cuSOLVER batched dense Cholesky factorization example

Description

This code demonstrates a usage of cuSOLVER potrs_batched function for doing batched dense Cholesky factorization to solve a sequence of linear systems

A[i] * x[i] = b[i]

each A[i] is a 3x3 dense Hermitian matrix. In this example, there are two matrices, A0 and A1. A0 is positive definite and A1 is not.

The code uses potrfBatched to do Cholesky factorization and potrsBatched to do backward and forward solve. potrfBatched would report singularity on A1.

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

• cusolverDnDpotrfBatched API
• cusolverDnDpotrsBatched API

Building (make)

Prerequisites

• A Linux/Windows system with recent NVIDIA drivers.
• CMake version 3.18 minimum
• Minimum CUDA 9.1 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_potrfBatched_example

Sample example output:

A0 = (matlab base-1)
1.00 2.00 3.00
2.00 5.00 5.00
3.00 5.00 12.00
=====
A1 = (matlab base-1)
1.00 2.00 3.00
2.00 4.00 5.00
3.00 5.00 12.00
=====
B0 = (matlab base-1)
1.00
1.00
1.00
=====
info[0] = 0
info[1] = 2
L = (matlab base-1), upper triangle is don't care
1.00 2.00 3.00
2.00 1.00 5.00
3.00 -1.00 1.41
=====
after potrsBatched: infoArray[0] = 0
X0 = (matlab base-1)
10.50
-2.50
-1.50
=====