1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
|
# Numerical Linear Algebra
This repo contains a small C++ dense numerical linear algebra library for `double`, with a companion experiments directory for evaluating performance.
The current matmul uses a vectorized dot-product kernel. The implementation supports compile-time SIMD backends for `AVX`, `AVX2`, `AVX512`, and `NEON` on `AArch64`/`ARM64` with FP64 vector support.
## Build
```bash
cmake -S . -B build
cmake --build build
```
On x86, you can explicitly choose a matmul SIMD target at configure time:
```bash
cmake -S . -B build -DLINEAR_ALGEBRA_SIMD=AVX2
```
Valid values are `AUTO`, `NONE`, `AVX`, `AVX2`, and `AVX512`. `AUTO` uses the compiler's current target. `NONE` forces the scalar fallback.
## Run tests
```bash
ctest --test-dir build --output-on-failure
```
## What's implemented
- Matrix / Vector core with SIMD matmul
- Triangular solvers (forward / backward substitution)
- LU factorization with partial pivoting (`lu_factor`, `lu_solve`)
- QR factorization — classical GS, modified GS, and Householder (`qr_classical_gs`, `qr_modified_gs`, `qr_householder`)
## Run examples
```bash
./build/linear_system
./build/matmul
```
## Run experiments
```bash
./build/pivoting_vs_no_pivoting
./build/hilbert_qr
```
|