def full(self, **kwargs):
"""convert a tucker representation to a full tensor object
A = CORE (*1) Basis1 (*2) Basis2 (*3) Basis3 ..., with (*n) means n-mode product.
from paper "A MULTILINEAR SINGULAR VALUE DECOMPOSITION" by LIEVEN DE LATHAUWER , BART DE MOOR , AND JOOS VANDEWALLE
"""
# if core is a single scalar value, make it in a n-D array shape
if np.prod(self.core.shape) == 1:
self.core = np.reshape(self.core, tuple(self.r))
if self.Fourier:
res = self.fourier()
else:
res = self
val = res.core.copy()
for i in range(self.order):
val = nModeProduct(val, res.basis[i].T, i)
T = Tensor(name=res.name,
val=val,
order=0,
N=val.shape,
Fourier=False,
**kwargs)
if self.Fourier:
T.fourier()
return T
def full(self, **kwargs):
"return a full tensor object"
if self.order == 2:
if self.Fourier:
res = self.fourier(copy=True)
else:
res = self
# generate Tensor in real domain
val = np.einsum('i,ik,il->kl', res.core, res.basis[0],
res.basis[1])
kwargsT = dict(name=res.name,
val=val,
order=0,
N=val.shape,
Fourier=False,
fft_form='c')
kwargsT.update(kwargs)
T = Tensor(**kwargsT)
if self.Fourier:
T.fourier()
return T
else:
raise NotImplementedError()
def test_even(self):
print('\nChecking Tensors with even grid points...')
for dim, n, fft_form in itertools.product([2, 3], [4, 5], fft_forms):
msg = 'Tensors with: dim={}, n={}, fft_form={}'.format(
dim, n, fft_form)
N = dim * (n, )
M = tuple(2 * np.array(N))
u = Tensor(name='test',
shape=(),
N=N,
Fourier=False,
fft_form=fft_form)
u.randomize()
Fu = u.fourier(copy=True)
FuM = Fu.project(M)
uM = FuM.fourier()
if n % 2 == 0:
self.assertGreaterEqual(u.norm(), FuM.norm(), msg=msg)
self.assertGreaterEqual(u.norm(componentwise=True),
FuM.norm(componentwise=True),
msg=msg)
self.assertGreaterEqual(u.norm(), uM.norm(), msg=msg)
self.assertGreaterEqual(u.norm(componentwise=True),
uM.norm(componentwise=True),
msg=msg)
else:
self.assertAlmostEqual(u.norm(), FuM.norm(), msg=msg)
self.assertAlmostEqual(u.norm(componentwise=True),
FuM.norm(componentwise=True),
msg=msg)
self.assertAlmostEqual(u.norm(), uM.norm(), msg=msg)
self.assertAlmostEqual(u.norm(componentwise=True),
uM.norm(componentwise=True),
msg=msg)
self.assertAlmostEqual(0, u.mean() - FuM.mean(), msg=msg)
self.assertAlmostEqual(u.mean(), uM.mean(), msg=msg)
# testing that that interpolation on double grid have exactly the same values
slc = tuple(u.order * [
slice(None),
] + [slice(0, M[i], 2) for i in range(dim)])
self.assertAlmostEqual(0,
np.linalg.norm(u.val - uM.val[slc]),
msg=msg)
print('...ok')
def full(self, **kwargs):
"""
convert TT to a full tensor object
"""
if self.Fourier:
res = self.fourier()
else:
res = self
val = vector.full(res)
# Tensor with the default fft_form for full tensor
T = Tensor(name=res.name,
val=val,
order=0,
N=val.shape,
Fourier=False,
**kwargs)
if self.Fourier:
T.fourier()
return T
def test_even(self):
print('\nChecking Tensors with even grid points...')
