pyttb.tenmat

class pyttb.tenmat(data: Optional[ndarray] = None, rdims: Optional[ndarray] = None, cdims: Optional[ndarray] = None, tshape: Optional[Tuple[int, ...]] = None)

Bases: object

TENMAT 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.

Examples

Create an empty pyttb.tenmat.

>>> ttb.tenmat() 
matrix corresponding to a tensor of shape ()
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(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().double() 
array([[[0., 1.],
        [2., 3.]],
       [[4., 5.],
        [6., 7.]]])

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

to_tensor() → tensor

Return copy of tenmat data as a tensor.

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)
data[0, :, :] =
[[0. 1.]
 [2. 3.]]
data[1, :, :] =
[[4. 5.]
 [6. 7.]]

ctranspose() → tenmat

Complex conjugate transpose for 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)
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)
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 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)
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 tenmat

norm() → float

Frobenius norm of a 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)
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 tenmat

isequal(other: tenmat) → bool

Exact equality for pyttb.tenmat

__setitem__(key, value)

SUBSASGN Subscripted assignment for a tensor.

__getitem__(item)

SUBSREF Subscripted reference for tenmat.

Parameters:

item

Returns:

numpy.ndarray, float, int

__mul__(other)

Multiplies two tenmat objects.

Parameters:

other (pyttb.tenmat)

Returns:

pyttb.tenmat

__rmul__(other)

Multiplies two tenmat objects.

Parameters:

other (pyttb.tenmat)

Returns:

pyttb.tenmat

__add__(other)

Binary addition (+) for tenmats

Parameters:

other (pyttb.tenmat, float, int)

Returns:

pyttb.tenmat

__radd__(other)

Reverse binary addition (+) for tenmats

Parameters:

other (pyttb.tenmat, float, int)

Returns:

pyttb.tenmat

__sub__(other)

Binary subtraction (-) for tenmats

Parameters:

other (pyttb.tenmat, float, int)

Returns:

pyttb.tenmat

__rsub__(other)

Reverse binary subtraction (-) for tenmats

Parameters:

other (pyttb.tenmat, float, int)

Returns:

pyttb.tenmat

__pos__()

Unary plus (+) for tenmats

Returns:

pyttb.tenmat – copy of tenmat

__neg__()

Unary minus (-) for tenmats

Returns:

pyttb.tenmat – copy of tenmat

__repr__()

String representation of a tenmat.

Returns:

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

__str__()

String representation of a tenmat.

Returns:

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