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 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")