Comparison of the acceleration of SOR algorithm

Comparison of the acceleration of Successive Over-Relaxation algorithm using C, MPI and ArgoDSM.

The implementations are located in the following directories:

Source Code Path	Binary Name
SOR-C-reference	sor_c
SOR-MPI	sor_mpi
SOR-DSM-1	sor_argo_1
SOR-DSM-2	sor_argo_2
SOR-DSM-3	sor_argo_3

Parameters

For each implementation, modify the corresponding sor_params.h file to build & test for different parameters.

Build

To build all implementations, run ./build.sh.

The binaries (sor_c, sor_mpi, sor_argo_1, sor_argo_2, sor_argo_3) will be generated in ./bin/.

Or, to build one certain implementation, follow the next steps:

# IMPL_PATH indicates the implementation source code path stated above.

mkdir -p build/$IMPL_PATH && cd build/$IMPL_PATH

cmake ../../$IMPL_PATH

# The corresponding binary will be generated.
make

Run

Run each implementation with mpirun -n <node-count>.

Test

Run 81 set of tests according to the following parameters:

Parameter	Values
im	128, 256, 512
jm	128, 256, 512
km	64, 128, 256
node_count	2, 8, 16

For each node_count, there are more than one pair of dsmNX and dsmNY:

Node Count	(dsmNX, dsmNY)
2	(1, 2), (2, 1)
8	(1, 8), (2, 4), (4, 2), (8, 1)
16	(1, 16), (2, 8), (4, 4), (8, 2), (16, 1)

Considering all possible parameters, we will launch 999 (27 * 3 * 1 + 27 * 1 * 1 + 27 * (2 + 4 + 5) * 3 = 999) single tests.

nohup python testing.py >> nohup.out 2>&1 &
tail -f nohup.out

Additionally, whether using the compiler -O3 optimization flag may also affect the performance. So there would be actually 1998 = 999 * 2 single tests to run.

Results

Manifest

The test result can be obtained from the misc directory.

There are 5 files within misc directory:

• cvm-info.txt is the test environment on Google Cloud Platform.
• results.tar.gz is the original test logs collected from main branch.
• results-flags.tar.gz is the original test logs collected from flags branch.
• test-results.csv is the test results in CSV format, containing 1998 records.
• test-results.json is the test results in JSON format, containing 1998 records.

How to read the results

For each test record, test-results.json stores the SOR times from all computing nodes, while test-results.csv only stores the worst SOR time among all computing nodes.

The explanation for test-results.csv headers is as follows:

• im: im from array size.
• jm: jm from array size.
• km: km from array size.
• method: numbers from 0 to 4 represents Reference C Code, ArgoDSM V1 Code, ArgoDSM V2 Code, ArgoDSM V3 Code, MPI Code, respectively.
• optimized: whether the -O3 optimization flag has been set within CMAKE_CXX_FLAGS. 0 means Not Set, and 1 means Set.
• node_count: number of computing nodes.
• dsm_nx: dsmNX parameter for ArgoDSM.
• dsm_ny: dsmNY parameter for ArgoDSM.
• time: SOR time in seconds.

It is highly recommended reading the results via Python:

>>> import pandas as pd
>>> df = pd.read_csv('test-results.csv')
>>> df
       im   jm   km  method  optimized  node_count  dsm_nx  dsm_ny      time
0     128  128   64       0          0           1       0       0  0.412469
1     128  128   64       0          1           1       0       0  0.079119
2     128  128   64       1          0           2       1       2  7.100646
3     128  128   64       1          0           2       2       1  6.763574
4     128  128   64       1          0           8       1       8  0.426822
...   ...  ...  ...     ...        ...         ...     ...     ...       ...
1993  512  512  256       4          0           8       0       0  6.401710
1994  512  512  256       4          0          16       0       0  4.882370
1995  512  512  256       4          1           2       0       0  8.194650
1996  512  512  256       4          1           8       0       0  1.832680
1997  512  512  256       4          1          16       0       0  1.667990

[1998 rows x 9 columns]

How to regenerate CSV and JSON result

To regenerate test-results.csv and test-results.json from original tset logs, follow the next steps:

cd misc

tar -xzf results.tar.gz
tar -xzf results-flags.tar.gz

# Golang is required.
go run ../collector/main.go

How to regenerate figures

To regenerate figures, follow the next steps:

cd misc

# numpy, pandas, matplotlib is required
python plot.py