def add_jacobian(self, name, surfs, ind_u, ind_v, ndim=1):
num = self._num
size = self._size
str_indices = self._str_indices
topo = self._topo
bspline = self._bspline
vec = self.vec
jac = self.jac
surfs = numpy.array(surfs, int) + 1
npt = surfs.shape[0]
nnz = BSElib.computesnnz(npt, num['surf'], num['group'],
topo['surf_group'], bspline['order'], surfs)
quant = ['', '_du', '_dv']
der_u = [0, 1, 0]
der_v = [0, 0, 1]
for ind in xrange(3):
data, rows, cols \
= BSElib.computesmtx(der_u[ind], der_v[ind],
nnz, npt,
num['surf'], num['group'],
str_indices['cp'], topo['surf_group'],
bspline['order'], bspline['num_cp'],
surfs, ind_u, ind_v)
qname = name + quant[ind]
jac['d(' + qname + ')/d(cp_str)'] \
= scipy.sparse.csr_matrix((data, (rows-1, cols-1)),
shape=(npt,
size['cp_str']))
vec[qname] = BSEvecUns(qname, npt, ndim, self.hidden)
def add_jacobian(self, name, surfs, ind_u, ind_v, ndim=1):
num = self._num
size = self._size
str_indices = self._str_indices
topo = self._topo
bspline = self._bspline
vec = self.vec
jac = self.jac
surfs = numpy.array(surfs, int) + 1
npt = surfs.shape[0]
nnz = BSElib.computesnnz(npt, num['surf'], num['group'],
topo['surf_group'], bspline['order'],
surfs)
quant = ['', '_du', '_dv']
der_u = [0, 1, 0]
der_v = [0, 0, 1]
for ind in xrange(3):
data, rows, cols \
= BSElib.computesmtx(der_u[ind], der_v[ind],
nnz, npt,
num['surf'], num['group'],
str_indices['cp'], topo['surf_group'],
bspline['order'], bspline['num_cp'],
surfs, ind_u, ind_v)
qname = name + quant[ind]
jac['d(' + qname + ')/d(cp_str)'] \
= scipy.sparse.csr_matrix((data, (rows-1, cols-1)),
shape=(npt,
size['cp_str']))
vec[qname] = BSEvecUns(qname, npt, ndim, self.hidden)
def add_jacobian(self, name, surfs, ind_u, ind_v, ndim=1):
num = self._num
size = self._size
str_indices = self._str_indices
topo = self._topo
bspline = self._bspline
vec = self.vec
jac = self.jac
surfs = numpy.array(surfs, int) + 1
npt = surfs.shape[0]
nnz = BSElib.computesnnz(npt, num['surf'], num['group'],
topo['surf_group'], bspline['order'],
surfs)
data, rows, cols \
= BSElib.computesmtx(0, 0, nnz, npt,
num['surf'], num['group'],
str_indices['cp'], topo['surf_group'],
bspline['order'], bspline['num_cp'],
surfs, ind_u, ind_v)
jac['d(' + name + ')/d(cp_str)'] \
= scipy.sparse.csr_matrix((data, (rows-1, cols-1)),
shape=(npt,
size['cp_str']))
vec[name] = BSEvecUns(name, npt, ndim)
def _compute_topology(self, initial_surfaces):
""" Load an initial set of surfaces and compute the topology
Arguments
---------
initial_surfaces : list(nsurf) of double(nu, nv, 3)
Returns
-------
nvert, nedge, ngroup : see __init__
surf_vert : [int(nsurf, 2, 2)] surface to vertex mapping, 1-based
(isurf, i, j) : u=i, v=j corner
surf_edge : [int(nsurf, 2, 2)] surface to edge mapping, 1-based
(isurf, 1, 1) : v=0 edge
(isurf, 1, 2) : v=1 edge
(isurf, 2, 1) : u=0 edge
(isurf, 2, 2) : u=1 edge
surf_group : [int(nsurf, 2)] surface to group mapping, 1-based
(isurf, d) : d=0 for v=0, v=1 edges; d=1 for u=0, u=1 edges
"""
nsurf = len(initial_surfaces)
surfaces = numpy.zeros((nsurf, 3, 3, 3), float, 'F')
for isurf in xrange(nsurf):
surface = initial_surfaces[isurf]
num_u, num_v = surface.shape[:2]
mid_u1 = int(numpy.floor((num_u - 1) / 2.0))
mid_u2 = int(numpy.ceil((num_u - 1) / 2.0))
mid_v1 = int(numpy.floor((num_v - 1) / 2.0))
