Module jacobian 

Jacobian approximation and handling utilities for ODE solvers

This module provides tools for computing, updating, and reusing Jacobian matrices in implicit ODE solvers. It implements various approximation strategies, reuse logic, and specialized techniques for different problem types.

Re-exports

pub use crate::ode::utils::common::finite_difference_jacobian;

Structs

JacobianManager

Manages Jacobian computation, updates, and reuse

NewtonParameters

Newton solver parameters

NewtonResult

Result of a Newton solve

ParallelJacobianStrategy

Struct to manage parallel Jacobian computation strategy

Enums

JacobianStrategy

Strategy for Jacobian approximation

JacobianStructure

Structure of the Jacobian matrix

Functions

adaptive_jacobian

Jacobian strategy that uses autodiff when available and falls back to finite differences when not

autodiff_jacobian

Fallback implementation when autodiff feature is not enabled

block_update

Performs a block-update of the Jacobian using block structure

broyden_update

Update the Jacobian using Broyden’s method (rank-1 update) J_{k+1} = J_k + (df - J_k * dy) * dy^T / (dy^T * dy)

compute_banded_jacobian

Computes Jacobian for a banded system with specified number of lower and upper diagonals

compute_colored_jacobian

Group variables based on their interactions to minimize function evaluations

compute_diagonal_jacobian

Computes Jacobian for a system with diagonal or block-diagonal structure

compute_jacobian

Compute Jacobian using finite differences (for compatibility)

generate_banded_coloring

Generate a simple coloring for a banded matrix

is_autodiff_available

Check if autodiff is available

modified_newton_solve

Modified Newton solve that reuses the same Jacobian for multiple iterations

newton_solve

Solve a nonlinear system F(x) = 0 using Newton’s method

parallel_finite_difference_jacobian

Compute Jacobian matrix using parallel finite differences

parallel_sparse_jacobian

Compute sparse Jacobian matrix in parallel using coloring

should_use_parallel_jacobian

Determine if parallel Jacobian computation should be used