def super_diagonal_tensor(shape, distr='ones', values=None):
""" Generates a tensor of any dimension with random or specified numbers across the super-diagonal and zeros elsewhere
Parameters
----------
shape : tuple
Specifies the dimensions of the tensor
``len(shape)`` defines the order of the tensor, whereas its values specify sizes of dimensions of the tensor.
distr : str, optional
Specifies the random generation using a class of the numpy.random module
values : list
Array of values on the super-diagonal of a tensor
Returns
-------
Tensor
Generated tensor according to the parameters specified
"""
if not isinstance(shape, tuple):
raise TypeError("Parameter `shape` should be passed as a tuple!")
if shape[1:] != shape[:-1]:
raise ValueError("All values in `shape` should have the same value!")
inds = shape[0]
data = np.zeros(shape)
if values is None:
values = _predefined_distr(distr, inds)
if len(values) != inds:
raise ValueError("Dimension mismatch! The specified values do not match "
"the specified shape of the tensor provided ({} != {})".format(len(values), inds))
values = np.asarray(values).flatten()
np.fill_diagonal(data, values)
return Tensor(array=data)
def dense_tensor(shape, distr='uniform', distr_type=0, fxdind=None):
""" Generates a dense tensor of any dimension and fills it accordingly
Parameters
----------
shape : tuple
Specifies the dimensions of the tensor
distr : str, optional
Specifies the random generation using a class of the numpy.random module
distr_type : int, optional
Number of indices to not fix. 0 will be applied globally, 1 will apply to fibers, 2 to slices, etc.
Returns
-------
Tensor
Generated tensor according to the parameters specified
"""
# fxdind: fixed indices
if distr_type == 0:
data = _predefined_distr(distr, shape)
else:
data = np.random.uniform(size=shape)
raise NotImplementedError('Not implemented in dataset (basic) class')
return Tensor(array=data)
def sparse_tensor(shape, distr='uniform', distr_type=0, fxdind=None, pct=0.05):
""" Generates a sparse tensor of any dimension and fills it accordingly
Parameters
----------
shape : tuple
Specifies the dimensions of the tensor
distr : str, optional
Specifies the random generation using a class of the numpy.random module
distr_type : int, optional
Number of indices to not fix. 0 will be applied globally, 1 will apply to fibers, 2 to slices, etc.
pct : float, optional
Percentage of the dataset to be filled
Returns
-------
Tensor
Generated tensor according to the parameters specified
"""
data_size = np.product(shape)
if distr_type == 0:
number_non_zero_values = int(data_size * pct)
data = np.zeros(data_size)
index = np.random.randint(low=0, high=data_size, size=number_non_zero_values)
data[index] = _predefined_distr(distr, number_non_zero_values)
data = data.reshape(shape)
else:
raise NotImplementedError('Not implemented in dataset (basic) class')
return Tensor(array=data)
def super_symmetric_tensor(shape, tensor=None):
""" Generates a tensor of equal dimensions with random or specified numbers, with a specified tensor.
Parameters
----------
shape : tuple
Specifies the dimensions of the tensor
``len(shape)`` defines the order of the tensor, whereas its values specify sizes of dimensions of the tensor.
