def test_vec_mag(self):
mesh = UnitSquareMesh(2, 2)
V = VectorFunctionSpace(mesh, 'CG', 1)
series = TempSeries([(interpolate(Expression(('x[0]', '0'), degree=1), V), 0),
(interpolate(Expression(('0', 'x[1]'), degree=1), V), 1)])
mag_series = Eval(sqrt(inner(series, series)))
self.assertTrue(error(Expression('x[0]', degree=1), mag_series.getitem(0)) < 1E-14)
self.assertTrue(error(Expression('x[1]', degree=1), mag_series.getitem(1)) < 1E-14)
def test_sliding_window(self):
mesh = UnitSquareMesh(4, 4)
V = FunctionSpace(mesh, 'CG', 1)
series = TempSeries([(interpolate(Constant(1), V), 0),
(interpolate(Constant(2), V), 1),
(interpolate(Constant(3), V), 2),
(interpolate(Constant(4), V), 3)])
f_series = Eval(SlidingWindowFilter(Mean, 2, series**2))
assert len(f_series) == 3
assert f_series.times == (1, 2, 3)
self.assertTrue(error(Constant(2.5), f_series.getitem(0)) < 1E-14)
self.assertTrue(error(Constant(6.5), f_series.getitem(1)) < 1E-14)
self.assertTrue(error(Constant(12.5), f_series.getitem(2)) < 1E-14)
def test_sanity11(self):
mesh = UnitSquareMesh(5, 5)
true = SpatialCoordinate(mesh)
me = Eval(true)
e = error(true, me)
self.assertTrue(e < 1E-14)
def test_comp_tensor_num_vec(self):
mesh = UnitSquareMesh(4, 4)
r = SpatialCoordinate(mesh)
true = Constant(2) * r
me = Eval(true)
e = error(true, me)
self.assertTrue(e < 1E-14)
def test_algebra_fail_different_times(self):
mesh = UnitSquareMesh(2, 2)
V = FunctionSpace(mesh, 'DG', 0)
series0 = TempSeries(((Function(V), 0), (Function(V), 1)))
series1 = TempSeries(((Function(V), 0), (Function(V), 2)))
with self.assertRaises(AssertionError):
Eval(series0 - series1)
def test_max(self):
mesh = UnitSquareMesh(4, 4)
x, y = SpatialCoordinate(mesh)
true = Max(x + y, 2 * y)
me = Eval(true)
e = error(true, me)
self.assertTrue(e < 1E-14)
def test_std(self):
mesh = UnitSquareMesh(4, 4)
V = FunctionSpace(mesh, 'CG', 1)
f = Expression('(x[0]+x[1])*t', t=0, degree=1)
ft_pairs = []
for t in np.linspace(0, 2, 80):
f.t = t
v = interpolate(f, V)
ft_pairs.append((v, t))
series = TempSeries(ft_pairs)
std = Eval(STD(series)) # Efficiently in PETSc
# From definition
std_ = Eval(sqrt(Mean(series**2) - Mean(series)**2))
self.assertTrue(error(std_, std) < 1E-14)
def test_sanity12(self):
mesh = UnitSquareMesh(5, 5)
x, y = SpatialCoordinate(mesh)
true = as_vector((x + y, x - y))
me = Eval(true)
e = error(true, me)
self.assertTrue(e < 1E-14)
def test_cond_logic(self):
errors = []
for n in (4, 8, 16, 32, 64):
mesh = UnitSquareMesh(n, n)
x, y = SpatialCoordinate(mesh)
true = conditional(And(x < y, Constant(0) < x), x + y, x - y)
me = Eval(true)
errors.append(error(true, me))
self.assertTrue((np.diff(errors) < 0).all())
def test_maybe_fix_future(self):
mesh = UnitSquareMesh(10, 10)
V = FunctionSpace(mesh, 'RT', 1)
x = Function(V)
y = Function(V)
for f in (inner(x, y), as_vector((x[0], y[1])), 2 * x + y):
with self.assertRaises(AssertionError):
Eval(f)
def test_eigv(self):
A = np.array([[1, -2], [-3, 1]])
mesh = UnitSquareMesh(10, 10)
V = TensorFunctionSpace(mesh, 'DG', 0)
f = interpolate(Constant(A), V)
# FIXME: 2*f leads to ComponentTensor which we don't handle well
me = Eval(Eigv(f))
true = Constant((np.linalg.eig(A)[1]).T)
self.assertTrue(error(true, me) < 1E-14)
def test_maximum(self):
A = np.array([[1, -2], [-3, 1]])
mesh = UnitSquareMesh(10, 10)
V = TensorFunctionSpace(mesh, 'DG', 0)
f = interpolate(Constant(A), V)
me = Eval(Maximum(Eigw(f - 3 * f))) # Eval o Declared
true = Constant(np.max(np.linalg.eigvals(A - 3 * A)))
self.assertTrue(error(true, me) < 1E-14)
def test_cond_simple_conv(self):
