Extend Jacobian Features in Calculus

[Kritika75]

Problem Description

The Jacobian function computes partial derivatives but does not include higher-order derivatives, sparsity checks, or structural features.

Proposed Solution

Feature that can be added:
Hessian Option: Include a hessian=True parameter to compute the Hessian matrix directly.
Sparse Jacobian: Provide an option to compute sparse Jacobians for large systems.
Rank Analysis: Add functionality to compute the rank of the Jacobian matrix.

Alternatives Considered

Implementing separate functions for Hessians and sparse matrices

Additional Information

The proposed features improve the Jacobian function to address advanced computational needs, such as higher-order derivatives, sparse representations, and structural analysis.

Adding a Hessian option enables direct computation of second-order derivatives, essential for optimization and curvature analysis.

Sparse Jacobians improve efficiency for large-scale systems by reducing memory and computation overhead.

Rank analysis provides insights into the dimensionality and feasibility of solutions, crucial for constraint systems and differential equations.

These features expand the function's versatility

Is there an existing issue for this?

• I have searched the existing issues for a bug report that matches the one I want to file, without success.

@mkoeppe can i work on this issue?