def _get_Q(self, ms, ns, P0):
nsurf = ns.shape[0]
Ps = []
for i in xrange(nsurf):
P = numpy.zeros((ns[i] + 1, 4, 3), order='F')
for j in xrange(4):
P[:, j, :] = P0[sum(ns[:i]):sum(ns[:i + 1]) + 1, :]
P[:, j, 2] = j
Ps.append(P)
bse = BSEmodel(Ps)
for i in xrange(nsurf):
bse.set_bspline_option('num_cp', i, 'u', ms[i] + 1)
bse.set_bspline_option('num_pt', i, 'u', ns[i] + 1)
bse.set_bspline_option('num_pt', i, 'v', 4)
bse.assemble()
cp = bse.vec['cp_str'].array
pt = bse.vec['pt_str'].array
jac = bse.jac['d(pt_str)/d(cp_str)']
for i in xrange(nsurf):
bse.vec['pt_str'].surfs[i][:, :, :] = Ps[i]
mtx = jac.T.dot(jac)
rhs = jac.T.dot(pt)
for dim in xrange(3):
cp[:, dim] = scipy.sparse.linalg.cg(mtx, rhs[:, dim])[0]
Q = numpy.zeros((sum(ms) + 1, 3), order='F')
for i in xrange(nsurf):
Q[sum(ms[:i]):sum(ms[:i+1])+1,:] = \
bse.vec['cp_str'].surfs[i][:,0,:]
return Q
def _get_Q(self, ms, ns, P0):
nsurf = ns.shape[0]
Ps = []
for i in xrange(nsurf):
P = numpy.zeros((ns[i]+1,4,3), order='F')
for j in xrange(4):
P[:,j,:] = P0[sum(ns[:i]):sum(ns[:i+1])+1,:]
P[:,j,2] = j
Ps.append(P)
bse = BSEmodel(Ps)
for i in xrange(nsurf):
bse.set_bspline_option('num_cp', i, 'u', ms[i]+1)
bse.set_bspline_option('num_pt', i, 'u', ns[i]+1)
bse.set_bspline_option('num_pt', i, 'v', 4)
bse.assemble()
cp = bse.vec['cp_str'].array
pt = bse.vec['pt_str'].array
jac = bse.jac['d(pt_str)/d(cp_str)']
for i in xrange(nsurf):
bse.vec['pt_str'].surfs[i][:,:,:] = Ps[i]
mtx = jac.T.dot(jac)
rhs = jac.T.dot(pt)
for dim in xrange(3):
cp[:, dim] = scipy.sparse.linalg.cg(mtx, rhs[:, dim])[0]
Q = numpy.zeros((sum(ms) + 1,3),order='F')
for i in xrange(nsurf):
Q[sum(ms[:i]):sum(ms[:i+1])+1,:] = \
bse.vec['cp_str'].surfs[i][:,0,:]
return Q
def _initialize_bse(self):
"""
Instantiates and sets up BSE model. 5 steps:
1. Recursively loops over comps' faces' surfs' to
collect initial list of surfaces from each surf
and give each surface a unique global index
2. Instantiates BSE B-spline surface model
3. Components set differentiability options
4. Set user-specified B-spline options
5. Assemble BSE Jacobians
"""
surf_index = 0
surfs_list = []
for comp in self.comps.values():
surf_index = comp.initialize_bse(surfs_list, surf_index)
self._bse = BSEmodel(surfs_list)
bse = self._bse
comp_num = 0
for comp_name in self.comps:
comp = self.comps[comp_name]
comp.set_info(comp_name, comp_num, bse)
comp.set_diff()
comp.set_hidden_surfaces()
comp_num += 1
self._set_bspline_options()
for isurf in range(len(surfs_list)):
surf = surfs_list[isurf]
if numpy.average(surf[:, :, 2]) < 0:
bse.hidden[isurf] = True
bse.assemble()
def _get_P(self, nP, airfoils, name, bunch_LE, bunch_TE):
def bunch_start(ind, a):
ind[:] = ind**a
def bunch_end(ind, a):
ind[:] = 1 - (1 - ind)**a
airfoil = airfoils[name]
P = numpy.zeros((airfoil.shape[0], 4, 3), order='F')
for j in range(4):
P[:, j, :2] = airfoil[:, :]
P[:, j, 2] = j
bse = BSEmodel([P])
bse.set_bspline_option('num_pt', 0, 'u', airfoil.shape[0])
bse.set_bspline_option('num_cp', 0, 'u', int(airfoil.shape[0] / 3))
bse.set_bspline_option('num_pt', 0, 'v', 4)
