pyttb.tenmat

class pyttb.tenmat(data: ndarray | None = None, rdims: ndarray | None = None, cdims: ndarray | None = None, tshape: int | Iterable[int] | None = None, copy: bool = True)

Bases: object

Store tensor as a matrix.

Construct a pyttb.tenmat from explicit components.

If you already have a tensor see pyttb.tensor.to_tenmat().

Parameters:

• data – Flattened tensor data.

• rdims – Which dimensions of original tensor map to rows.

• cdims – Which dimensions of original tensor map to columns.

• tshape – Original tensor shape.

• copy – Whether to make a copy of provided data or just reference it.

Examples

Create an empty pyttb.tenmat.

>>> ttb.tenmat()  
matrix corresponding to a tensor of shape () with order F
rindices = [  ] (modes of tensor corresponding to rows)
cindices = [  ] (modes of tensor corresponding to columns)
data = []

Create tensor shaped data.

>>> tshape = (2, 2, 2)
>>> data = np.reshape(np.arange(prod(tshape), dtype=np.double), tshape)
>>> data  
array([[[0., 1.],
        [2., 3.]],
       [[4., 5.],
        [6., 7.]]])

Manually matrize the tensor.

>>> flat_data = np.reshape(data, (2, 4), order="F")
>>> flat_data  
array([[0., 2., 1., 3.],
       [4., 6., 5., 7.]])

Encode matrication into pyttb.tenmat.

>>> tm = ttb.tenmat(flat_data, rdims=np.array([0]), tshape=tshape)

Extract original tensor shaped data.

>>> tm.to_tensor().double()  
array([[[0., 1.],
        [2., 3.]],
       [[4., 5.],
        [6., 7.]]])

property order: Literal['F']

Return the data layout of the underlying storage.

copy() → tenmat

Return a deep copy of the pyttb.tenmat.

Examples

Create a pyttb.tenmat (TM1) and make a deep copy. Verify the deep copy (TM3) is not just a reference (like TM2) to the original.

>>> T1 = ttb.tensor(np.ones((3, 2)))
>>> TM1 = T1.to_tenmat(np.array([0]))
>>> TM2 = TM1
>>> TM3 = TM1.copy()
>>> TM1[0, 0] = 3

# Item to convert numpy boolean to python boolena for nicer printing

>>> (TM1[0, 0] == TM2[0, 0]).item()
True
>>> (TM1[0, 0] == TM3[0, 0]).item()
False

__deepcopy__(memo)

Return deep copy of this tenmat.

to_tensor(copy: bool = True) → tensor

Return pyttb.tenmat data as a pyttb.tensor.

Parameters:

copy – Whether to make a copy of provided data or just reference it.

Examples

Create tensor shaped data.

>>> tshape = (2, 2, 2)
>>> data = np.reshape(np.arange(np.prod(tshape), dtype=np.double), tshape)
>>> data  
array([[[0., 1.],
        [2., 3.]],
       [[4., 5.],
        [6., 7.]]])

Manually matrize the tensor.

>>> flat_data = np.reshape(data, (2, 4), order="F")
>>> flat_data  
array([[0., 2., 1., 3.],
       [4., 6., 5., 7.]])

Encode matrication into pyttb.tenmat.

>>> tm = ttb.tenmat(flat_data, rdims=np.array([0]), tshape=tshape)

Extract original tensor shaped data.

>>> tm.to_tensor()  
tensor of shape (2, 2, 2) with order F
data[:, :, 0] =
[[0. 2.]
 [4. 6.]]
data[:, :, 1] =
[[1. 3.]
 [5. 7.]]

ctranspose() → tenmat

Complex conjugate transpose for pyttb.tenmat.

Examples

Create pyttb.tensor then convert to pyttb.tenmat.

>>> T = ttb.tenones((2, 2, 2))
>>> TM = T.to_tenmat(rdims=np.array([0]))
>>> TM  
matrix corresponding to a tensor of shape (2, 2, 2) with order F
rindices = [ 0 ] (modes of tensor corresponding to rows)
cindices = [ 1, 2 ] (modes of tensor corresponding to columns)
data[:, :] =
[[1. 1. 1. 1.]
 [1. 1. 1. 1.]]
>>> TM.ctranspose()  
matrix corresponding to a tensor of shape (2, 2, 2) with order F
rindices = [ 1, 2 ] (modes of tensor corresponding to rows)
cindices = [ 0 ] (modes of tensor corresponding to columns)
data[:, :] =
[[1. 1.]
 [1. 1.]
 [1. 1.]
 [1. 1.]]

double() → ndarray

Convert a pyttb.tenmat to an array of doubles.

