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 test_trans_dct(self):
print('\nChecking transposed DCT')
Ns = np.arange(4, 15, 1)
for dim, Ni in itertools.product([2], Ns):
N = np.array(dim * [
Ni,
], dtype=np.int)
print(N)
u = Chebyshev_element(name='u', N=N, shape=(), multype='scal')
u.set_nodal_coord()
u.val = np.random.rand(N[0], N[1]) * 1
u.Fourier = True
u.idct()
v = Chebyshev_element(name='u', N=N, shape=(), multype='scal')
v.set_nodal_coord()
v.val = np.random.rand(N[0], N[1]) * 1
v.Fourier = True
v.idct()
def transform(a, b):
b.dct()
b.idct()
scal = Chebyshev_element(name='scal',
N=N,
shape=(),
multype='scal')
scal.set_nodal_coord()
scal.val = np.multiply(a.val, b.val)
return scal.val
def transposed_transform(a, b):
# a.Fourier=True
a.idct_trans()
a.dct_trans()
scal2 = Chebyshev_element(name='scal2',
N=N,
shape=(),
multype='scal')
scal2.set_nodal_coord()
scal2.val = np.multiply(a.val, b.val)
return scal2.val
forward = transform(copy.deepcopy(u), copy.deepcopy(v))
transposed = transposed_transform(copy.deepcopy(u),
copy.deepcopy(v))
# print(' sum((u,Fv) ={})'.format(np.sum(forward)))
# print(' sum((Ftu,v) ={})'.format(np.sum(transposed)))
# print(' dif sum((Ftu,v)-(u,Fv)) ={})'.format(np.sum(transposed-forward)))
self.assertTrue(np.isclose(np.sum(forward),
np.sum(transposed),
rtol=1e-10,
atol=1e-08,
equal_nan=False),
msg="Transposed DCT does not work correctly")
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))
def test_grad_transpose(self):
print('\nChecking adjoin to gradient')
Ns = np.arange(4, 25, 1)
for dim, Ni in itertools.product([2], Ns):
N = np.array(dim * [
Ni,
], dtype=np.int)
print(N)
# u_val = lambda x: (x[0]**0 )*(x[1]**0 )
u = Chebyshev_element(name='u', N=N, shape=(2, ), multype='scal')
u.set_nodal_coord()
u.val[0] = np.random.rand(N[0], N[1]) * 1
u.val[1] = np.random.rand(N[0], N[1]) * 1
u.Fourier = True
u.idct()
# u.Fourier = True
v = Chebyshev_element(name='u', N=N, shape=(), multype='scal')
v.set_nodal_coord()
v.val = np.random.rand(N[0], N[1]) * 1 #u_val(u.coord)
v.Fourier = True
v.idct()
#v.Fourier = True
# u.grad_transpose()
# print(u.val)
def grad_forward(a, b):
b.dct()
b.grad()
b.idct()
scal = Chebyshev_element(name='scal',
N=N,
shape=(),
multype='scal')
scal.set_nodal_coord()
scal.val = np.multiply(a.val, b.val)
return scal.val
def transposed_grad(a, b):
# a.Fourier = True
a.idct_trans()
# a.Fourier = True
a.grad_transpose()
# a.Fourier = False
a.dct_trans()
scal2 = Chebyshev_element(name='scal2',
N=N,
shape=(),
multype='scal')
scal2.set_nodal_coord()
scal2.val = np.multiply(a.val, b.val)
return scal2.val
forward = grad_forward(copy.deepcopy(u), copy.deepcopy(v))
#print(forward)
transposed = transposed_grad(copy.deepcopy(u), copy.deepcopy(v))
#print(transposed)
#print(' sum((u,iFGFv) ={})'.format(np.sum(forward)))
#print(' sum((FtGtiFtu,v) ={})'.format(np.sum(transposed)))
# print(' dif sum((Ftu,v)-(u,Fv)) ={})'.format(np.sum(transposed)-np.sum(forward)))
self.assertTrue(np.isclose(np.sum(forward),
np.sum(transposed),
rtol=1e-10,
atol=1e-08,
equal_nan=False),
msg="Transposed DCT does not work correctly")