Average time (in seconds) to diagonalize randomly generated (nxn) (normal-distributed) matrices (of floats) as a function of matrix size (n):
| Matrix Size (n) | jacobi_pd (s) | Numerical Recipes (s) |
|---|---|---|
| 2 | 9.54e-08 | 1.64e-07 |
| 3 | 4.95e-07 | 9.57e-07 |
| 4 | 1.24e-06 | 2.00e-06 |
| 5 | 2.53e-06 | 3.96e-06 |
| 10 | 2.22e-05 | 2.37e-05 |
| 20 | 2.35e-04 | 1.86e-04 |
| 50 | 0.00348 | 0.00259 |
| 100 | 0.0271 | 0.0192 |
| 200 | 0.232 | 0.25 |
| 500 | 5.39 | 5.36 |
| 1000 | 66.3 | 73.9 |
Matrices of (32 bit) floats were generated with randomly chosen eigenvectors. The eigenvalues were selected from a normal (Gaussian) distribution with mean 0 and variance 1.0.
These times were measured on a single i5-4210U CPU core running at 1.70GHz.
cd tests/
sed -i 's/double/float/' test_jacobi.cpp
g++ -DNDEBUG -Ofast -I../include -o test_jacobi test_jacobi.cpp
for N in 2 3 4 5 10 20 50 100 200 500 1000; do
time ./test_jacobi $N 10 0 1 0 10
done
To make the test fair, the "test_jacobi.cpp" file was modified slightly to disable the sorting of eigenvalues. (I did this by invoking Diagonalize() with sort_criteria=DO_NOT_SORT. I did this because the "Numerical Recipes" version of jacobi() was not sorting the eigenvalues. Either way, this probably did not make a significant difference in the running times.)
If I have time, I will compare this with other popular matrix diagonalizers like Eigen and GSL.