Examples

>>> T = ttb.tenones((2, 2, 2))
>>> TM = T.to_tenmat(rdims=np.array([0]))
>>> TM  
matrix corresponding to a tensor of shape (2, 2, 2) with order F
rindices = [ 0 ] (modes of tensor corresponding to rows)
cindices = [ 1, 2 ] (modes of tensor corresponding to columns)
data[:, :] =
[[1. 1. 1. 1.]
 [1. 1. 1. 1.]]
>>> TM.double()  
array([[1., 1., 1., 1.],
       [1., 1., 1., 1.]])

Returns:

Copy of tenmat data.

property ndims: int

Return the number of dimensions of a pyttb.tenmat.

Examples

>>> TM = ttb.tenmat()  # empty tenmat
>>> TM.ndims
0

>>> TM = ttb.tenones((2, 2, 2)).to_tenmat(np.array([0]))
>>> TM.ndims
2

norm() → float

Frobenius norm of a pyttb.tenmat.

Examples

>>> T = ttb.tenones((2, 2, 2))
>>> TM = T.to_tenmat(rdims=np.array([0]))
>>> TM  
matrix corresponding to a tensor of shape (2, 2, 2) with order F
rindices = [ 0 ] (modes of tensor corresponding to rows)
cindices = [ 1, 2 ] (modes of tensor corresponding to columns)
data[:, :] =
[[1. 1. 1. 1.]
 [1. 1. 1. 1.]]
>>> TM.norm()  
2.82...

property shape: Tuple[int, ...]

Return the shape of a pyttb.tenmat.

Examples

>>> TM = ttb.tenmat()  # empty tenmat
>>> TM.shape
()

>>> TM = ttb.tenones((2, 2, 2)).to_tenmat(np.array([0]))
>>> TM.shape
(2, 4)

isequal(other: tenmat) → bool

Exact equality for pyttb.tenmat.

Examples

>>> TM1 = ttb.tenmat()  # empty tenmat
>>> TM2 = ttb.tenones((2, 2, 2)).to_tenmat(np.array([0]))
>>> TM1.isequal(TM2)
False
>>> TM1.isequal(TM1)
True

__setitem__(key, value)

Subscripted assignment for a pyttb.tenmat.

Examples

>>> TM = ttb.tenones((2, 2, 2)).to_tenmat(np.array([0]))
>>> TM  
matrix corresponding to a tensor of shape (2, 2, 2) with order F
rindices = [ 0 ] (modes of tensor corresponding to rows)
cindices = [ 1, 2 ] (modes of tensor corresponding to columns)
data[:, :] =
[[1. 1. 1. 1.]
 [1. 1. 1. 1.]]
>>> TM[0, 0] = 2.0
>>> TM  
matrix corresponding to a tensor of shape (2, 2, 2) with order F
rindices = [ 0 ] (modes of tensor corresponding to rows)
cindices = [ 1, 2 ] (modes of tensor corresponding to columns)
data[:, :] =
[[2. 1. 1. 1.]
 [1. 1. 1. 1.]]

__getitem__(item)

Subscripted reference for pyttb.tenmat.

Examples

>>> TM = ttb.tenones((2, 2, 2)).to_tenmat(np.array([0]))
>>> print(TM[0, 0])
1.0

Returns:

numpy.ndarray, float, int

__mul__(other)

Multiplies two pyttb.tenmat objects.

Parameters:

other (pyttb.tenmat)

Examples

>>> TM = ttb.tenones((2, 2)).to_tenmat(np.array([0]))
>>> TM * TM  
matrix corresponding to a tensor of shape (2, 2) with order F
rindices = [ 0 ] (modes of tensor corresponding to rows)
cindices = [ 1 ] (modes of tensor corresponding to columns)
data[:, :] =
[[2. 2.]
 [2. 2.]]

Returns:

pyttb.tenmat

__rmul__(other)

Multiplies two pyttb.tenmat objects.

Parameters:

other (pyttb.tenmat)

Examples

>>> TM = ttb.tenones((2, 2)).to_tenmat(np.array([0]))
>>> TM * TM  
matrix corresponding to a tensor of shape (2, 2) with order F
rindices = [ 0 ] (modes of tensor corresponding to rows)
cindices = [ 1 ] (modes of tensor corresponding to columns)
data[:, :] =
[[2. 2.]
 [2. 2.]]

Returns:

pyttb.tenmat

__add__(other)

Binary addition (+) for pyttb.tenmat.

Parameters:

other (pyttb.tenmat, float, int)

Examples

>>> TM = ttb.tenones((2, 2)).to_tenmat(np.array([0]))
>>> TM + TM  
matrix corresponding to a tensor of shape (2, 2) with order F
rindices = [ 0 ] (modes of tensor corresponding to rows)
cindices = [ 1 ] (modes of tensor corresponding to columns)
data[:, :] =
[[2. 2.]
 [2. 2.]]
>>> TM + 1.0  
matrix corresponding to a tensor of shape (2, 2)  with order F
rindices = [ 0 ] (modes of tensor corresponding to rows)
cindices = [ 1 ] (modes of tensor corresponding to columns)
data[:, :] =
[[2. 2.]
 [2. 2.]]

