FunctionSpace(mesh_B,
V_B.ufl_element().sub_elements()[0])
assert V_A.value_size == 1
assert V_B.value_size == 1
preallocator = PETSc.Mat().create(comm=mesh_A.comm)
preallocator.setType(PETSc.Mat.Type.PREALLOCATOR)
rset = V_B.dof_dset
cset = V_A.dof_dset
nrows = rset.layout_vec.getSizes()
ncols = cset.layout_vec.getSizes()
preallocator.setLGMap(rmap=rset.scalar_lgmap, cmap=cset.scalar_lgmap)
preallocator.setSizes(size=(nrows, ncols), bsize=1)
preallocator.setUp()
zeros = numpy.zeros((V_B.cell_node_map().arity, V_A.cell_node_map().arity),
dtype=ScalarType)
for cell_A, dofs_A in enumerate(V_A.cell_node_map().values):
for cell_B in likely(cell_A):
dofs_B = V_B.cell_node_map().values_with_halo[cell_B, :]
preallocator.setValuesLocal(dofs_B, dofs_A, zeros)
preallocator.assemble()
dnnz, onnz = get_preallocation(preallocator, nrows[0])
# Unroll from block to AIJ
dnnz = dnnz * cset.cdim
dnnz = numpy.repeat(dnnz, rset.cdim)
onnz = onnz * cset.cdim
onnz = numpy.repeat(onnz, cset.cdim)
preallocator.destroy()
assert V_A.value_size == V_B.value_size
rdim = V_B.dof_dset.cdim
cdim = V_A.dof_dset.cdim
#
# Preallocate M_AB.
#
mat = PETSc.Mat().create(comm=mesh_A.comm)
mat.setType(PETSc.Mat.Type.AIJ)
rsizes = tuple(n * rdim for n in nrows)
csizes = tuple(c * cdim for c in ncols)
mat.setSizes(size=(rsizes, csizes), bsize=(rdim, cdim))
mat.setPreallocationNNZ((dnnz, onnz))
mat.setLGMap(rmap=rset.lgmap, cmap=cset.lgmap)
# TODO: Boundary conditions not handled.
mat.setOption(mat.Option.IGNORE_OFF_PROC_ENTRIES, False)
mat.setOption(mat.Option.NEW_NONZERO_ALLOCATION_ERR, True)
mat.setOption(mat.Option.KEEP_NONZERO_PATTERN, True)
mat.setOption(mat.Option.UNUSED_NONZERO_LOCATION_ERR, False)
mat.setOption(mat.Option.IGNORE_ZERO_ENTRIES, True)
mat.setUp()
evaluate_kernel_A = compile_element(ufl.Coefficient(V_A),
name="evaluate_kernel_A")
evaluate_kernel_B = compile_element(ufl.Coefficient(V_B),
name="evaluate_kernel_B")
# We only need one of these since we assume that the two meshes both have CG1 coordinates
to_reference_kernel = to_reference_coordinates(
mesh_A.coordinates.ufl_element())
if dim == 2:
reference_mesh = UnitTriangleMesh(comm=COMM_SELF)
else:
reference_mesh = UnitTetrahedronMesh(comm=COMM_SELF)
evaluate_kernel_S = compile_element(ufl.Coefficient(
reference_mesh.coordinates.function_space()),
name="evaluate_kernel_S")
V_S_A = FunctionSpace(reference_mesh, V_A.ufl_element())
V_S_B = FunctionSpace(reference_mesh, V_B.ufl_element())
M_SS = assemble(inner(TrialFunction(V_S_A), TestFunction(V_S_B)) * dx)
M_SS = M_SS.M.handle[:, :]
node_locations_A = utils.physical_node_locations(
V_S_A).dat.data_ro_with_halos
node_locations_B = utils.physical_node_locations(
V_S_B).dat.data_ro_with_halos
num_nodes_A = node_locations_A.shape[0]
num_nodes_B = node_locations_B.shape[0]
to_reference_kernel = to_reference_coordinates(
mesh_A.coordinates.ufl_element())
supermesh_kernel_str = """
#include "libsupermesh-c.h"
#include <petsc.h>
%(to_reference)s
%(evaluate_S)s
%(evaluate_A)s
%(evaluate_B)s
#define complex_mode %(complex_mode)s
#define PrintInfo(...) do { if (PetscLogPrintInfo) printf(__VA_ARGS__); } while (0)
static void print_array(PetscScalar *arr, int d)
{
for(int j=0; j<d; j++)
