operators

class MatrixOperatorCompatibility

Bases: object

Compatibility check for objects of MatrixOperator

static compatible_for_addition(first_operator, second_operator)

Parameters

• first_operator (MatrixOperator) –

• second_operator (MatrixOperator) –

static compatible_for_composition(first_operator, second_operator)

Parameters

• first_operator (MatrixOperator) –

• second_operator (MatrixOperator) –

class MatrixOperator(flattened_operator, input_shape, output_shape, order, representing_matrix=None)

Bases: object

Parameters

• flattened_operator (Union[LinearOperator, ndarray, csr_matrix]) –

• input_shape (Tuple[int, int]) –

• output_shape (Tuple[int, int]) –

• order (IndexingOrder) –

• representing_matrix (Optional[Union[ndarray, csr_matrix]]) –

class IndexingOrder(value, names=None, *, module=None, qualname=None, type=None, start=1, boundary=None)

Bases: Enum

Enum for order argument for numpy.reshape() and numpy.flatten()

ROW_MAJOR = 'C'

COLUMN_MAJOR = 'F'

__init__(flattened_operator, input_shape, output_shape, order, representing_matrix=None)

Represents an operator

\[\Phi: \mathbb{C}^{d_1 \times d_2} \rightarrow \mathbb{C}^{m_1 \times m_2}.\]

Takes care on flattening and reshaping. Wraps a scipy linear operator or numpy array.

Parameters

• flattened_operator (Union[LinearOperator, ndarray, csr_matrix]) –

  Represents the flattened map

  \[\varphi: \mathbb{C}^{d_1 \cdot d_2} \rightarrow \mathbb{C}^{m_1 \cdot m_2},\]

  such that \(\varphi(\operatorname{vec}(x)) = \operatorname{vec}(\Phi(x))\).

• input_shape (Tuple[int, int]) – \((d_1,d_2)\)

• output_shape (Tuple[int, int]) – \((m_1,m_2)\)

• order (IndexingOrder) – order for vectorization \(\operatorname{vec}\)

• representing_matrix (Optional[Union[ndarray, csr_matrix]]) – matrix representation of flattened operator

dot(x)

Matrix-matrix multiplication (operator application) or operator composition.

Parameters

x (array_like of shape \((d_1, d_2)\) or MatrixOperator compatible for composition or scalar) –

Returns

• :math:`Phi(x)` (array or MatrixOperator that represents)

• the result of applying this linear operator on x.

property shape

property output_shape

property input_shape

property order

property flattened_operator

property representing_matrix

adjoint()

Hermitian adjoint.

Returns a MatrixOperator that represents the Hermitian adjoint of this one

Can be abbreviated self.H instead of self.adjoint().

Returns

:math:`Phi^{star}` – Hermitian adjoint of self.

Return type

MatrixOperator

property H

Hermitian adjoint.

Returns a MatrixOperator that represents the Hermitian adjoint of this one

Can be abbreviated self.H instead of self.adjoint().

Returns

:math:`Phi^{star}` – Hermitian adjoint of self.

Return type

MatrixOperator

transpose()

Transpose this linear operator.

Returns a MatrixOperator that represents the transpose of this one. Can be abbreviated self.T instead of self.transpose().

Returns

:math:`Phi^{star}` – adjoint of self.

Return type

MatrixOperator

property T

Transpose this linear operator.

Returns a MatrixOperator that represents the transpose of this one. Can be abbreviated self.T instead of self.transpose().

Returns

:math:`Phi^{star}` – adjoint of self.

Return type

MatrixOperator

class SamplingOperator(*args, **kwargs)

Bases: LinearOperator

Parameters

• indices (Union[List[int], ndarray]) –

• input_dimension (int) –

__init__(indices, input_dimension)

Parameters

• indices (linear indices) –

• input_dimension –

property indices

property input_dimension

property sampling_matrix

classmethod from_matrix_indices(row_indices, column_indices, shape, order=IndexingOrder.COLUMN_MAJOR)

Parameters

• row_indices (List[int]) –

• column_indices (List[int]) –

• shape (Tuple[int, int]) –

• order (IndexingOrder) –

class SamplingMatrixOperator(row_indices, column_indices, shape, order=IndexingOrder.COLUMN_MAJOR)

Bases: MatrixOperator

Parameters

• row_indices (List[int]) –

• column_indices (List[int]) –

• shape (Tuple[int, int]) –

• order (IndexingOrder) –

__init__(row_indices, column_indices, shape, order=IndexingOrder.COLUMN_MAJOR)

Represents an operator

\[\Phi: \mathbb{C}^{d_1 \times d_2} \rightarrow \mathbb{C}^{m_1 \times m_2}.\]

Takes care on flattening and reshaping. Wraps a scipy linear operator or numpy array.

Parameters

• flattened_operator –

  Represents the flattened map

  \[\varphi: \mathbb{C}^{d_1 \cdot d_2} \rightarrow \mathbb{C}^{m_1 \cdot m_2},\]

  such that \(\varphi(\operatorname{vec}(x)) = \operatorname{vec}(\Phi(x))\).

• input_shape – \((d_1,d_2)\)

• output_shape – \((m_1,m_2)\)

• order (IndexingOrder) – order for vectorization \(\operatorname{vec}\)

• representing_matrix – matrix representation of flattened operator

• row_indices (List[int]) –

• column_indices (List[int]) –

• shape (Tuple[int, int]) –

classmethod from_index_tuples(indices, shape)

Parameters

• indices (List[int]) –

• shape (Tuple[int, int]) –

class InverseWeightOperator(left_inverse_weight, right_inverse_weight, order)

Bases: MatrixOperator

Parameters

• left_inverse_weight (ndarray) –

• right_inverse_weight (ndarray) –

__init__(left_inverse_weight, right_inverse_weight, order)

Constructs inverse weight operator from one-sided inverse weights.

Parameters

• left_inverse_weight (ndarray) –

• right_inverse_weight (ndarray) –

• order –