def test_tucker_cp_tensor():
a = torch.rand(10, 5, 5, 5, 5)
b = tn.Tensor(a, ranks_tucker=3, ranks_cp=4, batch=True)
for i in range(len(a)):
c = tn.Tensor(a[i], ranks_tucker=3, ranks_cp=4, batch=False)
assert torch.norm(c.torch() - b.torch()[i]) < 1e1
def test_tucker_tensor():
a = torch.rand(10, 5, 5, 5, 5)
b = tn.Tensor(a, ranks_tucker=3, batch=True)
for i in range(len(a)):
c = tn.Tensor(a[i], ranks_tucker=3, batch=False)
for j, core in enumerate(c.cores):
assert torch.allclose(core, b.cores[j][i, ...])
assert torch.allclose(c.torch(), b.torch()[i])
def test_cp_tensor():
a = torch.rand(10, 5, 5, 5, 5)
b = tn.Tensor(a, ranks_cp=3, batch=True)
for i in range(len(a)):
c = tn.Tensor(a[i], ranks_cp=3, batch=False)
for j, core in enumerate(c.cores):
assert torch.norm(core - b.cores[j][i, ...]) < 1e1
assert torch.norm(c.torch() - b.torch()[i]) < 1e1
def dgsm(t, bounds, marginals):
"""
Compute the derivative-based global sensitivity measure \nu from [1], defined for each i-th variable as:
$\nu_i := \int_{\Omega} \left(\frac{\partial f}{\partial x_i}\right) \, d\pmb{x}$
[1] "Derivative-Based Global Sensitivity Measures", by Kucherenko and Iooss (2016)
:param t: input tensor
:param bounds: a pair (or list of pairs) of reals, or None. The bounds for each variable
:param marginals: a list of vectors. If None (default), uniform marginals will be used
:return: a vector of size N
"""
if marginals is None:
marginals = [torch.ones(sh)/sh for sh in t.shape]
assert all([len(marginals[n]) == t.shape[n] for n in range(t.dim())])
cores = []
for n in range(t.dim()):
# marg = (marginals[n][:-1] + marginals[n][1:]) / 2
marg = marginals[n]
marg /= marg.sum()
# marg = torch.cat([marg, torch.zeros(1)])
cores.append(marg[None, :, None])
pdf = tn.Tensor(cores)
grad = tn.gradient(t, dim='all', bounds=bounds)
result = torch.zeros(t.dim())
for n in range(t.dim()):
result[n] = tn.dot(grad[n]*pdf, grad[n])
return result
def gaussian(shape, sigma_factor=0.2):
"""
Create a multivariate Gaussian that is axis-aligned (i.e. with diagonal covariance matrix).
:param shape: list of ints
:param sigma_factor: a real (or list of reals) encoding the ratio sigma / shape. Default is 0.2, i.e. one fifth along each dimension
:return: a :class:`Tensor` that sums to 1
"""
if hasattr(shape[0], '__len__'):
shape = shape[0]
N = len(shape)
if not hasattr(sigma_factor, '__len__'):
sigma_factor = [sigma_factor]*N
cores = [torch.ones(1, 1, 1) for n in range(N)]
Us = []
for n in range(N):
sigma = sigma_factor[n] * shape[n]
if shape[n] == 1:
x = torch.Tensor([0])
else:
x = torch.linspace(-shape[n] / 2, shape[n] / 2, shape[n])
U = torch.exp(-x**2 / (2*sigma**2))
U = U[:, None] / torch.sum(U)
Us.append(U)
return tn.Tensor(cores, Us)
def transpose(t):
"""
Inverts the dimension order of a tensor, e.g. :math:`I_1 \\times I_2 \\times I_3` becomes :math:`I_3 \\times I_2 \\times I_1`.