PrintInfo(stderr, "%%+.2f ", arr[j]);
}
static void print_coordinates(PetscScalar *simplex, int d)
{
for(int i=0; i<d+1; i++)
{
PrintInfo("\t");
print_array(&simplex[d*i], d);
PrintInfo("\\n");
}
}
#if complex_mode
static void seperate_real_and_imag(PetscScalar *simplex, double *real_simplex, double *imag_simplex, int d)
{
for(int i=0; i<d+1; i++)
{
for(int j=0; j<d; j++)
{
real_simplex[d*i+j] = creal(simplex[d*i+j]);
imag_simplex[d*i+j] = cimag(simplex[d*i+j]);
}
}
}
static void merge_back_to_simplex(PetscScalar* simplex, double* real_simplex, double* imag_simplex, int d)
{
print_coordinates(simplex,d);
for(int i=0; i<d+1; i++)
{
for(int j=0; j<d; j++)
{
simplex[d*i+j] = real_simplex[d*i+j]+imag_simplex[d*i+j]*_Complex_I;
}
}
}
#endif
int supermesh_kernel(PetscScalar* simplex_A, PetscScalar* simplex_B, PetscScalar* simplices_C, PetscScalar* nodes_A, PetscScalar* nodes_B, PetscScalar* M_SS, PetscScalar* outptr, int num_ele)
{
#define d %(dim)s
#define num_nodes_A %(num_nodes_A)s
#define num_nodes_B %(num_nodes_B)s
double simplex_ref_measure;
PrintInfo("simplex_A coordinates\\n");
print_coordinates(simplex_A, d);
PrintInfo("simplex_B coordinates\\n");
print_coordinates(simplex_B, d);
int num_elements = num_ele;
if (d == 2) simplex_ref_measure = 0.5;
else if (d == 3) simplex_ref_measure = 1.0/6;
PetscScalar R_AS[num_nodes_A][num_nodes_A];
PetscScalar R_BS[num_nodes_B][num_nodes_B];
PetscScalar coeffs_A[%(num_nodes_A)s] = {0.};
PetscScalar coeffs_B[%(num_nodes_B)s] = {0.};
PetscScalar reference_nodes_A[num_nodes_A][d];
PetscScalar reference_nodes_B[num_nodes_B][d];
#if complex_mode
double real_simplex_A[d*(d+1)];
double imag_simplex_A[d*(d+1)];
seperate_real_and_imag(simplex_A, real_simplex_A, imag_simplex_A, d);
double real_simplex_B[d*(d+1)];
double imag_simplex_B[d*(d+1)];
seperate_real_and_imag(simplex_B, real_simplex_B, imag_simplex_B, d);
double real_simplices_C[num_elements*d*(d+1)];
double imag_simplices_C[num_elements*d*(d+1)];
for (int ii=0; ii<num_elements*d*(d+1); ++ii) imag_simplices_C[ii] = 0.;
%(libsupermesh_intersect_simplices)s(real_simplex_A, real_simplex_B, real_simplices_C, &num_elements);
merge_back_to_simplex(simplex_A, real_simplex_A, imag_simplex_A, d);
merge_back_to_simplex(simplex_B, real_simplex_B, imag_simplex_B, d);
for(int s=0; s<num_elements; s++)
{
PetscScalar* simplex_C = &simplices_C[s * d * (d+1)];
double* real_simplex_C = &real_simplices_C[s * d * (d+1)];
double* imag_simplex_C = &imag_simplices_C[s * d * (d+1)];
merge_back_to_simplex(simplex_C, real_simplex_C, imag_simplex_C, d);
}
#else
%(libsupermesh_intersect_simplices)s(simplex_A, simplex_B, simplices_C, &num_elements);
#endif
PrintInfo("Supermesh consists of %%i elements\\n", num_elements);
// would like to do this
//PetscScalar MAB[%(num_nodes_A)s][%(num_nodes_B)s] = (PetscScalar (*)[%(num_nodes_B)s])outptr;
// but have to do this instead because we don't grok C
PetscScalar (*MAB)[num_nodes_A] = (PetscScalar (*)[num_nodes_A])outptr;
PetscScalar (*MSS)[num_nodes_A] = (PetscScalar (*)[num_nodes_A])M_SS; // note the underscore
for ( int i = 0; i < num_nodes_B; i++ ) {
for (int j = 0; j < num_nodes_A; j++) {
MAB[i][j] = 0.0;
}
}
for(int s=0; s<num_elements; s++)
{
PetscScalar* simplex_S = &simplices_C[s * d * (d+1)];
