Matrix

This class is used to represent both numeric and symbolic complex matrices. Every matrix in perceval is an instance of this class.

>>> import perceval as pcvl
>>> M = pcvl.Matrix("1 2 3\n4 5 6\n7 8 9")
>>> pcvl.pdisplay(M)
⎡1  2  3⎤
⎢4  5  6⎥
⎣7  8  9⎦
>>> M.is_unitary()
False

It also comes with utility methods to create unitary matrices

>>> random_unitary = pcvl.Matrix.random_unitary(6)  # 6*6
>>> deterministic_unitary = pcvl.Matrix.parametrized_unitary(list(range(8)))  # 2*2 (requires 2*m**2 parameters)
>>> from_array_unitary = pcvl.Matrix.get_unitary_extension(numpy_2d_array)  # Size (row+col) * (row+col)

class perceval.utils.matrix.Matrix(source, use_symbolic=None)

This parent class is the gateway MatrixN or MatrixS - based on use_symbolic, and checking if input contains any parameter, it will create an instance of one or the other class.

MatrixS is a subclass of sympy.Matrix with slight API augmentations for compatibility with numpy
MatrixN is a subclass of numpy.ndarray

Both classes have additional utility functions - while Matrix class is also presenting additional static utility functions

static __new__(cls, source, use_symbolic=None)

Constructor for Matrix class

Parameters:

source – can be a string, a file, a list, a ndarray, another Matrix, or a integer
use_symbolic – True to force use of symbolic, False to force use of numeric, None to select based on source

static eye(n, use_symbolic=False)

Returns an identity matrix

Parameters:

n (int) – size of the matrix
use_symbolic (bool) – defines if matrix will be symbolic or numeric

Return type:

Matrix

Returns:

an identity matrix

static get_unitary_extension(M)

Embed the input matrix M into a unitary matrix U

U = | M/σ * |: * * |

\[\begin{split}U = \begin{matrix} M/σ & * \\ * & * \end{matrix}\end{split}\]

Parameters:: M (ndarray) – np.ndarray describing a row x col complex matrix
Return type:: MatrixN
Returns:: numeric matrix describing a (row + col) x (row + col) complex unitary matrix

abstract is_symbolic()

check if matrix is symbolic or numeric

Return type:: bool

abstract is_unitary()

check if matrix is unitary

Return type:: bool

static parametrized_unitary(n, parameters)

static method generating a parametrized unitary matrix

Parameters:

n (int) – size of the Matrix
parameters (np.ndarray | list) – \(2n^2\) parameters to use as generator

Return type:

MatrixN

Returns:

a numeric Matrix

static random_unitary(n)

static method generating a random unitary matrix

Parameters:: n (int) – size of the Matrix
Return type:: MatrixN
Returns:: a numeric Matrix

simp(): Simplify the matrix - only implemented for symbolic matrix

static zeros(shape, use_symbolic=False)

Generate an empty matrix

Parameters:

shape (tuple[int, int]) – 2D shape of the matrix
use_symbolic (bool) – defines if matrix will be symbolic or numeric

Return type:

Matrix

Returns:

an empty matrix