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import math
import pytest
from numpy import ndindex, reshape
from utils import LagrangeElement
from ufl import (
Coefficient,
FunctionSpace,
Mesh,
TestFunction,
TrialFunction,
VectorConstant,
acos,
as_tensor,
as_ufl,
asin,
atan,
cos,
cosh,
dx,
exp,
i,
j,
ln,
max_value,
min_value,
outer,
sin,
sinh,
tan,
tanh,
triangle,
)
from ufl.algorithms import compute_form_data
from ufl.constantvalue import Zero
from ufl.core.multiindex import FixedIndex, Index, MultiIndex, indices
from ufl.indexed import Indexed
from ufl.tensors import ComponentTensor, ListTensor
def xtest_zero_times_argument(self):
# FIXME: Allow zero forms
element = LagrangeElement(triangle, 1)
domain = Mesh(LagrangeElement(triangle, 1, (2,)))
space = FunctionSpace(domain, element)
v = TestFunction(space)
u = TrialFunction(space)
L = 0 * v * dx
a = 0 * (u * v) * dx
b = (0 * u) * v * dx
assert len(compute_form_data(L).arguments) == 1
assert len(compute_form_data(a).arguments) == 2
assert len(compute_form_data(b).arguments) == 2
def test_divisions(self):
element = LagrangeElement(triangle, 1)
domain = Mesh(LagrangeElement(triangle, 1, (2,)))
space = FunctionSpace(domain, element)
f = Coefficient(space)
# Test simplification of division by 1
a = f
b = f / 1
assert a == b
# Test simplification of division by 1.0
a = f
b = f / 1.0
assert a == b
# Test simplification of division by of zero by something
a = 0 / f
b = 0 * f
assert a == b
# Test simplification of division by self (this simplification has been disabled)
# a = f/f
# b = 1
# assert a == b
def test_products(self):
element = LagrangeElement(triangle, 1)
domain = Mesh(LagrangeElement(triangle, 1, (2,)))
space = FunctionSpace(domain, element)
f = Coefficient(space)
g = Coefficient(space)
# Test simplification of literal multiplication
assert f * 0 == as_ufl(0)
assert 0 * f == as_ufl(0)
assert 1 * f == f
assert f * 1 == f
assert as_ufl(2) * as_ufl(3) == as_ufl(6)
assert as_ufl(2.0) * as_ufl(3.0) == as_ufl(6.0)
# Test reordering of operands
assert f * g == g * f
# Test simplification of self-multiplication (this simplification has been disabled)
# assert f*f == f**2
def test_sums(self):
element = LagrangeElement(triangle, 1)
domain = Mesh(LagrangeElement(triangle, 1, (2,)))
space = FunctionSpace(domain, element)
f = Coefficient(space)
g = Coefficient(space)
# Test reordering of operands
assert f + g == g + f
# Test adding zero
assert f + 0 == f
assert 0 + f == f
# Test collapsing of basic sum (this simplification has been disabled)
# assert f + f == 2 * f
# Test reordering of operands and collapsing sum
a = f + g + f # not collapsed, but ordered
b = g + f + f # not collapsed, but ordered
c = (g + f) + f # not collapsed, but ordered
d = f + (f + g) # not collapsed, but ordered
assert a == b
assert a == c
assert a == d
# Test reordering of operands and collapsing sum
a = f + f + g # collapsed
b = g + (f + f) # collapsed
assert a == b
def test_mathfunctions(self):
for a in (0.1, 0.3, 0.9):
assert math.sin(a) == sin(a)
assert math.cos(a) == cos(a)
assert math.tan(a) == tan(a)
assert math.sinh(a) == sinh(a)
assert math.cosh(a) == cosh(a)
assert math.tanh(a) == tanh(a)
assert math.asin(a) == asin(a)
assert math.acos(a) == acos(a)
assert math.atan(a) == atan(a)
assert math.exp(a) == exp(a)
assert math.log(a) == ln(a)
# TODO: Implement automatic simplification of conditionals?
assert a == float(max_value(a, a - 1))