mid_v2 = int(numpy.ceil((num_v - 1) / 2.0))
for ind_u in xrange(2):
for ind_v in xrange(2):
surfaces[isurf, -ind_u, -ind_v] = surface[-ind_u, -ind_v]
for ind_u in xrange(2):
surfaces[isurf, -ind_u, 1] += 0.5 * surface[-ind_u, mid_v1] + \
0.5 * surface[-ind_u, mid_v2]
for ind_v in xrange(2):
surfaces[isurf, 1, -ind_v] += 0.5 * surface[mid_u1, -ind_v] + \
0.5 * surface[mid_u2, -ind_v]
nvert, nedge, surf_ptrs \
= BSElib.computesurfconnectivities(nsurf, 1e-16, 1e-10, surfaces)
edge_ptrs \
= BSElib.computeedgeconnectivities(nsurf, nedge, surf_ptrs)
ngroup, surf_group, edge_group \
= BSElib.computegroups(nsurf, nedge, surf_ptrs)
topology = [nvert, nedge, ngroup, \
surf_ptrs, edge_ptrs, \
surf_group, edge_group, \
]
return topology
def _compute_topology(self, initial_surfaces):
""" Load an initial set of surfaces and compute the topology
Arguments
---------
initial_surfaces : list(nsurf) of double(nu, nv, 3)
Returns
-------
nvert, nedge, ngroup : see __init__
surf_vert : [int(nsurf, 2, 2)] surface to vertex mapping, 1-based
(isurf, i, j) : u=i, v=j corner
surf_edge : [int(nsurf, 2, 2)] surface to edge mapping, 1-based
(isurf, 1, 1) : v=0 edge
(isurf, 1, 2) : v=1 edge
(isurf, 2, 1) : u=0 edge
(isurf, 2, 2) : u=1 edge
surf_group : [int(nsurf, 2)] surface to group mapping, 1-based
(isurf, d) : d=0 for v=0, v=1 edges; d=1 for u=0, u=1 edges
"""
nsurf = len(initial_surfaces)
surfaces = numpy.zeros((nsurf, 3, 3, 3), float, 'F')
for isurf in xrange(nsurf):
surface = initial_surfaces[isurf]
num_u, num_v = surface.shape[:2]
mid_u1 = int(numpy.floor((num_u - 1) / 2.0))
mid_u2 = int(numpy.ceil((num_u - 1) / 2.0))
mid_v1 = int(numpy.floor((num_v - 1) / 2.0))
mid_v2 = int(numpy.ceil((num_v - 1) / 2.0))
for ind_u in xrange(2):
for ind_v in xrange(2):
surfaces[isurf, -ind_u, -ind_v] = surface[-ind_u, -ind_v]
for ind_u in xrange(2):
surfaces[isurf, -ind_u, 1] += 0.5 * surface[-ind_u, mid_v1] + \
0.5 * surface[-ind_u, mid_v2]
for ind_v in xrange(2):
surfaces[isurf, 1, -ind_v] += 0.5 * surface[mid_u1, -ind_v] + \
0.5 * surface[mid_u2, -ind_v]
nvert, nedge, surf_ptrs \
= BSElib.computesurfconnectivities(nsurf, 1e-16, 1e-10, surfaces)
edge_ptrs \
= BSElib.computeedgeconnectivities(nsurf, nedge, surf_ptrs)
ngroup, surf_group, edge_group \
= BSElib.computegroups(nsurf, nedge, surf_ptrs)
topology = [nvert, nedge, ngroup, \
surf_ptrs, edge_ptrs, \
surf_group, edge_group, \
]
return topology
def _compute_indices(self):
num = self._num
topo = self._topo
diff = self.diff
bspline = self._bspline
vert_indices = self._vert_indices
edge_indices = self._edge_indices
surf_indices = self._surf_indices
str_indices = self._str_indices
mult = self._mult
size = self._size
vert_indices[:] \
= BSElib.computevertindices(num['surf'], num['edge'], num['vert'],
topo['surf_ptrs'], topo['edge_ptrs'],
diff['surf'], diff['edge'])
edge_indices['df'], edge_indices['cp'], edge_indices['pt'], \
= BSElib.computeedgeindices(num['surf'], num['edge'],
num['group'], topo['surf_ptrs'],
diff['surf'], topo['edge_group'],
bspline['num_cp'], bspline['num_pt'])
surf_indices['df'], surf_indices['cp'], surf_indices['pt'], \
= BSElib.computesurfindices(num['surf'], num['group'],
topo['surf_group'],
bspline['num_cp'], bspline['num_pt'])
str_indices['df'], str_indices['cp'], str_indices['pt'], \
