pykoop.lmi_regressors.LmiHinfZpkMeta

class LmiHinfZpkMeta(hinf_regressor=None, type='post', zeros=None, poles=None, gain=1, discretization='bilinear', t_step=1, units='rad/s')

Bases: RegressorMixin, BaseEstimator

Meta-estimator where H-infinity weight is specified in ZPK format.

H-infinity regularization weights must normally be specified in discrete-time state space format. This can make cross-validating pole or zero positions annoying. This meta-estimator wraps LmiEdmdHinfReg or LmiDmdcHinfReg and allows the weighting filter to be specified using zeros, poles, and a gain (i.e., ZPK format) in continuous-time.

All attributes with a trailing underscore are set by fit().

Parameters:
hinf_regressor_

Fit internal regressor.

Type:

koopman_pipeline.KoopmanRegressor

ss_ct_

Continuous-times state space weight.

Type:

scipy.signal.lti

ss_dt_

Discrete-times state space weight.

Type:

scipy.signal.dlti

n_features_in_

Number of features input, including episode feature.

Type:

int

n_states_in_

Number of states input.

Type:

int

n_inputs_in_

Number of inputs input.

Type:

int

episode_feature_

Indicates if episode feature was present during fit().

Type:

bool

feature_names_in_

Array of input feature name strings.

Type:

np.ndarray

coef_

Fit coefficient matrix.

Type:

np.ndarray

__init__(hinf_regressor=None, type='post', zeros=None, poles=None, gain=1, discretization='bilinear', t_step=1, units='rad/s')

Instantiate LmiHinfZpkMeta.

Parameters:

  • hinf_regressor (Optional[koopman_pipeline.KoopmanRegressor]) – Instance of LmiEdmdHinfReg or LmiDmdcHinfReg.

  • type (str) – Type of weight ('pre' or 'post').

  • zeros (Union[float, np.ndarray, None]) – Filter zeros. If None, no zeros are used. Accepts scalar input if only one zero is required.

  • poles (Union[float, np.ndarray, None]) – Filter poles. If None, no poles are used. Accepts scalar input if only one pole is required.

  • gain (float) – Filter gain.

  • discretization (str) –

    Discretization method supported by scipy.signal.cont2discrete() (except 'gbt'). Specifically, possible valued are

    • 'bilinear' – Tustin’s approximation (recommended),

    • 'euler' – Euler (or forward differencing) method,

    • 'backward_diff' – backwards differencing method,

    • 'zoh' – zero-order hold method,

    • 'foh' – first-order hold method, or

    • 'impulse' – equivalent impulse response method.

  • t_step (float) – Timestep beween samples. Used for discretization.

  • units (str) –

    Units of poles and zeros. Possible values are

    • 'rad/s' – radians per second,

    • 'hz' – Hertz, or

    • 'normalized' – normalized, where 1 is the Nyquist frequency.

Return type:

None

Notes

The zeros and poles in the weight should usually have negative real parts! If you want a pole at 10 rad/s, then poles must be -10.

Examples

>>> est = pykoop.lmi_regressors.LmiHinfZpkMeta(
...     hinf_regressor=pykoop.lmi_regressors.LmiEdmdHinfReg(),
...     type='post',
...     zeros=-0,
...     poles=-5,
...     gain=1,
...     discretization='bilinear',
...     t_step=0.1,
... )
>>> est.fit(X_msd, n_inputs=1, episode_feature=True)
LmiHinfZpkMeta(hinf_regressor=LmiEdmdHinfReg(), poles=-5, t_step=0.1,
zeros=0)

Methods

__init__([hinf_regressor, type, zeros, ...])

Instantiate LmiHinfZpkMeta.

fit(X[, y, n_inputs, episode_feature])

Fit the regressor.

get_metadata_routing()

Get metadata routing of this object.

get_params([deep])

Get parameters for this estimator.

predict(X)

Perform a single-step prediction for each state in each episode.

score(X, y[, sample_weight])

Return the coefficient of determination of the prediction.

set_fit_request(*[, episode_feature, n_inputs])

Request metadata passed to the fit method.

set_params(**params)

Set the parameters of this estimator.

set_score_request(*[, sample_weight])

Request metadata passed to the score method.
fit(X, y=None, n_inputs=0, episode_feature=False)

Fit the regressor.

If only X is specified, the regressor will compute its unshifted and shifted versions. If X and y are specified, X is treated as the unshifted data matrix, while y is treated as the shifted data matrix.

Parameters:

  • X (np.ndarray) – Full data matrix if y=None. Unshifted data matrix if y is specified.

  • y (Optional[np.ndarray]) – Optional shifted data matrix. If None, shifted data matrix is computed using X.

  • n_inputs (int) – Number of input features at the end of X.