tensor : Tensor, optional
Input tensor to be symmetricised
Returns
-------
Tensor
Generated tensor according to the parameters specified
"""
dims = len(shape)
inds = itertools.permutations(np.arange(dims))
inds = np.array(list(inds))
data = np.zeros(shape)
if tensor is None:
tensor = dense_tensor(shape)
for i, _ in enumerate(inds):
data = data + np.transpose(tensor.data, tuple(inds[i, :]))
return Tensor(array=data)
def is_toeplitz_tensor(tensor, modes=None):
""" Checks if ``tensor`` has Toeplitz structure
Parameters
----------
tensor : Tensor
Input tensor to check
Returns
-------
Boolean indicating if Toeplitz matrix
"""
if tensor.order <= 2:
return is_toeplitz_matrix(tensor.data)
if modes is None:
modes = [0, 1]
sz = np.asarray(tensor.shape)
availmodes = np.setdiff1d(np.arange(len(sz)), modes)
for idx, mode in enumerate(availmodes):
dim = sz[mode]
# Go through each dim
for i in range(dim):
t = tensor.access(i, mode)
t = Tensor(t)
if not (is_toeplitz_tensor(t)):
print("Wrong slice: \n{}\n{}".format(t, (i, idx)))
return False
return True
def test_init_fmat(self):
""" Tests for _init_fmat method """
np.random.seed(0)
shape = (4, 5, 6)
size = reduce(lambda x, y: x * y, shape)
tensor = Tensor(np.random.randn(size).reshape(shape))
cpd = CPD()
# ------ tests on getting factor matrices of the correct shape
for rank_value in range(min(tensor.shape) - 1, max(tensor.shape) + 2):
rank = (rank_value, )
fmat = cpd._init_fmat(tensor=tensor, rank=rank)
for mode, mat in enumerate(fmat):
assert mat.shape == (tensor.shape[mode], rank_value)
# ------ tests for the type of initialisation
# svd type initialisation should produce factor matrices with orthogonal columns
rank = (min(tensor.shape) - 1, )
cpd = CPD(init='svd')
fmat = cpd._init_fmat(tensor=tensor, rank=rank)
for mat in fmat:
result = np.dot(mat.T, mat)
true_result = np.eye(rank[0])
np.testing.assert_almost_equal(result, true_result)
# svd type initialisation but the `rank` is greater then one of the dimensions then you get random fmat
# and there would be a runtime warning
rank = (min(tensor.shape) + 1, )
cpd = CPD(init='svd', verbose=True)
with pytest.warns(RuntimeWarning):
fmat = cpd._init_fmat(tensor=tensor, rank=rank)
for mat in fmat:
result_1 = np.dot(mat.T, mat)
result_2 = np.eye(rank[0])
# since each mat is randomly initialized it is not orthonormal
with pytest.raises(AssertionError):
np.testing.assert_almost_equal(result_1, result_2)
# random type initialisation should produce factor matrices each of which is not orthonormal
rank = (3, )
cpd = CPD(init='random')
fmat = cpd._init_fmat(tensor=tensor, rank=rank)
for mat in fmat:
result_1 = np.dot(mat.T, mat)
result_2 = np.eye(rank[0])
# since each mat is randomly initialized it is not orthonormal
with pytest.raises(AssertionError):
np.testing.assert_almost_equal(result_1, result_2)
# unknown type of initialisation
with pytest.raises(NotImplementedError):
rank = (min(tensor.shape) - 1, )
cpd = CPD(init='qwerty')
cpd._init_fmat(tensor=tensor, rank=rank)
def test_mape():
""" Tests for mape """
# ------ tests for 1-d case
shape = (2, )
size = shape[0]
tensor_true = Tensor(np.arange(size).reshape(shape) + 1)
tensor_pred = Tensor(np.arange(size).reshape(shape) * 2)
true_mape = 0.5
result = mape(tensor_true, tensor_pred)
np.testing.assert_array_almost_equal(result, true_mape)
# ------ tests for 2-d case
shape = (2, 2)
size = reduce(lambda x, y: x * y, shape)
tensor_true = Tensor(np.arange(size).reshape(shape) + 1)
tensor_pred = Tensor(np.arange(size).reshape(shape) * 2)
true_mape = 0.4583333333333333
result = mape(tensor_true, tensor_pred)
np.testing.assert_array_almost_equal(result, true_mape)
# ------ tests for 3-d case
shape = (2, 2, 2)
size = reduce(lambda x, y: x * y, shape)