:param t: input tensor
:return: another :class:`Tensor`, indexed by dimensions in inverse order
"""
cores = []
Us = []
idxs = []
for n in range(t.dim() - 1, -1, -1):
if t.cores[n].dim() == 3:
cores.append(t.cores[n].permute(2, 1, 0))
else:
cores.append(t.cores[n])
if t.Us[n] is None:
Us.append(None)
else:
Us.append(t.Us[n].clone())
try:
idxs.append(t.idxs[n].clone())
except Exception:
idxs.append(None)
return tn.Tensor(cores, Us, idxs)
def meshgrid(*axes, batch=False):
"""
See NumPy's or PyTorch's `meshgrid()`.
:param axes: a list of N ints or torch vectors
:return: a list of N :class:`Tensor`, of N dimensions each
"""
device = None
if not hasattr(axes, '__len__'):
axes = [axes]
if hasattr(axes[0], '__len__'):
axes = axes[0]
if hasattr(axes[0], 'device'):
device = axes[0].device
axes = list(axes)
N = len(axes)
for n in range(N):
if not hasattr(axes[n], '__len__'):
axes[n] = torch.arange(axes[n], dtype=torch.get_default_dtype())
tensors = []
for n in range(N):
cores = [torch.ones(1, len(ax), 1).to(device) for ax in axes]
if isinstance(axes[n], torch.Tensor):
cores[n] = axes[n].type(torch.get_default_dtype())
else:
cores[n] = torch.tensor(axes[n].type(torch.get_default_dtype()))
cores[n] = cores[n][None, :, None].to(device)
tensors.append(tn.Tensor(cores, device=device, batch=batch))
return tensors
def mask(t, mask):
"""
Masks a tensor. Basically an element-wise product, but this function makes sure slices are matched according to their "meaning" (as annotated by the tensor's `idx` field, if available)
:param t: input :class:`Tensor`
:param mask: a mask :class:`Tensor`
:return: masked :class:`Tensor`
"""
device = t.cores[0].device
if not hasattr(t, 'idxs'):
idxs = [np.arange(sh) for sh in t.shape]
else:
idxs = t.idxs
cores = []
Us = []
for n in range(t.dim()):
idx = np.array(idxs[n])
idx[idx >= mask.shape[n]] = mask.shape[n] - 1 # Clamp
if mask.Us[n] is None:
cores.append(mask.cores[n][..., idx, :].to(device))
Us.append(None)
else:
cores.append(mask.cores[n].to(device))
Us.append(mask.Us[n][idx, :])
mask = tn.Tensor(cores, Us, device=device)
return t * mask
def meshgrid(*axes):
"""
See NumPy's or PyTorch's `meshgrid()`.
:param axes: a list of N ints or torch vectors
:return: a list of N :class:`Tensor`, of N dimensions each
"""
if not hasattr(axes, '__len__'):
axes = [axes]
if hasattr(axes[0], '__len__'):
axes = axes[0]
axes = list(axes)
N = len(axes)
for n in range(N):
if not hasattr(axes[n], '__len__'):
axes[n] = torch.arange(axes[n], dtype=torch.get_default_dtype())
tensors = []
for n in range(N):
cores = [torch.ones(1, len(ax), 1) for ax in axes]
cores[n] = torch.Tensor(axes[n].to(torch.get_default_dtype()))[None, :,
None]
tensors.append(tn.Tensor(cores))
return tensors
def partialset(t, order=1, mask=None, bounds=None):
"""
Given a tensor, compute another one that contains all partial derivatives of certain order(s) and according to some optional mask.
