pysindy.optimizers.STLSQ

class pysindy.optimizers.STLSQ(threshold=0.1, alpha=0.05, max_iter=20, ridge_kw=None, normalize_columns=False, copy_X=True, initial_guess=None, verbose=False, sparse_ind=None, unbias=True)[source]

Sequentially thresholded least squares algorithm. Defaults to doing Sequentially thresholded Ridge regression.

Attempts to minimize the objective function $\|y - Xw\|^2_2 + \alpha \|w\|^2_2$ by iteratively performing least squares and masking out elements of the weight array w that are below a given threshold.

See the following reference for more details:

Brunton, Steven L., Joshua L. Proctor, and J. Nathan Kutz. “Discovering governing equations from data by sparse identification of nonlinear dynamical systems.” Proceedings of the national academy of sciences 113.15 (2016): 3932-3937.

Parameters:

threshold (float, optional (default 0.1)) – Minimum magnitude for a coefficient in the weight vector. Coefficients with magnitude below the threshold are set to zero.
alpha (float, optional (default 0.05)) – Optional L2 (ridge) regularization on the weight vector.
max_iter (int, optional (default 20)) – Maximum iterations of the optimization algorithm.
ridge_kw (dict, optional (default None)) – Optional keyword arguments to pass to the ridge regression.
normalize_columns (boolean, optional (default False)) – Normalize the columns of x (the SINDy library terms) before regression by dividing by the L2-norm. Note that the ‘normalize’ option in sklearn is deprecated in sklearn versions >= 1.0 and will be removed.
copy_X (boolean, optional (default True)) – If True, X will be copied; else, it may be overwritten.
initial_guess (np.ndarray, shape (n_features) or (n_targets, n_features),) – optional (default None) Initial guess for coefficients coef_. If None, least-squares is used to obtain an initial guess.
verbose (bool, optional (default False)) – If True, prints out the different error terms every iteration.
sparse_ind (list, optional (default None)) – Indices to threshold and perform ridge regression upon. If None, sparse thresholding and ridge regression is applied to all indices.

Attributes:

coef_ (array, shape (n_features,) or (n_targets, n_features)) – Weight vector(s).
ind_ (array, shape (n_features,) or (n_targets, n_features)) – Array of 0s and 1s indicating which coefficients of the weight vector have not been masked out, i.e. the support of self.coef_.
history_ (list) – History of coef_. history_[k] contains the values of coef_ at iteration k of sequentially thresholded least-squares.

Examples

>>> import numpy as np
>>> from scipy.integrate import odeint
>>> from pysindy import SINDy
>>> from pysindy.optimizers import STLSQ
>>> lorenz = lambda z,t : [10*(z[1] - z[0]),
>>>                        z[0]*(28 - z[2]) - z[1],
>>>                        z[0]*z[1] - 8/3*z[2]]
>>> t = np.arange(0,2,.002)
>>> x = odeint(lorenz, [-8,8,27], t)
>>> opt = STLSQ(threshold=.1, alpha=.5)
>>> model = SINDy(optimizer=opt)
>>> model.fit(x, t=t[1]-t[0])
>>> model.print()
x0' = -9.999 1 + 9.999 x0
x1' = 27.984 1 + -0.996 x0 + -1.000 1 x1
x2' = -2.666 x1 + 1.000 1 x0

Methods

`set_fit_request`	Configure whether metadata should be requested to be passed to the `fit` method.
`set_score_request`	Configure whether metadata should be requested to be passed to the `score` method.

Attributes

`complexity`
`max_iter`
`normalize_columns`
`initial_guess`
`copy_X`
`unbias`
`coef_`
`intercept_`

set_fit_request(*, sample_weight: bool | None | str = '$UNCHANGED$', x_: bool | None | str = '$UNCHANGED$') → STLSQ

Configure whether metadata should be requested to be passed to the fit method.

Note that this method is only relevant when this estimator is used as a sub-estimator within a meta-estimator and metadata routing is enabled with enable_metadata_routing=True (see sklearn.set_config). Please check the 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.

Parameters:

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

Returns:

self – The updated object.

Return type:

object

set_score_request(*, sample_weight: bool | None | str = '$UNCHANGED$') → STLSQ

Configure whether metadata should be requested to be passed to the score method.

Note that this method is only relevant when this estimator is used as a sub-estimator within a meta-estimator and metadata routing is enabled with enable_metadata_routing=True (see sklearn.set_config). Please check the 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.

Parameters:: sample_weight (str, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED) – Metadata routing for sample_weight parameter in score.
Returns:: self – The updated object.
Return type:: object