Table below generated by cargo run -p multicalc-qa --bin gen_accuracy_tables; do not edit it by hand.
The linear-algebra routines are tested against numpy (LAPACK). Each case uses a random matrix A,
and for solves a random vector b, with x solving Ax = b. The table shows det(A) for the
LU/Cholesky solves, the residual ‖Ax − b‖ for QR least-squares, and the singular values σ(A)
for the SVD.
| Operation | Equation | Tolerance | Tested Against |
|---|---|---|---|
| LU decompose + solve, 3×3 | det(A) | 1e-10 | numpy/LAPACK 2.1.3 |
| LU decompose + solve, 4×4 | det(A) | 1e-10 | numpy/LAPACK 2.1.3 |
| LU decompose + solve, 5×5 | det(A) | 1e-10 | numpy/LAPACK 2.1.3 |
| Cholesky decompose + solve, 2×2 | det(A) | 1e-10 | numpy/LAPACK 2.1.3 |
| Cholesky decompose + solve, 3×3 | det(A) | 1e-10 | numpy/LAPACK 2.1.3 |
| Cholesky decompose + solve, 4×4 | det(A) | 1e-10 | numpy/LAPACK 2.1.3 |
| QR least-squares, 3×2 | ‖Ax − b‖ | 1e-10 | numpy/LAPACK 2.1.3 |
| QR least-squares, 3×3 | ‖Ax − b‖ | 1e-10 | numpy/LAPACK 2.1.3 |
| QR least-squares, 4×3 | ‖Ax − b‖ | 1e-10 | numpy/LAPACK 2.1.3 |
| QR least-squares, 20×7 | ‖Ax − b‖ | 1e-10 | numpy/LAPACK 2.1.3 |
| SVD, 3×2 | σ(A) | 1e-10 | numpy/LAPACK 2.1.3 |
| SVD, 3×3 | σ(A) | 1e-10 | numpy/LAPACK 2.1.3 |
| SVD, 4×3 | σ(A) | 1e-10 | numpy/LAPACK 2.1.3 |
| SVD, 12×6 | σ(A) | 1e-10 | numpy/LAPACK 2.1.3 |
| SVD, 20×6 | σ(A) | 1e-10 | numpy/LAPACK 2.1.3 |