Linear Algebra Performance Benchmarks

List of benchmarks

1. Create a random 1000x1000 matrix.

2. Invert a 1000x1000 random matrix.

3. Compute the Cholesky decomposition of a random 1000x1000 matrix.

4. Vector (1 000 000) dot product.

5. Matrix (1000x1000) transpose.

6. Matrix (1000x1000 <> 1000x1000) multiply.

7. Sigmoid

8. ReLU

9. Sum by rows

10. sum by columns

11. indices of max elements in rows

12. indices of max elements in columns

Results

• hmatrix: 0.18.0.0 (ghc: 8.0.2) & hmatrix-morpheus: 0.1.1.1
• numpy: 1.11.1 (python: 3.5.2)
• octave: 4.0.3
• gonum matrix: master (go: 1.8)
• LASwift: 0.1.2 (Apple Swift 3.0.2)

Benchmark	hmatrix (hmatrix-morpheus)	numpy	octave	gonum matrix	LASwift
1. Random matrix	16.10 ms	39.24 ms	18.48 ms	41.98 ms	15 ms
2. Invert matrix	84.85 ms	84.74 ms	57.00 ms	364.49 ms	39 ms
3. Cholesky decomposition	28.74 ms	29.40 ms	9.11 ms	116.60 ms	33 ms
4. Vector dot product	1.965 ms	0.80 ms	1.07 ms	0.990 ms	1 ms
5. Matrix transpose	41.80 ns	262.0 ns	22,860 ns	0.65 ns	11e9 ns
6. Matrix multiply	32.78 ms	37.01 ms	36.38 ms	185.65 ms	30 ms
7. Sigmoid	14.40 ms (9.835 ms)	19.76 ms	18.14 ms	2 333 ms	20 ms
8. ReLU	3.575 ms (1.389 ms)	7.39 ms	3.11 ms	10.5 ms	4 ms
9. sum by rows	3.276 ms (1.069 ms)	0.546 ms	0.830 ms		2 ms
10. sum by columns	14.690 ms (0.539 ms)	0.692 ms	1.049 ms		13 ms
11. max index by rows	1.540 ms (0.830 ms)	0.924 ms	1.131 ms		2 ms
12. max index by columns	12.980 ms (0.902 ms)	9.940 ms	1.460 ms		13 ms

TODO:

• dlib (http://dlib.net)
• eigen (http://eigen.tuxfamily.org/)
• MKL backend