fastest-matrices

This project benchmarks the following libraries:

• hmatrix
• dense-linear-algebra
• numhask
• matrix

instead of relying on hackage, the project's dependencies fetch the libraries directly from github (see stack.yaml).

To run:

(allocation) stack build :bench-alloc && stack exec bench-alloc

(runtime) stack build :bench-runtime && stack exec bench-runtime

The implementations of the "naive C" parts can be found in /naive. They were compiled with -O3

Results

Runtime

Matrix-matrix multiplication

Library	n = 10	n = 50	n = 100
DLA	3.400 μs	339.2 μs	2.377 ms
hmatrix	1.179 μs	56.76 μs	297.6 μs
NumHask	659.4 μs	87.64 ms	310.4 ms
Matrix	10.84 μs	974.9 μs	8.329 ms
Naive C	51 us	323 us	4.78 ms

Repeated matrix-matrix multiplication

Library	n = 10	n = 50	n = 100
DLA	9.217 μs	1.050 ms	7.566 ms
hmatrix	3.945 μs	168.5 μs	905.6 μs
NumHask	1.060 ms	139.9 ms	691.9 ms

Matrix-vector multiplication

Library	n = 10	n = 50	n = 100
DLA	257.7 ns	5.904 μs	21.36 μs
hmatrix	450.3 ns	1.867 μs	11.54 μs

QR factorization

Library	n = 10	n = 50	n = 100
DLA	3.050 μs	312.8 μs	2.375 ms
hmatrix	68.20 μs	5.653 ms	46.28 ms

Transpose

Library	n = 10	n = 50	n = 100
DLA	1.285 μs	29.84 μs	130.8 μs
hmatrix	12.02 ns	10.14 ns	11.93 ns
NumHask	446.9 ns	10.85 μs	35.28 μs
Matrix	2.267 μs	58.81 μs	355.8 μs

Norm

Library	n = 10	n = 50	n = 100
DLA	154.3 ns	3.716 μs	15.83 μs
hmatrix	99.41 ns	824.0 ns	3.579 μs
NumHask	20.76 μs	605.9 μs	3.428 ms
Naive C	350 ns	12.65 us	40.96 μs

Row

Library	n = 10	n = 50	n = 100
DLA	16.01 ns	16.32 ns	17.05 ns
hmatrix	704.6 ns	696.4 ns	739.7 ns
NumHask	41.40 ns	175.1 ns	377.8 ns
Matrix	42.94 ns	185.9 ns	340.5 ns

Column

Library	n = 10	n = 50	n = 100
DLA	38.04 ns	134.5 ns	195.2 ns
hmatrix	817.4 ns	811.2 ns	1.078 μs
NumHask	192.4 ns	1.151 μs	1.708 μs
Matrix	222.0 ns	887.0 ns	1.954 μs

Identity

Library	n = 10	n = 50	n = 100
DLA	90.64 ns	1.021 μs	2.841 μs
hmatrix	1.804 μs	28.01 μs	150.9 μs
Matrix	1.845 μs	38.73 μs	210.5 μs

Diagonal

Library	n = 10	n = 50	n = 100
DLA	87.47 ns	839.2 ns	2.816 μs
hmatrix	1.665 μs	27.49 μs	143.3 μs

Allocation

Matrix-matrix multiplication

Library	n = 10	n = 50	n = 100
DLA	976	20,176	80,176
hmatrix	904	20,936	80,936
NumHask	1,691,432	179,093,816	1,400,273,872
Matrix	18,160	392,288	1,544,056

QR factorization

Library	n = 10	n = 50	n = 100
DLA	1,848	40,248	160,248
hmatrix	201,192	9,074,048	67,457,120

Transpose

Library	n = 10	n = 50	n = 100
DLA	880	20,080	80,080
hmatrix	64	64	64
NumHask	0	0	0
Matrix	9,840	239,952	959,664

Norm

Library	n = 10	n = 50	n = 100
DLA	16	16	16
hmatrix	232	232	232
NumHask	146,800	2,919,552	11,641,752

Row

Library	n = 10	n = 50	n = 100
DLA	64	64	64
hmatrix	2,128	2,128	2,128
NumHask	256	256	256
Matrix	896	20,112	80,168

Column

Library	n = 10	n = 50	n = 100
DLA	160	480	880
hmatrix	2,128	2,128	2,128
NumHask	800	2,720	5,120
Matrix	1,648	23,744	87,400

Identity

Library	n = 10	n = 50	n = 100
DLA	1,008	20,528	80,928
hmatrix	3,208	66,440	252,440
Matrix	5,752	139,848	559,504