tensor_true = Tensor(np.arange(size).reshape(shape) + 1)
tensor_pred = Tensor(np.arange(size).reshape(shape) * 2)
true_mape = 0.5705357142857143
result = mape(tensor_true, tensor_pred)
np.testing.assert_array_almost_equal(result, true_mape)
def test_rmse():
""" Tests for rmse """
# ------ tests for 1-d case
shape = (2, )
size = shape[0]
tensor_true = Tensor(np.arange(size).reshape(shape))
tensor_pred = Tensor(np.arange(size).reshape(shape) * 2)
true_rmse = 0.7071067811865476
result = rmse(tensor_true, tensor_pred)
np.testing.assert_array_almost_equal(result, true_rmse)
# ------ tests for 2-d case
shape = (2, 2)
size = reduce(lambda x, y: x * y, shape)
tensor_true = Tensor(np.arange(size).reshape(shape))
tensor_pred = Tensor(np.arange(size).reshape(shape) * 2)
true_rmse = 1.8708286933869707
result = rmse(tensor_true, tensor_pred)
np.testing.assert_array_almost_equal(result, true_rmse)
# ------ tests for 3-d case
shape = (2, 2, 2)
size = reduce(lambda x, y: x * y, shape)
tensor_true = Tensor(np.arange(size).reshape(shape))
tensor_pred = Tensor(np.arange(size).reshape(shape) * 2)
true_rmse = 4.183300132670378
result = rmse(tensor_true, tensor_pred)
np.testing.assert_array_almost_equal(result, true_rmse)
def test_residual_rel_error():
# ------ tests for 1-d case
shape = (2, )
size = shape[0]
tensor_true = Tensor(np.arange(size).reshape(shape))
tensor_pred = Tensor(np.arange(size).reshape(shape) * 2)
true_res_rel_error = 1
result = residual_rel_error(tensor_true, tensor_pred)
np.testing.assert_array_almost_equal(result, true_res_rel_error)
# ------ tests for 2-d case
shape = (2, 2)
size = reduce(lambda x, y: x * y, shape)
tensor_true = Tensor(np.arange(size).reshape(shape))
tensor_pred = Tensor(np.arange(size).reshape(shape) * 2)
true_res_rel_error = 1
result = residual_rel_error(tensor_true, tensor_pred)
np.testing.assert_array_almost_equal(result, true_res_rel_error)
# ------ tests for 3-d case
shape = (2, 2, 2)
size = reduce(lambda x, y: x * y, shape)
tensor_true = Tensor(np.arange(size).reshape(shape))
tensor_pred = Tensor(np.arange(size).reshape(shape) * 2)
true_res_rel_error = 1
result = residual_rel_error(tensor_true, tensor_pred)
np.testing.assert_array_almost_equal(result, true_res_rel_error)
def residual_tensor(tensor_orig, tensor_approx):
""" Residual tensor
Parameters
----------
tensor_orig : Tensor
tensor_approx : {Tensor, TensorCPD, TensorTKD, TensorTT}
Returns
-------
residual : Tensor
"""
if not isinstance(tensor_orig, Tensor):
raise TypeError("Unknown data type of original tensor.\n"
"The available type for `tensor_A` is `Tensor`")
# TODO: make use of direct subtraction of tensors
if isinstance(tensor_approx, Tensor):
residual = Tensor(tensor_orig.data - tensor_approx.data)
elif isinstance(tensor_approx, BaseTensorTD):
residual = Tensor(tensor_orig.data - tensor_approx.reconstruct().data)
else:
raise TypeError("Unknown data type of the approximation tensor!\n"
"The available types for `tensor_B` are `Tensor`, `TensorCPD`, `TensorTKD`, `TensorTT`")
return residual
def test_init(self):
""" Tests for constructor of BaseCPD class """
# Even though we can create such object we shouldn't do that
default_params = dict(init='svd',
max_iter=50,
epsilon=10e-3,
tol=10e-5,
random_state=None,
verbose=False)
# basically for coverage tests object of
with pytest.raises(NotImplementedError):
tensor = Tensor(np.arange(2))
rank = 5
keep_meta = 0
base_cpd = BaseCPD(**default_params)
base_cpd.decompose(tensor, rank, keep_meta)
with pytest.raises(NotImplementedError):
base_cpd = BaseCPD(**default_params)
base_cpd.plot()
def super_diag_tensor(shape, values=None):
""" Super-diagonal tensor of the specified `order`.
Parameters
----------
shape : tuple
Desired shape of the tensor.