# TODO: Implement automatic simplification of conditionals?
assert a == float(min_value(a, a + 1))
def test_indexing(self):
domain = Mesh(LagrangeElement(triangle, 1, (2,)))
u = VectorConstant(domain)
v = VectorConstant(domain)
A = outer(u, v)
A2 = as_tensor(A[i, j], (i, j))
assert A2 == A
Bij = u[i] * v[j]
Bij2 = as_tensor(Bij, (i, j))[i, j]
as_tensor(Bij, (i, j))
assert Bij2 == Bij
@pytest.mark.parametrize("shape", [(3,), (3, 2)], ids=("vector", "matrix"))
def test_tensor_from_indexed(self, shape):
element = LagrangeElement(triangle, 1, shape)
domain = Mesh(LagrangeElement(triangle, 1, (2,)))
space = FunctionSpace(domain, element)
f = Coefficient(space)
assert as_tensor(reshape([f[i] for i in ndindex(f.ufl_shape)], f.ufl_shape).tolist()) is f
def test_nested_indexed(self):
# Test that a nested Indexed expression simplifies to the existing Indexed object
shape = (2,)
element = LagrangeElement(triangle, 1, shape)
domain = Mesh(LagrangeElement(triangle, 1, (2,)))
space = FunctionSpace(domain, element)
f = Coefficient(space)
comps = tuple(f[i] for i in range(2))
assert all(isinstance(c, Indexed) for c in comps)
expr = as_tensor(list(reversed(comps)))
multiindex = MultiIndex((FixedIndex(0),))
assert Indexed(expr, multiindex) is expr[0]
assert Indexed(expr, multiindex) is comps[1]
def test_repeated_indexing(self):
# Test that an Indexed with repeated indices does not contract indices
shape = (2, 2)
element = LagrangeElement(triangle, 1, shape)
domain = Mesh(LagrangeElement(triangle, 1, (2,)))
space = FunctionSpace(domain, element)
x = Coefficient(space)
C = as_tensor([x, x])
fi = FixedIndex(0)
i = Index()
ii = MultiIndex((fi, i, i))
expr = Indexed(C, ii)
assert i.count() in expr.ufl_free_indices
assert isinstance(expr, Indexed)
B, jj = expr.ufl_operands
assert B is x
assert tuple(jj) == tuple(ii[1:])
def test_untangle_indexed_component_tensor(self):
shape = (2, 2, 2, 2)
element = LagrangeElement(triangle, 1, shape)
domain = Mesh(LagrangeElement(triangle, 1, (2,)))
space = FunctionSpace(domain, element)
C = Coefficient(space)
r = len(shape)
kk = indices(r)
# Untangle as_tensor(C[kk], kk) -> C
B = as_tensor(Indexed(C, MultiIndex(kk)), kk)
assert B is C
# Untangle as_tensor(C[kk], jj)[ii] -> C[ll]
jj = kk[2:]
A = as_tensor(Indexed(C, MultiIndex(kk)), jj)
assert A is not C
ii = kk
expr = Indexed(A, MultiIndex(ii))
assert isinstance(expr, Indexed)
B, ll = expr.ufl_operands
assert B is C
rep = dict(zip(jj, ii))
expected = tuple(rep.get(k, k) for k in kk)
assert tuple(ll) == expected
def test_simplify_indexed(self):
element = LagrangeElement(triangle, 1, (3,))
domain = Mesh(LagrangeElement(triangle, 1, (2,)))
space = FunctionSpace(domain, element)
u = Coefficient(space)
z = Zero(())
i = Index()
j = Index()
# ListTensor
lt = ListTensor(z, z, u[1])
assert Indexed(lt, MultiIndex((FixedIndex(2),))) == u[1]
# ListTensor -- nested
l0 = ListTensor(z, u[1], z)
l1 = ListTensor(z, z, u[2])
l2 = ListTensor(u[0], z, z)
ll = ListTensor(l0, l1, l2)
assert Indexed(ll, MultiIndex((FixedIndex(1), FixedIndex(2)))) == u[2]
assert Indexed(ll, MultiIndex((FixedIndex(2), i))) == l2[i]
# ComponentTensor + ListTensor
c = ComponentTensor(Indexed(ll, MultiIndex((i, j))), MultiIndex((j, i)))
assert Indexed(c, MultiIndex((FixedIndex(1), FixedIndex(2)))) == l2[1]
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