double simplex_S_measure;
#if complex_mode
double real_simplex_S[d*(d+1)];
double imag_simplex_S[d*(d+1)];
seperate_real_and_imag(simplex_S, real_simplex_S, imag_simplex_S, d);
%(libsupermesh_simplex_measure)s(real_simplex_S, &simplex_S_measure);
merge_back_to_simplex(simplex_S, real_simplex_S, imag_simplex_S, d);
#else
%(libsupermesh_simplex_measure)s(simplex_S, &simplex_S_measure);
#endif
PrintInfo("simplex_S coordinates with measure %%f\\n", simplex_S_measure);
print_coordinates(simplex_S, d);
PrintInfo("Start mapping nodes for V_A\\n");
PetscScalar physical_nodes_A[num_nodes_A][d];
for(int n=0; n < num_nodes_A; n++) {
PetscScalar* reference_node_location = &nodes_A[n*d];
PetscScalar* physical_node_location = physical_nodes_A[n];
for (int j=0; j < d; j++) physical_node_location[j] = 0.0;
pyop2_kernel_evaluate_kernel_S(physical_node_location, simplex_S, reference_node_location);
PrintInfo("\\tNode ");
print_array(reference_node_location, d);
PrintInfo(" mapped to ");
print_array(physical_node_location, d);
PrintInfo("\\n");
}
PrintInfo("Start mapping nodes for V_B\\n");
PetscScalar physical_nodes_B[num_nodes_B][d];
for(int n=0; n < num_nodes_B; n++) {
PetscScalar* reference_node_location = &nodes_B[n*d];
PetscScalar* physical_node_location = physical_nodes_B[n];
for (int j=0; j < d; j++) physical_node_location[j] = 0.0;
pyop2_kernel_evaluate_kernel_S(physical_node_location, simplex_S, reference_node_location);
PrintInfo("\\tNode ");
print_array(reference_node_location, d);
PrintInfo(" mapped to ");
print_array(physical_node_location, d);
PrintInfo("\\n");
}
PrintInfo("==========================================================\\n");
PrintInfo("Start pulling back dof from S into reference space for A.\\n");
for(int n=0; n < num_nodes_A; n++) {
for(int i=0; i<d; i++) reference_nodes_A[n][i] = 0.;
to_reference_coords_kernel(reference_nodes_A[n], physical_nodes_A[n], simplex_A);
PrintInfo("Pulling back ");
print_array(physical_nodes_A[n], d);
PrintInfo(" to ");
print_array(reference_nodes_A[n], d);
PrintInfo("\\n");
}
PrintInfo("Start pulling back dof from S into reference space for B.\\n");
for(int n=0; n < num_nodes_B; n++) {
for(int i=0; i<d; i++) reference_nodes_B[n][i] = 0.;
to_reference_coords_kernel(reference_nodes_B[n], physical_nodes_B[n], simplex_B);
PrintInfo("Pulling back ");
print_array(physical_nodes_B[n], d);
PrintInfo(" to ");
print_array(reference_nodes_B[n], d);
PrintInfo("\\n");
}
PrintInfo("Start evaluating basis functions of V_A at dofs for V_A on S\\n");
for(int i=0; i<num_nodes_A; i++) {
coeffs_A[i] = 1.;
for(int j=0; j<num_nodes_A; j++) {
R_AS[i][j] = 0.;
pyop2_kernel_evaluate_kernel_A(&R_AS[i][j], coeffs_A, reference_nodes_A[j]);
}
print_array(R_AS[i], num_nodes_A);
PrintInfo("\\n");
coeffs_A[i] = 0.;
}
PrintInfo("Start evaluating basis functions of V_B at dofs for V_B on S\\n");
for(int i=0; i<num_nodes_B; i++) {
coeffs_B[i] = 1.;
for(int j=0; j<num_nodes_B; j++) {
R_BS[i][j] = 0.;
pyop2_kernel_evaluate_kernel_B(&R_BS[i][j], coeffs_B, reference_nodes_B[j]);
}
print_array(R_BS[i], num_nodes_B);
PrintInfo("\\n");
coeffs_B[i] = 0.;
}
PrintInfo("Start doing the matmatmat mult\\n");
for ( int i = 0; i < num_nodes_B; i++ ) {
