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 transposed_transform(a, b):
# a.Fourier = True
a.idct_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
def transform(a, b):
b.Fourier = True
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 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 test_gradient(self): ## TODO : NOT FINISHED
print('\nChecking gradient')
#solution = [0, 0.8, 8.3317]
for dim, Ni in itertools.product([2], [10]):
N = np.array(dim * [
Ni,
], dtype=np.int)
print(N)
fun_val = lambda x: ((x[0]**4) * x[1]**4) + (
(x[0]**3) * x[1]**4) + (
(x[0]**4) * x[1]**3) - x[1]**3 - x[0]**4
grad_fun_x = lambda x: ((4 * x[0]**3) * x[1]**4) + (
(3 * x[0]**2) * x[1]**4) + (
(4 * x[0]**3) * x[1]**3) - 4 * x[0]**3
grad_fun_y = lambda x: ((4 * x[0]**4) * x[1]**3) + (
(x[0]**3) * 4 * x[1]**3) + (
(x[0]**4) * 3 * x[1]**2) - 3 * x[1]**2
x0 = Chebyshev_element(name='x', N=N, shape=())
x0.set_nodal_coord()
x0.val = fun_val(x0.coord)
x0.dct_ortho()
x0.grad_ortho()
x0.idct_ortho()
# x0.plot_grad()
control = Chebyshev_element(name='control',
N=N,
shape=(2, ),
multype='scal')
control.set_nodal_coord()
control.val[0] = grad_fun_x(control.coord)
control.val[1] = grad_fun_y(control.coord)
# control.dct()
# control.plot_grad()
plt.show()
self.assertTrue(np.allclose(x0.val,
control.val,
rtol=1e-010,
atol=1e-08,
equal_nan=False),
msg="Gradient does not work correctly")
plt.show()
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 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_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")
def test_adjoin_operator(self):
print('\nChecking adjoin_operator form')
coll_BF = []
GaNi_BF = []
adjoin_GaNi_BF = []
adjoin_GaNi_T = []
adjoin_Ga_BF = []
testers = []
Ns = np.arange(2, 12, 1) # [10, 50, 100, 155, 200]
i = 0
for dim, Ni in itertools.product([2], Ns):
N = np.array(dim * [
Ni,
], dtype=np.int)
dN = tuple(np.array(N * 2 - 1, dtype=np.int))
print(N)
# (((x[0]**2)*x[1]**3) - x[0]**2*x[1] - x[1]**3 + x[1])#*np.cos(np.pi*x[0]/2)*np.cos(np.pi*x[1]/2)
u_val1 = lambda x: x[
0]**2 #-x[0]**3 # 4*x[0]**3 -x[0]#(x[0]**2 -x[1]**3 - 3)
u_val2 = lambda x: x[
0] * 0 # x[1]**2 -x[0]**3 # 3*x[1]**2 -x[0]**3
v_val = lambda x: (x[0]**3 - x[0]) * (x[0]**3 - x[
0]) #(x[0]**2 - 1)*(x[1]**3 - x[1]**1)+x[0]**3
exp_val = lambda x: 3 * x[0]
# (((x[0]**2)*x[1]**3) - x[0]**2*x[1] - x[1]**3 + x[1])#*np.cos(np.pi*x[0]/2)*np.cos(np.pi*x[1]*2)
u = Chebyshev_element(name='u', N=N, shape=(2, ), multype='scal')
u.set_nodal_coord()
u.val[0] = u_val1(u.coord)
u.val[1] = u_val2(u.coord)
v = Chebyshev_element(name='v', N=N, shape=(), multype='scal')
v.set_nodal_coord()
v.val = v_val(v.coord)
exp = Chebyshev_element(name='exp', N=N, shape=(), multype='scal')
exp.set_nodal_coord()
exp.val = exp_val(exp.coord)
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 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 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 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 # #
coll_BF.append(coll(copy.deepcopy(u), copy.deepcopy(v)))
print(' sum((FDFu,v) ={})'.format(coll_BF[i]))
testers.append(tester(copy.deepcopy(exp), copy.deepcopy(v)))
print(' sum((exp,v) ={})'.format(testers[i]))
# print(' sum((-FDFAFGFu,v).*W={})'.format(coll_BF[i]/(N[0]*N[1])))
GaNi_BF.append(GaNi(copy.deepcopy(u), copy.deepcopy(v)))
