pysindy.feature_library.SINDyPILibrary

class pysindy.feature_library.SINDyPILibrary(library_functions=None, t=None, x_dot_library_functions=None, function_names=None, interaction_only=True, differentiation_method=None, include_bias=False)[source]

WARNING: This library is deprecated in PySINDy versions > 1.7. Please use the PDE or WeakPDE libraries instead.

Generate a library with custom functions. The Library takes custom libraries for X and Xdot respectively, and then tensor-products them together. For a 3D system, a library of constant and linear terms in x_dot, i.e. [1, x_dot0, …, x_dot3], is good enough for most problems and implicit terms. The function names list should include both X and Xdot functions, without the mixed terms.

Parameters:

library_functions (list of mathematical functions) – Functions to include in the library. Each function will be applied to each input variable x.
x_dot_library_functions (list of mathematical functions) – Functions to include in the library. Each function will be applied to each input variable x_dot.
t (np.ndarray of time slices) – Time base to compute Xdot from X for the implicit terms
differentiation_method (differentiation object, optional) – Method for differentiating the data. This must be a class extending pysindy.differentiation_methods.base.BaseDifferentiation class. The default option is centered difference.
function_names (list of functions, optional (default None)) – List of functions used to generate feature names for each library function. Each name function must take a string input (representing a variable name), and output a string depiction of the respective mathematical function applied to that variable. For example, if the first library function is sine, the name function might return $\sin(x)$ given $x$ as input. The function_names list must be the same length as library_functions. If no list of function names is provided, defaults to using $[ f_0(x),f_1(x), f_2(x), \ldots ]$. For SINDy-PI, function_names should include the names of the functions in both the x and x_dot libraries (library_functions and x_dot_library_functions), but not the mixed terms, which are computed in the code.
interaction_only (boolean, optional (default True)) – Whether to omit self-interaction terms. If True, function evaulations of the form $f(x,x)$ and $f(x,y,x)$ will be omitted, but those of the form $f(x,y)$ and $f(x,y,z)$ will be included. If False, all combinations will be included.
include_bias (boolean, optional (default False)) – If True (default), then include a bias column, the feature in which all polynomial powers are zero (i.e. a column of ones - acts as an intercept term in a linear model). This is hard to do with just lambda functions, because if the system is not 1D, lambdas will generate duplicates.

Attributes:

functions (list of functions) – Mathematical library functions to be applied to each input feature.
function_names (list of functions) – Functions for generating string representations of each library function.
n_features_in_ (int) – The total number of input features.
n_output_features_ (int) – The total number of output features. The number of output features is the product of the number of library functions and the number of input features.

Examples

>>> import numpy as np
>>> from pysindy.feature_library import SINDyPILibrary
>>> t = np.linspace(0, 1, 5)
>>> x = np.ones((5, 2))
>>> functions = [lambda x: 1, lambda x : np.exp(x),
                 lambda x,y : np.sin(x+y)]
>>> x_dot_functions = [lambda x: 1, lambda x : x]
>>> function_names = [lambda x: '',
                      lambda x : 'exp(' + x + ')',
                      lambda x, y : 'sin(' + x + y + ')',
                      lambda x: '',
              lambda x : x]
>>> lib = ps.SINDyPILibrary(library_functions=functions,
                            x_dot_library_functions=x_dot_functions,
                            function_names=function_names, t=t
                            ).fit(x)
>>> lib.transform(x)
        [[ 1.00000000e+00  2.71828183e+00  2.71828183e+00  9.09297427e-01
           2.22044605e-16  6.03579815e-16  6.03579815e-16  2.01904588e-16
           2.22044605e-16  6.03579815e-16  6.03579815e-16  2.01904588e-16]
         [ 1.00000000e+00  2.71828183e+00  2.71828183e+00  9.09297427e-01
           0.00000000e+00  0.00000000e+00  0.00000000e+00  0.00000000e+00
           0.00000000e+00  0.00000000e+00  0.00000000e+00  0.00000000e+00]
         [ 1.00000000e+00  2.71828183e+00  2.71828183e+00  9.09297427e-01
           0.00000000e+00  0.00000000e+00  0.00000000e+00  0.00000000e+00
           0.00000000e+00  0.00000000e+00  0.00000000e+00  0.00000000e+00]
         [ 1.00000000e+00  2.71828183e+00  2.71828183e+00  9.09297427e-01
           0.00000000e+00  0.00000000e+00  0.00000000e+00  0.00000000e+00
           0.00000000e+00  0.00000000e+00  0.00000000e+00  0.00000000e+00]
         [ 1.00000000e+00  2.71828183e+00  2.71828183e+00  9.09297427e-01
          -2.22044605e-16 -6.03579815e-16 -6.03579815e-16 -2.01904588e-16
          -2.22044605e-16 -6.03579815e-16 -6.03579815e-16 -2.01904588e-16]]
>>> lib.get_feature_names()
    ['', 'exp(x0)', 'exp(x1)', 'sin(x0x1)', 'x0_dot', 'exp(x0)x0_dot',
     'exp(x1)x0_dot', 'sin(x0x1)x0_dot', 'x1_dot', 'exp(x0)x1_dot',
     'exp(x1)x1_dot', 'sin(x0x1)x1_dot']

Methods

`fit`	Compute number of output features.
`get_feature_names`	Return feature names for output features.
`set_fit_request`	Configure whether metadata should be requested to be passed to the `fit` method.
`set_transform_request`	Configure whether metadata should be requested to be passed to the `transform` method.
`transform`	Transform data to custom features

Attributes

`n_features_in_`
`n_output_features_`

fit(x_full, y=None)[source]

Compute number of output features.

Parameters:: x (array-like, shape (n_samples, n_features)) – Measurement data.
Returns:: self
Return type:: instance

get_feature_names(input_features=None)[source]

Return feature names for output features.

Parameters:: input_features (list of string, length n_features, optional) – String names for input features if available. By default, “x0”, “x1”, … “xn_features” is used.
Returns:: output_feature_names
Return type:: list of string, length n_output_features

set_fit_request(*, x_full: bool | None | str = '$UNCHANGED$') → SINDyPILibrary

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

set_transform_request(*, x_full: bool | None | str = '$UNCHANGED$') → SINDyPILibrary

Configure whether metadata should be requested to be passed to the transform 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 transform 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 transform.
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:: x_full (str, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED) – Metadata routing for x_full parameter in transform.
Returns:: self – The updated object.
Return type:: object

transform(x_full)[source]

Transform data to custom features

Parameters:: x (array-like, shape (n_samples, n_features)) – The data to transform, row by row.
Returns:: xp – The matrix of features, where n_output_features is the number of features generated from applying the custom functions to the inputs.
Return type:: np.ndarray, shape (n_samples, n_output_features)