def mbfv(x, p, poly_type):
assert np.min(x) >= -1 and np.max(x) <= 1, "x should be in [-1,1]"
assert p >= 1 and isinstance(p, int), "p should be positve integer"
if poly_type == "LobN": # lobatto polynomials
nodes, weights = lobatto_quad(p)
basis = lagrange_basis(nodes, x)
return basis
elif poly_type == "LobE": # lobatto edges functions
nodes, weights = lobatto_quad(p)
basis = edge_basis(nodes, x)
return basis
elif poly_type == "GauN": # gauss polynomials
nodes, weights = gauss_quad(p)
basis = lagrange_basis(nodes, x)
return basis
elif poly_type == "GauE": # gauss edges functions
nodes, weights = gauss_quad(p)
basis = edge_basis(nodes, x)
return basis
elif poly_type == "etGN": # extended-gauss polynomials
nodes, weights = extended_gauss_quad(p)
basis = lagrange_basis(nodes, x)
return basis
elif poly_type == "etGE": # extended-gauss edges functions
nodes, weights = extended_gauss_quad(p)
basis = edge_basis(nodes, x)
return basis
else:
raise Exception("Error, poly_type wrong......")
def evaluate_basis(self, domain=None):
"""
#SUMMARY: Update self.xi, eta and basis.
"""
if domain is None:
# evaluate the lagrange basis at the default quad nodes
self._xi, self._eta = np.meshgrid(self._quad_nodes[0],
self._quad_nodes[1])
nodal_basis_1d = [
functionals.lagrange_basis(self._nodal_nodes[i],
self._quad_nodes[i])
for i in range(2)
]
self._evaluate_basis_domain = (self._quad_nodes[0],
self._quad_nodes[1])
else:
self._xi, self._eta = np.meshgrid(*domain)
nodal_basis_1d = [
functionals.lagrange_basis(self._nodal_nodes[i], domain[i])
for i in range(2)
]
self._evaluate_basis_domain = domain
self._basis = np.kron(nodal_basis_1d[0], nodal_basis_1d[1])
def evaluate_basis(self, domain=None):
"""
#SUMMARY: Update self.xi, eta and basis.
# UPDATE: xi, eta, basis
basis: A list, [0], [1] corresponding to S;N, W;E
"""
if domain is None:
# evaluate the lagrange basis at the default quad nodes
self._xi, self._eta = self._quad_nodes[0], self._quad_nodes[1]
self._basis = [
functionals.lagrange_basis(self._nodal_nodes[i],
self._quad_nodes[i])
for i in range(2)
]
self._evaluate_basis_domain = (self._quad_nodes[0],
self._quad_nodes[1])
else:
self._xi, self._eta = domain[0], domain[1]
self._basis = [
functionals.lagrange_basis(self._nodal_nodes[i], domain[i])
for i in range(2)
]
self._evaluate_basis_domain = domain
self._basis_SN = self._basis[0]
self._basis_WE = self._basis[1]
def evaluate_basis(self, domain=None):
"""
#SUMMARY: Update self.xi, eta and basis.
"""
if domain is None:
self._xi, self._eta = np.meshgrid(self._quad_nodes[0],
self._quad_nodes[1])
nodal_basis_1d = [
functionals.lagrange_basis(self._nodal_nodes[i],
self._quad_nodes[1 - i])
for i in range(2)
]
edge_basis_1d = [
functionals.edge_basis(self._edge_nodes[i],
self._quad_nodes[i]) for i in range(2)
]
self._basis = np.zeros(
(self.num_basis,
np.size(self._quad_nodes[0]) * np.size(self._quad_nodes[1])))
self._evaluate_basis_domain = (self._quad_nodes[0],
self._quad_nodes[1])
else:
self._xi, self._eta = np.meshgrid(domain[0], domain[1])
nodal_basis_1d = [
functionals.lagrange_basis(self._nodal_nodes[i], domain[1 - i])
for i in range(2)
]
edge_basis_1d = [
functionals.edge_basis(self._edge_nodes[i], domain[i])
for i in range(2)
]
self._basis = np.zeros(
(self.num_basis, np.size(domain[0]) * np.size(domain[1])))
self._evaluate_basis_domain = domain
if self.numbering_scheme == 'symmetric1':
self._basis[:self.num_basis_xi] = np.kron(nodal_basis_1d[0],
edge_basis_1d[0])
self._basis[-self.num_basis_eta:] = np.kron(
nodal_basis_1d[1], edge_basis_1d[1])
# self.basis_1edge = np.kron(edge_basis_1d[0], np.ones(np.shape(edge_basis_1d[0])))
# self.basis_1node = np.kron(nodal_basis_1d[0], np.ones(np.shape(nodal_basis_1d[0])))
# self.basis_1node = nodal_basis_1d[0]
# sio.savemat('edgebasis', mdict={'edgebasis': self.basis_1node})
# TODO
if self.numbering_scheme == 'general' or None:
self._basis[:self.num_basis_xi] = np.kron(edge_basis_1d[0],
nodal_basis_1d[0])
self._basis[-self.num_basis_eta:] = np.kron(
nodal_basis_1d[1], edge_basis_1d[1])
def evaluate_basis(self, domain=None):
"""Evaluate the basis."""
pass
if domain is None:
edge_basis_eg = [functionals.edge_basis(self._ext_gauss_nodes, self._quad_nodes[i]) for i in range(2)]
edge_basis_gl = [functionals.edge_basis(self._lobatto_nodes , self._quad_nodes[i]) for i in range(2)]
node_basis_eg = [functionals.lagrange_basis(self._ext_gauss_nodes, self._quad_nodes[i]) for i in range(2)]
node_basis_gl = [functionals.lagrange_basis(self._lobatto_nodes , self._quad_nodes[i]) for i in range(2)]
self.xi, self.eta = np.meshgrid(self._quad_nodes, self._quad_nodes)
else:
edge_basis_eg = [functionals.edge_basis(self._ext_gauss_nodes, domain[i]) for i in range(2)]
edge_basis_gl = [functionals.edge_basis(self._lobatto_nodes , domain[i]) for i in range(2)]
node_basis_eg = [functionals.lagrange_basis(self._ext_gauss_nodes, domain[i]) for i in range(2)]
node_basis_gl = [functionals.lagrange_basis(self._lobatto_nodes , domain[i]) for i in range(2)]
self.xi, self.eta = np.meshgrid(*domain)
self.basis_dxodx = np.kron(edge_basis_eg[0], node_basis_gl[1]) # OK
self.basis_dyodx = np.kron(node_basis_eg[0], edge_basis_gl[1]) # OK
self.basis_dxody = np.kron(edge_basis_gl[0], node_basis_eg[1]) # OK
self.basis_dyody = np.kron(node_basis_gl[0], edge_basis_eg[1]) # OK
self.basis = np.vstack( ( self.basis_dxodx, self.basis_dyodx, self.basis_dxody, self.basis_dyody ) )