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__authors__ = "Martin Sandve Alnæs"
__date__ = "2009-02-17 -- 2014-10-14"
import pytest
from utils import LagrangeElement
from ufl import (
Coefficient,
FunctionSpace,
Mesh,
SpatialCoordinate,
as_vector,
atan,
cos,
diff,
exp,
indices,
ln,
sin,
tan,
triangle,
variable,
)
from ufl.algorithms import expand_derivatives
from ufl.constantvalue import as_ufl
def get_variables():
xv = None
vv = 5.0
return (xv, variable(vv))
@pytest.fixture
def v():
_xv, vv = get_variables()
return vv
def _test(f, df):
x, v = get_variables()
dfv1 = diff(f(v), v)
dfv2 = df(v)
dfv1 = dfv1(x)
dfv2 = dfv2(x)
assert round(dfv1 - dfv2, 7) == 0
dfv1 = diff(f(7 * v), v)
dfv2 = 7 * df(7 * v)
dfv1 = dfv1(x)
dfv2 = dfv2(x)
assert round(dfv1 - dfv2, 7) == 0
def testVariable(v):
def f(v):
return v
def df(v):
return as_ufl(1)
_test(f, df)
def testSum(v):
def f(v):
return v + 1
def df(v):
return as_ufl(1)
_test(f, df)
def testProduct(v):
def f(v):
return 3 * v
def df(v):
return as_ufl(3)
_test(f, df)
def testPower(v):
def f(v):
return v**3
def df(v):
return 3 * v**2
_test(f, df)
def testDivision(v):
def f(v):
return v / 3.0
def df(v):
return as_ufl(1.0 / 3.0)
_test(f, df)
def testDivision2(v):
def f(v):
return 3.0 / v
def df(v):
return -3.0 / v**2
_test(f, df)
def testExp(v):
def f(v):
return exp(v)
def df(v):
return exp(v)
_test(f, df)
def testLn(v):
def f(v):
return ln(v)
def df(v):
return 1.0 / v
_test(f, df)
def testSin(v):
def f(v):
return sin(v)
def df(v):
return cos(v)
_test(f, df)
def testCos(v):
def f(v):
return cos(v)
def df(v):
return -sin(v)
_test(f, df)
def testTan(v):
def f(v):
return tan(v)
def df(v):
return 2.0 / (cos(2.0 * v) + 1.0)
_test(f, df)
# TODO: Check the following tests. They run into strange math domain errors.
# def testAsin(v):
# def f(v): return asin(v)
# def df(v): return 1/sqrt(1.0 - v**2)
# _test(f, df)
# def testAcos(v):
# def f(v): return acos(v)
# def df(v): return -1/sqrt(1.0 - v**2)
# _test(f, df)
def testAtan(v):
def f(v):
return atan(v)
def df(v):
return 1 / (1.0 + v**2)
_test(f, df)
def testIndexSum(v):
def f(v):
# 3*v + 4*v**2 + 5*v**3
a = as_vector((v, v**2, v**3))
b = as_vector((3, 4, 5))
(i,) = indices(1)
return a[i] * b[i]
def df(v):
return 3 + 4 * 2 * v + 5 * 3 * v**2
_test(f, df)
def testCoefficient():
coord_elem = LagrangeElement(triangle, 1, (3,))
mesh = Mesh(coord_elem)
V = FunctionSpace(mesh, LagrangeElement(triangle, 1))
v = Coefficient(V)
assert round(expand_derivatives(diff(v, v)) - 1.0, 7) == 0
def testDiffX():
cell = triangle
domain = Mesh(LagrangeElement(cell, 1, (2,)))
x = SpatialCoordinate(domain)
f = x[0] ** 2 * x[1] ** 2
(i,) = indices(1)
df1 = diff(f, x)
df2 = as_vector(f.dx(i), i)
xv = (2, 3)
df10 = df1[0](xv)
df11 = df1[1](xv)
df20 = df2[0](xv)
df21 = df2[1](xv)
assert round(df10 - df20, 7) == 0
assert round(df11 - df21, 7) == 0
assert round(df10 - 2 * 2 * 9, 7) == 0
assert round(df11 - 2 * 4 * 3, 7) == 0
# TODO: More tests involving wrapper types and indices
|
