def make_diagonal_mat(engine, fes1, fes2, value):
if fes1 == fes2:
bf = engine.new_bf(fes1)
bf.Assemble()
bf.Finalize()
mat = engine.a2A(bf)
else:
bf = engine.new_mixed_bf(fes1, fes2)
#one = mfem.ConstantCoefficient(0.0001)
#itg = mfem.MixedScalarMassIntegrator()
#bf.AddDomainIntegrator(itg)
bf.Assemble()
mat = engine.a2Am(bf)
if use_parallel:
mat.CopyRowStarts()
mat.CopyColStarts()
from mfem.common.chypre import MfemMat2PyMat
m1 = MfemMat2PyMat(mat, None)
if not use_parallel:
from petram.helper.block_matrix import convert_to_ScipyCoo
m1 = convert_to_ScipyCoo(m1)
shape = m1.shape
assert shape[0]==shape[1], "Identity Operator must be square"
idx = range(shape[0])
m1.setDiag(idx, value=value)
return m1
def convert_mat_to_operator(self, mat):
'''
a utility routine to convert locally assembled mat
to linear operator
'''
is_complex = np.iscomplexobj(mat)
m_coo = mat.tocoo()
row = m_coo.row
col = m_coo.col
col = np.unique(col)
from scipy.sparse import coo_matrix, csr_matrix
if use_parallel:
if is_complex:
m1 = csr_matrix(mat.real, dtype=float)
m2 = csr_matrix(mat.imag, dtype=float)
else:
m1 = csr_matrix(mat.real, dtype=float)
m2 = None
from mfem.common.chypre import CHypreMat
start_col = self.fes1.GetMyTDofOffset()
end_col = self.fes1.GetMyTDofOffset() + self.fes1.GetTrueVSize()
col_starts = [start_col, end_col, mat.shape[1]]
M = CHypreMat(m1, m2, col_starts=col_starts)
else:
from petram.helper.block_matrix import convert_to_ScipyCoo
M = convert_to_ScipyCoo(coo_matrix(mat, dtype=mat.dtype))
def assemble(self, *args, **kwargs):
engine = self._engine()
self.process_kwargs(engine, kwargs)
fes1 = self._fes1()
fes2 = fes1 if self._fes2 is None else self._fes2()
if fes1 == fes2:
bf = engine.new_bf(fes1)
#one = mfem.ConstantCoefficient(0.0001)
#itg = mfem.MassIntegrator()
#bf.AddDomainIntegrator(itg)
bf.Assemble()
bf.Finalize()
mat = engine.a2A(bf)
else:
bf = engine.new_mixed_bf(fes1, fes2)
#one = mfem.ConstantCoefficient(0.0001)
#itg = mfem.MixedScalarMassIntegrator()
#bf.AddDomainIntegrator(itg)
bf.Assemble()
mat = engine.a2Am(bf)
if use_parallel:
mat.CopyRowStarts()
mat.CopyColStarts()
from mfem.common.chypre import MfemMat2PyMat
m1 = MfemMat2PyMat(mat, None)
if not use_parallel:
from petram.helper.block_matrix import convert_to_ScipyCoo
m1 = convert_to_ScipyCoo(m1)
shape = m1.shape
assert shape[0]==shape[1], "Identity Operator must be square"
idx = range(shape[0])
m1.setDiag(idx)
return m1
def projection_matrix(idx1, idx2, fes, tdof1, fes2=None, tdof2=None,
trans1=None, trans2 = None, dphase=0.0, weight = None,
tol = 1e-7, mode = 'surface', filldiag=True):
'''
map: destinatiom mapping
smap: source mapping
'''
fec_name = fes.FEColl().Name()
if fec_name.startswith('ND') and mode == 'volume':
mapper = map_volume_nd
elif fec_name.startswith('ND') and mode == 'surface':
mapper = map_surface_nd
elif fec_name.startswith('ND') and mode == 'edge':
mapper = map_edge_nd
elif fec_name.startswith('H1') and mode == 'volume':
mapper = map_volume_h1
elif fec_name.startswith('H1') and mode == 'surface':
mapper = map_surface_h1
elif fec_name.startswith('H1') and mode == 'edge':
mapper = map_edge_h1
elif fec_name.startswith('RT') and mode == 'volume':
mapper = map_volume_rt
elif fec_name.startswith('RT') and mode == 'surface':
mapper = map_surface_rt
else:
raise NotImplementedError("mapping :" + fec_name + ", mode: " + mode)
map = mapper(idx2, idx1, fes, fes2=fes2, trans1=trans1, trans2=trans2, tdof1=tdof1,
tdof2=tdof2, tol=tol)
if weight is None:
iscomplex = False
if (dphase == 0.):
pass
elif (dphase == 180.):
map = -map
else:
iscomplex = True
map = map.astype(complex)
map *= np.exp(-1j*np.pi/180*dphase)
else:
iscomplex = np.iscomplexobj(weight)
if iscomplex:
map = map.astype(complex)
if map.nnz > 0:
map *= -weight
m_coo = map.tocoo()
row = m_coo.row
col = m_coo.col
col = np.unique(col)
if use_parallel:
start_row = fes.GetMyTDofOffset()
end_row = fes.GetMyTDofOffset() + fes.GetTrueVSize()
col = np.unique(allgather_vector(col))
row = row + start_row
