QuarticSolver 0.1.5

A CPU/GPU library for finding the minimum of a quartic function

CUDA-quartic-solver

A general cubic equation solver and quartic equation minimisation solver written for CPU and Nvidia GPUs, for more details and results, see: https://arxiv.org/abs/1903.10041. The library is available for C++/CUDA as well as Python using Pybind11.

Running the solver

Requirements

1. CUDA 9.0+ capable GPU and nvcc required to run the GPU solvers
2. CMake 3.8+
3. Python 3.6, numpy (if using Python)
4. Pybind11 v2.5.0+ (installation instructions)

CMake

CMake can be used to build the project, for example:

git clone --recursive https://github.com/qureshizawar/CUDA-quartic-solver
mkdir build && cd build
cmake -D CMAKE_BUILD_TYPE=Release ../ -D CPP_exe=true -D GPU_build=false
make

When the CPP_exe flag is set to true, CMake will build a c++ executable, then quartic_solver_main can be executed to run the example code. When the GPU_build flag is set to true, CMake will build the CUDA capable version of the library.

Python

The Python package can be installed by building its .whl file, for example:

git clone --recursive https://github.com/qureshizawar/CUDA-quartic-solver
python setup.py bdist_wheel --GPU_build True

When the GPU_build flag is set to True, the CUDA capable version of the library will be built. The built .whl can then be used to install the package, for example:

pip install ./dist/QuarticSolver-0.1.1-cp36-cp36m-linux_x86_64.whl

Usage

Please see src/main.cu, src/cpu_main.cpp, and the examples in the /tests folder for detailed usage examples

C++

Given quartic functions of the form Ax^4 + Bx^3 + Cx^2 + Dx + E the minimiser for the quartic functions can calculated on the CPU by calling the following function from cpu_solver.cpp:

QuarticMinimumCPU(N, A, B, C, D, E, min);

Where:

• N is the number of functions
• A is an array containing the coefficient A for each of the quartic functions
• B is an array containing the coefficient B for each of the quartic functions
• C is an array containing the coefficient C for each of the quartic functions
• D is an array containing the coefficient D for each of the quartic functions
• E is an array containing the coefficient E for each of the quartic functions
• min is an array which will contain the corresponding minimums for each of the quartic functions

The calculations can be carried out on a GPU by using QuarticMinimumGPU or QuarticMinimumGPUStreams. Please note signifcant performance improvement is observed when N>10000 for QuarticMinimumGPU vs QuarticMinimumGPUStreams

Python

The Python version of the library can be used as follows:

import numpy as np
import QuarticSolver

minimum = QuarticSolver.QuarticMinimum(A,B,C,D,E,True)

Where A,B,C,D,E are numpy arrays containing the quartic function coefficients and the final arg is a boolean flag which if set to True will use the GPU if possible. minimum is the returned numpy array containing the corresponding minimisers.

TODO

1. Add multi-gpu support