``len(shape)`` defines the order of the tensor, whereas its values specify sizes of dimensions of the tensor.
values : np.ndarray
Array of values on the super-diagonal of a tensor. By default contains only ones.
Length of this vector defines Kryskal rank which is equal to ``shape[0]``.
Returns
-------
tensor : Tensor
"""
order = len(shape)
rank = shape[0]
if not isinstance(shape, tuple):
raise TypeError("Parameter `shape` should be passed as a tuple!")
if not all(mode_size == shape[0] for mode_size in shape):
raise ValueError("All values in `shape` should have the same value!")
if values is None:
values = np.ones(rank) # set default values
elif isinstance(values, np.ndarray):
if values.ndim != 1:
raise ValueError("The `values` should be 1-dimensional numpy array!")
if values.size != rank:
raise ValueError("Dimension mismatch! Not enough or too many `values` for the specified `shape`:\n"
"{} != {} (values.size != shape[0])".format(values.size, rank))
else:
raise TypeError("The `values` should be passed as a numpy array!")
core = np.zeros(shape)
core[np.diag_indices(rank, ndim=order)] = values
tensor = Tensor(core)
return tensor
def _reconstruct(fmat_a, fmat_b, n_mat):
""" Reconstruct the tensor and matrix after the coupled factorisation
Parameters
----------
fmat_a : List(np.ndarray)
Multidimensional data obtained from the factorisation
fmat_b : List(np.ndarray)
Multidimensional data obtained from the factorisation
n_mat : int
Number of matrices provided to fuse
Returns
-------
(core_tensor, lrecon) : np.ndarray or List(np.ndarray)
Reconstructed tensor and list of matrices obtained from the factorisation
"""
core_values = np.repeat(np.array([1]), fmat_a[0].shape[1])
_r = (fmat_a[0].shape[1], )
core_shape = _r * len(fmat_a)
core_tensor = super_diag_tensor(core_shape, values=core_values)
for mode, fmat in enumerate(fmat_a):
core_tensor.mode_n_product(fmat, mode=mode, inplace=True)
lrecon = [Tensor(fmat_a[i].dot(fmat_b[i].T)) for i in range(n_mat)]
return core_tensor, lrecon
def test_residual_tensor():
""" Tests for computing/creating a residual tensor """
true_default_mode_names = ['mode-0', 'mode-1', 'mode-2']
# ------ tests for residual tensor with the Tensor
array_3d = np.array([[[0, 1, 2, 3],
[4, 5, 6, 7],
[8, 9, 10, 11]],
[[12, 13, 14, 15],
[16, 17, 18, 19],
[20, 21, 22, 23]]])
true_residual_data = np.zeros(array_3d.shape)
tensor_1 = Tensor(array=array_3d)
tensor_2 = Tensor(array=array_3d)
residual = residual_tensor(tensor_orig=tensor_1, tensor_approx=tensor_2)
assert isinstance(residual, Tensor)
assert (residual.mode_names == true_default_mode_names)
np.testing.assert_array_equal(residual.data, true_residual_data)
# ------ tests for residual tensor with the TensorCPD
array_3d = np.array([[[100., 250., 400., 550.],
[250., 650., 1050., 1450.],
[400., 1050., 1700., 2350.]],
[[250., 650., 1050., 1450.],
[650., 1925., 3200., 4475.],
[1050., 3200., 5350., 7500.]]]