else:
start_row = 0
end_row = map.shape[0]
if filldiag:
for i in range(min(map.shape[0], map.shape[1])):
r = start_row+i
if not r in col: map[i, r] = 1.0
from scipy.sparse import coo_matrix, csr_matrix
if use_parallel:
if iscomplex:
m1 = csr_matrix(map.real, dtype=float)
m2 = csr_matrix(map.imag, dtype=float)
else:
m1 = csr_matrix(map.real, dtype=float)
m2 = None
from mfem.common.chypre import CHypreMat
start_col = fes2.GetMyTDofOffset()
end_col = fes2.GetMyTDofOffset() + fes2.GetTrueVSize()
col_starts = [start_col, end_col, map.shape[1]]
M = CHypreMat(m1, m2, col_starts=col_starts)
else:
from petram.helper.block_matrix import convert_to_ScipyCoo
M = convert_to_ScipyCoo(coo_matrix(map, dtype=map.dtype))
return M, row, col
def hcurln(fes1,
fes2,
coeff,
is_complex=False,
bdr='all',
orderinc=1,
verbose=False):
mat, rstart = get_empty_map(fes2, fes1, is_complex=is_complex)
mat2, rstart = get_empty_map(fes2, fes1, is_complex=is_complex)
from petram.helper.element_map import map_element
name_fes1 = fes1.FEColl().Name()[:2]
name_fes2 = fes2.FEColl().Name()[:2]
if verbose:
if myid == 0:
dprint1("fes", name_fes1, name_fes2)
mesh1 = fes1.GetMesh()
mesh2 = fes2.GetMesh()
mesh2.Print("/home/shiraiwa/part.mesh")
if verbose:
if myid == 0:
dprint1("NE", mesh1.GetNE(), mesh2.GetNE())
elmap, elmap_r = map_element(mesh1, mesh2, bdr, map_bdr=True)
sdim1 = mesh1.SpaceDimension()
sdim2 = mesh1.SpaceDimension()
dim1 = mesh1.Dimension()
dim2 = mesh2.Dimension()
shape1 = mfem.DenseMatrix()
shape2 = mfem.Vector()
ip = mfem.IntegrationPoint()
nor = mfem.Vector(sdim1)
if USE_PARALLEL:
# this is global TrueDoF (offset is not subtracted)
P = fes1.Dof_TrueDof_Matrix()
P1mat = ToScipyCoo(P).tocsr()
#VDoFtoGTDoF1 = P.indices
#P = fes2.Dof_TrueDof_Matrix()
#P = ToScipyCoo(P).tocsr()
#VDoFtoGTDoF2 = P.indices
#P2mat = P
vdofs1_senddata = []
shared_data = []
el2_2_node = {}
el2_2_el1 = {}
for d in elmap_r:
for x in list(elmap_r[d]):
el2_2_node[x] = d
for x in list(elmap_r[d]):
el2_2_el1[x] = elmap_r[d][x]
# working for fes2
# find boundary element on mesh1 using mesh2 boundary
el2_arr = [list() for x in range(nprc)]
el1_arr = [list() for x in range(nprc)]
fe2o_arr = [list() for x in range(nprc)]
for i_el in range(fes2.GetNE()):
attr = fes2.GetAttribute(i_el)
if bdr != 'all' and not attr in bdr:
continue
el1_arr[el2_2_node[i_el]].append(el2_2_el1[i_el])
el2_arr[el2_2_node[i_el]].append(i_el)
fe2 = fes2.GetFE(i_el)
fe2o_arr[el2_2_node[i_el]].append(fe2.GetOrder())
if USE_PARALLEL:
el1_arr = alltoall_vector(el1_arr, int) # transfer to mesh1 owners
# working for fes1
# find elemet order on mesh1
fe1o_arr = [list() for x in range(nprc)]
i_fe1_arr = [list() for x in range(nprc)]
rank = 0
for rank, i_bdrs in enumerate(el1_arr):
for i_bdr in i_bdrs:
iface = mesh1.GetBdrElementEdgeIndex(i_bdr)
transs = mesh1.GetFaceElementTransformations(iface)
i_el1 = transs.Elem1No
assert transs.Elem2No == -1, "boundary must be exterior for this operator"
fe1 = fes1.GetFE(i_el1)
fe1o_arr[rank].append(fe1.GetOrder())
i_fe1_arr[rank].append(i_el1)
rank = rank + 1
if USE_PARALLEL:
fe1o_arr = alltoall_vector(fe1o_arr, int) # transfer to mesh2
# working for fes2
locnor_arr = [list() for x in range(nprc)]
data2_arr = [list() for x in range(nprc)]
verbose1 = verbose
for rank, i_el2s in enumerate(el2_arr):
for i_el2, fe1o in zip(i_el2s, fe1o_arr[rank]):
eltrans = fes2.GetElementTransformation(i_el2)
fe2 = fes2.GetFE(i_el2)
nd2 = fe2.GetDof()
ir = get_rule(fe1o,
fe2,
eltrans,
orderinc=orderinc,
verbose=verbose1)
verbose1 = False
shape2.SetSize(nd2)
data2 = []
locnors = []
for jj in range(ir.GetNPoints()):
ip1 = ir.IntPoint(jj)
eltrans.SetIntPoint(ip1)
w = eltrans.Weight() * ip1.weight
mfem.CalcOrtho(eltrans.Jacobian(), nor)
nor2 = nor.GetDataArray() / np.linalg.norm(nor.GetDataArray())
fe2.CalcShape(ip1, shape2)
if dim2 == 1:
d = np.array([ip1.x] + list(eltrans.Transform(ip1)) +
list(nor2))
locnors.append(d)
elif dim2 == 2:
d = np.array([ip1.x, ip1.y] +
list(eltrans.Transform(ip1)) + list(nor2))
