cristal.helper_classes.incrementers module#

Incrementers for moments matrix using various methods.

class cristal.helper_classes.incrementers.IMPLEMENTED_INCREMENTERS_OPTIONS(*values)#

Bases: Enum

The implemented incrementers classes.

INVERSE = <class 'cristal.helper_classes.incrementers.InverseIncrementer'>#
SHERMAN = <class 'cristal.helper_classes.incrementers.ShermanIncrementer'>#
WOODBURY = <class 'cristal.helper_classes.incrementers.WoodburyIncrementer'>#
class cristal.helper_classes.incrementers.InverseIncrementer#

Bases: BaseIncrementer

Incrementer for moments matrix using the inverse method. This method updates the moments matrix and then computes the inverse of the updated moments matrix directly.

static increment(mm, x, n, inv_class, sym=True)#

Increment the moments matrix using the inverse method.

Parameters:

  • mm (MomentsMatrix) – The moments matrix to increment.

  • x (np.ndarray (N', d)) – The input data.

  • n (int) – The number of points integrated in the moments matrix.

  • inv_class (type[BaseInverter]) – The inversion class to use.

  • sym (bool, optional) – Not used in this implementation, by default True

update_moments_matrix: bool = True#

Whether the method updates the moments matrix during incrementing

class cristal.helper_classes.incrementers.ShermanIncrementer#

Bases: BaseIncrementer

Incrementer for moments matrix using the Sherman-Morrison formula. This method updates the inverse moments matrix iteratively and not modifies the moments matrix.

static increment(mm, x, n, inv_class=None, sym=True)#

Increment the moments matrix using the Sherman-Morrison formula iteratively.

Sherman-Morrison formula:

\[(A + uv^T)^{-1} = A^{-1} - \frac{(A^{-1} u v^T A^{-1})}{(1 + v^T A^{-1} u)}\]
\[\text{Here } u = v^T\]
Parameters:

  • mm (MomentsMatrix) – The moments matrix to increment.

  • x (np.ndarray (N', d)) – The input data.

  • n (int) – The number of points integrated in the moments matrix.

  • inv_class (type[BaseInverter] | None, optional) – Not used in this implementation, by default None

  • sym (bool, optional) – Whether to consider the matrix as symmetric, by default True

class cristal.helper_classes.incrementers.WoodburyIncrementer#

Bases: BaseIncrementer

Incrementer for moments matrix using the Woodbury matrix identity. This method updates the inverse moments matrix and not modifies the moments matrix.

static increment(mm, x, n, inv_class, sym=True)#

Increment the moments matrix using the Woodbury matrix identity.

Woodbury matrix identity:

\[(A + UCV)^{-1} = A^{-1} - A^{-1} U (C^{-1} + V A^{-1} U)^{-1} V A^{-1}\]
\[\text{Here } C = I \text{ and } U = V^T = \begin{bmatrix} v_1, v_2, \cdots, v_{N'} \end{bmatrix}\]
Parameters:

  • mm (MomentsMatrix) – The moments matrix to increment.

  • x (np.ndarray (N', d)) – The input data.

  • n (int) – The number of points integrated in the moments matrix.

  • inv_class (type[BaseInverter]) – The inversion class to use.

  • sym (bool, optional) – Whether to consider the matrix as symmetric, by default True