OpenCV vs. Armadillo vs. Eigen on Linux

In this post I’ll be comparing 3 popular C++ matrix libraries found on Linux.

OpenCV 2.3.1
Armadillo 2.2.1
Eigen 3.0.3

OpenCV is a large computer vision library with matrix support. Armadillo wraps around LAPACK. Eigen is an interesting library, all the implementation is in the C++ header, much like boost. So it is simple to link into, but takes more time compile.

The 5 matrix operations I’ll be focusing on are: add, multiply, transpose, inversion, SVD. These are the most common functions I use. All the libraries are open source and run on a variety of platforms but I’ll just be comparing them on Ubuntu Linux.

Each of the 5 operations were tested on randomly generated matrices of different size NxN with the average running time recorded.

I was tossing up whether to use a bar chart to display the result but the results span over a very large interval. A log graph would show all the data easily but make numerical comparisons harder. So in the end I opted to show the raw data plus a normalised version to compare relative speed ups. Values highlight in red indicate the best results.

Add

Performing C = A + B

Raw data

Results in ms	OpenCV	Armadillo	Eigen
4×4	0.00098	0.00003	0.00002
8×8	0.00034	0.00006	0.00017
16×16	0.00048	0.00029	0.00077
32×32	0.00142	0.00208	0.00185
64×64	0.00667	0.00647	0.00688
128×128	0.02190	0.02776	0.03318
256×256	0.23900	0.27900	0.30400
512×512	1.04700	1.17600	1.33900

Normalised

Speed up over slowest	OpenCV	Armadillo	Eigen
4×4	1.00x	30.53x	44.41x
8×8	1.00x	5.56x	2.02x
16×16	1.62x	2.66x	1.00x
32×32	1.46x	1.00x	1.12x
64×64	1.03x	1.06x	1.00x
128×128	1.52x	1.20x	1.00x
256×256	1.27x	1.09x	1.00x
512×512	1.28x	1.14x	1.00x

The average running time for all 3 libraries are very similar so I would say there is no clear winner here. In the 4×4 case where OpenCV is much slower it might be due to overhead in error checking.

Multiply

Performing C = A * B

Raw data

Results in ms	OpenCV	Armadillo	Eigen
4×4	0.00104	0.00007	0.00030
8×8	0.00070	0.00080	0.00268
16×16	0.00402	0.00271	0.00772
32×32	0.02059	0.02104	0.02527
64×64	0.14835	0.18493	0.06987
128×128	1.83967	1.10590	0.60047
256×256	15.54500	9.18000	2.65200
512×512	133.32800	35.43100	21.53300

Normalised

Speed up over slowest	OpenCV	Armadillo	Eigen
4×4	1.00x	16.03x	3.52x
8×8	3.84x	3.35x	1.00x
16×16	1.92x	2.84x	1.00x
32×32	1.23x	1.20x	1.00x
64×64	1.25x	1.00x	2.65x
128×128	1.00x	1.66x	3.06x
256×256	1.00x	1.69x	5.86x
512×512	1.00x	3.76x	6.19x

Average running time for all 3 are similar up to 64×64, where Eigen comes out as the clear winner.

Transpose

Performing C = A^T.

Raw data

Results in ms	OpenCV	Armadillo	Eigen
4×4	0.00029	0.00002	0.00002
8×8	0.00024	0.00007	0.00009
16×16	0.00034	0.00019	0.00028
32×32	0.00071	0.00088	0.00111
64×64	0.00458	0.00591	0.00573
128×128	0.01636	0.13390	0.04576
256×256	0.12200	0.77400	0.32400
512×512	0.68700	3.44700	1.17600

Normalised

Speed up over slowest	OpenCV	Armadillo	Eigen
4×4	1.00x	17.00x	12.57x
8×8	1.00x	3.45x	2.82x
16×16	1.00x	1.81x	1.20x
32×32	1.56x	1.26x	1.00x
64×64	1.29x	1.00x	1.03x
128×128	8.18x	1.00x	2.93x
256×256	6.34x	1.00x	2.39x
512×512	5.02x	1.00x	2.93x

Comparable running time up to 64×64, after which OpenCV is the winner by quite a bit. Some clever memory manipulation?

Inversion

Performing C = A^-1

Raw data

Results in ms	OpenCV	Armadillo	Eigen
4×4	0.00189	0.00018	0.00090
8×8	0.00198	0.00414	0.00271
16×16	0.01118	0.01315	0.01149
32×32	0.06602	0.05445	0.05464
64×64	0.42008	0.32378	0.30324
128×128	3.67776	4.52664	2.35105
256×256	35.45200	16.41900	17.12700
512×512	302.33500	122.48600	97.62200

Normalised

Speed up over slowest	OpenCV	Armadillo	Eigen
4×4	1.00x	10.22x	2.09x
8×8	2.09x	1.00x	1.53x
16×16	1.18x	1.00x	1.15x
32×32	1.00x	1.21x	1.21x
64×64	1.00x	1.30x	1.39x
128×128	1.23x	1.00x	1.93x
256×256	1.00x	2.16x	2.07x
512×512	1.00x	2.47x	3.10x

Some mix results up until 128×128, where Eigen appears to be better choice.

SVD

Performing [U,S,V] = SVD(A)

Raw data

Results in ms	OpenCV	Armadillo	Eigen
4×4	0.00815	0.01752	0.00544
8×8	0.01498	0.05514	0.03522
16×16	0.08335	0.17098	0.21254
32×32	0.53363	0.73960	1.21068
64×64	3.51651	3.37326	6.89069
128×128	25.86869	24.34282	71.48941
256×256	293.54300	226.95800	722.12400
512×512	1823.72100	1595.14500	7747.46800

Normalised

Speed up over slowest	OpenCV	Armadillo	Eigen
4×4	2.15x	1.00x	3.22x
8×8	3.68x	1.00x	1.57x
16×16	2.55x	1.24x	1.00x
32×32	2.27x	1.64x	1.00x
64×64	1.96x	2.04x	1.00x
128×128	2.76x	2.94x	1.00x
256×256	2.46x	3.18x	1.00x
512×512	4.25x	4.86x	1.00x

Looks like OpenCV and Armadillo are the winners, depending on the size of the matrix.

Discussion

With mix results left, right and centre it is hard to come to any definite conclusion. The benchmark itself is very simple. I only focused on square matrices of power of two, comparing execution speed, not accuracy, which is important for SVD.

What’s interesting from the benchmark is the clear difference in speed for some of the operations depending on the matrix size. Since the margins can be large it can have a noticeable impact on your application’s running time. It would be pretty cool if there was a matrix library that could switch between different algorithms depending on the size/operation requested, fine tuned to the machine it is running on. Sort of like what Atlas/Blas does.

So which library is faster? I have no idea, try them all for your application and see