# Outside of CG1 with nonlinearity?
errors = []
for n in (4, 8, 16, 32, 64):
mesh = UnitSquareMesh(n, n)
x, y = SpatialCoordinate(mesh)
true = conditional(x < y, x + y, x - y)
me = Eval(true)
errors.append(error(true, me))
self.assertTrue((np.diff(errors) < 0).all())
def test_comp_tensor_col_slice(self):
mesh = UnitSquareMesh(4, 4)
x, y = SpatialCoordinate(mesh)
A = as_matrix(((x, 2 * y), (3 * y, 4 * x)))
true = A[:, 0]
me = Eval(true)
e = error(true, me)
self.assertTrue(e < 1E-14)
def test_comp_tensor_num_mat(self):
mesh = UnitSquareMesh(4, 4)
x, y = SpatialCoordinate(mesh)
A = as_matrix(((x, y), (y, -x)))
true = Constant(2) * A
me = Eval(true)
e = error(true, me)
self.assertTrue(e < 1E-14)
def test_sanity10(self):
mesh = UnitSquareMesh(5, 5)
V = FunctionSpace(mesh, 'CG', 1)
a0 = interpolate(Expression('x[0]', degree=1), V)
a1 = interpolate(Expression('x[1]', degree=1), V)
true = as_vector((as_vector((a0, a1)), as_vector((-a0, -a1))))
me = Eval(true)
e = error(true, me)
self.assertTrue(e < 1E-14)
def test_sanity5(self):
mesh = UnitSquareMesh(5, 5)
T = TensorFunctionSpace(mesh, 'CG', 1)
A = interpolate(Expression((('1', 'x[0]'), ('2', 'x[1]')), degree=1),
T)
expr = det(A)
me = Eval(expr)
true = Expression('x[1]-2*x[0]', degree=1)
e = error(true, me)
self.assertTrue(e < 1E-14)
def test_comp_tensor_mat_mat_mat(self):
mesh = UnitSquareMesh(4, 4)
T = TensorFunctionSpace(mesh, 'DG', 0)
A = interpolate(Constant(((1, 2), (3, 4))), T)
B = interpolate(Constant(((1, -2), (-1, 4))), T)
true = A * B * A
me = Eval(true)
e = error(true, me)
self.assertTrue(e < 1E-14)
def test_sanity8(self):
mesh = UnitSquareMesh(5, 5)
V = VectorFunctionSpace(mesh, 'CG', 1)
v0 = interpolate(Expression(('x[0]+x[1]', '1'), degree=1), V)
v1 = interpolate(Expression(('1', 'x[0]'), degree=1), V)
me = Eval(inner(v0, v1))
true = Expression('x[1]+2*x[0]', degree=1)
e = error(true, me)
self.assertTrue(e < 1E-14)
def test_cond_simple(self):
mesh = UnitSquareMesh(4, 4)
V = FunctionSpace(mesh, 'DG', 0)
x = interpolate(Constant(1), V)
y = interpolate(Constant(2), V)
true = conditional(x < y, x + y, x - y)
me = Eval(true)
e = error(true, me)
self.assertTrue(e < 1E-14)
def test_get(self):
mesh = UnitSquareMesh(2, 2)
V = VectorFunctionSpace(mesh, 'CG', 1)
series = TempSeries([(interpolate(Expression(('x[0]', '0'), degree=1), V), 0),
(interpolate(Expression(('0', 'x[1]'), degree=1), V), 1)])
mag_series = Eval(series[0]) # series of first componentsts
self.assertTrue(error(Expression('x[0]', degree=1), mag_series.getitem(0)) < 1E-14)
self.assertTrue(error(Expression('0', degree=1), mag_series.getitem(1)) < 1E-14)
mag_series = Eval(series[1]) # series of secon componentsts
self.assertTrue(error(Expression('0', degree=1), mag_series.getitem(0)) < 1E-14)
self.assertTrue(error(Expression('x[1]', degree=1), mag_series.getitem(1)) < 1E-14)
def test_sanity4(self):
mesh = UnitSquareMesh(5, 5)
T = TensorFunctionSpace(mesh, 'CG', 1)
A = interpolate(
Expression((('x[0]', 'x[1]'), ('2*x[0]+x[1]', 'x[0]+3*x[1]')),
degree=1), T)
expr = (sym(A) + skew(A))[:, 0]
me = Eval(expr)
true = Expression(('x[0]', '2*x[0]+x[1]'), degree=1)
e = error(true, me)
self.assertTrue(e < 1E-14)
def test_cond_logic_simple(self):
