def _visit_LogicalValueNode(self, expr, **kwargs):
mapping = self.mapping
expr = expr.expr
if isinstance(expr, SymbolicDeterminant):
return SymbolicExpr(mapping.det_jacobian)
elif isinstance(expr, SymbolicInverseDeterminant):
return SymbolicExpr(1. / SymbolicDeterminant(mapping))
elif isinstance(expr, WeightedVolumeQuadrature):
l_quad = TensorQuadrature()
l_quad = self._visit(l_quad, **kwargs)
points, weights = list(zip(*l_quad))
wvol = Mul(*weights)
return wvol
elif isinstance(expr, SymbolicWeightedVolume):
wvol = self._visit(expr, **kwargs)
det_jac = SymbolicDeterminant(mapping)
det_jac = SymbolicExpr(det_jac)
return wvol * Abs(det_jac)
else:
raise TypeError('{} not available'.format(type(expr)))
def _visit_PhysicalValueNode(self, expr, **kwargs):
mapping = self.mapping
expr = LogicalExpr(mapping, expr.expr)
expr = SymbolicExpr(expr)
inv_jac = SymbolicInverseDeterminant(mapping)
jac = SymbolicExpr(mapping.det_jacobian)
expr = expr.subs(1 / jac, inv_jac)
return expr
def test_derivatives_2d_with_mapping():
dim = 2
M = Mapping('M', dim=dim)
O = M(Domain('Omega', dim=dim))
V = ScalarFunctionSpace('V', O, kind='h1')
u = element_of(V, 'u')
det_jac = Jacobian(M).det()
J = Symbol('J')
expr = M
assert SymbolicExpr(expr) == Symbol('M')
expr = M[0]
assert SymbolicExpr(expr) == Symbol('x')
expr = M[1]
assert SymbolicExpr(expr) == Symbol('y')
expr = dx2(M[0])
assert SymbolicExpr(expr) == Symbol('x_x2')
expr = dx1(M[1])
assert SymbolicExpr(expr) == Symbol('y_x1')
expr = LogicalExpr(dx(u), O).subs(det_jac, J)
expected = '(u_x1 * y_x2 - u_x2 * y_x1)/J'
difference = SymbolicExpr(expr) - sympify(expected)
assert difference.simplify() == 0
def test_derivatives_2d_without_mapping():
O = Domain('Omega', dim=2)
V = ScalarFunctionSpace('V', O)
u = element_of(V, 'u')
expr = u
assert SymbolicExpr(expr) == Symbol('u')
expr = dx(u)
assert SymbolicExpr(expr) == Symbol('u_x')
expr = dx(dx(u))
assert SymbolicExpr(expr) == Symbol('u_xx')
expr = dx(dy(u))
assert SymbolicExpr(expr) == Symbol('u_xy')
expr = dy(dx(u))
assert SymbolicExpr(expr) == Symbol('u_xy')
expr = dy(dx(dz(u)))
assert SymbolicExpr(expr) == Symbol('u_xyz')
expr = dy(dy(dx(u)))
assert SymbolicExpr(expr) == Symbol('u_xyy')
expr = dy(dz(dy(u)))
assert SymbolicExpr(expr) == Symbol('u_yyz')
def _visit_MatrixLocalBasis(self, expr, **kwargs):
dim = self.dim
rank = self._visit(expr.rank)
target = SymbolicExpr(expr.target)
name = 'arr_{}'.format(target.name)
return IndexedVariable(name, dtype='real', rank=rank)
def _visit_AtomicNode(self, expr, **kwargs):
if isinstance(expr.expr, WeightedVolumeQuadrature):
mapping = self.mapping
expr = SymbolicWeightedVolume(mapping)
return self._visit(expr, **kwargs)
else:
return SymbolicExpr(expr.expr)
def _visit_ComputeKernelExpr(self, expr, op=None, lhs=None, **kwargs):
expr = expr.expr
if lhs is None:
if not isinstance(expr, (Add, Mul)):
lhs = self._visit(BasisAtom(expr), **kwargs)
else:
lhs = random_string(6)
lhs = Symbol('tmp_{}'.format(lhs))
weight = SymbolicWeightedVolume(self.mapping)
weight = SymbolicExpr(weight)
rhs = self._visit(expr, **kwargs)
rhs *= weight
if op is None:
stmt = Assign(lhs, rhs)
else:
stmt = AugAssign(lhs, op, rhs)
return self._visit(stmt, **kwargs)
def _visit_LogicalBasisValue(self, expr, **kwargs):
# ...
dim = self.dim
coords = ['x1', 'x2', 'x3'][:dim]
expr = expr.expr
atom = BasisAtom(expr).atom
atoms = _split_test_function(atom)
ops = [dx1, dx2, dx3][:dim]
d_atoms = dict(zip(coords, atoms))
d_ops = dict(zip(coords, ops))
d_indices = get_index_logical_derivatives(expr)
args = []
for k, u in d_atoms.items():
d = d_ops[k]
n = d_indices[k]
for i in range(n):
u = d(u)
args.append(u)
# ...
expr = Mul(*args)
return SymbolicExpr(expr)
def test_symbolic_expr_1d_1():
rdim = 1
M = Mapping('M', rdim)
domain = M(Domain('Omega', dim=rdim))
alpha = Constant('alpha')
V = ScalarFunctionSpace('V', domain, kind='h1')
u = element_of(V, name='u')
det_M = Jacobian(M).det()
det_M = SymbolicExpr(det_M)
#print('>>> ', det_M)
det = Symbol('det')
# ...
expr = u
expr = LogicalExpr(expr, mapping=M, dim=rdim)
expr = SymbolicExpr(expr)
#print(expr)
