gemseo / algos / sequence_transformer

Hide inherited members

sequence_transformer module

Sequence transformer methods.

class gemseo.algos.sequence_transformer.sequence_transformer.SequenceTransformer

Bases: object

A vector sequence transformer for fixed-point iteration method.

For any function \(G : \mathbb{R}^n \rightarrow \mathbb{R}^n\), the fixed point iteration method computes the sequence \(x_{n+1} = G(x_n)\), whih is exepcted to converge towards a fixed point of \(G\).

A sequence transformer is a function \(f : \mathbb{R}^n \rightarrow \mathbb{R}^n\) so that the new iterate is instead computed as .. math:

x_{n+1}' = f(G, x_n, \dots, x_{n-k}, G(x_n)),

for a given \(k \geq 0\).

The transformed sequence is expected to exhibit faster convergence and/or better numerical stability.

clear()

Clear the iterates.

Return type:

None

compute_transformed_iterate(iterate, residual)

Compute the next transformed iterate.

Parameters:

• iterate (NDArray) – The iterate \(G(x_n)\).

• residual (NDArray) – The associated residual \(G(x_n) - x_n\).

Returns:

The next transformed iterate \(x_{n+1}\).

Return type:

NDArray