SphericalHarmonicAnalysis#

class ktch.harmonic.SphericalHarmonicAnalysis(n_harmonics=10, n_jobs=None, verbose=0)[source]#

Spherical Harmonic (SPHARM) Analysis

Parameters:

n_harmonics: int, default=10: Number of harmonics to use ($l_mathrm{max}$).
n_jobs: int, default=None: The number of jobs to run in parallel. None means 1 unless in a joblib.parallel_backend context. -1 means using all processors.
verbose: int, default=0: The verbosity level.

Notes

[Ritche_Kemp_1999], [Shen_etal_2009]

A surface point $\mathbf{p}(\theta, \phi)$ is expanded as

\[\mathbf{p}(\theta, \phi) = \sum_{l=0}^{L} \sum_{m=-l}^l a_l^m \, S_l^m(\theta, \phi)\]

where $S_l^m$ are real orthonormal spherical harmonics defined in terms of the complex harmonics $Y_l^m$:

$S_l^0 = Y_l^0$
$S_l^m = \sqrt{2}\,(-1)^m\,\mathrm{Re}(Y_l^m)$ for $m > 0$
$S_l^m = \sqrt{2}\,(-1)^{|m|}\,\mathrm{Im}(Y_l^{|m|})$ for $m < 0$

The coefficients $a_l^m$ are real-valued, so transform returns a float64 array. Conversion utilities _complex_to_real_sph_coef and _real_to_complex_sph_coef are available for interoperability with complex-basis representations.

References

[Ritche_Kemp_1999]

Ritchie, D.W., Kemp, G.J.L. (1999) Fast computation, rotation, and comparison of low resolution spherical harmonic molecular surfaces. J. Comput. Chem. 20: 383–395.

[Shen_etal_2009]

Shen, L., Farid, H., McPeek, M.A. (2009) Modeling three-dimensional morphological structures using spherical harmonics. Evolution (N. Y). 63: 1003–1016.

fit(X, y=None)[source]#

Fit the model (no-op for stateless transformer).

Parameters:

Xignored
yignored

Returns:

self

fit_transform(X, y=None, theta_phi=None)[source]#

Fit and transform in a single step.

Overridden to support metadata routing of theta_phi.

Parameters:

Xlist of array-like of shape (n_coords_i, 3): Coordinate values of n_samples.
yignored
theta_philist of array-like of shape (n_coords_i, 2): Surface parameterization of n_samples.

Returns:

X_transformedndarray of shape (n_samples, n_coefficients)

get_feature_names_out(input_features: None | npt.ArrayLike = None) → np.ndarray[source]#

Get output feature names.

Parameters:

input_featuresignored

Returns:

feature_names_outndarray of str objects: Transformed feature names.

get_metadata_routing()#

Get metadata routing of this object.

Please check User Guide on how the routing mechanism works.

Returns:

routingMetadataRequest: A MetadataRequest encapsulating routing information.

get_params(deep=True)#

Get parameters for this estimator.

Parameters:

deepbool, default=True: If True, will return the parameters for this estimator and contained subobjects that are estimators.

Returns:

paramsdict: Parameter names mapped to their values.

inverse_transform(X_transformed, theta_range=None, phi_range=None, l_max=None)[source]#

Reconstruct surfaces from SPHARM coefficients.

Parameters:

X_transformedarray-like of shape (n_samples, 3 * (l_max + 1)**2): Flat SPHARM coefficient vectors as returned by transform(). Layout is axis-major: [cx_0_0, cx_1_-1, ..., cy_0_0, ..., cz_0_0, ...].
theta_rangearray-like of shape (n_theta,), optional: Polar angle values (colatitude). Defaults to np.linspace(0, pi, 90).
phi_rangearray-like of shape (n_phi,), optional: Azimuthal angle values. Defaults to np.linspace(0, 2*pi, 180).
l_maxint, optional: Maximum degree of harmonics to use. Defaults to self.n_harmonics. When smaller, the input coefficient vector is truncated to the leading (l_max + 1) ** 2 terms per axis. Values greater than self.n_harmonics raise ValueError.

Returns:

X_coordsndarray of shape (n_samples, n_theta, n_phi, 3): Reconstructed surface coordinates.

Raises:

ValueError: If l_max is negative or greater than self.n_harmonics.

Configure whether metadata should be requested to be passed to the inverse_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 inverse_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 inverse_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_transformedstr, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED: Metadata routing for X_transformed parameter in inverse_transform.
l_maxstr, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED: Metadata routing for l_max parameter in inverse_transform.
phi_rangestr, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED: Metadata routing for phi_range parameter in inverse_transform.
theta_rangestr, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED: Metadata routing for theta_range parameter in inverse_transform.

Returns:

selfobject: The updated object.

set_output(*, transform=None)#

Set output container.

Refer to the user guide for more details and Introducing the set_output API for an example on how to use the API.

Parameters:

transform{“default”, “pandas”, “polars”}, default=None

Configure output of transform and fit_transform.

“default”: Default output format of a transformer
“pandas”: DataFrame output
“polars”: Polars output
None: Transform configuration is unchanged

Added in version 1.4: “polars” option was added.

Returns:

selfestimator instance: Estimator instance.

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:

**paramsdict: Estimator parameters.

Returns:

selfestimator instance: Estimator instance.

set_transform_request(*, theta_phi: bool | None | str = '$UNCHANGED$') → SphericalHarmonicAnalysis#

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

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:

theta_phistr, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED: Metadata routing for theta_phi parameter in transform.

Returns:

selfobject: The updated object.

transform(X, theta_phi=None)[source]#

Compute SPHARM coefficients.

Parameters:

X: list of array-like: Coordinate values of n_samples. The i-th array-like whose shape (n_coords_i, 3) represents 3D coordinate values of the i-th sample .
theta_phi: list of array-like of shape (n_coords, 2): Surface parameter of n_samples. The i-th array-like of theta and phi values whose shape is (n_coords_i, 2).

Returns:

X_transformed: array-like of shape (n_samples, n_coefficients): Returns the array-like of SPHARM coefficients.