gemseo / algos / sequence_transformer

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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(current_iterate, next_iterate)

Compute the next transformed iterate.

Parameters:

• current_iterate (NDArray) – The current iterate \(x_n\).

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

Returns:

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

Return type:

NDArray