for dim, n, fft_form in itertools.product([2,3], [4,5], fft_forms):
msg='Tensors with: dim={}, n={}, fft_form={}'.format(dim, n, fft_form)
N=dim*(n,)
M=tuple(2*np.array(N))
u=Tensor(name='test', shape=(), N=N, Fourier=False, fft_form=fft_form)
u.randomize()
Fu=u.fourier(copy=True)
FuM=Fu.project(M)
uM=FuM.fourier()
if n%2 == 0:
self.assertGreaterEqual(u.norm(), FuM.norm(), msg=msg)
self.assertGreaterEqual(u.norm(componentwise=True), FuM.norm(componentwise=True),
msg=msg)
self.assertGreaterEqual(u.norm(), uM.norm(), msg=msg)
self.assertGreaterEqual(u.norm(componentwise=True), uM.norm(componentwise=True),
msg=msg)
else:
self.assertAlmostEqual(u.norm(), FuM.norm(), msg=msg)
self.assertAlmostEqual(u.norm(componentwise=True), FuM.norm(componentwise=True),
msg=msg)
self.assertAlmostEqual(u.norm(), uM.norm(), msg=msg)
self.assertAlmostEqual(u.norm(componentwise=True), uM.norm(componentwise=True),
msg=msg)
self.assertAlmostEqual(0, u.mean()-FuM.mean(), msg=msg)
self.assertAlmostEqual(u.mean(), uM.mean(), msg=msg)
# testing that that interpolation on double grid have exactly the same values
slc=tuple(u.order*[slice(None),]+[slice(0,M[i],2) for i in range(dim)])
self.assertAlmostEqual(0, np.linalg.norm(u.val-uM.val[slc]), msg=msg)
print('...ok')
def test_Fourier(self):
print('\nChecking Fourier functions ...')
for opt in [0, 'c']:
a = SparseTensor(kind='cano', val=self.T2d, fft_form=opt)
T = Tensor(val=self.T2d,
order=0,
N=self.T2d.shape,
Fourier=False,
fft_form=opt)
self.assertAlmostEqual(
norm(a.fourier().full(fft_form=opt).val -
T.fourier(copy=True).val), 0)
self.assertEqual(
norm(a.fourier().fourier(real_output=True).full().val.imag), 0)
a = SparseTensor(kind='tucker', val=self.T3d, fft_form=opt)
T = Tensor(val=self.T3d,
order=0,
N=self.T3d.shape,
Fourier=False,
fft_form=opt)
self.assertAlmostEqual(
norm(a.fourier().full(fft_form=opt) - T.fourier(copy=True)), 0)
self.assertEqual(
norm(a.fourier().fourier(real_output=True).full().val.imag), 0)
a = SparseTensor(kind='tt', val=self.T3d, fft_form=opt)
T = Tensor(val=self.T3d,
order=0,
N=self.T3d.shape,
Fourier=False,
fft_form=opt)
self.assertAlmostEqual(
norm(a.fourier().full(fft_form=opt) -
T.fourier(copy=True).val), 0)
self.assertEqual(
norm(a.fourier().fourier(real_output=True).full().val.imag), 0)
# checking shifting fft_forms
sparse_opt = 'sr'
for full_opt in [0, 'c']:
a = SparseTensor(kind='cano', val=self.T2d, fft_form=sparse_opt)
T = Tensor(val=self.T2d,
order=0,
N=self.T2d.shape,
Fourier=False,
fft_form=full_opt)
self.assertAlmostEqual(
norm(a.fourier().full(fft_form=full_opt) -
T.fourier(copy=True)), 0)
self.assertAlmostEqual((a.fourier().set_fft_form(full_opt) -
a.set_fft_form(full_opt).fourier()).norm(),
0)
a = SparseTensor(kind='tucker', val=self.T3d, fft_form=sparse_opt)
T = Tensor(val=self.T3d,
order=0,
N=self.T3d.shape,
Fourier=False,
fft_form=full_opt)
self.assertAlmostEqual(
norm(a.fourier().full(fft_form=full_opt) -
T.fourier(copy=True)), 0)
self.assertAlmostEqual((a.fourier().set_fft_form(full_opt) -
a.set_fft_form(full_opt).fourier()).norm(),
0)
a = SparseTensor(kind='tt', val=self.T3d, fft_form=sparse_opt)
T = Tensor(val=self.T3d,
order=0,
N=self.T3d.shape,
Fourier=False,
fft_form=full_opt)
self.assertAlmostEqual(
norm(a.fourier().full(fft_form=full_opt) -
T.fourier(copy=True)), 0)
self.assertAlmostEqual((a.fourier().set_fft_form(full_opt) -
a.set_fft_form(full_opt).fourier()).norm(),
0)
print('...ok')