# We're outside of the CG1!
mesh = UnitSquareMesh(4, 4)
V = FunctionSpace(mesh, 'DG', 0)
x = interpolate(Constant(1), V)
y = interpolate(Constant(2), V)
true = conditional(And(x < y, 0 < x), x + y, x - y)
me = Eval(true)
e = error(true, me)
self.assertTrue(e < 1E-14)
def test_eigw(self):
# FIxME: more advances
A = np.array([[1, -2], [-3, 1]])
mesh = UnitSquareMesh(10, 10)
V = TensorFunctionSpace(mesh, 'DG', 0)
f = interpolate(Constant(A), V)
me = Eval(Eigw(f + f)) # Eval o Declared
true = Constant(np.linalg.eigvals(A + A))
self.assertTrue(error(true, me) < 1E-14)
def test_sanity1(self):
mesh = UnitSquareMesh(5, 5)
T = TensorFunctionSpace(mesh, 'DG', 0)
u = interpolate(
Expression((('x[0]', 'x[1]'), ('2*x[0]+x[1]', 'x[0]+3*x[1]')),
degree=1), T)
expr = sym(u) + skew(u)
me = Eval(expr)
true = u
e = error(true, me)
self.assertTrue(e < 1E-14)
def test_sanity9(self):
mesh = UnitSquareMesh(5, 5)
V = FunctionSpace(mesh, 'CG', 1)
a0 = interpolate(Expression('x[0]', degree=1), V)
a1 = interpolate(Expression('x[1]', degree=1), V)
me = Eval(as_vector((a0, a1)))
x, y = SpatialCoordinate(mesh)
true = as_vector((x, y))
e = error(true, me)
self.assertTrue(e < 1E-14)
def test_comp_tensor_mat_vec(self):
mesh = UnitSquareMesh(4, 4)
x, y = SpatialCoordinate(mesh)
A = as_matrix(((x, 2 * y), (3 * y, 4 * x)))
V = VectorFunctionSpace(mesh, 'CG', 1)
b = interpolate(Constant((1, 2)), V)
true = A * b
me = Eval(true)
e = error(true, me)
self.assertTrue(e < 1E-14)
def test_sanity8(self):
mesh = UnitSquareMesh(5, 5)
T = TensorFunctionSpace(mesh, 'CG', 1)
A = interpolate(Expression((('1', 'x[0]'), ('2', 'x[1]')), degree=1),
T)
V = VectorFunctionSpace(mesh, 'CG', 1)
v = interpolate(Expression(('x[0]+x[1]', '1'), degree=1), V)
me = Eval(dot(v, transpose(A)))
true = Expression(('x[1]+2*x[0]', '2*x[0]+3*x[1]'), degree=1)
e = error(true, me)
self.assertTrue(e < 1E-14)
def test_mean(self):
mesh = UnitSquareMesh(2, 2)
V = FunctionSpace(mesh, 'CG', 1)
f = Expression('(x[0]+x[1])*t', t=0, degree=1)
ft_pairs = []
for t in (0, 0.1, 0.4, 0.6, 2.0):
f.t = t
v = interpolate(f, V)
ft_pairs.append((v, t))
mean = Eval(Mean(TempSeries(ft_pairs))) # Eval o Declared
f.t = 1.0
self.assertTrue(error(f, mean) < 1E-14)
def test_algebra(self):
mesh = UnitSquareMesh(2, 2)
V = FunctionSpace(mesh, 'DG', 0)
series0 = TempSeries([(interpolate(Constant(1), V), 0),
(interpolate(Constant(2), V), 1)])
series1 = TempSeries([(interpolate(Constant(2), V), 0),
(interpolate(Constant(3), V), 1)])
series01 = Eval(series1 - series0)
self.assertTrue(np.linalg.norm(series01.times - np.array([0, 1])) < 1E-14)
# Now each should be 1
for f in series01:
self.assertTrue(error(Constant(1), f) < 1E-14)