Conjugate Gradient Method Library implement the linear CG method and non-linear CG menthod by numpy and C++. Furthermore, Conjugate Gradient Method Library supports OpenMP and CUDA operations, that can further accelerate the C++ library.
Conjugate gradient method is a numerical method that can find the minima of the function in the hyper-dimensional space, and conjugate gradient method includes linear conjugate method and non-linear conjugate method.
Linear CG algorithm can precisely calculate the step length in every iteration, but in order to calculate the precise step length, the objective function could only be quadratic function. Compared with the steepest gradient method, the minima could be found in the finite step by conjugate gradient method in theory (if we don't consider the floating-point error and ill-conditioned), and the convergence iteration of conjugate gradient method is less than those of steepest gradient method.
Non-linear CG algorithm can approximately calculate the step length by line search, or gradient descent method, and the advantage of non-linear CG algorithm is that the target function could be convex nonlinear objective functions.
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Clone this repo.
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Install numpy, autograd, OpenMP, and CUDA, or build and run the dockerfile in /contrib/docker (under construction).
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Here are the commands for the CPU implementations:
| Command | Utility |
|---|---|
make |
Compile the module |
make test |
Run the pytest |
make demo |
Run the simple example and analysis. |
For the GPU implementations, simply add the GPU=1 flag:
| Command | Utility |
|---|---|
make GPU=1 |
Compile the module |
make test GPU=1 |
Run the pytest |
make demo GPU=1 |
Run the simple example and analysis. |
Run python3 demo/demo_cg_method.py for reproducing the results in the paper (which is also included in make demo).