= BSElib.computestrindices(num['surf'], num['group'],
topo['surf_group'],
bspline['num_cp'], bspline['num_pt'])
mult['vert'], mult['edge'], mult['diff_vert'], mult['diff_edge'] \
= BSElib.computemults(num['surf'], num['edge'], num['vert'],
topo['surf_ptrs'], topo['edge_ptrs'],
diff['surf'], diff['edge'])
nvert_df = numpy.max(vert_indices)
edge_indices['df'][:] += nvert_df
edge_indices['cp'][:] += num['vert']
edge_indices['pt'][:] += num['vert']
surf_indices['df'][:] += numpy.max(edge_indices['df'])
surf_indices['cp'][:] += numpy.max(edge_indices['cp'])
surf_indices['pt'][:] += numpy.max(edge_indices['pt'])
size['df_str'] = str_indices['df'][-1, -1]
size['df'] = surf_indices['df'][-1, -1]
size['cp'] = surf_indices['cp'][-1, -1]
size['cp_str'] = str_indices['cp'][-1, -1]
size['pt_str'] = str_indices['pt'][-1, -1]
size['pt'] = surf_indices['pt'][-1, -1]
def _compute_indices(self):
num = self._num
topo = self._topo
diff = self.diff
bspline = self._bspline
vert_indices = self._vert_indices
edge_indices = self._edge_indices
surf_indices = self._surf_indices
str_indices = self._str_indices
mult = self._mult
size = self._size
vert_indices[:] \
= BSElib.computevertindices(num['surf'], num['edge'], num['vert'],
topo['surf_ptrs'], topo['edge_ptrs'],
diff['surf'], diff['edge'])
edge_indices['df'], edge_indices['cp'], edge_indices['pt'], \
= BSElib.computeedgeindices(num['surf'], num['edge'],
num['group'], topo['surf_ptrs'],
diff['surf'], topo['edge_group'],
bspline['num_cp'], bspline['num_pt'])
surf_indices['df'], surf_indices['cp'], surf_indices['pt'], \
= BSElib.computesurfindices(num['surf'], num['group'],
topo['surf_group'],
bspline['num_cp'], bspline['num_pt'])
str_indices['df'], str_indices['cp'], str_indices['pt'], \
= BSElib.computestrindices(num['surf'], num['group'],
topo['surf_group'],
bspline['num_cp'], bspline['num_pt'])
mult['vert'], mult['edge'], mult['diff_vert'], mult['diff_edge'] \
= BSElib.computemults(num['surf'], num['edge'], num['vert'],
topo['surf_ptrs'], topo['edge_ptrs'],
diff['surf'], diff['edge'])
nvert_df = numpy.max(vert_indices)
edge_indices['df'][:] += nvert_df
edge_indices['cp'][:] += num['vert']
edge_indices['pt'][:] += num['vert']
surf_indices['df'][:] += numpy.max(edge_indices['df'])
surf_indices['cp'][:] += numpy.max(edge_indices['cp'])
surf_indices['pt'][:] += numpy.max(edge_indices['pt'])
size['df_str'] = str_indices['df'][-1, -1]
size['df'] = surf_indices['df'][-1, -1]
size['cp'] = surf_indices['cp'][-1, -1]
size['cp_str'] = str_indices['cp'][-1, -1]
size['pt_str'] = str_indices['pt'][-1, -1]
size['pt'] = surf_indices['pt'][-1, -1]
def compute_projection(self, name, pts, surf_pts=None, ndim=1):
num = self._num
size = self._size
str_indices = self._str_indices
topo = self._topo
bspline = self._bspline
cp_str = self.vec['cp_str'].array
pt_str = self.vec['pt_str'].array
pts = numpy.array(pts, order='F')
if surf_pts is None:
surf_pts = numpy.linspace(1, num['surf'], num['surf'])
else:
surf_pts = numpy.array(surf_pts, int) + 1
npts = pts.shape[0]
nsurf_pts = surf_pts.shape[0]
nrefine = 10
surfs, ind_u, ind_v \
= BSElib.computeproj(npts, nsurf_pts,
size['cp_str'], size['pt_str'],
num['surf'], num['group'], nrefine,
surf_pts,
str_indices['cp'], str_indices['pt'],
topo['surf_group'], bspline['order'],