)
true_residual_data = np.zeros(array_3d.shape)
tensor = Tensor(array=array_3d)
ft_shape = (2, 3, 4) # define shape of the tensor in full form
R = 5 # define Kryskal rank of a tensor in CP form
core_values = np.ones(R)
fmat = [np.arange(orig_dim * R).reshape(orig_dim, R)
for orig_dim in ft_shape]
tensor_cpd = TensorCPD(fmat=fmat, core_values=core_values)
residual = residual_tensor(tensor_orig=tensor, tensor_approx=tensor_cpd)
assert isinstance(residual, Tensor)
assert (residual.mode_names == true_default_mode_names)
np.testing.assert_array_equal(residual.data, true_residual_data)
# ------ tests for residual tensor with the TensorTKD
array_3d = np.array([[[378, 1346, 2314, 3282, 4250],
[1368, 4856, 8344, 11832, 15320],
[2358, 8366, 14374, 20382, 26390],
[3348, 11876, 20404, 28932, 37460]],
[[1458, 5146, 8834, 12522, 16210],
[5112, 17944, 30776, 43608, 56440],
[8766, 30742, 52718, 74694, 96670],
[12420, 43540, 74660, 105780, 136900]],
[[2538, 8946, 15354, 21762, 28170],
[8856, 31032, 53208, 75384, 97560],
[15174, 53118, 91062, 129006, 166950],
[21492, 75204, 128916, 182628, 236340]]])
true_residual_data = np.zeros(array_3d.shape)
tensor = Tensor(array=array_3d)
ft_shape = (3, 4, 5) # define shape of the tensor in full form
ml_rank = (2, 3, 4) # define multi-linear rank of a tensor in Tucker form
core_size = reduce(lambda x, y: x * y, ml_rank)
core_values = np.arange(core_size).reshape(ml_rank)
fmat = [np.arange(ft_shape[mode] * ml_rank[mode]).reshape(ft_shape[mode],
ml_rank[mode]) for mode in range(len(ft_shape))]
tensor_tkd = TensorTKD(fmat=fmat, core_values=core_values)
residual = residual_tensor(tensor_orig=tensor, tensor_approx=tensor_tkd)
assert isinstance(residual, Tensor)
assert (residual.mode_names == true_default_mode_names)
np.testing.assert_array_equal(residual.data, true_residual_data)
# ------ tests for residual tensor with the TensorTT
array_3d = np.array([[[300, 348, 396, 444, 492, 540],
[354, 411, 468, 525, 582, 639],
[408, 474, 540, 606, 672, 738],
[462, 537, 612, 687, 762, 837],
[516, 600, 684, 768, 852, 936]],
[[960, 1110, 1260, 1410, 1560, 1710],
[1230, 1425, 1620, 1815, 2010, 2205],
[1500, 1740, 1980, 2220, 2460, 2700],
[1770, 2055, 2340, 2625, 2910, 3195],
[2040, 2370, 2700, 3030, 3360, 3690]],
[[1620, 1872, 2124, 2376, 2628, 2880],
[2106, 2439, 2772, 3105, 3438, 3771],
[2592, 3006, 3420, 3834, 4248, 4662],
[3078, 3573, 4068, 4563, 5058, 5553],
[3564, 4140, 4716, 5292, 5868, 6444]],
[[2280, 2634, 2988, 3342, 3696, 4050],
[2982, 3453, 3924, 4395, 4866, 5337],
[3684, 4272, 4860, 5448, 6036, 6624],
[4386, 5091, 5796, 6501, 7206, 7911],
[5088, 5910, 6732, 7554, 8376, 9198]]])
true_residual_data = np.zeros(array_3d.shape)
tensor = Tensor(array=array_3d)
r1, r2 = 2, 3
I, J, K = 4, 5, 6
core_1 = np.arange(I * r1).reshape(I, r1)
core_2 = np.arange(r1 * J * r2).reshape(r1, J, r2)
core_3 = np.arange(r2 * K).reshape(r2, K)
core_values = [core_1, core_2, core_3]
ft_shape = (I, J, K)
tensor_tt = TensorTT(core_values=core_values)
residual = residual_tensor(tensor_orig=tensor, tensor_approx=tensor_tt)
assert isinstance(residual, Tensor)
assert (residual.mode_names == true_default_mode_names)
np.testing.assert_array_equal(residual.data, true_residual_data)
# ------ tests that should FAIL for residual tensor due to wrong input type
array_3d = np.array([[[0, 1, 2, 3],
[4, 5, 6, 7],
[8, 9, 10, 11]],
[[12, 13, 14, 15],
[16, 17, 18, 19],
[20, 21, 22, 23]]])
tensor_1 = Tensor(array=array_3d)
tensor_2 = array_3d
with pytest.raises(TypeError):
residual_tensor(tensor_orig=tensor_1, tensor_approx=tensor_2)
tensor_1 = array_3d
tensor_2 = Tensor(array=array_3d)
with pytest.raises(TypeError):
residual_tensor(tensor_orig=tensor_1, tensor_approx=tensor_2)
def test_decompose(self):
""" Tests for decompose method """
# ------ tests for termination conditions
captured_output = io.StringIO(
) # Create StringIO object for testing verbosity
sys.stdout = captured_output # and redirect stdout.
