pykoop.lmi_regressors.LmiEdmdHinfReg
- class LmiEdmdHinfReg(alpha=1, ratio=1, weight=None, max_iter=100, iter_atol=1e-06, iter_rtol=0, inv_method='svd', tsvd=None, square_norm=False, picos_eps=1e-06, solver_params=None)
Bases:
LmiRegressor
LMI-based EDMD with H-infinity norm regularization.
Optionally supports additional Tikhonov regularization.
- Parameters:
- tsvd_
Fit truncated SVD object.
- Type:
- P_
P
matirx for debugging.- Type:
np.ndarray
- gamma_
H-infinity norm for debugging.
- Type:
np.ndarray
- solver_params_
Solver parameters used (defaults merged with constructor input).
- Type:
Optional[Dict[str, Any]]
- feature_names_in_
Array of input feature name strings.
- Type:
np.ndarray
- coef_
Fit coefficient matrix.
- Type:
np.ndarray
Examples
Apply EDMD with H-infinity regularization to mass-spring-damper data
>>> kp = pykoop.KoopmanPipeline( ... regressor=pykoop.lmi_regressors.LmiEdmdHinfReg( ... alpha=1e-3, ... ) ... ) >>> kp.fit(X_msd, n_inputs=1, episode_feature=True) KoopmanPipeline(regressor=LmiEdmdHinfReg(alpha=0.001))
Apply EDMD with weighted H-infinity regularization to mass-spring-damper data
>>> from scipy import signal >>> ss_ct = signal.ZerosPolesGain([0], [-4], [1]).to_ss() >>> ss_dt = ss_ct.to_discrete(dt=0.1, method='bilinear') >>> kp = pykoop.KoopmanPipeline( ... regressor=pykoop.lmi_regressors.LmiEdmdHinfReg( ... alpha=1e-3, ... weight=('pre', ss_dt.A, ss_dt.B, ss_dt.C, ss_dt.D), ... ) ... ) >>> kp.fit(X_msd, n_inputs=1, episode_feature=True) KoopmanPipeline(regressor=LmiEdmdHinfReg(alpha=0.001, weight=('pre', array([[...]]), array([[...]]), array([[...]]), array([[...]]))))
- __init__(alpha=1, ratio=1, weight=None, max_iter=100, iter_atol=1e-06, iter_rtol=0, inv_method='svd', tsvd=None, square_norm=False, picos_eps=1e-06, solver_params=None)
Instantiate
LmiEdmdHinfReg
.Supports cascading the plant with an LTI weighting function.
- Parameters:
alpha (float) – Regularization coefficient. Cannot be zero.
ratio (float) – Ratio of H-infinity norm to use in mixed regularization. If
ratio=1
, no Tikhonov regularization is used. Cannot be zero.weight (Optional[Tuple[str, np.ndarray, np.ndarray, np.ndarray,) – np.ndarray]] Tuple containing weight type (
'pre'
or'post'
), and the weight state space matrices (A
,B
,C
, andD
). IfNone
, no weighting is used.max_iter (int) – Maximum number of solver iterations.
iter_atol (float) – Absolute tolerance for change in objective function value.
iter_rtol (float) – Relative tolerance for change in objective function value.
inv_method (str) –
- Method to handle or avoid inversion of the
H
matrix when forming the LMI problem. Possible values are
'inv'
– invertH
directly,'pinv'
– apply the Moore-Penrose pseudoinverse toH
,'eig'
– splitH
using an eigendecomposition,'ldl'
– splitH
using an LDL decomposition,'chol'
– splitH
using a Cholesky decomposition,'sqrt'
– splitH
usingscipy.linalg.sqrtm()
, or'svd'
– splitH
using a singular value decomposition.
- tsvdOptional[pykoop.Tsvd]
Singular value truncation method if
inv_method='svd'
. IfNone
, economy SVD is used.
- Method to handle or avoid inversion of the
square_norm (bool) – Square norm H-infinity norm in regularizer. Enabling may increase computation time. Frobenius norm used in Tikhonov regularizer is always squared.
picos_eps (float) – Tolerance used for strict LMIs. If nonzero, should be larger than solver tolerance.
solver_params (Optional[Dict[str, Any]]) – Parameters passed to PICOS
picos.Problem.solve()
. By default, allows chosen solver to select its own tolerances.tsvd (Tsvd | None)
- Return type:
None
Methods
__init__
([alpha, ratio, weight, max_iter, ...])Instantiate
LmiEdmdHinfReg
.fit
(X[, y, n_inputs, episode_feature])Fit the regressor.
frequency_response
(t_step[, f_min, f_max, ...])Compute frequency response of Koopman system.
