The currently available tools for sparse linear algebra in Scipy are not very good for larger problems. The goal is to develop a high-performance sparse linear algebra interface for a single workstation that integrates fully within Scipy.
• Interfacing to algebraic multigrid (AMG) solvers and other preconditioners. Create interfaces to widely used algebraic multigrid packages (e.g. ML, others) and preconditioners.
Potentially write a custom AMG Implementation referred on PyAMG git-repository https://github.com/pyamg.
Our aim is to speed up PyAMG on the using of finite elements.
All software developments must be well implemented using PEP8 Python coding standards, easy to use, well documented and easy to install using conda or pip.
System enviroment:
sudo apt-get install gcc gfortran python3-dev libopenblas-dev liblapack-dev
Use conda create 2 enviroment scipy numba
conda create -n scipy python=3.6 -y
conda activate scipy
conda install numba tbb cudatoolkit -y
pip install pyamg
pip install -r requirements.txt
conda create -n numba python=3.6 -y
conda activate numba
conda install numba tbb cudatoolkit Cython -y
pip install pyamg
pip install -r requirements.txt
build scipy: bash install_scipy.sh
~/anaconda3/envs/scipy/bin/python -m cProfile -o result_scipy profile_ruge_stuben_solver.py
~/anaconda3/envs/numba/bin/python -m cProfile -o result_numba profile_ruge_stuben_solver.py
python test_csr_matvec.py
| operator | A | B | scipy sparse |
|---|---|---|---|
| *,@ | sparse matrix | vector | matrix multiplication,dot,call csr_matvec |
| *,@ | sparse matrix | sparse matrix | matrix multiplication, dot, call _mul_sparse_matrix->csr_matmat |
multiply |
sparse matrix(M,N) | sparse matrix(M,N) | (M,N)*(M,N)，multiply-> _binopt->csr_elmul_csr |
multiply |
sparse matrix(M,1) | sparse matrix(1,N) | (M,1)@(1,N),multiply-> _mul_sparse_matrix |
multiply |
sparse matrix(1,N) | sparse matrix(M,1) | (M,1)@(1,N)，multiply-> _mul_sparse_matrix |
multiply |
sparse matrix(M,N) | sparse matrix(1,N) | (M,N)*(1,N)，multiply-> _mul_sparse_matrix |
multiply |
sparse matrix(M,N) | sparse matrix(M,1) | (M,N)*(M,1)，multiply-> _mul_sparse_matrix |
multiply |
sparse matrix(M,1) | sparse matrix(M,N) | (M,1)*(M,N)，multiply-> _mul_sparse_matrix |
| + | sparse matrix(M,N) | sparse matrix(M,N) | (M,N)+(M,N), _add_sparse->_binopt->csr_plus_csr |
| - | sparse matrix(M,N) | sparse matrix(M,N) | (M,N)+(M,N), _add_sparse->_binopt->csr_minus_csr |
- matvec
- profile: find the bottleneck operator
python -m cProfile -o result profile_ruge_stuben_solver.py
snakeviz result
the top 2 operators of sparse matrixes using in ruge_stuben_solver are csr_matvec,csr_elmul_csr ,csr_matmat
- optimize
csr_matvec
The calling interface is _mul_vector of nb_compresed
The implementaation operator is csr_matvec of nb_sparsetools
Ref to Sparse Matrix data structures,it is found that the implementation speed of numba is very slow.
-Install numba tbb with conda instead of pip.
- When the number of calculations is < 100, it is slightly slower than SciPy
- Between 100 and 200, speed is almost the same
- Calculation times > 200, slightly faster than SciPy
-
optimize
csr_elmul_csr -
optimize
csr_matmat
Little acceleration effect
NumbaWarning: The TBB threading layer requires TBB version 2019.5 or later i.e., TBB_INTERFACE_VERSION >= 11005. Found TBB_INTERFACE_VERSION = 9002. The TBB threading layer is disabled.
see numba -s has a section Threading Layer Information
Solution: Use conda to install rather than pip