print(' sum((u,FGFv) ={})'.format(GaNi_BF[i]))
# print(' sum((WAFGFu,FGFv) ={})'.format(GaNi_BF[i]/(N[0]*N[1])))
adjoin_GaNi_BF.append(
adjoin_GaNi(copy.deepcopy(u), copy.deepcopy(v)))
print(' sum((FGtFiu,v) ={})'.format(adjoin_GaNi_BF[i]))
# print(' sum((FGtFWAFGFu,v) ={})'.format(adjoin_GaNi_BF[i]/(N[0]*N[1])))
adjoin_GaNi_T.append(
adjoin_GaNi_Tran(copy.deepcopy(u), copy.deepcopy(v)))
print(' sum((FitGtFtu,v) ={})'.format(adjoin_GaNi_T[i]))
i = i + 1
plt.plot(Ns, coll_BF, label="Collocation")
plt.plot(Ns, GaNi_BF, label=" GaNi_BF")
plt.plot(Ns, adjoin_GaNi_BF, label="adjoin_GaNi_BF")
plt.plot(Ns, adjoin_GaNi_T, label="adjoin_GaNi_T")
plt.legend()
plt.show()
def test_elliptic_BF(self):
print('\nChecking elliptic bilinear form')
coll_BF = []
GaNi_BF = []
adjoin_GaNi_BF = []
adjoin_Ga_BF = []
Ns = np.arange(2, 12, 1) #[10, 50, 100, 155, 200]
i = 0
for dim, Ni in itertools.product([2], Ns):
N = np.array(dim * [
Ni,
], dtype=np.int)
dN = tuple(np.array(N * 2 - 1, dtype=np.int))
# (((x[0]**2)*x[1]**3) - x[0]**2*x[1] - x[1]**3 + x[1])#*np.cos(np.pi*x[0]/2)*np.cos(np.pi*x[1]/2)
u_val = lambda x: (x[0]**2 - 1) * (x[1]**3 - x[1]**1)
v_val = lambda x: (x[0]**2 - 1) * (
x[1]**3 - x[1]**1
) # (((x[0]**2)*x[1]**3) - x[0]**2*x[1] - x[1]**3 + x[1])#*np.cos(np.pi*x[0]/2)*np.cos(np.pi*x[1]*2)
u = Chebyshev_element(name='u', N=N, shape=(), multype='scal')
u.set_nodal_coord()
u.val = u_val(u.coord)
v = Chebyshev_element(name='v', N=N, shape=(), multype='scal')
v.set_nodal_coord()
v.val = v_val(v.coord)
material = Chebyshev_element(name='A_mat',
N=N,
shape=2 * [dim],
multype='21')
material.set_nodal_coord()
material.val = mat_fun(material.coord, kind='constant')
materialDG = Chebyshev_element(name='A_mat',
N=dN,
shape=2 * [dim],
multype='21')
materialDG.set_nodal_coord()
materialDG.val = mat_fun(materialDG.coord, kind='constant')
#materialDG.mul_by_cc_weights()
def collocation(a, b, mat):
a.dct()
a.grad()
a.idct()
a.val = (mat * a).val
a.dct()
a.div()
original = Chebyshev_element(name='original',
N=N,
shape=(),
multype='scal')
original.val = np.multiply(-a.val, b.val)
original.integrate()
return original.integral
def GaNi(a, b, mat):
a.dct()
a.grad()
a.idct()
a.val = (mat * a).val
a.mul_by_cc_weights()
b.dct()
b.grad()
b.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 scalar # both_side.integral
def adjoin_GaNi(a, b, mat):
a.dct()
a.grad()
a.idct()
a.val = (mat * a).val
a.mul_by_cc_weights()
a.idct_trans()
a.grad_transpose()
a.dct_trans()
adjoin = Chebyshev_element(name='adjoin',
N=N,
shape=(),
multype='scal')
adjoin.val = np.multiply(a.val, b.val)
scalar = np.sum(adjoin.val)
return scalar
def adjoin_Ga(a, b, mat):
a.dct()
a.grad()
a.enlarge()
a.idct()
mat.mul_by_cc_weights()
a.val = (mat * a).val
#a.mul_by_cc_weights()
a.idct_trans()
a.shrink()
a.grad_transpose()
a.dct_trans()
adjoin = Chebyshev_element(name='adjoin',
N=N,
shape=(),
multype='scal')
adjoin.val = np.multiply(a.val, b.val)
#adjoin.integrate()
scalar = np.sum(adjoin.val)
return scalar
print("solutions for N={}".format(N))
coll_BF.append(
collocation(copy.deepcopy(u), copy.deepcopy(v),
copy.deepcopy(material)))
print(' sum((-FDFAFGFu,v).*W={})'.format(coll_BF[i]))
GaNi_BF.append(
GaNi(copy.deepcopy(u), copy.deepcopy(v),
