datasets

Load and fetch sample data for benchmarking and testing purposes.

Functions:

Name	Description
gen_gbn_seq	Generate sequence of inputs GBN.
gen_rw_seq	Generate a sequence of inputs as Random walk.
make_tf	Generate a Transfer Function object of a system.
white_noise	Add a white noise to a signal y.
white_noise_var	Generate a white noise matrix (rows with zero mean).

gen_gbn_seq

gen_gbn_seq(
    n_samples: int,
    p_swd: float,
    n_min: int = 1,
    scale: tuple[float, float] = (-1.0, 1.0),
    tol: float = 0.01,
    nit_max: int = 30,
    seed: int | None = None,
) -> tuple[ndarray, float, int]

Generate sequence of inputs GBN.

Generate Generalized Binary Noise (GBN), apseudo-random binary sequence.

Parameters:

Name	Type	Description	Default
n_samples	int	sequence length (total number of samples)	required
p_swd	float	desired probability of switching (no switch: 0<x<1 :always switch)	required
n_min	int	minimum number of samples between two switches	1
scale	tuple[float, float]	upper and lower values of the sequence	(-1.0, 1.0)
tol	float	tolerance on switching probability relative error	0.01
nit_max	int	maximum number of iterations to get the desired switching probability	30

Return

array of given length and switching probability. actual probability of switching (which may differ a little from p_swd according to tol. number of switches in the sequence.

Examples:

Generating an array of length equal to 1000, 10% of switch probability, switching at least every 20 samples, between -10 or 5;

>>> bn_b, p_sw_b, Nswb = gen_gbn_seq(1000, 0.1, 20, (-10, 5))

References

Y. Zhu. Multivariable System Identification For Process Control. 2001.

gen_rw_seq

gen_rw_seq(
    n_samples: int,
    rw0: float,
    sigma: float = 1.0,
    seed: int | None = None,
) -> ndarray

Generate a sequence of inputs as Random walk.

Generate a random signal sequence (a random walk from a normal distribution).

Parameters:

Name	Type	Description	Default
n_samples	int	sequence length (total number of samples);	required
sigma	float	standard deviation (mobility) of randow walk	1.0
rw0	float	initial value	required

Parameters:

Name	Type	Description	Default
n_samples	int	sequence length (total number of samples)	required
rw0	float	initial value	required
sigma	float	standard deviation (mobility) of random walk	1.0
seed	int | None	seed for random number generator	None

Return

array of given length and switching probability. actual probability of switching (which may differ a little from p_swd according to tol. number of switches in the sequence.

Examples:

Generating an array of length equal to 1000, 10% of switch probability, switching at least every 20 samples, between -10 or 5;

>>> bn_b, p_sw_b, Nswb = gen_gbn_seq(1000, 0.1, 20, (-10, 5))

References

Y. Zhu. Multivariable System Identification For Process Control. 2001.

make_tf

make_tf(
    numerator: list[float],
    denominator: list[float],
    ts: float = 1.0,
    noise: float = 0.0,
    random_state: int | None = None,
) -> TransferFunction

make_tf(
    numerator: list[list[float]],
    denominator: list[list[float]],
    ts: float = 1.0,
    noise: float = 0.0,
    random_state: int | None = None,
) -> NestedTransferFunction

make_tf(
    numerator: list[float] | list[list[float]],
    denominator: list[float] | list[list[float]],
    ts: float = 1.0,
    noise: float = 0.0,
    random_state: int | None = None,
) -> TransferFunction | NestedTransferFunction

Generate a Transfer Function object of a system.

Parameters:

Name	Type	Description	Default
numerator	list[float] | list[list[float]]	Numerator coefficients of the transfer function.	required
denominator	list[float] | list[list[float]]	Denominator coefficients of the transfer function.	required
ts	float	Sampling time, by default 1.0.	1.0
noise	float	Standard deviation of Gaussian noise, by default 0.0.	0.0
random_state	int | None	Random seed, by default None.	None

Returns:

Type	Description
TransferFunction | NestedTransferFunction	TransferFunction or nested structure of TransferFunctions.

white_noise

white_noise(
    y: ndarray, A_rel: float, seed: int | None = None
)

Add a white noise to a signal y.

noise amplitude= A_rel*(standard deviation of y)

Parameters:

Name	Type	Description	Default
y	ndarray	original signal	required
A_rel	float	relative amplitude (0<x<1) to the standard deviation of y	required
seed	int | None	random seed	None

white_noise_var

white_noise_var(
    L: int, Var: ndarray, seed: int | None = None
) -> ndarray

Generate a white noise matrix (rows with zero mean).

Parameters:

Name	Type	Description	Default
L	int	size (columns)	required
Var	ndarray	variance vector	required

Returns:

Type	Description
ndarray	white_noise_var(100,[1,1]) , noise matrix has two row vectors with variance=1