bse.set_bspline_option('num_cp', 0, 'v', 4)
bse.assemble()
cp = bse.vec['cp_str'].array
pt = bse.vec['pt_str'].array
jac = bse.jac['d(pt_str)/d(cp_str)']
bse.vec['pt_str'].surfs[0][:, :, :] = P
mtx = jac.T.dot(jac)
rhs = jac.T.dot(pt)
for dim in xrange(3):
cp[:, dim] = scipy.sparse.linalg.cg(mtx, rhs[:, dim])[0]
fit = numpy.array(cp)
bse.set_bspline_option('num_pt', 0, 'u', nP)
bse.assemble()
cp = bse.vec['cp_str'].array
pt = bse.vec['pt_str'].array
cp[:, :] = fit[:, :]
surfs = numpy.zeros(nP).astype(int)
ind_u = numpy.linspace(0, 1, nP)
if name == 'upp':
bunch_start(ind_u, bunch_TE)
bunch_end(ind_u, bunch_LE)
elif name == 'low':
bunch_start(ind_u, bunch_LE)
bunch_end(ind_u, bunch_TE)
ind_v = numpy.zeros(nP)
bse.add_jacobian('new', surfs, ind_u, ind_v, 3)
bse.apply_jacobian('new', 'd(new)/d(cp_str)', 'cp_str')
return bse.vec['new'].array[:, :]
def _get_P(self, nP, airfoils, name, bunch_LE, bunch_TE):
def bunch_start(ind, a):
ind[:] = ind**a
def bunch_end(ind, a):
ind[:] = 1 - (1-ind)**a
airfoil = airfoils[name]
P = numpy.zeros((airfoil.shape[0],4,3),order='F')
for j in range(4):
P[:,j,:2] = airfoil[:,:]
P[:,j,2] = j
bse = BSEmodel([P])
bse.set_bspline_option('num_pt', 0, 'u',
airfoil.shape[0])
bse.set_bspline_option('num_cp', 0, 'u',
int(airfoil.shape[0]/3))
bse.set_bspline_option('num_pt', 0, 'v', 4)
bse.set_bspline_option('num_cp', 0, 'v', 4)
bse.assemble()
cp = bse.vec['cp_str'].array
pt = bse.vec['pt_str'].array
jac = bse.jac['d(pt_str)/d(cp_str)']
bse.vec['pt_str'].surfs[0][:, :, :] = P
mtx = jac.T.dot(jac)
rhs = jac.T.dot(pt)
for dim in xrange(3):
cp[:, dim] = scipy.sparse.linalg.cg(mtx, rhs[:, dim])[0]
fit = numpy.array(cp)
bse.set_bspline_option('num_pt', 0, 'u', nP)
bse.assemble()
cp = bse.vec['cp_str'].array
pt = bse.vec['pt_str'].array
cp[:, :] = fit[:, :]
surfs = numpy.zeros(nP).astype(int)
ind_u = numpy.linspace(0, 1, nP)
if name == 'upp':
bunch_start(ind_u, bunch_TE)
bunch_end(ind_u, bunch_LE)
elif name == 'low':
bunch_start(ind_u, bunch_LE)
bunch_end(ind_u, bunch_TE)
ind_v = numpy.zeros(nP)
bse.add_jacobian('new', surfs, ind_u, ind_v, 3)
bse.apply_jacobian('new', 'd(new)/d(cp_str)', 'cp_str')
return bse.vec['new'].array[:, :]
def _get_P(self, nP, airfoil):
P = numpy.zeros((airfoil.shape[0],4,3),order='F')
for j in range(4):
P[:,j,:2] = airfoil[:,:]
P[:,j,2] = j
bse = BSEmodel([P])
bse.set_bspline_option('num_pt', 0, 'u',
airfoil.shape[0])
bse.set_bspline_option('num_cp', 0, 'u',
int(airfoil.shape[0]/3))
bse.set_bspline_option('num_pt', 0, 'v', 4)
bse.set_bspline_option('num_cp', 0, 'v', 4)
bse.assemble()
cp = bse.vec['cp_str'].array
pt = bse.vec['pt_str'].array
jac = bse.jac['d(pt_str)/d(cp_str)']
bse.vec['pt_str'].surfs[0][:, :, :] = P
mtx = jac.T.dot(jac)
rhs = jac.T.dot(pt)
for dim in xrange(3):
cp[:, dim] = scipy.sparse.linalg.cg(mtx, rhs[:, dim])[0]
fit = numpy.array(cp)
bse.set_bspline_option('num_pt', 0, 'u', nP)
bse.assemble()
cp = bse.vec['cp_str'].array
pt = bse.vec['pt_str'].array
cp[:, :] = fit[:, :]
bse.apply_jacobian('pt_str', 'd(pt_str)/d(cp_str)', 'cp_str')
return bse.vec['pt_str'].surfs[0][:, 0, :]