copy.deepcopy(material)))
print(' sum((WAFGFu,FGFv) ={})'.format(GaNi_BF[i]))
adjoin_GaNi_BF.append(
adjoin_GaNi(copy.deepcopy(u), copy.deepcopy(v),
copy.deepcopy(material)))
print(' sum((FGtFWAFGFu,v) ={})'.format(adjoin_GaNi_BF[i]))
adjoin_Ga_BF.append(
adjoin_Ga(copy.deepcopy(u), copy.deepcopy(v),
copy.deepcopy(materialDG)))
print('sum((FGtPFWAFPGFu,v) ={})'.format(adjoin_Ga_BF[i]))
i = i + 1
plt.plot(Ns, coll_BF, label="Collocation")
plt.plot(Ns, GaNi_BF, label=" GaNi_BF")
plt.plot(Ns, adjoin_GaNi_BF, label="adjoin_GaNi_BF")
plt.plot(Ns, adjoin_Ga_BF, label="adjoin_Ga_BF")
plt.legend()
plt.show()
def test_weighted_projection_BF(self):
print('\nChecking weighted projection')
coll_BF = []
GaNi_BF = []
adjoin_GaNi_BF = []
adjoin_Ga_BF = []
Ns = np.arange(4, 10, 1) #[6,10, 50, 100, 155, 200]#
i = 0
for dim, Ni in itertools.product([2], Ns):
N = np.array(dim * [
Ni,
], dtype=np.int)
# u_val = lambda x: (((x[0]**2)*x[1]**3) - x[0]**2*x[1] - x[1]**3 + x[1])*np.cos(np.pi*x[0]/2)*np.cos(np.pi*x[1]/2)
u_val = lambda x: (x[0]**2 - 1) * (
x[1]**3 - x[1]**1
) #*np.cos(4*np.pi*x[0]/2)*np.cos(np.pi*x[1]*2)#*(-x[2]**2+1)
# v_val = lambda x: (((x[0]**2)*x[1]**3) - x[0]**2*x[1] - x[1]**3 + x[1])*np.cos(np.pi*x[0]/2)*np.cos(np.pi*x[1]*2)
v_val = lambda x: (x[0]**2 - 1) * (
x[1]**3 - x[1]**1
) #*np.cos(4*np.pi*x[0]/2)*np.cos(np.pi*x[1]*2)#*(-x[2]**2 + 1)
u = Chebyshev_element(name='u', N=N, shape=(), multype='scal')
u.set_nodal_coord()
u.val = u_val(u.coord)
material = Chebyshev_element(name='A_mat',
N=N,
shape=(),
multype='21')
material.set_nodal_coord()
material.val = load(material.coord,
kind='constant') # (x[0]**4 ) + (x[1]**3)
v = Chebyshev_element(name='v', N=N, shape=(), multype='scal')
v.set_nodal_coord()
v.val = v_val(v.coord)
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 GaNi(a, b, mat):
a.dct()
a.idct()
a.val = np.multiply(mat.val, a.val)
a.mul_by_cc_weights()
b.dct()
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.integrate()
scalar = np.sum(both_side.val)
return scalar #both_side.integral
def adjoin_GaNi(a, b, mat):
a.dct()
a.idct()
a.val = np.multiply(mat.val, a.val)
a.mul_by_cc_weights()
a.dct()
a.idct()
adjoin = Chebyshev_element(name='adjoin',
N=N,
shape=(),
multype='scal')
adjoin.val = np.multiply(a.val, b.val)
scalar = np.sum(adjoin.val)
return scalar
def adjoin_Ga(a, b, mat):
mat.dct()
mat.enlarge()
mat.idct()
a.dct()
a.enlarge()
a.idct()
a.val = (2**dim) * np.multiply(mat.val, a.val)
a.mul_by_cc_weights()
a.dct()
a.shrink()
a.idct()
adjoin = Chebyshev_element(name='adjoin',
N=N,
shape=(),
multype='scal')
adjoin.val = np.multiply(a.val, b.val)
scalar = np.sum(adjoin.val)
return scalar
print("solutions for N={}".format(N))
coll_BF.append(
collocation(copy.deepcopy(u), copy.deepcopy(v),
copy.deepcopy(material)))
print(' sum((-FFAFFu,v).*W={})'.format(coll_BF[i]))
GaNi_BF.append(
GaNi(copy.deepcopy(u), copy.deepcopy(v),
copy.deepcopy(material)))
print(' sum((WAFFu,FFv) ={})'.format(GaNi_BF[i]))
adjoin_GaNi_BF.append(
adjoin_GaNi(copy.deepcopy(u), copy.deepcopy(v),
copy.deepcopy(material)))
print(' sum((FFWAFFu,v) ={})'.format(adjoin_GaNi_BF[i]))
adjoin_Ga_BF.append(
adjoin_Ga(copy.deepcopy(u), copy.deepcopy(v),
copy.deepcopy(material)))
print(' sum((FPFWAFPFu,v) ={})'.format(adjoin_Ga_BF[i]))
i = i + 1