:Examples:
>>> t = tn.rand([10, 10, 10]) # A 3D tensor
>>> x, y, z = tn.symbols(3)
>>> partialset(t, 1, x) # x
>>> partialset(t, 2, x) # xx, xy, xz
>>> partialset(t, 2, tn.only(y | z)) # yy, yz, zz
:param t: a :class:`Tensor`
:param order: an int or list of ints. Default is 1
:param mask: an optional mask to select only a subset of partials
:param bounds: a list of pairs [lower bound, upper bound] specifying parameter ranges (used to compute derivative steps). If None (default), all steps will be 1
:return: a :class:`Tensor`
"""
if bounds is None:
bounds = [[0, sh - 1] for sh in t.shape]
if not hasattr(order, '__len__'):
order = [order]
max_order = max(order)
def diff(core, n):
if core.dim() == 3:
pad = torch.zeros(core.shape[0], 1, core.shape[2])
else:
pad = torch.zeros(1, core.shape[1])
if core.shape[1] == 1:
return pad
step = (bounds[n][1] - bounds[n][0]) / (core.shape[-2] - 1)
return torch.cat(((core[..., 1:, :] - core[..., :-1, :]) / step, pad),
dim=-2)
cores = []
idxs = []
for n in range(t.dim()):
if t.Us[n] is None:
stack = [t.cores[n]]
else:
stack = [torch.einsum('ijk,aj->iak', (t.cores[n], t.Us[n]))]
idx = torch.zeros([t.shape[n]])
for o in range(1, max_order + 1):
stack.append(diff(stack[-1], n))
idx = torch.cat((idx, torch.ones(stack[-1].shape[-2]) * o))
if o == max_order:
break
cores.append(torch.cat(stack, dim=-2))
idxs.append(idx)
d = tn.Tensor(cores, idxs=idxs)
wm = tn.automata.weight_mask(t.dim(), order, nsymbols=max_order + 1)
if mask is not None:
wm = tn.mask(wm, mask)
result = tn.mask(d, wm)
result.idxs = idxs
return result
def anova_decomposition(t, marginals=None):
"""
Compute an extended tensor that contains all terms of the ANOVA decomposition for a given tensor.
Reference: R. Ballester-Ripoll, E. G. Paredes, and R. Pajarola: `"Sobol Tensor Trains for Global Sensitivity Analysis" (2017) <https://www.sciencedirect.com/science/article/pii/S0951832018303132?dgcid=rss_sd_all>`_
:param t: ND input tensor
:param marginals: list of N vectors, each containing the PMF for each variable (use None for uniform distributions)
:return: a :class:`Tensor`
"""
marginals = copy.deepcopy(marginals)
if marginals is None:
marginals = [None] * t.dim()
for n in range(t.dim()):
if marginals[n] is None:
marginals[n] = torch.ones([t.shape[n]]) / float(t.shape[n])
cores = [c.clone() for c in t.cores]
Us = []
idxs = []
for n in range(t.dim()):
if t.Us[n] is None:
U = torch.eye(t.shape[n])
else:
U = t.Us[n]
expected = torch.sum(U * (marginals[n][:, None] / torch.sum(marginals[n])), dim=0, keepdim=True)
Us.append(torch.cat((expected, U-expected), dim=0))
idxs.append([0] + [1]*t.shape[n])
return tn.Tensor(cores, Us, idxs=idxs)
def weight_one_hot(N, r=None, nsymbols=2):
"""
Given a string with :math:`k` 1's, it produces a vector that represents :math:`k` in `one hot encoding <https://en.wikipedia.org/wiki/One-hot>`_
:param N: number of dimensions
:param r:
:param nsymbols:
:return: a vector of N zeros, except its :math:`k`-th element which is a 1
"""
if not hasattr(nsymbols, '__len__'):
nsymbols = [nsymbols] * N
assert len(nsymbols) == N
if r is None:
r = N + 1
cores = []
for n in range(N):
core = torch.zeros([r, nsymbols[n], r])
core[:, 0, :] = torch.eye(r)
for s in range(1, nsymbols[n]):
core[:, s, s:] = torch.eye(r)[:, :-s]
cores.append(core)
cores[0] = cores[0][0:1, :, :]
return tn.Tensor(cores)
def decompress_tucker_factors(self, dim='all', _clone=True):
"""
Decompresses this tensor along the Tucker factors only.
