def adjoin_GaNi(a, b):
print('Gani')
a.dct()
# print(a.val)
a.grad_transpose()
# print(a.val)
a.idct()
adjoin = Chebyshev_element(name='adjoin',
N=N,
shape=(),
multype='scal')
adjoin.val = np.multiply(a.val, b.val)
adjoin.dct()
# print(adjoin.val)
adjoin.idct()
# print('ab')
# print(adjoin.val)
adjoin.integrate()
#scalar = np.sum(adjoin.val)
return adjoin.integral #scalar # #
def test_interpolate(self):
print('\nChecking enlarge and decrease')
for dim, Ni in itertools.product([2], [5, 15, 55]):
N = np.array(dim * [
Ni,
], dtype=np.int)
dN = tuple(np.array(N * 2 - 1, dtype=np.int))
x0 = Chebyshev_element(name='x', N=N, shape=(), Fourier=False)
x0.set_nodal_coord()
x0.val = load(x0.coord, 'continuous')
a = copy.deepcopy(x0)
# print(x0.val)
x0.interpolate()
# print(x0.val)
x0.dct()
# print(x0.val)
x0.shrink()
# print(x0.val)
x0.idct()
# print(x0.val)
self.assertTrue(np.allclose(
a.val,
x0.val,
atol=1e-12,
),
msg="Enlarge and shrink does not preserve values")
def tester(a, b):
a.dct()
# print(a.val)
a.idct()
adjoin = Chebyshev_element(name='test',
N=N,
shape=(),
multype='scal')
adjoin.val = np.multiply(a.val, b.val)
adjoin.dct()
# print(adjoin.val)
adjoin.idct()
# print('ab')
# print(adjoin.val)
adjoin.integrate()
#scalar = np.sum(adjoin.val)
return adjoin.integral #scalar # #
def test_integral_w_projection(self):
print('\nChecking integral with projection')
solution = [0, 0.8, 8.3317]
for dim, Ni in itertools.product([2, 3], [100, 155]):
N = np.array(dim * [
Ni,
], dtype=np.int)
dN = tuple(np.array(N * 2 - 1, dtype=np.int))
integrant = lambda x: (x[0]**4) + (x[1]**3) if x.__len__(
) == 2 else (x[0]**4) + (x[1]**3) + np.cos(x[2])
u = Chebyshev_element(name='u', N=N, shape=(), multype='scal')
u.set_nodal_coord()
u.val = integrant(u.coord)
u.integrate()
i_1 = u.integral
u.dct()
u.enlarge()
u.idct()
u.integrate()
i_2 = u.integral
u.dct()
u.shrink()
u.idct()
i_3 = u.integral
self.assertTrue(np.isclose(i_1,
i_2,
rtol=1e-05,
atol=1e-08,
equal_nan=False),
msg="Integral does not work correctly")
self.assertTrue(np.isclose(i_1,
i_3,
rtol=1e-05,
atol=1e-08,
equal_nan=False),
msg="Integral does not work correctly")
def test_dct(self):
print('\nChecking discrete cosine transform...')
for dim, Ni in itertools.product([2, 3], [2, 4, 8]):
N = tuple(np.array(dim * [
Ni,
], dtype=np.int))
values = np.random.random_sample(N)
Element = Chebyshev_element(name='x', N=N, shape=())
Element.val = values
u1 = copy.deepcopy(Element.val)
Element.dct()
Element.idct()
u2 = copy.deepcopy(Element.val)
self.assertTrue(
np.allclose(
u1,
u2,
atol=1e-15,
),
msg="dct does not preserve values for dim {} and N{}".format(
dim, Ni))