Get metadata routing of this object.
get_params
([deep])Get parameters for this estimator.
plot_bode
(t_step[, f_min, f_max, n_points, ...])Plot frequency response of Koopman system.
plot_eigenvalues
([unit_circle, figure_kw, ...])Plot eigenvalues of Koopman
A
matrix.plot_koopman_matrix
([subplots_kw, plot_kw])Plot heatmap of Koopman matrices.
plot_svd
([subplots_kw, plot_kw])Plot singular values of Koopman matrices.
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. IfX
andy
are specified,X
is treated as the unshifted data matrix, whiley
is treated as the shifted data matrix.- Parameters:
X (np.ndarray) – Full data matrix if
y=None
. Unshifted data matrix ify
is specified.y (Optional[np.ndarray]) – Optional shifted data matrix. If
None
, shifted data matrix is computed usingX
.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:
- Raises:
ValueError – If constructor or fit parameters are incorrect.
- frequency_response(t_step, f_min=0, f_max=None, n_points=1000, decibels=True)
Compute frequency response of Koopman system.
- Parameters:
- Returns:
Frequency (Hz) and frequency response (gain or dB).
- Return type:
Tuple[np.ndarray, np.ndarray]
- Raises:
ValueError – If
f_min
is less than zero orf_max
is greater than the Nyquist frequency.
- 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.
- plot_bode(t_step, f_min=0, f_max=None, n_points=1000, decibels=True, subplots_kw=None, plot_kw=None)
Plot frequency response of Koopman system.
- Parameters:
t_step (float) – Sampling timestep.
f_min (float) – Minimum frequency to plot.
f_max (Optional[float]) – Maximum frequency to plot. If
None
, uses Nyquist frequency.n_points (int) – Number of frequecy points to plot.
decibels (bool) – Plot gain in dB (default is true).
subplots_kw (Optional[Dict[str, Any]]) – Keyword arguments for
plt.subplots()
.plot_kw (Optional[Dict[str, Any]]) – Keyword arguments for Matplotlib
plt.Axes.plot()
.
- Returns:
Matplotlib
plt.Figure
andplt.Axes
objects.- Return type:
Tuple[plt.Figure, plt.Axes]
- Raises:
ValueError – If
f_min
is less than zero orf_max
is greater than the Nyquist frequency.
- plot_eigenvalues(unit_circle=True, figure_kw=None, subplot_kw=None, plot_kw=None)
Plot eigenvalues of Koopman
A
matrix.- Parameters:
- Returns:
Matplotlib
plt.Figure
andplt.Axes
objects.- Return type:
Tuple[plt.Figure, plt.Axes]
- plot_koopman_matrix(subplots_kw=None, plot_kw=None)
Plot heatmap of Koopman matrices.
- plot_svd(subplots_kw=None, plot_kw=None)
Plot singular values of Koopman matrices.
- 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)
, wheren_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:
Notes
The \(R^2\) score used when calling
score
on a regressor usesmultioutput='uniform_average'
from version 0.23 to keep consistent with default value ofr2_score()
. This influences thescore
method of all the multioutput regressors (except forMultiOutputRegressor
).
- 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
(seesklearn.set_config()
). Please see User Guide on how the routing mechanism works.The options for each parameter are:
True
: metadata is requested, and passed tofit
if provided. The request is ignored if metadata is not provided.False
: metadata is not requested and the meta-estimator will not pass it tofit
.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 infit
.n_inputs (str, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED) – Metadata routing for
n_inputs
parameter infit
.self (LmiEdmdHinfReg)
- Returns:
self – The updated object.
- Return type:
- 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
(seesklearn.set_config()
). Please see User Guide on how the routing mechanism works.The options for each parameter are:
True
: metadata is requested, and passed toscore
if provided. The request is ignored if metadata is not provided.False
: metadata is not requested and the meta-estimator will not pass it toscore
.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 inscore
.self (LmiEdmdHinfReg)
- Returns:
self – The updated object.
- Return type: