Non-uniform grid Laplacian operator in matrix_ops

[jc-macdonald]

Non-uniform grid Laplacian operator

Add a 1D Laplacian operator for non-uniform grids to matrix_ops.py. Currently make_1d_laplacian only supports uniform grids. The structured-observables chemostat model requires a Neumann-BC tridiagonal Laplacian on curvature-weighted non-uniform grids.

Implementation

• make_1d_laplacian(n, dx=None, grid=None, bc='neumann') — extend existing function to accept a non-uniform grid array
• For non-uniform grid: second-order FD stencil with variable spacing h_i = grid[i+1] - grid[i]
• Neumann BC: ghost-node approach, one-sided differences at boundaries
• Return sparse CSC matrix compatible with existing CachedImplicitSolve
• Optional: 4th-order Laplacian for biharmonic diffusion (used in Chemostat_Simulator)

Source code reference

• Thoery_1_Code.ipynb: neumann_tridiag_laplacian_1d(theta_grid) — FD on non-uniform 1D grid
• Chemostat_Simulator.ipynb: 4th-order Laplacian in simulate_model2_explicit

Tests

• Uniform grid: matches existing make_1d_laplacian output
• Non-uniform grid: second-order convergence on smooth test function
• Neumann BC: constant function in null space
• Symmetric matrix for symmetric grids