la.jacobi: fix incorrect eigen values/vectors

[PottierLoic]

This PR resolves issue #202, where the Jacobi eigenvalue algorithm in vsl.la produced incorrect results. The original rotation logic failed to zero off-diagonal elements and broke the symmetry of the matrix a, resulting in incorrect eigenvalues (v) and eigenvectors (q).

I retained the initial test with a diagonal matrix:

mut a := la.Matrix.deep2([
  [2.0, 0.0, 0.0],
  [0.0, 2.0, 0.0],
  [0.0, 0.0, 2.0],
])

Expected : v = [2, 2, 2], q = identity, a unchanged. It still passes.

I added a new test for a more complex symmetric matrix, which was failing prior to the fix:

mut a := la.Matrix.deep2([
  [4.0, 1.0, 1.0],
  [1.0, 3.0, 0.0],
  [1.0, 0.0, 2.0],
])	

Expected : v = [4.879385241571816, 2.652703644666139, 1.467911113762045], q matches computed eigenvectors, a diagonalized. It now passes.

I compared the outputs against an online eigenvalue calculator. v match exactly and q_values are matching the results from the solver once normalized.

I re-ran the code from #202 and it still doesn't return the expected values from the issue. I think there may be a problem in the code snippet provided too.

Summary by CodeRabbit

• Refactor
  • Improved the matrix algorithm’s logic by revising convergence checks and updating numerical computations for enhanced clarity and correctness.
• Tests
  • Expanded test coverage by introducing a new case for a symmetric 3x3 matrix and enhancing existing validations to ensure precise outputs.

[coderabbitai[bot]]

Walkthrough

The Jacobi method implementation has been updated to adjust its control flow and numerical updates. The convergence check now uses a break statement instead of an immediate return, and the computation of the difference variable has been reversed. Additional tolerance conditions have been added before processing further calculations. The matrix update logic has been refactored using a single loop, and the final matrix assembly now explicitly sets both diagonal and off-diagonal elements. In parallel, a new test case for a 3x3 symmetric matrix and additional assertions in an existing test have been introduced.

Changes

File	Change Summary
la/jacobi.v	Modified the jacobi function: convergence check now uses a break; reversed the computation of h; added extra tolerance checks; refactored matrix update loops; explicitly set diagonal/off-diagonal values; updated convergence validation.
la/jacobi_test.v	Added a new test function test_jacobi_3x3_symmetric() for a 3x3 symmetric matrix; enhanced test_jacobi01() with additional assertions for updated matrix output.

Sequence Diagram(s)

sequenceDiagram
    participant Caller as Caller/Test
    participant Jacobi as jacobi()
    participant Matrix as Matrix (a, v, q)
    
    Caller->>Jacobi: Call jacobi(q, v, a)
    Note over Jacobi: Start iterations for Jacobi rotation
    
    Jacobi->>Jacobi: Compute h = v[j] - v[i]
    alt Tolerance Condition Met & Convergence Check
        Jacobi->>Jacobi: Break loop
    else Continue Calculations
        Jacobi->>Jacobi: Calculate t based on h and a.get(i, j)
        Jacobi->>Matrix: Update matrix values (aii, ajj, aij) and set a[i][j] to 0.0
    end
    
    Jacobi->>Matrix: Update remaining matrix entries (excluding i and j)
    Jacobi->>Matrix: Set diagonal elements to v and off-diagonals to zero
    Jacobi-->>Caller: Return updated matrices or error if not converged

Poem

I'm a bunny with a coder's delight,
Hopping through changes both day and night.
Jacobi's loop now twists and turns,
With each new check, my code burns.
Matrices dance with precision and cheer,
For in this code field, I’m the rabbit engineer!
🥕🐇 Happy coding!

---

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