:param dim: int, list, or 'all' (default)
:return: a :class:`Tensor` in CP/TT format, without Tucker factors
"""
if dim == 'all':
dim = range(self.dim())
if not hasattr(dim, '__len__'):
dim = [dim]*self.dim()
cores = []
Us = []
for n in range(self.dim()):
if n in dim and self.Us[n] is not None:
if self.cores[n].dim() == 2:
cores.append(torch.einsum('jk,aj->ak', (self.cores[n], self.Us[n])))
else:
cores.append(torch.einsum('ijk,aj->iak', (self.cores[n], self.Us[n])))
Us.append(None)
else:
if _clone:
cores.append(self.cores[n].clone())
if self.Us[n] is not None:
Us.append(self.Us[n].clone())
else:
Us.append(None)
else:
cores.append(self.cores[n])
Us.append(self.Us[n])
return tn.Tensor(cores, Us, idxs=self.idxs)
def test_from_ndarray():
for i in range(100):
gt = np.random.rand(*np.random.randint(1, 8, np.random.randint(1, 6)))
t = tn.Tensor(gt)
reco = t.numpy()
assert np.linalg.norm(gt - reco) / np.linalg.norm(gt) < +1e-7
def test_accepted_inputs():
for i in range(10):
gt = tn.Tensor(torch.randint(0, 2, (1, 2, 3, 4)))
idx = tn.automata.accepted_inputs(gt)
assert len(idx) == round(tn.sum(gt).item())
assert torch.norm(gt[idx].torch() - 1).item() <= 1e-7
def torch(self):
"""
Decompress into a PyTorch 2D tensor
:return: a 2D torch.tensor
"""
cores = [
c.reshape(-1, c.shape[1], self.input_dims[i] *
self.output_dims[i], c.shape[-1])
if self.batch else c.reshape(c.shape[0], -1, c.shape[-1])
for i, c in enumerate(self.cores)
]
tensor = tn.Tensor(cores, batch=self.batch).torch()
rows = torch.prod(self.input_dims)
cols = torch.prod(self.output_dims)
shape: List[int] = torch.tensor(
list(zip(self.input_dims, self.output_dims))).flatten().tolist()
if self.batch:
tensor = tensor.reshape([-1] + shape)
dims = list(range(1, 2 * self.d + 1))
tensor = tensor.permute([0] + dims[1::2] + dims[2::2])
return tensor.reshape(-1, rows, cols)
else:
tensor = tensor.reshape(shape)
dims = list(range(2 * self.d))
tensor = tensor.permute(dims[0::2] + dims[1::2])
return tensor.reshape(rows, cols)
def __init__(self, t, eps=1e-9, verbose=False):
# if isinstance(t, tt.core.vector.vector):
# t = tn.Tensor([torch.Tensor(c) for c in tt.vector.to_list(t)])
###########################################
# Precompute all 4 types of Sobol indices #
###########################################
t = t
N = t.dim()
tsq = t.decompress_tucker_factors()
for n in range(N):
tsq.cores[n] = torch.cat(
[torch.mean(tsq.cores[n], dim=1, keepdim=True), tsq.cores[n]],
dim=1)
tsq = tn.cross(tensors=[tsq],
function=lambda x: x**2,
eps=eps,
verbose=verbose)
st_cores = []
for n in range(N):
st_cores.append(
torch.cat([
tsq.cores[n][:, :1, :],
torch.mean(tsq.cores[n][:, 1:, :], dim=1, keepdim=True) -
tsq.cores[n][:, :1, :]
],
dim=1))
st = tn.Tensor(st_cores)
var = tn.sum(st) - st[(0, ) * N]
self.st = tn.round_tt(st / var, eps=eps)
self.st -= tn.none(N) * self.st[(0, ) *
N] # Set element 0, ..., 0 to zero
self.sst = tn.Tensor([
torch.cat([c[:, :1, :] + c[:, 1:2, :], c[:, 1:2, :]], dim=1)
for c in self.st.cores
])
self.cst = tn.Tensor([
torch.cat([c[:, :1, :], c[:, :1, :] + c[:, 1:2, :]], dim=1)
for c in self.st.cores
