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Diffstat (limited to 'README.md')
| -rw-r--r-- | README.md | 45 |
1 files changed, 17 insertions, 28 deletions
@@ -4,7 +4,7 @@ I mostly follow Trefethen & Bau, "Numerical Linear Algebra" and Golub & Van Loan Computations." The implementation uses `NEON` SIMD on ARM64 systems when available. -## Build +### Build The library is packaged as a C++20 named module (`linalgebra`): @@ -14,8 +14,7 @@ The library is packaged as a C++20 named module (`linalgebra`): doesn't yet support module dependency scanning) ```bash -cmake -S . -B build -G Ninja \ - -DCMAKE_CXX_COMPILER=/opt/homebrew/opt/llvm/bin/clang++ +cmake -S . -B build -G Ninja -DCMAKE_CXX_COMPILER=/opt/homebrew/opt/llvm/bin/clang++ cmake --build build ``` @@ -29,7 +28,7 @@ cmake -S . -B build -G Ninja \ Valid values are `AUTO` (uses available SIMD) and `NONE` (forces scalar fallback). -## Usage +### Usage Import the module: @@ -44,13 +43,13 @@ int main() { } ``` -## Run tests +### Run tests ```bash ctest --test-dir build --output-on-failure ``` -## What's implemented +### What's implemented - Matrix / Vector core with SIMD matmul - Triangular solvers (forward / backward substitution) @@ -67,25 +66,15 @@ ctest --test-dir build --output-on-failure - Francis double-shift QR (`eigenvalues_francis`) — implicit bulge chasing on Hessenberg form; handles complex conjugate eigenvalue pairs without complex arithmetic; robust subdiagonal + 2×2 block deflation with exceptional shifts (GVL §7.5) -- Cholesky factorization (`cholesky_factor`, `cholesky_solve`) — for symmetric positive definite systems - -## TODO: -- [ ] Symmetric tridiagonalization — Householder reduction before symmetric QR (tridiagonalize) -- [ ] Eigenvectors via inverse iteration (eigenvectors_inverse_iteration) -- [ ] SVD — Golub-Kahan bidiagonalization + QR (svd) -- [ ] Conjugate Gradient (solve_cg) — for symmetric positive definite systems -- [ ] GMRES (solve_gmres) — for general non-symmetric systems -- [ ] BiCGSTAB (solve_bicgstab) — lighter alternative to GMRES -- [ ] Condition number estimation — norm-based LINPACK estimator -- [ ] Preconditioners (precond_jacobi, precond_ilu0) — diagonal and ILU(0) -- [ ] Least squares solver (lstsq) — via QR or SVD with rank-deficient handling -- [ ] Arnoldi iteration (arnoldi) — falls out naturally from GMRES -- [ ] Matrix exponential (expm) — via Padé approximation - -## Run experiments - -```bash -./build/matmul -./build/pivoting_vs_no_pivoting -./build/hilbert_qr -``` +- Cholesky factorization (`cholesky_factor`, `cholesky_solve`) +- Symmetric tridiagonalization +- Eigenvectors via inverse iteration (eigenvectors_inverse_iteration) +- SVD — Golub-Kahan bidiagonalization + QR (svd) +- Conjugate Gradient (solve_cg) +- GMRES (solve_gmres) +- BiCGSTAB (solve_bicgstab) +- Condition number estimation +- Preconditioners (precond_jacobi, precond_ilu0) +- Least squares solver (lstsq) +- Arnoldi iteration (arnoldi) +- Matrix exponential (expm) |