bspline['num_cp'], bspline['num_pt'],
cp_str, pt_str, pts)
self.add_jacobian(name, surfs-1, ind_u, ind_v, ndim)
def compute_projection(self, name, pts, surf_pts=None, ndim=1):
num = self._num
size = self._size
str_indices = self._str_indices
topo = self._topo
bspline = self._bspline
cp_str = self.vec['cp_str'].array
pt_str = self.vec['pt_str'].array
pts = numpy.array(pts, order='F')
if surf_pts is None:
surf_pts = numpy.linspace(1, num['surf'], num['surf'])
else:
surf_pts = numpy.array(surf_pts, int) + 1
npts = pts.shape[0]
nsurf_pts = surf_pts.shape[0]
nrefine = 10
surfs, ind_u, ind_v \
= BSElib.computeproj(npts, nsurf_pts,
size['cp_str'], size['pt_str'],
num['surf'], num['group'], nrefine,
surf_pts,
str_indices['cp'], str_indices['pt'],
topo['surf_group'], bspline['order'],
bspline['num_cp'], bspline['num_pt'],
cp_str, pt_str, pts)
self.add_jacobian(name, surfs - 1, ind_u, ind_v, ndim)
def _compute_jacobians(self, nbs_jac=1):
num = self._num
topo = self._topo
diff = self.diff
bspline = self._bspline
mult = self._mult
vert_indices = self._vert_indices
edge_indices = self._edge_indices
surf_indices = self._surf_indices
str_indices = self._str_indices
size = self._size
jac = self.jac
nnz = BSElib.computeennz(num['surf'], num['edge'],
num['vert'], num['group'],
topo['surf_ptrs'], topo['surf_group'],
mult['diff_vert'], mult['diff_edge'],
bspline['num_cp'])
data, rows, cols \
= BSElib.computeemtx(nnz, num['surf'], num['edge'],
num['vert'], num['group'],
topo['surf_ptrs'], topo['surf_group'],
surf_indices['df'], edge_indices['df'],
str_indices['df'], vert_indices,
mult['vert'], mult['edge'],
mult['diff_vert'], mult['diff_edge'],
bspline['num_cp'])
jac['d(df)/d(df_str)'] \
= scipy.sparse.csr_matrix((data, (rows-1, cols-1)),
shape=(size['df'],
size['df_str']))
nnz = BSElib.computednnz(num['surf'], num['edge'],
num['vert'], num['group'],
topo['surf_group'], topo['edge_group'],
diff['surf'], diff['edge'],
mult['diff_vert'], mult['diff_edge'],
bspline['num_cp'])
data, rows, cols \
= BSElib.computedmtx(nnz, num['surf'], num['edge'],
num['vert'], num['group'],
topo['surf_group'], topo['edge_group'],
topo['surf_ptrs'], topo['edge_ptrs'],
diff['surf'], diff['edge'],
mult['diff_vert'], mult['diff_edge'],
surf_indices['df'], surf_indices['cp'],
edge_indices['df'], edge_indices['cp'],
vert_indices, bspline['num_cp'])
jac['d(cp)/d(df)'] \
= scipy.sparse.csr_matrix((data, (rows-1, cols-1)),
shape=(size['cp'],
size['df']))
nnz = size['cp_str']
data, rows, cols \
= BSElib.computecmtx(nnz, num['surf'], num['edge'], num['group'],
topo['surf_ptrs'], topo['surf_group'],
surf_indices['cp'], edge_indices['cp'],
str_indices['cp'], bspline['num_cp'])
jac['d(cp_str)/d(cp)'] \
= scipy.sparse.csr_matrix((data, (rows-1, cols-1)),
shape=(size['cp_str'],
size['cp']))
nnz = BSElib.computebnnz(num['surf'], num['group'],
topo['surf_group'],
bspline['order'], bspline['num_pt'])
uder = [0, 1, 0, 2, 1, 0]
vder = [0, 0, 1, 0, 1, 2]
name = ['', '_du', '_dv', '_duu', '_duv', '_dvv']
for k in xrange(nbs_jac):
data, rows, cols \
= BSElib.computebmtx(nnz, num['surf'], num['group'],
uder[k], vder[k],
str_indices['cp'], str_indices['pt'],
topo['surf_group'], bspline['order'],
bspline['num_cp'], bspline['num_pt'])
jac['d(pt_str)/d(cp_str)' + name[k]] \