for (int j = 0; j < num_nodes_A; j++) {
for ( int k = 0; k < num_nodes_B; k++) {
for ( int l = 0; l < num_nodes_A; l++) {
MAB[i][j] += (simplex_S_measure/simplex_ref_measure) * R_BS[i][k] * MSS[k][l] * R_AS[j][l];
}
}
}
}
}
return num_elements;
}
""" % {
"evaluate_S":
str(evaluate_kernel_S),
"evaluate_A":
str(evaluate_kernel_A),
"evaluate_B":
str(evaluate_kernel_B),
"to_reference":
str(to_reference_kernel),
"num_nodes_A":
num_nodes_A,
"num_nodes_B":
num_nodes_B,
"libsupermesh_simplex_measure":
"libsupermesh_triangle_area"
if dim == 2 else "libsupermesh_tetrahedron_volume",
"libsupermesh_intersect_simplices":
"libsupermesh_intersect_tris_real"
if dim == 2 else "libsupermesh_intersect_tets_real",
"dim":
dim,
"complex_mode":
1 if complex_mode else 0
}
dirs = get_petsc_dir() + (sys.prefix, )
includes = ["-I%s/include" % d for d in dirs]
libs = ["-L%s/lib" % d for d in dirs]
libs = libs + ["-Wl,-rpath,%s/lib" % d
for d in dirs] + ["-lpetsc", "-lsupermesh"]
lib = load(supermesh_kernel_str,
"c",
"supermesh_kernel",
cppargs=includes,
ldargs=libs,
argtypes=[
ctypes.c_voidp, ctypes.c_voidp, ctypes.c_voidp,
ctypes.c_voidp, ctypes.c_voidp, ctypes.c_voidp,
ctypes.c_voidp
],
restype=ctypes.c_int)
ammm(V_A, V_B, likely, node_locations_A, node_locations_B, M_SS,
ctypes.addressof(lib), mat)
if orig_value_size == 1:
return mat
else:
(lrows, grows), (lcols, gcols) = mat.getSizes()
lrows *= orig_value_size
grows *= orig_value_size
lcols *= orig_value_size
gcols *= orig_value_size
size = ((lrows, grows), (lcols, gcols))
context = BlockMatrix(mat, orig_value_size)
blockmat = PETSc.Mat().createPython(size,
context=context,
comm=mat.comm)
blockmat.setUp()
return blockmat
def create_interpolation(dmc, dmf):
_, clvl = utils.get_level(dmc)
_, flvl = utils.get_level(dmf)
cctx = dmc.getAppCtx()
fctx = dmf.getAppCtx()
V_c = dmc.getAttr("__fs__")()
V_f = dmf.getAttr("__fs__")()
nrow = sum(x.dof_dset.size * x.dof_dset.cdim for x in V_f)
ncol = sum(x.dof_dset.size * x.dof_dset.cdim for x in V_c)
cfn = firedrake.Function(V_c)
ffn = firedrake.Function(V_f)
cbcs = cctx._problems[clvl].bcs
fbcs = fctx._problems[flvl].bcs
class Interpolation(object):
def __init__(self, cfn, ffn, cbcs=None, fbcs=None):
self.cfn = cfn
self.ffn = ffn
self.cbcs = cbcs or []
self.fbcs = fbcs or []
def mult(self, mat, x, y, inc=False):
with self.cfn.dat.vec as v:
x.copy(v)
firedrake.prolong(self.cfn, self.ffn)
for bc in self.fbcs:
bc.zero(self.ffn)
with self.ffn.dat.vec_ro as v:
if inc:
y.axpy(1.0, v)
else:
v.copy(y)
def multAdd(self, mat, x, y, w):
if y.handle == w.handle:
self.mult(mat, x, w, inc=True)
else:
self.mult(mat, x, w)
w.axpy(1.0, y)
def multTranspose(self, mat, x, y, inc=False):
with self.ffn.dat.vec as v:
x.copy(v)
firedrake.restrict(self.ffn, self.cfn)
for bc in self.cbcs:
bc.zero(self.cfn)
with self.cfn.dat.vec_ro as v:
if inc:
y.axpy(1.0, v)
else:
v.copy(y)
def multTransposeAdd(self, mat, x, y, w):
if y.handle == w.handle:
self.multTranspose(mat, x, w, inc=True)
else:
self.multTranspose(mat, x, w)
w.axpy(1.0, y)
ctx = Interpolation(cfn, ffn, cbcs, fbcs)
mat = PETSc.Mat().create()
mat.setSizes(((nrow, None), (ncol, None)))
mat.setType(mat.Type.PYTHON)
mat.setPythonContext(ctx)
mat.setUp()
return mat, None