locnors.append(d)
else:
assert False, "boundary mesh must be dim=1 or 2"
data2.append(w * shape2.GetDataArray().copy())
# np.vstack(locnors).shape = (#Npoints, dim2+sdim2*2)
# np.vstack(data2).shape = (#Npoints, #NDoF2)
#print("size here", np.vstack(locnors).shape, np.vstack(data2).shape)
locnor_arr[rank].append(np.vstack(locnors))
data2_arr[rank].append(np.vstack(data2))
if USE_PARALLEL:
locnor_arr = alltoall_vectorv(locnor_arr, float) # transfer to mesh1
ll = dim2 + 2 * sdim2
vdofs1_arr = [list() for x in range(nprc)]
data1_arr = [list() for x in range(nprc)]
# space to compute the coefficient
MV = [mfem.Vector(sdim1), mfem.DenseMatrix(sdim1, sdim1)]
max_misalignment = -np.inf
for rank, i_fe1s in enumerate(i_fe1_arr):
locnorss = locnor_arr[rank]
sign_dict = {}
for k, i_fe1 in enumerate(i_fe1s):
fe1 = fes1.GetFE(i_fe1)
nd1 = fe1.GetDof()
eltrans = fes1.GetElementTransformation(i_fe1)
doftrans = fes1.GetElementDofTransformation(i_fe1)
#ctr = eval_element_center(fe1, eltrans)
locnors2 = locnorss[k]
shape1.SetSize(nd1, sdim1)
vdofs1 = fes1.GetElementVDofs(i_fe1)
dof_sign1 = np.array([
[1 if vv >= 0 else -1 for vv in vdofs1],
])
vdofs1 = [-1 - x if x < 0 else x for x in vdofs1]
mat_doftrans = get_inv_doftrans(doftrans, dof_sign1)
if USE_PARALLEL:
# After DofTransformation is introduced we can not use GetGlobalTDofNumber, because
# element local DoF could be linked with two TrueDoFs in neighber processes
# We construct submatrix of Prolongation to construct element matrix
# in TrueDof space
vv1 = [
P1mat.indices[P1mat.indptr[ii]:P1mat.indptr[ii + 1]]
for ii in vdofs1
]
vv3 = [
P1mat.data[P1mat.indptr[ii]:P1mat.indptr[ii + 1]]
for ii in vdofs1
]
ngtof = np.sum([len(x) for x in vv3])
sub_p = np.zeros((nd1, ngtof))
k1 = 0
k2 = 0
for gtofs, weights in zip(vv1, vv3):
for g, w in zip(gtofs, weights):
sub_p[k1, k2] = w
k2 = k2 + 1
k1 = k1 + 1
vdofs1 = np.hstack(vv1).flatten()
mat_doftrans = mat_doftrans.dot(sub_p)
res, misalignment = map_ir(fe1, eltrans, coeff, shape1, dim2,
sdim2, locnors2, dof_sign1,
mat_doftrans, MV)
vdofs1_arr[rank].append(np.array(vdofs1))
data1_arr[rank].append(res)
max_misalignment = np.max([max_misalignment, np.max(misalignment)])
# res.shape = (#Npoints, #DoF1)
if USE_PARALLEL:
vdofs1_arr = alltoall_vectorv(vdofs1_arr, int) # transfer to mesh2
if is_complex:
data1_arr = alltoall_vectorv(data1_arr,
complex) # transfer to mesh2
else:
data1_arr = alltoall_vectorv(data1_arr, float) # transfer to mesh2
max_misalignment = np.max(
MPI.COMM_WORLD.gather(max_misalignment, root=0))
dprint1("Max misalignment: ", max_misalignment)
shared_data = []
for rank, i_el2s in enumerate(el2_arr):
for k, i_el2 in enumerate(i_el2s):
vdofs1 = vdofs1_arr[rank][k]
fe2 = fes2.GetFE(i_el2)
eltrans2 = fes2.GetElementTransformation(i_el2)
vdofs2 = fes2.GetElementVDofs(i_el2)
vdofs2 = [-1 - x if x < 0 else x for x in vdofs2]
d1 = data1_arr[rank][k]
d2 = data2_arr[rank][k]
mm = d2.transpose().dot(d1)
if USE_PARALLEL:
# prepare data for not-owned DoFs, which will be shared later
vdofs22 = [fes2.GetLocalTDofNumber(ii) for ii in vdofs2]
vdofs22g = [fes2.GetGlobalTDofNumber(ii) for ii in vdofs2]
kkk = 0
for v2, v2g in zip(vdofs22, vdofs22g):
if v2 < 0:
shared_data.append([v2g, mm[kkk, :], vdofs1])
kkk = kkk + 1
else:
vdofs22 = vdofs2
for i, ltdof2 in enumerate(vdofs22):
if ltdof2 < 0:
continue
for j, gtdof1 in enumerate(vdofs1):
mat[ltdof2, gtdof1] = mat[ltdof2, gtdof1] + mm[i, j]
if USE_PARALLEL:
#nicePrint("shared data", shared_data)
for source_id in range(nprc):
data = comm.bcast(shared_data, root=source_id)
myoffset = fes2.GetMyTDofOffset()
for v2g, elmat, vdofs1 in data:
if v2g >= myoffset and v2g < myoffset + mat.shape[0]:
i = v2g - myoffset
for j, gtdof1 in enumerate(vdofs1):
mat[i, gtdof1] = mat[i, gtdof1] + elmat[j]
#mat[i, vdofs1] = mat[i, vdofs1] + elmat
from scipy.sparse import coo_matrix, csr_matrix
if USE_PARALLEL:
if is_complex:
m1 = csr_matrix(mat.real, dtype=float)
m2 = csr_matrix(mat.imag, dtype=float)
else:
m1 = csr_matrix(mat.real, dtype=float)
m2 = None
from mfem.common.chypre import CHypreMat
start_col = fes1.GetMyTDofOffset()
end_col = fes1.GetMyTDofOffset() + fes1.GetTrueVSize()
col_starts = [start_col, end_col, mat.shape[1]]
M = CHypreMat(m1, m2, col_starts=col_starts)
else:
from petram.helper.block_matrix import convert_to_ScipyCoo
M = convert_to_ScipyCoo(coo_matrix(mat, dtype=mat.dtype))
return M
def dof_mapping_matrix(src,
dst,
fes,
tdof,
engine=None,
dphase=0.0,
map_to_u=def_map_u,
map_to_v=def_map_v,
smap_to_u=None,
smap_to_v=None,
tol=1e-7):
'''
map: destinatiom mapping
smap: source mapping
'''
fec_name = fes.FEColl().Name()
if fec_name.startswith('ND'):
mapper = find_dof_map_nd
elif fec_name.startswith('H1'):
mapper = find_dof_map_h1
else:
raise NotImplementedError("mapping for " + fec_name)
if smap_to_u is None:
smap_to_u = map_to_u
if smap_to_v is None:
smap_to_v = map_to_v
map = mapper(src,
dst,
map_to_u,
map_to_v,
smap_to_u,
smap_to_v,
fes,
engine,
tdof,
tol=tol)
if (dphase == 0.):
pass
elif (dphase == 180.):
map = -map
else:
map = map.astype(complex)
map *= np.exp(-1j * np.pi / 180 * dphase)
coo = coo_matrix(map)
r = coo.row
c = coo.col
idx = range(map.shape[0])
map.setdiag(1.0)
for k in c:
map[k, k] = 0.0
if use_parallel:
start_row = fes.GetMyTDofOffset()
end_row = fes.GetMyTDofOffset() + fes.GetTrueVSize()
c = allgather_vector(c)
map = map.transpose()
m1 = csr_matrix(map.real[start_row:end_row, :], dtype=float)
m2 = csr_matrix(map.imag[start_row:end_row, :], dtype=float)
m1.eliminate_zeros()
m2.eliminate_zeros()
from mfem.common.chypre import CHypreMat
dprint1(m1.shape, m2.shape)
M = CHypreMat(m1, m2).transpose()
else:
from petram.helper.block_matrix import convert_to_ScipyCoo
M = convert_to_ScipyCoo(coo_matrix(map, dtype=map.dtype))
#idx = range(M.shape[0])
#M.setDiag(idx, 1.0)
#M.setDiag(c, 0.0)
return M, r, c
def convolve2d(fes1,
fes2,
kernel=delta,
support=None,
orderinc=5,
is_complex=False,
trial_domain='all',
test_domain='all',
verbose=False,
coeff=None):
'''
fill linear operator for convolution
\int phi_test(x) func(x-x') phi_trial(x') dx
Genralized version to multi-dim
test/trial
ScalarFE, ScalarFE : func is scalar
VectorFE, ScalarFE : func is vector (vertical)
ScalarFE, VectorFE : func is vector (horizontal)
VectorFE, VectorFE : func matrix
'''
mat, rstart = get_empty_map(fes2, fes1, is_complex=is_complex)
if fes1.GetNE() == 0:
assert False, "FESpace does not have element"
eltrans1 = fes1.GetElementTransformation(0)
ir = get_rule(fes1.GetFE(0), fes2.GetFE(0), eltrans1, orderinc, verbose)
name_fes1 = fes1.FEColl().Name()[:2]
name_fes2 = fes2.FEColl().Name()[:2]
sdim = fes1.GetMesh().SpaceDimension()
if name_fes1 in ['RT', 'ND']:
shape1 = mfem.DenseMatrix()
vdim1 = fes1.GetMesh().SpaceDimension()
else:
shape1 = mfem.Vector()
vdim1 = 1
if name_fes2 in ['RT', 'ND']:
shape2 = mfem.DenseMatrix()
vdim2 = fes1.GetMesh().SpaceDimension()
else:
shape2 = mfem.Vector()
vdim1 = 1
#nicePrint("shape", mat.shape, fes2.GetNE(), fes1.GetNE())
# communication strategy
# (1) x2 (ir points on test space) is collected in each nodes
# (2) x2 is send to other nodes
# (3) each nodes compute \int f(x2-x1) phi(x1)
# (4) non-zero results of (3) and global index should be send back
# Step (1, 2)
if verbose:
dprint1("Step 1,2")
x2_arr = []
i2_arr = []
ptx = mfem.DenseMatrix(ir.GetNPoints(), sdim)
attrs1 = fes2.GetMesh().GetAttributeArray()
attrs2 = fes2.GetMesh().GetAttributeArray()
for i in range(fes2.GetNE()): # scan test space
if test_domain != 'all':
if not attrs1[i] in test_domain: continue
eltrans = fes2.GetElementTransformation(i)
eltrans.Transform(ir, ptx)
x2_arr.append(ptx.GetDataArray().copy().transpose())
i2_arr.append(i)
if support is not None:
supports = np.array([support(np.mean(xxx, 0)) for xxx in x2_arr])
else:
supports = -np.ones(len(x2_arr))
if len(i2_arr) > 0:
ptx_x2 = np.stack(x2_arr)
i2_arr = np.hstack(i2_arr)
else:
ptx_x2 = np.array([[[]]])
i2_arr = np.array([])
#nicePrint("x2 shape", ptx_x2.shape)
if USE_PARALLEL:
