def set_dofs(self, fun=0.0, region=None, dpn=None, warn=None):
"""
Set the values of DOFs given by the `region` using a function of space
coordinates or value `fun`.
If `fun` is a function, the l2 projection that is global for all region
facets is used to set the DOFs.
If `dpn > 1`, and `fun` is a function, it has to return the values
DOF-by-DOF, i.e. a single one-dimensional vector with all values of the
first component, then of the second one etc. concatenated
together.
Parameters
----------
fun : float or array of length dpn or callable
The DOF values.
region : Region
The region containing the DOFs.
dpn : int, optional
The DOF-per-node count. If not given, the number of field
components is used.
warn : str, optional
The warning message printed when the region selects no DOFs.
Returns
-------
nods : array, shape (n_dof,)
The field DOFs (or node indices) given by the region.
vals : array, shape (dpn, n_dof)
The values of the DOFs, DOF-by-DOF when raveled in C (row-major)
order.
"""
if region is None:
region = self.region
if dpn is None:
dpn = self.n_components
nods = []
vals = []
aux = self.get_dofs_in_region(region)
nods = nm.unique(nm.hstack(aux))
if nm.isscalar(fun):
vals = nm.repeat([fun], nods.shape[0] * dpn)
elif isinstance(fun, nm.ndarray):
assert_(len(fun) == dpn)
vals = nm.repeat(fun, nods.shape[0])
elif callable(fun):
import scipy.sparse as sps
from sfepy.solvers.ls import solve
from sfepy.discrete.integrals import Integral
from sfepy.discrete.fem.utils import prepare_remap
import sfepy.discrete.iga as iga
from sfepy.discrete.iga.extmods.igac import eval_mapping_data_in_qp
nurbs = self.nurbs
facets = self._get_facets(region.kind_tdim)
# Region facet connectivity.
rconn = self.get_econn('surface', region)
# Local connectivity.
remap = prepare_remap(nods, nods.max() + 1)
lconn = [remap[ii] for ii in rconn]
# Cell and face(cell) ids for each facet.
fis = region.get_facet_indices()
# Integral given by max. NURBS surface degree.
fdegrees = iga.get_surface_degrees(nurbs.degrees)
order = fdegrees.max()
integral = Integral('i', order=2*order)
vals, weights = integral.get_qp(self.domain.gel.surface_facet_name)
# Boundary QP - use tensor product structure.
bvals = iga.create_boundary_qp(vals, region.tdim)
# Compute facet basis, jacobians and physical BQP.
n_dof = len(nods)
rhs = nm.zeros((dpn, n_dof), dtype=nm.float64)
rows, cols, mvals = [], [], []
all_qp = []
all_fbfs = []
all_dets = []
for ii, (ie, ifa) in enumerate(fis):
qp_coors = bvals[ifa]
bfs, _, dets = eval_mapping_data_in_qp(qp_coors, nurbs.cps,
nurbs.weights,
nurbs.degrees,
nurbs.cs,
nurbs.conn,
nm.array([ie]))
# Facet basis.
fbfs = bfs[..., facets[ifa]][0, :, 0, :]
# Weight Jacobians by quadrature point weights.
dets = nm.abs(dets) * weights[None, :, None, None]
dets = dets[0, :, 0, :]
# Physical BQP.
fcps = nurbs.cps[nurbs.conn[ie, facets[ifa]]]
qp = nm.dot(fbfs, fcps)
all_qp.append(qp)
all_fbfs.append(fbfs)
all_dets.append(dets)
# DOF values in the physical BQP.
qps = nm.concatenate(all_qp)
vals = nm.asarray(fun(qps))
vals.shape = (dpn, qps.shape[0])
n_qp_face = len(bvals[0])
# Assemble l2 projection system.
for ii, (ie, ifa) in enumerate(fis):
# Assembling indices.
elc = lconn[ii]
fvals = vals[:, n_qp_face * ii : n_qp_face * (ii + 1)]
fbfs = all_fbfs[ii]
dets = all_dets[ii]
