The matmul.py file contains Python code for matrix multiplication with NumPy,
Python, and CUDA. The program generates two matrices A and B and multiplies them
using the three approaches. For each approach the elapsed time is printed.
The CUDA code is implemented with the help of Numba, see Numba for CUDA GPUs. It still follows the concepts explained in the CUDA C++ Programming Guide.
First the numpy matmul() function is compared with a self written naive Python
function matmul_python(). This can only be done for small dimensions. The
example below shows it for N = 200.
# python matmul.py
Matrix dimension N = 200
[[5 0 3 ... 8 2 3]
[9 7 5 ... 4 0 0]
[8 4 6 ... 3 7 9]
...
[4 9 1 ... 4 5 9]
[9 4 0 ... 0 0 9]
[4 6 0 ... 0 5 9]]
[[5 2 6 ... 6 3 0]
[7 7 0 ... 2 1 5]
[9 1 4 ... 7 0 5]
...
[1 0 8 ... 0 9 8]
[3 4 9 ... 4 8 3]
[8 1 9 ... 5 1 4]]
Multiply A x B with numpy
time: 0.008651971817016602 seconds
[[4047 3968 4008 ... 3925 4108 3894]
[4217 4156 4187 ... 4248 4187 3933]
[3913 4041 3953 ... 4285 3895 3986]
...
[3854 3993 4180 ... 4219 4201 4051]
[3862 3935 3626 ... 4059 3779 3538]
[4119 4409 3970 ... 4054 4188 4037]]
Multiply A x B with python
time: 3.1456005573272705 seconds
[[4047. 3968. 4008. ... 3925. 4108. 3894.]
[4217. 4156. 4187. ... 4248. 4187. 3933.]
[3913. 4041. 3953. ... 4285. 3895. 3986.]
...
[3854. 3993. 4180. ... 4219. 4201. 4051.]
[3862. 3935. 3626. ... 4059. 3779. 3538.]
[4119. 4409. 3970. ... 4054. 4188. 4037.]]
Now the numpy matmul() function is compared with a CUDA Kernel which is run
on the GPU by many threads in parallel. The example below shows it for N = 2000.
The naive Python function is commented out as it would take way too long.
$ python matmul.py
Matrix dimension N = 2000
[[5 0 3 ... 6 4 2]
[3 2 0 ... 7 5 6]
[9 9 5 ... 7 0 6]
...
[2 5 2 ... 4 9 3]
[6 9 4 ... 5 3 0]
[7 9 5 ... 8 4 0]]
[[0 0 1 ... 6 9 8]
[7 7 1 ... 2 1 0]
[6 5 6 ... 4 5 4]
...
[3 8 0 ... 8 0 3]
[2 8 7 ... 2 8 5]
[3 0 7 ... 0 4 4]]
Multiply A x B with numpy
time: 13.221363067626953 seconds
[[40057 40045 39818 ... 39471 39177 40292]
[41191 40602 41106 ... 40001 40606 40081]
[41209 41222 41510 ... 40900 39753 40128]
...
[40808 41009 40877 ... 40428 39166 40515]
[39352 38838 38865 ... 39285 38904 39338]
[39667 40245 38818 ... 39127 39668 40084]]
Multiply A x B with cuda
threads_per_block=(8, 8), blocks_per_grid=(250, 250)
time: 0.6066441535949707 seconds
[[40057. 40045. 39818. ... 39471. 39177. 40292.]
[41191. 40602. 41106. ... 40001. 40606. 40081.]
[41209. 41222. 41510. ... 40900. 39753. 40128.]
...
[40808. 41009. 40877. ... 40428. 39166. 40515.]
[39352. 38838. 38865. ... 39285. 38904. 39338.]
[39667. 40245. 38818. ... 39127. 39668. 40084.]]