utils

class nfoursid.utils.Decomposition(left_orthogonal, eigenvalues, right_orthogonal)

Bases: tuple

Eigenvalue decomposition of a matrix matrix such that left_orthogonal @ eigenvalues @ right_orthogonal equals matrix.

property eigenvalues

Alias for field number 1

property left_orthogonal

Alias for field number 0

property right_orthogonal

Alias for field number 2

class nfoursid.utils.Utils

Bases: object

static block_hankel_matrix(matrix: numpy.ndarray, num_block_rows: int) → numpy.ndarray

Calculate a block Hankel matrix based on input matrix matrix with num_block_rows block rows. The shape of matrix is interpreted in row-order, like the structure of a pd.DataFrame: the rows are measurements and the columns are data sources.

The returned block Hankel matrix has a columnar structure. Every column of the returned matrix consists of num_block_rows block rows (measurements). See the examples for details.

Suppose that the input matrix contains 4 measurements of 2-dimensional data:

>>> matrix = np.array([
>>>     [0, 1],
>>>     [2, 3],
>>>     [4, 5],
>>>     [6, 7]
>>> ])

If the number of block rows is set to num_block_rows=2, then the block Hankel matrix will be

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

static eigenvalue_decomposition(matrix: numpy.ndarray) → nfoursid.utils.Decomposition

Calculate eigenvalue decomposition of matrix as a Decomposition.

static reduce_decomposition(decomposition: nfoursid.utils.Decomposition, rank: int) → nfoursid.utils.Decomposition

Reduce an eigenvalue decomposition decomposition such that only rank number of biggest eigenvalues remain. Returns another Decomposition.

static unvectorize(vector: numpy.ndarray, num_rows: int) → numpy.ndarray

Given a vector vector of shape (num_rows*b, 1), return a matrix of shape (num_rows, b) such that the stacked columns of the returned matrix equal vector.

static validate_matrix_shape(matrix: numpy.ndarray, shape: Tuple[float, float], name: str)

Raises if matrix does not have shape shape. The error message will contain name.

static vectorize(matrix: numpy.ndarray) → numpy.ndarray

Given a matrix matrix of shape (a, b), return a vector of shape (a*b, 1) with all columns of matrix stacked on top of eachother.