Version 2.1 will allow the user to define the shape (structure) of the Jacobian matrix. I.e., instead of providing analytic Jacobian (or not providing it at all, which is slow), the user can specify the positions of non-zero elements in the Jacobian. The solver will use automatic differentiation for the specified elements only. This should work as fast as analytic Jacobian without requiring the user to differentiate the vector function manually.

Tasks:

• Upgrade Eigen, autodiff, googletest
• Add Jacobian shape class and a helper function to populate an array containing positions of non-zero elements
• Compute Jacobian using the given matrix shape
• Add utility function that compares fully automatic Jacobian with the one computed from the given shape
• Add utility function that compares fully automatic Jacobian with the one provided by the user
• Update tests
• Update examples
• Update README and CHANGELOG
• Update docs
• Add performance tests (added locally for now)

Implemented changes:

• Updated autodiff to v1.1.2
• Updated Eigen (commit from 28th March 2024)
• Updated googletest from v.1.14.x to v1.15.2
• Added JacobianMatrixShape and VectorFunctionElements helper classes to define the Jacobian matrix shape and the vector function
• Added JacobianCompare class that helps the user to compare the user-defined Jacobian (either defined explicitly or using Jacobian shape) with the one computed automatically from the system RHS
• Added jacobian_shape and jacobian_compare examples
• Added integration test that uses Jacobian derived from the given shape
• Added unit tests for all new classes (JacobianMatrixShape, VectorFunctionElements, JacobianCompare)