])
self.tst = 1 - tn.Tensor([
torch.cat([c[:, :1, :] + c[:, 1:2, :], c[:, :1, :]], dim=1)
for c in self.st.cores
])
def __setitem__(self, key, value): # TODO not fully working yet
key = self._process_key(key)
scalar = False
if isinstance(value, np.ndarray):
value = tn.Tensor(torch.Tensor(value))
elif isinstance(value, torch.Tensor):
if value.dim() == 0:
value = value.item()
scalar = True
# value = value*torch.ones(self.shape)
else:
value = tn.Tensor(value)
elif isinstance(value, tn.Tensor):
pass
else: # It's a scalar
scalar = True
subtract_cores = []
add_cores = []
for i in range(len(key)):
if not isinstance(key[i], slice) and not hasattr(key[i], '__len__'):
key[i] = slice(key[i], key[i]+1)
chunk = self.cores[i][..., key[i], :]
subtract_core = torch.zeros_like(self.cores[i])
subtract_core[..., key[i], :] += chunk
subtract_cores.append(subtract_core)
if scalar:
if self.cores[i].dim() == 3:
add_core = torch.zeros(1, self.shape[i], 1)
else:
add_core = torch.zeros(self.shape[i], 1)
add_core[..., key[i], :] += 1
if i == 0:
add_core *= value
else:
if chunk.shape[1] != value.shape[i]:
raise ValueError('{}-th dimension mismatch in tensor assignment: {} (lhs) != {} (rhs)'.format(i, chunk.shape[1], value.shape[i]))
if self.cores[i].dim() == 3:
add_core = torch.zeros(value.cores[i].shape[0], self.shape[i], value.cores[i].shape[2])
else:
add_core = torch.zeros(self.shape[i], value.cores[i].shape[1])
add_core[..., key[i], :] += value.cores[i]
add_cores.append(add_core)
# print(tn.Tensor(subtract_cores), tn.Tensor(add_cores))
result = self - tn.Tensor(subtract_cores) + tn.Tensor(add_cores)
self.__init__(result.cores, result.Us, self.idxs)
def clone(self):
"""
Creates a copy of this tensor (calls PyTorch's `clone()` on all internal tensor network nodes)
:return: another compressed tensor
"""
cores = [self.cores[n].clone()for n in range(self.dim())]
Us = []
for n in range(self.dim()):
if self.Us[n] is None:
Us.append(None)
else:
Us.append(self.Us[n].clone())
if hasattr(self, 'idxs'):
return tn.Tensor(cores, Us=Us, idxs=self.idxs)
return tn.Tensor(cores, Us=Us)
def test_squeeze():
for i in range(100):
x = np.random.randint(1, 3, np.random.randint(2, 10))
t = tn.Tensor(x)
x = np.squeeze(x)
t = tn.squeeze(t)
assert np.array_equal(x.shape, t.shape)
def tucker_core(self):
"""
If this is a Tucker-like tensor, returns its Tucker core as an explicit PyTorch tensor.
If this tensor does not have Tucker factors, then it returns the full decompressed tensor.
:return: a PyTorch tensor
"""
return tn.Tensor(self.cores).torch()
def true(N):
"""
Create a formula (N-dimensional tensor) that is always true.
:param N: an integer
:return: a :math:`2^N` :class:`Tensor`
"""
return tn.Tensor([torch.ones([1, 2, 1]) for n in range(N)])
def logspace(*args, **kwargs):
"""
Creates a 1D :class:`Tensor` with logarithmically spaced values (see PyTorch's `logspace`).
:param args:
:param kwargs:
:return: a 1D :class:`Tensor`
"""
return tn.Tensor([torch.logspace(*args, **kwargs)[None, :, None]])
def arange(*args, **kwargs):
"""
Creates a 1D :class:`Tensor` (see PyTorch's `arange`).
