cuSOLVER Cholesky Factorization example

Description

This code demonstrates a usage of cuSOLVER Xpotrf/Xpotrs 64-bit functions for using dense Cholesky factorization of a Hermitian positive-definite matrix

A * X = 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 |

where A is a n×n Hermitian matrix, only lower or upper part is meaningful using the generic API interface. The input parameter uplo indicates which part of the matrix is used. The function would leave other part untouched.

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

• cusolverDnXpotrf API
• cusolverDnXpotrs API

Building (make)

Prerequisites

• A Linux/Windows system with recent NVIDIA drivers.
• CMake version 3.18 minimum
• Minimum CUDA 11.1 toolkit is required.

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_Xpotrf_example

Sample example output:

A = (matlab base-1)
1.00 2.00 3.00
2.00 5.00 5.00
3.00 5.00 12.00
=====
B = (matlab base-1)
1.00
2.00
3.00
=====
after Xpotrf: info = 0
L and U = (matlab base-1)
1.00 2.00 3.00
2.00 1.00 5.00
3.00 -1.00 1.41
=====
X = (matlab base-1)
1.00
0.00
0.00
=====