## note: we could implement more advanced alg. to reduce
## the amount of data exchange..
x2_all = comm.allgather(ptx_x2)
i2_all = comm.allgather(i2_arr)
s_all = comm.allgather(supports)
else:
x2_all = [ptx_x2]
i2_all = [i2_arr]
s_all = [supports]
#nicePrint("x2_all shape", supports.shape, len(x2_all), [tmp.shape for tmp in x2_all])
if USE_PARALLEL:
#this is global TrueDoF (offset is not subtracted)
P = fes1.Dof_TrueDof_Matrix()
P = ToScipyCoo(P).tocsr()
VDoFtoGTDoF1 = P.indices
P = fes2.Dof_TrueDof_Matrix()
P = ToScipyCoo(P).tocsr()
VDoFtoGTDoF2 = P.indices
# Step 3
if verbose:
dprint1("Step 3")
vdofs1_senddata = []
elmats_senddata = []
for knode1 in range(len(x2_all)):
#dprint1("new knode1", myid, knode1)
x2_onenode = x2_all[knode1]
i2_onenode = i2_all[knode1]
s_onenode = s_all[knode1]
elmats_all = []
vdofs1_all = []
# collect vdofs
for j in range(fes1.GetNE()):
local_vdofs = fes1.GetElementVDofs(j)
local_vdofs = [vv if vv >= 0 else -1 - vv for vv in local_vdofs]
if USE_PARALLEL:
subvdofs2 = [VDoFtoGTDoF1[i] for i in local_vdofs]
vdofs1_all.append(subvdofs2)
else:
vdofs1_all.append(local_vdofs)
#if myid == 0:
# pr = profile_start()
for i, x2s, su in zip(i2_onenode, x2_onenode,
s_onenode): # loop over fes2
nd2 = len(x2s)
#nicePrint("x2s", i, x2s.shape, x2s)
elmats = []
for j in range(fes1.GetNE()):
if trial_domain != 'all':
if not attrs1[j] in trial_domain: continue
# collect integration
fe1 = fes1.GetFE(j)
nd1 = fe1.GetDof()
eltrans = fes1.GetElementTransformation(j)
dof_sign1 = np.array(
[1 if vv >= 0 else -1 for vv in fes1.GetElementVDofs(j)])
if name_fes1 in ['RT', 'ND']:
shape1.SetSize(nd1, vdim1)
else:
shape1.SetSize(nd1)
elmat = np.zeros((nd2, vdim2, nd1), dtype=mat.dtype)
tmp_int = np.zeros((vdim2, nd1), dtype=mat.dtype).squeeze()
#if myid == 0: print("fes1 idx", j)
dataset = []
shapes = []
for jj in range(ir.GetNPoints()):
ip1 = ir.IntPoint(jj)
eltrans.SetIntPoint(ip1)
x1 = eltrans.Transform(ip1)
if name_fes1 in ['RT', 'ND']:
fe1.CalcVShape(eltrans, shape1)
else:
fe1.CalcShape(ip1, shape1)
w = eltrans.Weight() * ip1.weight
ss = shape1.GetDataArray().copy()
if len(ss.shape) > 1:
#dof_sign1 = dof_sign1.reshape(-1, 1)
ss = np.transpose(ss)
ss = ss * dof_sign1
dataset.append((x1, w, ss))
has_contribution = False
for kkk, x2 in enumerate(x2s):
tmp_int *= 0.0
has_contribution2 = False
for x1, w, shape_arr in dataset:
s = np.sqrt(np.sum((x1 - x2)**2))
if su >= 0 and s > su:
continue
val = kernel(x2 - x1, (x2 + x1) / 2.0, w=w)
if val is None:
continue
if coeff is not None:
val = val * coeff((x2 + x1) / 2.0)
tmp_int += np.dot(val, shape_arr) * w
has_contribution2 = True
if has_contribution2:
elmat[kkk, ...] = tmp_int
has_contribution = True
if has_contribution:
elmats.append((j, elmat))
#if myid == 0:
# pr.dump_stats("/home/shiraiwa/test.prf")
# profile_stop(pr)
# assert False, "hoge"
# pr = profile_start()
if len(elmats) > 0:
elmats_all.append((i, elmats))
vdofs1_senddata.append(vdofs1_all)
elmats_senddata.append(elmats_all)
# send this information to knodes;
'''
if USE_PARALLEL:
#nicePrint(vdofs1_all)
#nicePrint("elmats", [len(x) for x in elmats_all])
if myid == knode1:
vdofs1_data = comm.gather(vdofs1_all, root=knode1)
elmats_data = comm.gather(elmats_all, root=knode1)
else:
_ = comm.gather(vdofs1_all, root=knode1)
_ = comm.gather(elmats_all, root=knode1)
else:
vdofs1_data = [vdofs1_all,]
elmats_data = [elmats_all,]
'''
if USE_PARALLEL:
knode1 = 0
for vdofs1_all, elmats_all in zip(vdofs1_senddata, elmats_senddata):
if myid == knode1:
vdofs1_data = comm.gather(vdofs1_all, root=knode1)
elmats_data = comm.gather(elmats_all, root=knode1)
else:
_ = comm.gather(vdofs1_all, root=knode1)
_ = comm.gather(elmats_all, root=knode1)
knode1 = knode1 + 1
else:
vdofs1_data = vdofs1_senddata
elmats_data = elmats_senddata
# Step 4
if verbose:
dprint1("Step 4")
shared_data = []
mpi_rank = 0
for vdofs1, elmats_all in zip(vdofs1_data,
elmats_data): # loop over MPI nodes
#nicePrint("len elmats", len(elmats_all))
#for i, elmats in enumerate(elmats_all): # corresponds to loop over fes2
if verbose:
coupling = [len(elmats) for i, elmats in elmats_all]
nicePrint("Element coupling for rank/count", mpi_rank,
len(coupling))
nicePrint(" Average :",