# ...
# ...
expr = dx1(u)
expr = LogicalExpr(expr, mapping=M, dim=rdim)
expr = SymbolicExpr(expr)
#print(expr)
# ...
# ...
expr = dx1(M[0])
expr = LogicalExpr(expr, mapping=M, dim=rdim)
expr = SymbolicExpr(expr)
#print(expr)
# ...
# ...
expr = dx(u)
expr = LogicalExpr(expr, mapping=M, dim=rdim)
expr = SymbolicExpr(expr)
expr = expr.subs(det_M, det)
#print(expr)
# ...
# ...
expr = dx(Jacobian(M).det())
expr = LogicalExpr(expr, mapping=M, dim=rdim)
expr = SymbolicExpr(expr)
expr = expr.subs(det_M, det)
#print(expand(expr))
# ...
# ...
expr = dx(dx(u))
expr = LogicalExpr(expr, mapping=M, dim=rdim)
expr = SymbolicExpr(expr)
expr = expr.subs(det_M, det)
#print(expand(expr))
# ...
# ...
expr = dx(dx(dx(u)))
expr = LogicalExpr(expr, mapping=M, dim=rdim)
expr = SymbolicExpr(expr)
expr = expr.subs(det_M, det)
def test_symbolic_expr_3d_1():
dim = 3
M = Mapping('M', dim=dim)
domain = M(Domain('Omega', dim=dim))
V = ScalarFunctionSpace('V', domain, kind='h1')
u = element_of(V, 'u')
det_M = Jacobian(M).det()
det_M = SymbolicExpr(det_M)
#print('>>> ', det_M)
det = Symbol('det')
# ...
expr = u
expr = LogicalExpr(expr, domain)
expr = SymbolicExpr(expr)
#print(expr)
# ...
# ...
expr = dx1(u)
expr = LogicalExpr(expr, domain)
expr = SymbolicExpr(expr)
#print(expr)
# ...
# ...
expr = dx1(dx2(u))
expr = LogicalExpr(expr, domain)
expr = SymbolicExpr(expr)
#print(expr)
# ...
# ...
expr = dx1(M[0])
expr = LogicalExpr(expr, domain)
expr = SymbolicExpr(expr)
#print(expr)
# ...
# ...
expr = dx(u)
expr = LogicalExpr(expr, domain)
expr = SymbolicExpr(expr)
expr = expr.subs(det_M, det)
#print(expr)
# ...
# ...
expr = dx(Jacobian(M).det())
expr = LogicalExpr(expr, domain)
expr = SymbolicExpr(expr)
expr = expr.subs(det_M, det)
#print(expand(expr))
# ...
# ...
expr = dx(dx(u))
expr = LogicalExpr(expr, domain)
expr = SymbolicExpr(expr)
expr = expr.subs(det_M, det)
#print(expand(expr))
# ...
# ...
expr = dx(dx(dx(u)))
expr = LogicalExpr(expr, domain)
expr = SymbolicExpr(expr)
expr = expr.subs(det_M, det)
def test_symbolic_expr_3d_1():
rdim = 3
M = Mapping('M', rdim)
domain = Domain('Omega', dim=rdim)
alpha = Constant('alpha')
V = ScalarFunctionSpace('V', domain)
u = element_of(V, 'u')
det_M = DetJacobian(M)
det_M = SymbolicExpr(det_M)
#print('>>> ', det_M)
det = Symbol('det')
# ...
expr = u
expr = LogicalExpr(M, expr)
expr = SymbolicExpr(expr)
#print(expr)
# ...
# ...
expr = dx1(u)
expr = LogicalExpr(M, expr)
expr = SymbolicExpr(expr)
#print(expr)
# ...
# ...
expr = dx1(dx2(u))
expr = LogicalExpr(M, expr)
expr = SymbolicExpr(expr)
#print(expr)
# ...
# ...
expr = dx1(M[0])
expr = LogicalExpr(M, expr)
expr = SymbolicExpr(expr)
#print(expr)
# ...
# ...
expr = dx(u)
expr = LogicalExpr(M, expr)
expr = SymbolicExpr(expr)
expr = expr.subs(det_M, det)
#print(expr)
# ...
# ...
expr = dx(DetJacobian(M))
expr = LogicalExpr(M, expr)
expr = SymbolicExpr(expr)
expr = expr.subs(det_M, det)
#print(expand(expr))
# ...
# ...
expr = dx(dx(u))
expr = LogicalExpr(M, expr)
expr = SymbolicExpr(expr)
expr = expr.subs(det_M, det)
#print(expand(expr))
# ...
# ...
expr = dx(dx(dx(u)))
expr = LogicalExpr(M, expr)
expr = SymbolicExpr(expr)
expr = expr.subs(det_M, det)
def _visit_Expr(self, expr, **kwargs):
return SymbolicExpr(expr)
def _visit_PhysicalGeometryValue(self, expr, **kwargs):
mapping = self.mapping
expr = LogicalExpr(mapping, expr.expr)
return SymbolicExpr(expr)
def _visit_BasisAtom(self, expr, **kwargs):
symbol = SymbolicExpr(expr.expr)
return symbol
def _visit_CoefficientBasis(self, expr, **kwargs):
target = SymbolicExpr(expr.target)
name = 'coeff_{}'.format(target.name)
return Variable('real', name)