  • episode_feature (bool) – True if first feature indicates which episode a timestep is from.

Returns:

Instance of itself.

Return type:

LmiHinfZpkMeta

Raises:

ValueError – If constructor or fit parameters are incorrect.

get_metadata_routing()

Get metadata routing of this object.

Please check User Guide on how the routing mechanism works.

Returns:

routing – A MetadataRequest encapsulating routing information.

Return type:

MetadataRequest

get_params(deep=True)

Get parameters for this estimator.

Parameters:

deep (bool, default=True) – If True, will return the parameters for this estimator and contained subobjects that are estimators.

Returns:

params – Parameter names mapped to their values.

Return type:

dict

predict(X)

Perform a single-step prediction for each state in each episode.

Parameters:

X (np.ndarray) – Data matrix.

Returns:

Predicted data matrix.

Return type:

np.ndarray

score(X, y, sample_weight=None)

Return the coefficient of determination of the prediction.

The coefficient of determination \(R^2\) is defined as \((1 - \frac{u}{v})\), where \(u\) is the residual sum of squares ((y_true - y_pred)** 2).sum() and \(v\) is the total sum of squares ((y_true - y_true.mean()) ** 2).sum(). The best possible score is 1.0 and it can be negative (because the model can be arbitrarily worse). A constant model that always predicts the expected value of y, disregarding the input features, would get a \(R^2\) score of 0.0.

Parameters:

  • X (array-like of shape (n_samples, n_features)) – Test samples. For some estimators this may be a precomputed kernel matrix or a list of generic objects instead with shape (n_samples, n_samples_fitted), where n_samples_fitted is the number of samples used in the fitting for the estimator.

  • y (array-like of shape (n_samples,) or (n_samples, n_outputs)) – True values for X.

  • sample_weight (array-like of shape (n_samples,), default=None) – Sample weights.

Returns:

score – \(R^2\) of self.predict(X) w.r.t. y.

Return type:

float

Notes

The \(R^2\) score used when calling score on a regressor uses multioutput='uniform_average' from version 0.23 to keep consistent with default value of r2_score(). This influences the score method of all the multioutput regressors (except for MultiOutputRegressor).

set_fit_request(*, episode_feature='$UNCHANGED$', n_inputs='$UNCHANGED$')

Request metadata passed to the fit method.

Note that this method is only relevant if enable_metadata_routing=True (see sklearn.set_config()). Please see User Guide on how the routing mechanism works.

The options for each parameter are:

  • True: metadata is requested, and passed to fit if provided. The request is ignored if metadata is not provided.

  • False: metadata is not requested and the meta-estimator will not pass it to fit.

  • None: metadata is not requested, and the meta-estimator will raise an error if the user provides it.

  • str: metadata should be passed to the meta-estimator with this given alias instead of the original name.

The default (sklearn.utils.metadata_routing.UNCHANGED) retains the existing request. This allows you to change the request for some parameters and not others.

Added in version 1.3.

Note

This method is only relevant if this estimator is used as a sub-estimator of a meta-estimator, e.g. used inside a Pipeline. Otherwise it has no effect.

Parameters:

  • episode_feature (str, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED) – Metadata routing for episode_feature parameter in fit.

  • n_inputs (str, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED) – Metadata routing for n_inputs parameter in fit.

  • self (LmiHinfZpkMeta)

Returns:

self – The updated object.

Return type:

object

set_params(**params)

Set the parameters of this estimator.

The method works on simple estimators as well as on nested objects (such as Pipeline). The latter have parameters of the form <component>__<parameter> so that it’s possible to update each component of a nested object.

Parameters:

**params (dict) – Estimator parameters.

Returns:

self – Estimator instance.

Return type:

estimator instance

set_score_request(*, sample_weight='$UNCHANGED$')

Request metadata passed to the score method.

Note that this method is only relevant if enable_metadata_routing=True (see sklearn.set_config()). Please see User Guide on how the routing mechanism works.

The options for each parameter are:

  • True: metadata is requested, and passed to score if provided. The request is ignored if metadata is not provided.

  • False: metadata is not requested and the meta-estimator will not pass it to score.

  • None: metadata is not requested, and the meta-estimator will raise an error if the user provides it.

  • str: metadata should be passed to the meta-estimator with this given alias instead of the original name.

The default (sklearn.utils.metadata_routing.UNCHANGED) retains the existing request. This allows you to change the request for some parameters and not others.

Added in version 1.3.

Note

This method is only relevant if this estimator is used as a sub-estimator of a meta-estimator, e.g. used inside a Pipeline. Otherwise it has no effect.

Parameters:

  • sample_weight (str, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED) – Metadata routing for sample_weight parameter in score.

  • self (LmiHinfZpkMeta)

Returns:

self – The updated object.

Return type:

object