(0 if len(coupling) == 0 else np.mean(coupling)))
nicePrint(" Max/Min :",
(0 if len(coupling) == 0 else np.max(coupling)),
(0 if len(coupling) == 0 else np.min(coupling)))
mpi_rank += 1
for i, elmats in elmats_all: # corresponds to loop over fes2
vdofs2 = fes2.GetElementVDofs(i)
dof_sign2 = np.array([
[1 if vv >= 0 else -1 for vv in vdofs2],
]).transpose()
vdofs2 = [-1 - x if x < 0 else x for x in vdofs2]
fe2 = fes2.GetFE(i)
nd2 = fe2.GetDof()
if name_fes2 in ['RT', 'ND']:
shape2.SetSize(nd2, vdim2)
else:
shape2.SetSize(nd2)
eltrans = fes2.GetElementTransformation(i)
#for j, elmat in enumerate(elmats):
for j, elmat in elmats:
#print(vdofs1[j], elmat.shape)
#if elmat is None:
# continue
mm = np.zeros((len(vdofs2), len(vdofs1[j])), dtype=float)
for ii in range(ir.GetNPoints()):
ip2 = ir.IntPoint(ii)
eltrans.SetIntPoint(ip2)
ww = eltrans.Weight() * ip2.weight
if name_fes2 in ['RT', 'ND']:
fe2.CalcVShape(eltrans, shape2)
else:
fe2.CalcShape(ip2, shape2)
shape2 *= ww
ss = shape2.GetDataArray().reshape(-1, vdim2)
ss = ss * dof_sign2
tmp_int = elmat[ii, ...].reshape(vdim1, -1)
tmp = np.dot(ss, tmp_int)
mm = mm + tmp
# preapre shared data
if USE_PARALLEL:
vdofs22 = [fes2.GetLocalTDofNumber(ii) for ii in vdofs2]
vdofs22g = [VDoFtoGTDoF2[ii] for ii in vdofs2]
kkk = 0
#for v2, v2g in zip(vdofs22, vdofs22g):
for v2, v2g in zip(vdofs22, vdofs22g):
if v2 < 0:
shared_data.append([v2g, mm[kkk, :], vdofs1[j]])
kkk = kkk + 1
# merge contribution to final mat
for k, vv in enumerate(vdofs1[j]):
try:
if USE_PARALLEL:
mmm = mm[np.where(np.array(vdofs22) >= 0)[0], :]
vdofs222 = [x for x in vdofs22 if x >= 0]
else:
vdofs222 = vdofs2
mmm = mm
#if myid == 1:
# print("check here", vdofs2, vdofs22, vdofs222)
#print(mmm[:, [k]])
tmp = mat[vdofs222, vv] + mmm[:, [k]]
mat[vdofs222, vv] = tmp.flatten()
except:
import traceback
print("error", myid)
#print(vdofs1, vdofs22, vdofs222, mmm.shape, k)
traceback.print_exc()
if USE_PARALLEL:
for source_id in range(nprc):
data = comm.bcast(shared_data, root=source_id)
myoffset = fes2.GetMyTDofOffset()
for v2g, elmat, vdofs1 in data:
if v2g >= myoffset and v2g < myoffset + mat.shape[0]:
i = v2g - myoffset
#print("procesising this", myid, i, v2g, elmat, vdofs1)
mat[i, vdofs1] = mat[i, vdofs1] + elmat
from scipy.sparse import coo_matrix, csr_matrix
if USE_PARALLEL:
if is_complex:
m1 = csr_matrix(mat.real, dtype=float)
m2 = csr_matrix(mat.imag, dtype=float)
else:
m1 = csr_matrix(mat.real, dtype=float)
m2 = None
from mfem.common.chypre import CHypreMat
start_col = fes1.GetMyTDofOffset()
end_col = fes1.GetMyTDofOffset() + fes1.GetTrueVSize()
col_starts = [start_col, end_col, mat.shape[1]]
M = CHypreMat(m1, m2, col_starts=col_starts)
else:
from petram.helper.block_matrix import convert_to_ScipyCoo
M = convert_to_ScipyCoo(coo_matrix(mat, dtype=mat.dtype))
return M
def convolve1d(fes1,
fes2,
kernel=delta,
support=None,
orderinc=5,
is_complex=False,
trial_domain='all',
test_domain='all',
verbose=False,
coeff=None):
'''
fill linear operator for convolution
\int phi_test(x) func(x-x') phi_trial(x') dx
'''
mat, rstart = get_empty_map(fes2, fes1, is_complex=is_complex)
eltrans1 = fes1.GetElementTransformation(0)
ir = get_rule(fes1.GetFE(0), fes2.GetFE(0), eltrans1, orderinc, verbose)
shape1 = mfem.Vector()
shape2 = mfem.Vector()
#nicePrint("shape", mat.shape, fes2.GetNE(), fes1.GetNE())
# communication strategy
# (1) x2 (ir points on test space) is collected in each nodes
# (2) x2 is send to other nodes
# (3) each nodes compute \int f(x2-x1) phi(x1)
# (4) non-zero results of (3) and global index should be send back
# Step (1, 2)
if verbose:
dprint1("Step 1,2")
x2_arr = []
i2_arr = []
ptx = mfem.DenseMatrix(ir.GetNPoints(), 1)
attrs1 = fes2.GetMesh().GetAttributeArray()
attrs2 = fes2.GetMesh().GetAttributeArray()
for i in range(fes2.GetNE()): # scan test space
if test_domain != 'all':
if not attrs1[i] in test_domain: continue
eltrans = fes2.GetElementTransformation(i)
eltrans.Transform(ir, ptx)
x2_arr.append(ptx.GetDataArray().copy())
i2_arr.append(i)
if len(i2_arr) > 0:
ptx_x2 = np.vstack(x2_arr)
i2_arr = np.hstack(i2_arr)
else:
ptx_x2 = np.array([[]])
i2_arr = np.array([])
#nicePrint("x2 shape", ptx_x2.shape)
if USE_PARALLEL:
## note: we could implement more advanced alg. to reduce
## the amount of data exchange..
x2_all = comm.allgather(ptx_x2)
i2_all = comm.allgather(i2_arr)
else:
x2_all = [ptx_x2]
i2_all = [i2_arr]
#nicePrint("x2_all shape", x2_all.shape)
if USE_PARALLEL:
#this is global TrueDoF (offset is not subtracted)
P = fes1.Dof_TrueDof_Matrix()
P = ToScipyCoo(P).tocsr()
VDoFtoGTDoF1 = P.indices
P = fes2.Dof_TrueDof_Matrix()
P = ToScipyCoo(P).tocsr()
VDoFtoGTDoF2 = P.indices
# Step 3
if verbose:
dprint1("Step 3")
vdofs1_senddata = []
elmats_senddata = []
for knode1 in range(len(x2_all)):
x2_onenode = x2_all[knode1]
i2_onenode = i2_all[knode1]
elmats_all = []
vdofs1_all = []
# collect vdofs
for j in range(fes1.GetNE()):
local_vdofs = fes1.GetElementVDofs(j)
if USE_PARALLEL:
subvdofs2 = [VDoFtoGTDoF1[i] for i in local_vdofs]
vdofs1_all.append(subvdofs2)
else:
vdofs1_all.append(local_vdofs)
for i, x2s in zip(i2_onenode, x2_onenode): # loop over fes2
nd2 = len(x2s)
#nicePrint(x2s)
elmats = []
for j in range(fes1.GetNE()):
if trial_domain != 'all':
if not attrs1[j] in trial_domain: continue
# collect integration
fe1 = fes1.GetFE(j)
nd1 = fe1.GetDof()
shape1.SetSize(nd1)
eltrans = fes1.GetElementTransformation(j)
tmp_int = np.zeros(shape1.Size(), dtype=mat.dtype)
elmat = np.zeros((nd2, nd1), dtype=mat.dtype)
#if myid == 0: print("fes1 idx", j)
dataset = []
for jj in range(ir.GetNPoints()):
ip1 = ir.IntPoint(jj)
eltrans.SetIntPoint(ip1)
x1 = eltrans.Transform(ip1)[0]
fe1.CalcShape(ip1, shape1)
w = eltrans.Weight() * ip1.weight
dataset.append((x1, w, shape1.GetDataArray().copy()))
has_contribution = False
for kkk, x2 in enumerate(x2s):
tmp_int *= 0.0
for x1, w, shape_arr in dataset:
if support is not None:
s = support((x1 + x2) / 2.0)
if np.abs(x1 - x2) > s:
continue
has_contribution = True
#if myid == 0: print("check here", x1, x2)
val = kernel(x2 - x1, (x2 + x1) / 2.0, w=w)
if coeff is not None:
val = val * coeff((x2 + x1) / 2.0)
#shape_arr *= w*val
tmp_int += shape_arr * w * val
elmat[kkk, :] = tmp_int
if has_contribution:
elmats.append((j, elmat))
#print(elmats)
if len(elmats) > 0:
elmats_all.append((i, elmats))
vdofs1_senddata.append(vdofs1_all)
elmats_senddata.append(elmats_all)
# send this information to knodes;
'''
if USE_PARALLEL:
#nicePrint(vdofs1_all)
#nicePrint("elmats", [len(x) for x in elmats_all])
if myid == knode1:
vdofs1_data = comm.gather(vdofs1_all, root=knode1)
elmats_data = comm.gather(elmats_all, root=knode1)
else:
_ = comm.gather(vdofs1_all, root=knode1)
_ = comm.gather(elmats_all, root=knode1)
else:
vdofs1_data = [vdofs1_all,]
elmats_data = [elmats_all,]
'''
if USE_PARALLEL:
knode1 = 0
for vdofs1_all, elmats_all in zip(vdofs1_senddata, elmats_senddata):
if myid == knode1:
vdofs1_data = comm.gather(vdofs1_all, root=knode1)
elmats_data = comm.gather(elmats_all, root=knode1)
else:
_ = comm.gather(vdofs1_all, root=knode1)
_ = comm.gather(elmats_all, root=knode1)
knode1 = knode1 + 1
else:
vdofs1_data = vdofs1_senddata
elmats_data = elmats_senddata
# Step 4
if verbose:
dprint1("Step 4")
shared_data = []
mpi_rank = 0
for vdofs1, elmats_all in zip(vdofs1_data,
elmats_data): # loop over MPI nodes
#nicePrint("len elmats", len(elmats_all))
#for i, elmats in enumerate(elmats_all): # corresponds to loop over fes2
if verbose:
coupling = [len(elmats) for i, elmats in elmats_all]
nicePrint("Element coupling for rank", mpi_rank)
nicePrint(" Average :",
(0 if len(coupling) == 0 else np.mean(coupling)))
nicePrint(" Max/Min :",
(0 if len(coupling) == 0 else np.max(coupling)),
(0 if len(coupling) == 0 else np.min(coupling)))
mpi_rank += 1
for i, elmats in elmats_all: # corresponds to loop over fes2
vdofs2 = fes2.GetElementVDofs(i)
fe2 = fes2.GetFE(i)
nd2 = fe2.GetDof()
shape2.SetSize(nd2)
eltrans = fes2.GetElementTransformation(i)
#for j, elmat in enumerate(elmats):
for j, elmat in elmats:
#print(vdofs1[j], elmat.shape)
#if elmat is None:
# continue
mm = np.zeros((len(vdofs2), len(vdofs1[j])), dtype=float)
for ii in range(ir.GetNPoints()):
ip2 = ir.IntPoint(ii)
eltrans.SetIntPoint(ip2)
ww = eltrans.Weight() * ip2.weight
fe2.CalcShape(ip2, shape2)
shape2 *= ww
tmp_int = elmat[ii, :]
tmp = np.dot(
np.atleast_2d(shape2.GetDataArray()).transpose(),
np.atleast_2d(tmp_int))
mm = mm + tmp
#print("check here", myid, mm.shape, tmp.shape)
# merge contribution to final mat
if USE_PARALLEL:
vdofs22 = [fes2.GetLocalTDofNumber(ii) for ii in vdofs2]
vdofs22g = [VDoFtoGTDoF2[ii] for ii in vdofs2]
kkk = 0
for v2, v2g in zip(vdofs22, vdofs22g):
if v2 < 0:
shared_data.append([v2g, mm[kkk, :], vdofs1[j]])
kkk = kkk + 1
for k, vv in enumerate(vdofs1[j]):
try:
if USE_PARALLEL:
mmm = mm[np.where(np.array(vdofs22) >= 0)[0], :]
vdofs222 = [x for x in vdofs22 if x >= 0]
else:
vdofs222 = vdofs2
mmm = mm
#if myid == 1:
# print("check here", vdofs2, vdofs22, vdofs222)
#print(mmm[:, [k]])
tmp = mat[vdofs222, vv] + mmm[:, [k]]
mat[vdofs222, vv] = tmp.flatten()
except:
import traceback
print("error", myid)
#print(vdofs1, vdofs22, vdofs222, mmm.shape, k)
traceback.print_exc()
if USE_PARALLEL:
for source_id in range(nprc):
data = comm.bcast(shared_data, root=source_id)
myoffset = fes2.GetMyTDofOffset()
for v2g, elmat, vdofs1 in data:
if v2g >= myoffset and v2g < myoffset + mat.shape[0]:
i = v2g - myoffset
#print("procesising this", myid, i, v2g, elmat, vdofs1)
mat[i, vdofs1] = mat[i, vdofs1] + elmat
from scipy.sparse import coo_matrix, csr_matrix
if USE_PARALLEL:
if is_complex:
m1 = csr_matrix(mat.real, dtype=float)
m2 = csr_matrix(mat.imag, dtype=float)
else:
m1 = csr_matrix(mat.real, dtype=float)
m2 = None
from mfem.common.chypre import CHypreMat
start_col = fes1.GetMyTDofOffset()
end_col = fes1.GetMyTDofOffset() + fes1.GetTrueVSize()
col_starts = [start_col, end_col, mat.shape[1]]
M = CHypreMat(m1, m2, col_starts=col_starts)
#print("mat", M)
else:
from petram.helper.block_matrix import convert_to_ScipyCoo
M = convert_to_ScipyCoo(coo_matrix(mat, dtype=mat.dtype))
return M
def projection_matrix(idx1,
idx2,
fes,
tdof1,
fes2=None,
tdof2=None,
trans1=None,
trans2=None,
dphase=0.0,
weight=None,
tol=1e-7,
mode='surface',
filldiag=True,
old_mapping=True):
'''
map: destinatiom mapping
smap: source mapping
old_mapping: True : periodic boundary conditions are implemented this way
x = M*y
False: projection operator should use this flag.
y = M*x
the difference is only when mapping two/three DoFs sitting at the
same location. therefore, it only matters for ND and RT cases
'''
fec_name = fes.FEColl().Name()
dprint1("constructing mapping to fec_name", fec_name, mode)
if fec_name.startswith('ND') and mode == 'volume':
mapper = map_volume_nd
elif fec_name.startswith('ND') and mode == 'surface':
mapper = map_surface_nd
elif fec_name.startswith('ND') and mode == 'edge':
mapper = map_edge_nd
elif fec_name.startswith('H1') and mode == 'volume':
mapper = map_volume_h1
elif fec_name.startswith('H1') and mode == 'surface':
mapper = map_surface_h1
elif fec_name.startswith('H1') and mode == 'edge':
mapper = map_edge_h1
elif fec_name.startswith('H1') and mode == 'point':
mapper = map_point_h1
elif fec_name.startswith('L2') and mode == 'volume':
mapper = map_volume_h1
elif fec_name.startswith('L2') and mode == 'surface':
mapper = map_surface_h1
elif fec_name.startswith('L2') and mode == 'edge':
mapper = map_edge_h1
elif fec_name.startswith('RT') and mode == 'volume':
mapper = map_volume_rt
elif fec_name.startswith('RT') and mode == 'surface':
mapper = map_surface_rt
else:
raise NotImplementedError("mapping :" + fec_name + ", mode: " + mode)
map = mapper(idx2,
idx1,
fes,
fes2=fes2,
trans1=trans1,
trans2=trans2,
tdof1=tdof1,
tdof2=tdof2,
tol=tol,
old_mapping=old_mapping)
if weight is None:
iscomplex = False
if (dphase == 0.):
pass
elif (dphase == 180.):
map = map.tocsr()
map *= -1
map = map.tolil()
else:
iscomplex = True
map = map.astype(complex)
# need to this to make efficient....
map = map.tocsr()
map *= np.exp(-1j * np.pi / 180 * dphase)
map = map.tolil()
else:
iscomplex = np.iscomplexobj(weight)
if iscomplex:
map = map.astype(complex)
if map.nnz > 0:
map = map.tocsr()
map *= -weight
map = map.tolil()
m_coo = map.tocoo()
row = m_coo.row
col = m_coo.col
col = np.unique(col)
if use_parallel:
start_row = fes.GetMyTDofOffset()
end_row = fes.GetMyTDofOffset() + fes.GetTrueVSize()
col = np.unique(allgather_vector(col))
row = row + start_row
else:
start_row = 0
end_row = map.shape[0]
if filldiag:
for i in range(min(map.shape[0], map.shape[1])):
r = start_row + i
if not r in col:
map[i, r] = 1.0
from scipy.sparse import coo_matrix, csr_matrix
if use_parallel:
if iscomplex:
m1 = csr_matrix(map.real, dtype=float)
m2 = csr_matrix(map.imag, dtype=float)
else:
m1 = csr_matrix(map.real, dtype=float)
m2 = None
from mfem.common.chypre import CHypreMat
start_col = fes2.GetMyTDofOffset()
end_col = fes2.GetMyTDofOffset() + fes2.GetTrueVSize()
col_starts = [start_col, end_col, map.shape[1]]
M = CHypreMat(m1, m2, col_starts=col_starts)
else:
from petram.helper.block_matrix import convert_to_ScipyCoo
M = convert_to_ScipyCoo(coo_matrix(map, dtype=map.dtype))
return M, row, col