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 adjoin_GaNi_Tran(
a,
b,
):
# print('Gani')
# print(a.val)
a.Fourier = True
a.idct_trans()
# print(a.val)
# iFa=a.idct()
# print(iFa.val)
a.Fourier = True
a.grad_transpose()
# print(a.val)
# print(a.val)
a.Fourier = False
a.dct_trans()
# print(a.val)
# b.idct()
# plt.show()
a.Fourier = False
adjoin = Chebyshev_element(name='adjoin',
N=N,
shape=(),
multype='scal')
adjoin.val = np.multiply(a.val, b.val)
# print('ab')
# print(adjoin.val)
adjoin.integrate()
# scalar = np.sum(adjoin.val)
return adjoin.integral # scalar # #
def collocation(a, b, mat):
a.dct()
a.idct()
a.val = np.multiply(mat.val, a.val)
a.dct()
a.idct()
original = Chebyshev_element(name='original',
N=N,
shape=(),
multype='scal')
original.val = np.multiply(a.val, b.val)
original.integrate()
return original.integral
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 coll(a, b):
# print('coll a dct')
# print(a.val)
a.dct()
# print(a.val)
a.div()
# print(a.val)
#a.idct()
both_side = Chebyshev_element(name='both_side',
N=N,
shape=(2, ),
multype='scal')
both_side.val = np.multiply(a.val, b.val)
# print('ab')
# print(both_side.val)
both_side.integrate()
#scalar = np.sum(both_side.val)
return both_side.integral # scalar #
def test_integral(self):
print('\nChecking integral')
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))
x0 = Chebyshev_element(name='x', N=N, shape=())
x0.set_nodal_coord()
integrant = lambda x: (x[0]**4) + (x[1]**3) if x.__len__(
) == 2 else (x[0]**4) + (x[1]**3) + np.cos(x[2])
x0.val = integrant(x0.coord)
x0.integrate()
self.assertTrue(np.isclose(x0.integral,
solution[dim - 1],
rtol=1e-05,
atol=1e-08,
equal_nan=False),
msg="Integral does not work correctly")
def GaNi(a, b):
b.dct()
b.grad()
# print(b.val)
b.idct()
both_side = Chebyshev_element(name='both_side',
N=N,
shape=(2, ),
multype='scal')
both_side.val = np.multiply(a.val, b.val)
# both_side.dct()
# print(both_side.val)
# both_side.idct()
# print('ab')
# print(both_side.val)
both_side.integrate()
#scalar = np.sum(both_side.val)
return both_side.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")