# Local projection system.
for idof in xrange(dpn):
lrhs = (fbfs * (fvals[idof, :, None] * dets)).sum(0)
rhs[idof, elc] += lrhs
lmtx = ((fbfs[..., None] * fbfs[:, None, :])
* dets[..., None]).sum(0)
er, ec = nm.meshgrid(elc, elc)
rows.append(er.ravel())
cols.append(ec.ravel())
mvals.append(lmtx.ravel())
rows = nm.concatenate(rows)
cols = nm.concatenate(cols)
mvals = nm.concatenate(mvals)
mtx = sps.coo_matrix((mvals, (rows, cols)), shape=(n_dof, n_dof))
vals = nm.zeros((dpn, n_dof), dtype=nm.float64)
# Solve l2 projection system.
for idof in xrange(dpn):
dofs = solve(mtx, rhs[idof, :])
vals[idof, remap[nods]] = dofs
else:
raise ValueError('unknown function/value type! (%s)' % type(fun))
return nods, vals
def set_dofs(self, fun=0.0, region=None, dpn=None, warn=None):
"""
Set the values of DOFs given by the `region` using a function of space
coordinates or value `fun`.
If `fun` is a function, the l2 projection that is global for all region
facets is used to set the DOFs.
If `dpn > 1`, and `fun` is a function, it has to return the values
DOF-by-DOF, i.e. a single one-dimensional vector with all values of the
first component, then of the second one etc. concatenated
together.
Parameters
----------
fun : float or array of length dpn or callable
The DOF values.
region : Region
The region containing the DOFs.
dpn : int, optional
The DOF-per-node count. If not given, the number of field
components is used.
warn : str, optional
The warning message printed when the region selects no DOFs.
Returns
-------
nods : array, shape (n_dof,)
The field DOFs (or node indices) given by the region.
vals : array, shape (dpn, n_dof)
The values of the DOFs, DOF-by-DOF when raveled in C (row-major)
order.
"""
if region is None:
region = self.region
if dpn is None:
dpn = self.n_components
nods = []
vals = []
aux = self.get_dofs_in_region(region)
nods = nm.unique(nm.hstack(aux))
if nm.isscalar(fun):
vals = nm.repeat([fun], nods.shape[0] * dpn)
elif isinstance(fun, nm.ndarray):
assert_(len(fun) == dpn)
vals = nm.repeat(fun, nods.shape[0])
elif callable(fun):
import scipy.sparse as sps
from sfepy.solvers.ls import solve
from sfepy.discrete.integrals import Integral
from sfepy.discrete.fem.utils import prepare_remap
import sfepy.discrete.iga as iga
from sfepy.discrete.iga.extmods.igac import eval_mapping_data_in_qp
nurbs = self.nurbs
facets = self._get_facets(region.kind_tdim)
# Region facet connectivity.
rconn = self.get_econn('surface', region)
# Local connectivity.
remap = prepare_remap(nods, nods.max() + 1)
lconn = [remap[ii] for ii in rconn]
# Cell and face(cell) ids for each facet.
fis = region.get_facet_indices()
# Integral given by max. NURBS surface degree.
fdegrees = iga.get_surface_degrees(nurbs.degrees)
order = fdegrees.max()
integral = Integral('i', order=2 * order)
vals, weights = integral.get_qp(self.domain.gel.surface_facet_name)
# Boundary QP - use tensor product structure.
bvals = iga.create_boundary_qp(vals, region.tdim)
# Compute facet basis, jacobians and physical BQP.
n_dof = len(nods)
rhs = nm.zeros((dpn, n_dof), dtype=nm.float64)
rows, cols, mvals = [], [], []
all_qp = []
all_fbfs = []
all_dets = []
for ii, (ie, ifa) in enumerate(fis):
qp_coors = bvals[ifa]
bfs, _, dets = eval_mapping_data_in_qp(qp_coors, nurbs.cps,
nurbs.weights,
nurbs.degrees, nurbs.cs,
nurbs.conn,
nm.array([ie]))
# Facet basis.
fbfs = bfs[..., facets[ifa]][0, :, 0, :]