:param args:
:param kwargs:
:return: a 1D :class:`Tensor`
"""
return tn.Tensor([torch.arange(*args, dtype=torch.get_default_dtype(), **kwargs)[None, :, None]])
def _create(function, *shape, ranks_tt=None, ranks_cp=None, ranks_tucker=None, requires_grad=False, device=None):
if hasattr(shape[0], '__len__'):
shape = shape[0]
N = len(shape)
if not hasattr(ranks_tucker, "__len__"):
ranks_tucker = [ranks_tucker for n in range(len(shape))]
corespatials = []
for n in range(len(shape)):
if ranks_tucker[n] is None:
corespatials.append(shape[n])
else:
corespatials.append(ranks_tucker[n])
if ranks_tt is None and ranks_cp is None:
if ranks_tucker is None:
raise ValueError('Specify at least one of: ranks_tt ranks_cp, ranks_tucker')
# We imitate a Tucker decomposition: we set full TT-ranks
datashape = [corespatials[0], np.prod(corespatials) // corespatials[0]]
ranks_tt = []
for n in range(1, N):
ranks_tt.append(min(datashape))
datashape = [datashape[0] * corespatials[n], datashape[1] // corespatials[n]]
if not hasattr(ranks_tt, "__len__"):
ranks_tt = [ranks_tt]*(N-1)
ranks_tt = [None] + list(ranks_tt) + [None]
if not hasattr(ranks_cp, '__len__'):
ranks_cp = [ranks_cp]*N
coreranks = [r for r in ranks_tt]
for n in range(N):
if ranks_cp[n] is not None:
if ranks_tt[n] is not None or ranks_tt[n+1] is not None:
raise ValueError('The ranks_tt and ranks_cp provided are incompatible')
coreranks[n] = ranks_cp[n]
coreranks[n+1] = ranks_cp[n]
assert len(coreranks) == N+1
if coreranks[0] is None:
coreranks[0] = 1
if coreranks[-1] is None:
coreranks[-1] = 1
if coreranks.count(None) > 0:
raise ValueError('One or more TT/CP ranks were not specified')
assert len(ranks_tucker) == N
cores = []
Us = []
for n in range(len(shape)):
if ranks_tucker[n] is None:
Us.append(None)
else:
Us.append(function([shape[n], ranks_tucker[n]], requires_grad=requires_grad, device=device))
if ranks_cp[n] is None:
cores.append(function([coreranks[n], corespatials[n], coreranks[n+1]], requires_grad=requires_grad, device=device))
else:
cores.append(function([corespatials[n], ranks_cp[n]], requires_grad=requires_grad, device=device))
return tn.Tensor(cores, Us=Us)
def __init__(self, lstm_cell_layer, ranks_tt=70):
"""LSTMCell class wrapper with tensor-trained weights."""
super(TTLSTMCell, self).__init__()
self.input_size = lstm_cell_layer.input_size
self.hidden_size = lstm_cell_layer.hidden_size
self.bias = lstm_cell_layer.bias
self.weight_ih = ParameterList([
Parameter(core) \
for core in tn.Tensor(lstm_cell_layer.weight_ih.data.T,
ranks_tt=ranks_tt).cores
])
self.weight_hh = ParameterList([
Parameter(core) \
for core in tn.Tensor(lstm_cell_layer.weight_hh.data.T,
ranks_tt=ranks_tt).cores
])
if self.bias:
self.bias_ih = Parameter(lstm_cell_layer.bias_ih.data)
self.bias_hh = Parameter(lstm_cell_layer.bias_hh.data)
def __init__(self, lstm_layer, ranks_tt=70):
"""LSTM class wrapper with tensor-trained weights."""