Returns:

pyttb.tenmat

__radd__(other)

Right binary addition (+) for pyttb.tenmat.

Parameters:

other (pyttb.tenmat, float, int)

Examples

>>> TM = ttb.tenones((2, 2)).to_tenmat(np.array([0]))
>>> 1.0 + TM  
matrix corresponding to a tensor of shape (2, 2) with order F
rindices = [ 0 ] (modes of tensor corresponding to rows)
cindices = [ 1 ] (modes of tensor corresponding to columns)
data[:, :] =
[[2. 2.]
 [2. 2.]]

Returns:

pyttb.tenmat

__sub__(other)

Binary subtraction (-) for pyttb.tenmat.

Parameters:

other (pyttb.tenmat, float, int)

Examples

>>> TM = ttb.tenones((2, 2)).to_tenmat(np.array([0]))
>>> TM - TM  
matrix corresponding to a tensor of shape (2, 2) with order F
rindices = [ 0 ] (modes of tensor corresponding to rows)
cindices = [ 1 ] (modes of tensor corresponding to columns)
data[:, :] =
[[0. 0.]
 [0. 0.]]
>>> TM - 1.0  
matrix corresponding to a tensor of shape (2, 2) with order F
rindices = [ 0 ] (modes of tensor corresponding to rows)
cindices = [ 1 ] (modes of tensor corresponding to columns)
data[:, :] =
[[0. 0.]
 [0. 0.]]

Returns:

pyttb.tenmat

__rsub__(other)

Right binary subtraction (-) for pyttb.tenmat.

Parameters:

other (pyttb.tenmat, float, int)

Examples

>>> TM = ttb.tenones((2, 2)).to_tenmat(np.array([0]))
>>> 1.0 - TM  
matrix corresponding to a tensor of shape (2, 2) with order F
rindices = [ 0 ] (modes of tensor corresponding to rows)
cindices = [ 1 ] (modes of tensor corresponding to columns)
data[:, :] =
[[0. 0.]
 [0. 0.]]

Returns:

pyttb.tenmat

__pos__()

Unary plus (+) for pyttb.tenmat.

Examples

>>> TM = ttb.tenones((2, 2)).to_tenmat(np.array([0]))
>>> +TM  
matrix corresponding to a tensor of shape (2, 2) with order F
rindices = [ 0 ] (modes of tensor corresponding to rows)
cindices = [ 1 ] (modes of tensor corresponding to columns)
data[:, :] =
[[1. 1.]
 [1. 1.]]

Returns:

pyttb.tenmat – copy of tenmat

__neg__()

Unary minus (-) for pyttb.tenmat.

Examples

>>> TM = ttb.tenones((2, 2)).to_tenmat(np.array([0]))
>>> -TM  
matrix corresponding to a tensor of shape (2, 2) with order F
rindices = [ 0 ] (modes of tensor corresponding to rows)
cindices = [ 1 ] (modes of tensor corresponding to columns)
data[:, :] =
[[-1. -1.]
 [-1. -1.]]

Returns:

pyttb.tenmat – Copy of original tenmat with negated data.

__repr__()

Return string representation of a pyttb.tenmat.

Examples

Print an empty pyttb.tenmat.

>>> ttb.tenmat()  
matrix corresponding to a tensor of shape () with order F
rindices = [  ] (modes of tensor corresponding to rows)
cindices = [  ] (modes of tensor corresponding to columns)
data = []

Print a non-empty pyttb.tenmat.

>>> TM = ttb.tenones((2, 2)).to_tenmat(np.array([0]))
>>> TM  
matrix corresponding to a tensor of shape (2, 2) with order F
rindices = [ 0 ] (modes of tensor corresponding to rows)
cindices = [ 1 ] (modes of tensor corresponding to columns)
data[:, :] =
[[1. 1.]
 [1. 1.]]

Returns:

str – Contains the shape, row indices (rindices), column indices (cindices) and data as strings on different lines.

__str__()

Return string representation of a pyttb.tenmat.

Examples

Print an empty pyttb.tenmat.

>>> ttb.tenmat()  
matrix corresponding to a tensor of shape () with order F
rindices = [  ] (modes of tensor corresponding to rows)
cindices = [  ] (modes of tensor corresponding to columns)
data = []

Print a non-empty pyttb.tenmat.

>>> TM = ttb.tenones((2, 2)).to_tenmat(np.array([0]))
>>> TM  
matrix corresponding to a tensor of shape (2, 2) with order F
rindices = [ 0 ] (modes of tensor corresponding to rows)
cindices = [ 1 ] (modes of tensor corresponding to columns)
data[:, :] =
[[1. 1.]
 [1. 1.]]

Returns:

str – Contains the shape, row indices (rindices), column indices (cindices) and data as strings on different lines.