# Weight Jacobians by quadrature point weights.
dets = nm.abs(dets) * weights[None, :, None, None]
dets = dets[0, :, 0, :]
# Physical BQP.
fcps = nurbs.cps[nurbs.conn[ie, facets[ifa]]]
qp = nm.dot(fbfs, fcps)
all_qp.append(qp)
all_fbfs.append(fbfs)
all_dets.append(dets)
# DOF values in the physical BQP.
qps = nm.concatenate(all_qp)
vals = nm.asarray(fun(qps))
vals.shape = (dpn, qps.shape[0])
n_qp_face = len(bvals[0])
# Assemble l2 projection system.
for ii, (ie, ifa) in enumerate(fis):
# Assembling indices.
elc = lconn[ii]
fvals = vals[:, n_qp_face * ii:n_qp_face * (ii + 1)]
fbfs = all_fbfs[ii]
dets = all_dets[ii]
# Local projection system.
for idof in range(dpn):
lrhs = (fbfs * (fvals[idof, :, None] * dets)).sum(0)
rhs[idof, elc] += lrhs
lmtx = ((fbfs[..., None] * fbfs[:, None, :]) *
dets[..., None]).sum(0)
er, ec = nm.meshgrid(elc, elc)
rows.append(er.ravel())
cols.append(ec.ravel())
mvals.append(lmtx.ravel())
rows = nm.concatenate(rows)
cols = nm.concatenate(cols)
mvals = nm.concatenate(mvals)
mtx = sps.coo_matrix((mvals, (rows, cols)), shape=(n_dof, n_dof))
vals = nm.zeros((dpn, n_dof), dtype=nm.float64)
# Solve l2 projection system.
for idof in range(dpn):
dofs = solve(mtx, rhs[idof, :])
vals[idof, remap[nods]] = dofs
else:
raise ValueError('unknown function/value type! (%s)' % type(fun))
return nods, vals
def project_to_facets(region, fun, dpn, field):
"""
Project a function `fun` to the `field` in facets of the given `region`.
"""
aux = field.get_dofs_in_region(region)
nods = nm.unique(aux)
n_dof = len(nods)
# Region facet connectivity.
lconn = field.get_econn('surface', region, local=True)
# Cell and face(cell) ids for each facet.
fis = region.get_facet_indices()
all_qps, all_fbfs, all_dets = field.get_surface_basis(region)
# DOF values in the physical BQP.
all_qps = nm.concatenate(all_qps)
vals = nm.asarray(fun(all_qps))
if (vals.ndim > 1) and (vals.shape != (len(all_qps), dpn)):
raise ValueError('The projected function return value should be'
' (n_point, dpn) == %s, instead of %s!' %
((len(all_qps), dpn), vals.shape))
vals.shape = (len(all_qps), dpn)
n_qp_face = all_dets[0].shape[0]
# Assemble l2 projection system.
rhs = nm.zeros((dpn, n_dof), dtype=nm.float64)
rows, cols, mvals = [], [], []
for ii, (ie, ifa) in enumerate(fis):
# Assembling indices.
elc = lconn[ii]
fvals = vals[n_qp_face * ii:n_qp_face * (ii + 1)]
fbfs = all_fbfs[ii]
dets = all_dets[ii]
# Local projection system.
for idof in range(dpn):
lrhs = (fbfs * (fvals[:, idof, None] * dets)).sum(0)
rhs[idof, elc] += lrhs
lmtx = ((fbfs[..., None] * fbfs[:, None, :]) * dets[..., None]).sum(0)
er, ec = nm.meshgrid(elc, elc)
rows.append(er.ravel())
cols.append(ec.ravel())
mvals.append(lmtx.ravel())
rows = nm.concatenate(rows)
cols = nm.concatenate(cols)
mvals = nm.concatenate(mvals)
mtx = sps.coo_matrix((mvals, (rows, cols)), shape=(n_dof, n_dof))
vals = nm.zeros((n_dof, dpn), dtype=nm.float64)
# Solve l2 projection system.
for idof in range(dpn):
dofs = solve(mtx, rhs[idof, :])
vals[:, idof] = dofs
return vals