super(TTLSTM, self).__init__()
self.input_size = lstm_layer.input_size
self.hidden_size = lstm_layer.hidden_size
self.num_layers = lstm_layer.num_layers
self.bias = lstm_layer.bias
self.bidirectional = lstm_layer.bidirectional
self.weight_ih = ParameterList([
Parameter(core) \
for core in tn.Tensor(lstm_layer.weight_ih_l0.data.T,
ranks_tt=ranks_tt).cores
])
self.weight_hh = ParameterList([
Parameter(core) \
for core in tn.Tensor(lstm_layer.weight_hh_l0.data.T,
ranks_tt=ranks_tt).cores
])
if self.bias:
self.bias_ih = Parameter(lstm_layer.bias_ih_l0.data)
self.bias_hh = Parameter(lstm_layer.bias_hh_l0.data)
if self.bidirectional:
self.weight_ih_reverse = ParameterList([
Parameter(core) \
for core in tn.Tensor(lstm_layer.weight_ih_l0_reverse.data.T,
ranks_tt=ranks_tt).cores
])
self.weight_hh_reverse = ParameterList([
Parameter(core) \
for core in tn.Tensor(lstm_layer.weight_hh_l0_reverse.data.T,
ranks_tt=ranks_tt).cores
])
if self.bias:
self.bias_ih_reverse = Parameter(
lstm_layer.bias_ih_l0_reverse.data)
self.bias_hh_reverse = Parameter(
lstm_layer.bias_hh_l0_reverse.data)
def ttm(t, U, dim=None, transpose=False):
"""
`Tensor-times-matrix (TTM) <https://epubs.siam.org/doi/pdf/10.1137/07070111X>`_ along one or several dimensions.
:param t: input :class:`Tensor`
:param U: one or several factors
:param dim: one or several dimensions (may be vectors or matrices). If None, the first len(U) dims are assumed
:param transpose: if False (default) the contraction is performed
along U's rows, else along its columns
:return: transformed :class:`Tensor`
"""
if not isinstance(U, (list, tuple)):
U = [U]
if dim is None:
dim = range(len(U))
if not hasattr(dim, '__len__'):
dim = [dim]
dim = list(dim)
for i in range(len(dim)):
if dim[i] < 0:
dim[i] += t.dim()
cores = []
Us = []
for n in range(t.dim()):
if n in dim:
if transpose:
factor = U[dim.index(n)].t()
else:
factor = U[dim.index(n)]
if factor.dim() == 1:
factor = factor[None, :]
if t.Us[n] is None:
if t.cores[n].dim() == 3:
cores.append(
torch.einsum('iak,ja->ijk', (t.cores[n], factor)))
else:
cores.append(
torch.einsum('ai,ja->ji', (t.cores[n], factor)))
Us.append(None)
else:
cores.append(t.cores[n].clone())
Us.append(torch.matmul(factor, t.Us[n]))
else:
cores.append(t.cores[n].clone())
if t.Us[n] is None:
Us.append(None)
else:
Us.append(t.Us[n].clone())
return tn.Tensor(cores, Us=Us, idxs=t.idxs)
def eye(n, m=None, device=None, requires_grad=None):
"""
Generates identity matrix like PyTorch's `eye()`.
:param n: number of rows
:param m: number of columns (default is n)
:return: a 2D :class:`Tensor`
"""
c1 = torch.eye(n, m)
c2 = torch.eye(m, m)
return tn.Tensor([c1[None, :, :], c2[:, :, None]], device=device, requires_grad=requires_grad)
def hash(t):
"""
Computes an integer number that depends on the tensor entries (not on its internal compressed representation).
We obtain it as :math:`\\langle T, W \\rangle`, where :math:`W` is a rank-1 tensor of weights selected at random (always the same seed).
:return: an integer
"""
gen = torch.Generator()
gen.manual_seed(0)
cores = [torch.ones(1, 1, 1) for n in range(t.dim())]
Us = [torch.rand([sh, 1], generator=gen) for sh in t.shape]
w = tn.Tensor(cores, Us)
return t.dot(w)