np.random.seed(0)
shape = (6, 7, 8)
size = reduce(lambda x, y: x * y, shape)
array_3d = np.random.randn(size).reshape(shape)
tensor = Tensor(array_3d)
rank = (2, )
cpd = RandomisedCPD(verbose=True)
# check for termination at max iter
cpd.max_iter = 10
cpd.epsilon = 0.01
cpd.tol = 0.0001
cpd.decompose(tensor=tensor, rank=rank)
assert not cpd.converged
assert len(cpd.cost) == cpd.max_iter
assert cpd.cost[-1] > cpd.epsilon
# Repeat cpd, test is self.cost is reset
cpd.decompose(tensor=tensor, rank=rank)
assert len(cpd.cost) == cpd.max_iter
# check for termination when acceptable level of approximation is achieved
cpd.max_iter = 20
cpd.epsilon = 0.98
cpd.tol = 0.0001
cpd.decompose(tensor=tensor, rank=rank)
assert not cpd.converged
assert len(cpd.cost) < cpd.max_iter
assert cpd.cost[-1] <= cpd.epsilon
# check for termination at convergence
cpd.max_iter = 20
cpd.epsilon = 0.01
cpd.tol = 0.03
cpd.decompose(tensor=tensor, rank=rank)
assert cpd.converged
assert len(cpd.cost) < cpd.max_iter
assert cpd.cost[-1] > cpd.epsilon
assert captured_output.getvalue(
) != '' # to check that something was actually printed
# ------ tests for correct output type and values
shape = (4, 5, 6)
size = reduce(lambda x, y: x * y, shape)
array_3d = np.arange(size, dtype='float32').reshape(shape)
tensor = Tensor(array_3d)
rank = (7, )
cpd = RandomisedCPD(init='random',
max_iter=50,
epsilon=10e-3,
tol=10e-5)
tensor_cpd = cpd.decompose(tensor=tensor, rank=rank)
assert isinstance(tensor_cpd, TensorCPD)
assert tensor_cpd.order == tensor.order
assert tensor_cpd.rank == rank
# check dimensionality of computed factor matrices
for mode, fmat in enumerate(tensor_cpd.fmat):
assert fmat.shape == (tensor.shape[mode], rank[0])
tensor_rec = tensor_cpd.reconstruct()
np.testing.assert_almost_equal(tensor_rec.data, tensor.data)
# ------ tests that should FAIL due to wrong input type
cpd = RandomisedCPD()
# tensor should be Tensor class
with pytest.raises(TypeError):
shape = (5, 5, 5)
size = reduce(lambda x, y: x * y, shape)
incorrect_tensor = np.arange(size).reshape(shape)
correct_rank = (2, )
cpd.decompose(tensor=incorrect_tensor, rank=correct_rank)
# rank should be a tuple
with pytest.raises(TypeError):
shape = (5, 5, 5)
size = reduce(lambda x, y: x * y, shape)
correct_tensor = Tensor(np.arange(size).reshape(shape))
incorrect_rank = [2]
cpd.decompose(tensor=correct_tensor, rank=incorrect_rank)
# incorrect length of rank
with pytest.raises(ValueError):
shape = (5, 5, 5)
size = reduce(lambda x, y: x * y, shape)
correct_tensor = Tensor(np.arange(size).reshape(shape))
incorrect_rank = (2, 3)
cpd.decompose(tensor=correct_tensor, rank=incorrect_rank)
# invalid sample size
with pytest.raises(ValueError):
cpd = RandomisedCPD(sample_size=0)
shape = (5, 5, 5)
size = reduce(lambda x, y: x * y, shape)
correct_tensor = Tensor(np.arange(size).reshape(shape))
incorrect_rank = (2, )
cpd.decompose(tensor=correct_tensor, rank=incorrect_rank)
def decompose(self, tenl, rank):
""" Performs Direct fitting using ALS on a list of tensors of order 2 with respect to the specified ``rank``.
