def test_derivatives_2d_with_mapping():
rdim = 2
O = Domain('Omega', dim=rdim)
V = ScalarFunctionSpace('V', O)
u = element_of(V, 'u')
M = Mapping('M', rdim)
det_jac = DetJacobian(M)
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(M, dx(u)).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_logical_expr_2d_1():
rdim = 2
M = Mapping('M', rdim)
domain = Domain('Omega', dim=rdim)
alpha = Constant('alpha')
V = ScalarFunctionSpace('V', domain)
W = VectorFunctionSpace('V', domain)
u, v = [element_of(V, name=i) for i in ['u', 'v']]
w = element_of(W, name='w')
det_M = DetJacobian(M)
#print('det = ', det_M)
det = Symbol('det')
# ...
expr = 2 * u + alpha * v
expr = LogicalExpr(M, expr)
#print(expr)
#print('')
# ...
# ...
expr = dx(u)
expr = LogicalExpr(M, expr)
#print(expr.subs(det_M, det))
#print('')
# ...
# ...
expr = dy(u)
expr = LogicalExpr(M, expr)
#print(expr.subs(det_M, det))
#print('')
# ...
# ...
expr = dx(det_M)
expr = LogicalExpr(M, expr)
expr = expr.subs(det_M, det)
expr = expand(expr)
#print(expr)
#print('')
# ...
# ...
expr = dx(dx(u))
expr = LogicalExpr(M, expr)
#print(expr.subs(det_M, det))
#print('')
# ...
# ...
expr = dx(w[0])
expr = LogicalExpr(M, expr)
def test_symbolic_expr_1d_1():
rdim = 1
M = Mapping('M', rdim)
domain = Domain('Omega', dim=rdim)
alpha = Constant('alpha')
V = ScalarFunctionSpace('V', domain)
u = element_of(V, name='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(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 eval(cls, *_args, **kwargs):
"""."""
if not _args:
return
if not len(_args) == 1:
raise ValueError('Expecting one argument')
expr = _args[0]
d_atoms = kwargs.pop('d_atoms', {})
mapping = kwargs.pop('mapping', None)
if isinstance(expr, Add):
args = [
cls.eval(a, d_atoms=d_atoms, mapping=mapping)
for a in expr.args
]
return Add(*args)
elif isinstance(expr, Mul):
coeffs = [a for a in expr.args if isinstance(a, _coeffs_registery)]
stests = [
a for a in expr.args
if not (a in coeffs) and a.atoms(ScalarTestFunction)
]
vtests = [
a for a in expr.args
if not (a in coeffs) and a.atoms(VectorTestFunction)
]
vectors = [
a for a in expr.args if
(not (a in coeffs) and not (a in stests) and not (a in vtests))
]
a = S.One
if coeffs:
a = Mul(*coeffs)
b = S.One
if vectors:
args = [cls(i, evaluate=False) for i in vectors]
b = Mul(*args)
sb = S.One
if stests:
args = [
cls.eval(i, d_atoms=d_atoms, mapping=mapping)
for i in stests
]
sb = Mul(*args)
vb = S.One
if vtests:
args = [
cls.eval(i, d_atoms=d_atoms, mapping=mapping)
for i in vtests
]
vb = Mul(*args)
return Mul(a, b, sb, vb)
elif isinstance(expr, _coeffs_registery):
return expr
elif isinstance(expr, Pow):
b = expr.base
e = expr.exp
return Pow(cls.eval(b), e)
elif isinstance(expr, (Matrix, ImmutableDenseMatrix)):
n_rows, n_cols = expr.shape
lines = []
for i_row in range(0, n_rows):
line = []
for i_col in range(0, n_cols):
line.append(
cls.eval(expr[i_row, i_col],
d_atoms=d_atoms,
mapping=mapping))
lines.append(line)
return Matrix(lines)
elif isinstance(expr, DomainExpression):
# TODO to be removed
target = expr.target
expr = expr.expr
return cls.eval(expr, d_atoms=d_atoms, mapping=mapping)
elif isinstance(expr, BilinearForm):
trials = list(expr.variables[0])
tests = list(expr.variables[1])
# ... # TODO improve
terminal_expr = TerminalExpr(expr)[0]
# ...
# ...
variables = list(terminal_expr.atoms(ScalarTestFunction))
variables += list(terminal_expr.atoms(IndexedTestTrial))
d_atoms = {}
for a in variables:
new = _split_test_function(a)
d_atoms[a] = new
# ...
# ...
logical = False
if not (mapping is None):
logical = True
terminal_expr = LogicalExpr(mapping, terminal_expr.expr)
det_M = DetJacobian(mapping)
det = SymbolicDeterminant(mapping)
terminal_expr = terminal_expr.subs(det_M, det)
terminal_expr = expand(terminal_expr)
# ...
# ...
expr = cls.eval(terminal_expr, d_atoms=d_atoms, mapping=mapping)
# ...
# ...
trials = [
a for a in variables
if ((isinstance(a, ScalarTestFunction) and a in trials) or (
isinstance(a, IndexedTestTrial) and a.base in trials))
]
tests = [
a for a in variables
if ((isinstance(a, ScalarTestFunction) and a in tests) or (
isinstance(a, IndexedTestTrial) and a.base in tests))
]
# ...
expr = _replace_atomic_expr(expr,
trials,
tests,
d_atoms,
logical=logical)
return expr
if expr.atoms(ScalarTestFunction) or expr.atoms(IndexedTestTrial):
return _tensorize_atomic_expr(expr, d_atoms)
return cls(expr, evaluate=False)