spateo.tdr.morphometrics.morphofield_dg.GPVectorField#

Module Contents#

Classes#

GPVectorField

Functions#

compute_acceleration(vf, f_jac, X[, Js, return_all])

Calculate acceleration.

compute_curvature(vf, f_jac, X[, Js, formula])

Calculate curvature.

compute_curl(f_jac, X)

Calculate curl for 2D or 3D systems.

compute_torsion(vf, f_jac, X)

Calculate torsion.

compute_divergence(→ numpy.ndarray)

Calculate divergence for many samples by taking the trace of a Jacobian matrix.

compute_sensitivity(f_jac, X)

Calculate sensitivity.

Jacobian_GP_gaussian_kernel(→ numpy.ndarray)

analytical Jacobian for RKHS vector field functions with Gaussian kernel.
spateo.tdr.morphometrics.morphofield_dg.GPVectorField.compute_acceleration(vf, f_jac, X, Js=None, return_all=False)[source]#

Calculate acceleration.

spateo.tdr.morphometrics.morphofield_dg.GPVectorField.compute_curvature(vf, f_jac, X, Js=None, formula=2)[source]#

Calculate curvature.

spateo.tdr.morphometrics.morphofield_dg.GPVectorField.compute_curl(f_jac, X)[source]#

Calculate curl for 2D or 3D systems.

spateo.tdr.morphometrics.morphofield_dg.GPVectorField.compute_torsion(vf, f_jac, X)[source]#

Calculate torsion.

spateo.tdr.morphometrics.morphofield_dg.GPVectorField.compute_divergence(f_jac, X: numpy.ndarray, Js: numpy.ndarray | None = None, vectorize_size: int = 1000) → numpy.ndarray[source]#

Calculate divergence for many samples by taking the trace of a Jacobian matrix.

vectorize_size is used to control the number of samples computed in each vectorized batch.

If vectorize_size = 1, there’s no vectorization whatsoever. If vectorize_size = None, all samples are vectorized.

Parameters:
f_jac

function for calculating Jacobian from cell states

X

cell states

Js

Jacobian matrices for each sample, if X is not provided

vectorize_size

number of Jacobian matrices to process at once in the vectorization

Returns:

divergence np.ndarray across Jacobians for many samples

spateo.tdr.morphometrics.morphofield_dg.GPVectorField.compute_sensitivity(f_jac, X)[source]#

Calculate sensitivity.

spateo.tdr.morphometrics.morphofield_dg.GPVectorField.Jacobian_GP_gaussian_kernel(X: numpy.ndarray, vf_dict: dict, vectorize: bool = False) → numpy.ndarray[source]#

analytical Jacobian for RKHS vector field functions with Gaussian kernel.

Args: x: Coordinates where the Jacobian is evaluated. vf_dict: A dictionary containing RKHS vector field control points, Gaussian bandwidth,

and RKHS coefficients. Essential keys: ‘X_ctrl’, ‘beta’, ‘C’

Returns:

Jacobian matrices stored as d-by-d-by-n numpy arrays evaluated at x.

d is the number of dimensions and n the number of coordinates in x.

class spateo.tdr.morphometrics.morphofield_dg.GPVectorField.GPVectorField[source]#
from_adata(adata: anndata.AnnData, vf_key: str = 'VecFld')[source]#
get_data() → Tuple[numpy.ndarray, numpy.ndarray][source]#
compute_velocity(X: numpy.ndarray)[source]#
compute_acceleration(X: numpy.ndarray | None = None, **kwargs)[source]#
compute_curvature(X: numpy.ndarray | None = None, formula: int = 2, **kwargs)[source]#
compute_curl(X: numpy.ndarray | None = None, dim1: int = 0, dim2: int = 1, dim3: int = 2, **kwargs) → numpy.ndarray[source]#
compute_torsion(X: numpy.ndarray | None = None, **kwargs) → numpy.ndarray[source]#
compute_divergence(X: numpy.ndarray | None = None, **kwargs) → numpy.ndarray[source]#
get_Jacobian(method: str = 'analytical', **kwargs) → Callable[source]#

Get the Jacobian of the vector field function. The analytical Jacobian will be returned and it always take row vectors as input no matter what input_vector_convention is.

The returned Jacobian is of the following format:

df_1/dx_1 df_1/dx_2 df_1/dx_3 … df_2/dx_1 df_2/dx_2 df_2/dx_3 … df_3/dx_1 df_3/dx_2 df_3/dx_3 … … … … …