Parameters
----------
tenl : List(np.ndarray)
List of np.ndarray of dimension 2 to be decomposed
rank : tuple
Desired Kruskal rank for the given ``tensor``. Should contain only one value.
If it is greater then any of dimensions then random initialisation is used
Returns
-------
fmat_u, fmat_s, fmat_v, reconstructed : Tuple(np.ndarray)
fmat_u,fmat_s,fmat_v are PARAFAC2 representation of list of tensors
reconstructed is the reconstruction of the original tensor directly using fmat_u, fmat_s, fmat_v
Notes
-----
khatri-rao product should be of matrices in reversed order. But this will duplicate original data (e.g. images)
Probably this has something to do with data ordering in Python and how it relates to kr product
"""
if not isinstance(tenl, list):
raise TypeError(
"Parameter `tenl` should be a list of np.ndarray objects!")
if not all(isinstance(m, np.ndarray) for m in tenl):
raise TypeError(
"Parameter `tenl` should be a list of np.ndarray objects!")
if not isinstance(rank, tuple):
raise TypeError("Parameter `rank` should be passed as a tuple!")
if len(rank) != 1:
raise ValueError(
"Parameter `rank` should be tuple with only one value!")
self.cost = [] # Reset cost every time when method decompose is called
sz = np.array([t.shape for t in tenl])
_m = list(sz[:, 1])
if _m[1:] != _m[:-1]:
raise ValueError("Tensors must be of shape I[k] x J")
num_t = len(sz)
mode_b = _m[0]
# Initialisations
cpd = CPD(max_iter=1)
fmat_h, fmat_v, fmat_s, fmat_u = self._init_fmat(rank, sz)
cpd_fmat = None
for n_iter in range(self.max_iter):
for k in range(num_t):
p, _, q = svd(fmat_h.dot(fmat_s[:, :, k]).dot(fmat_v.T).dot(
tenl[k].T),
rank=rank[0])
fmat_u[k] = q.T.dot(p.T)
y = np.zeros((rank[0], mode_b, num_t))
for k in range(num_t):
y[:, :, k] = fmat_u[k].T.dot(tenl[k])
fmat = [fmat_h, fmat_v, cpd_fmat]
if n_iter == 0:
fmat = None
decomposed_cpd = cpd.decompose(Tensor(y), rank, factor_mat=fmat)
fmat_h, fmat_v, cpd_fmat = decomposed_cpd.fmat
cpd_fmat = cpd_fmat.dot(np.diag(decomposed_cpd._core_values))
for k in range(num_t):
fmat_s[:, :, k] = np.diag(cpd_fmat[k, :])
reconstructed = [
(fmat_u[k].dot(fmat_h).dot(fmat_s[:, :, k])).dot(fmat_v.T)
for k in range(num_t)
]
err = np.sum([
np.sum((tenl[k] - reconstructed[k])**2) for k in range(num_t)
])
self.cost.append(err)
if self.verbose:
print('Iter {}: relative error of approximation = {}'.format(
n_iter, self.cost[-1]))
# Check termination conditions
if self.cost[-1] <= self.epsilon:
if self.verbose:
print(
'Relative error of approximation has reached the acceptable level: {}'
.format(self.cost[-1]))
break
if self.converged:
if self.verbose:
print('Converged in {} iteration(s)'.format(len(
self.cost)))
break
if self.verbose and not self.converged and self.cost[-1] > self.epsilon:
print('Maximum number of iterations ({}) has been reached. '
'Variation = {}'.format(self.max_iter,
abs(self.cost[-2] - self.cost[-1])))
# TODO: possibly make another structure
return fmat_u, fmat_s, fmat_v, reconstructed