README.md

cuSOLVER LU Factorization example

Description

This code demonstrates a usage of cuSOLVER getrf/getrs functions for using dense LU factorization to solve a linear system

Ax = b

All matrices A_i are small perturbations of

A = | 1.0 | 2.0 | 3.0 |
    | 4.0 | 5.0 | 6.0 |
    | 7.0 | 8.0 | 10.0 |

The code uses getrf to do LU factorization and getrs to do backward and forward solve. The parameter pivot_on decides whether partial pivoting is performed or not.

Supported SM Architectures

All GPUs supported by CUDA Toolkit (https://developer.nvidia.com/cuda-gpus)

Supported OSes

Linux
Windows

Supported CPU Architecture

x86_64
ppc64le
arm64-sbsa

CUDA APIs involved

• cusolverDnDgetrf API
• cusolverDnDgeqrs API

Building (make)

Prerequisites

• A Linux/Windows system with recent NVIDIA drivers.
• CMake version 3.18 minimum

Build command on Linux

$ mkdir build
$ cd build
$ cmake ..
$ make

Make sure that CMake finds expected CUDA Toolkit. If that is not the case you can add argument -DCMAKE_CUDA_COMPILER=/path/to/cuda/bin/nvcc to cmake command.

Build command on Windows

$ mkdir build
$ cd build
$ cmake -DCMAKE_GENERATOR_PLATFORM=x64 ..
$ Open cusolver_examples.sln project in Visual Studio and build

Usage

$  ./cusolver_getrf_example

Sample example output:

pivot is on : compute P*A = L*U
A = (matlab base-1)
1.00 2.00 3.00
4.00 5.00 6.00
7.00 8.00 10.00
=====
B = (matlab base-1)
1.00
2.00
3.00
=====
pivoting sequence, matlab base-1
Ipiv(1) = 3
Ipiv(2) = 3
Ipiv(3) = 3
L and U = (matlab base-1)
7.00 8.00 10.00
0.14 0.86 1.57
0.57 0.50 -0.50
=====
X = (matlab base-1)
-0.33
0.67
0.00
=====

pivot is off: compute A = L*U (not numerically stable)
A = (matlab base-1)
1.00 2.00 3.00
4.00 5.00 6.00
7.00 8.00 10.00
=====
B = (matlab base-1)
1.00
2.00
3.00
=====
L and U = (matlab base-1)
1.00 2.00 3.00
4.00 -3.00 -6.00
7.00 2.00 1.00
=====
X = (matlab base-1)
-0.33
0.67
0.00
=====