= scipy.sparse.csr_matrix((data, (rows-1, cols-1)),
shape=(size['pt_str'],
size['cp_str']))
nnz = size['pt_str']
data, rows, cols \
= BSElib.computepmtx(nnz, num['surf'], num['edge'],
num['vert'], num['group'],
topo['surf_ptrs'], topo['surf_group'],
surf_indices['pt'], edge_indices['pt'],
str_indices['pt'], mult['vert'],
mult['edge'], bspline['num_pt'])
jac['d(pt)/d(pt_str)'] \
= scipy.sparse.csr_matrix((data, (rows-1, cols-1)),
shape=(size['pt'],
size['pt_str']))
def _compute_jacobians(self, nbs_jac=1):
num = self._num
topo = self._topo
diff = self.diff
bspline = self._bspline
mult = self._mult
vert_indices = self._vert_indices
edge_indices = self._edge_indices
surf_indices = self._surf_indices
str_indices = self._str_indices
size = self._size
jac = self.jac
nnz = BSElib.computeennz(num['surf'], num['edge'], num['vert'],
num['group'], topo['surf_ptrs'],
topo['surf_group'], mult['diff_vert'],
mult['diff_edge'], bspline['num_cp'])
data, rows, cols \
= BSElib.computeemtx(nnz, num['surf'], num['edge'],
num['vert'], num['group'],
topo['surf_ptrs'], topo['surf_group'],
surf_indices['df'], edge_indices['df'],
str_indices['df'], vert_indices,
mult['vert'], mult['edge'],
mult['diff_vert'], mult['diff_edge'],
bspline['num_cp'])
jac['d(df)/d(df_str)'] \
= scipy.sparse.csr_matrix((data, (rows-1, cols-1)),
shape=(size['df'],
size['df_str']))
nnz = BSElib.computednnz(num['surf'], num['edge'], num['vert'],
num['group'], topo['surf_group'],
topo['edge_group'], diff['surf'],
diff['edge'], mult['diff_vert'],
mult['diff_edge'], bspline['num_cp'])
data, rows, cols \
= BSElib.computedmtx(nnz, num['surf'], num['edge'],
num['vert'], num['group'],
topo['surf_group'], topo['edge_group'],
topo['surf_ptrs'], topo['edge_ptrs'],
diff['surf'], diff['edge'],
mult['diff_vert'], mult['diff_edge'],
surf_indices['df'], surf_indices['cp'],
edge_indices['df'], edge_indices['cp'],
vert_indices, bspline['num_cp'])
jac['d(cp)/d(df)'] \
= scipy.sparse.csr_matrix((data, (rows-1, cols-1)),
shape=(size['cp'],
size['df']))
nnz = size['cp_str']
data, rows, cols \
= BSElib.computecmtx(nnz, num['surf'], num['edge'], num['group'],
topo['surf_ptrs'], topo['surf_group'],
surf_indices['cp'], edge_indices['cp'],
str_indices['cp'], bspline['num_cp'])
jac['d(cp_str)/d(cp)'] \
= scipy.sparse.csr_matrix((data, (rows-1, cols-1)),
shape=(size['cp_str'],
size['cp']))
nnz = BSElib.computebnnz(num['surf'], num['group'], topo['surf_group'],
bspline['order'], bspline['num_pt'])
uder = [0, 1, 0, 2, 1, 0]
vder = [0, 0, 1, 0, 1, 2]
name = ['', '_du', '_dv', '_duu', '_duv', '_dvv']
for k in xrange(nbs_jac):
data, rows, cols \
= BSElib.computebmtx(nnz, num['surf'], num['group'],
uder[k], vder[k],
str_indices['cp'], str_indices['pt'],
topo['surf_group'], bspline['order'],
bspline['num_cp'], bspline['num_pt'])
jac['d(pt_str)/d(cp_str)' + name[k]] \
= scipy.sparse.csr_matrix((data, (rows-1, cols-1)),
shape=(size['pt_str'],
size['cp_str']))
nnz = size['pt_str']
data, rows, cols \
= BSElib.computepmtx(nnz, num['surf'], num['edge'],
num['vert'], num['group'],
topo['surf_ptrs'], topo['surf_group'],
surf_indices['pt'], edge_indices['pt'],
str_indices['pt'], mult['vert'],
mult['edge'], bspline['num_pt'])
jac['d(pt)/d(pt_str)'] \
= scipy.sparse.csr_matrix((data, (rows-1, cols-1)),
shape=(size['pt'],
size['pt_str']))