cuSOLVER Standard Non-Hermitian Dense Eigenvalue solver example

Description

This chapter provides three examples that demonstrate the usage of cuSOLVER geev for computing the eigenvalues λ_k and corresponding eigenvectors x_k of a non-Hermitian matrix A such that

A x_k = λ_k x_k.

Example 1 and Example 2 compute the eigenvalues and right eigenvectors of the real 3x3 matrix

A = | 1.0 | 2.0 | -3.0 |
    | 7.0 | 4.0 | -2.0 |
    | 4.0 | 2.0 |  1.0 |.

The matrix has one real eigenvalue and two complex eigenvalues that appear as conjugate pair. Example 1 computes the eigenpairs using double precision for all types. Example 2 demonstrates the usage of the mixed real-complex interface.

Example 3 computes the eigenvalues and right eigenvectors of the complex 3x3 matrix

A = | 2.00 + 1.00j | -1.00 + 0.00j | 1.00 + 2.00j |
    | 2.00 + 1.00j | -3.00 + 1.00j | 2.00 + 3.00j |
    | 1.00 + 2.00j | -1.00 + 2.00j | 0.00 + 1.00j |.

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

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

Example 1

$  ./cusolver_geev_example1

Sample example output:

A = (matlab base -1)
1.00 2.00 -3.00
7.00 4.00 -2.00
4.00 2.00 1.00
=====
info = 0 : Xgeev converged
eigenvalues = (matlab base -1)
WR[1] + 1i* WI[1] = -9.209319E-01 + 1i*0.000000E+00
WR[2] + 1i* WI[2] = 3.460466E+00 + 1i*2.323549E+00
WR[3] + 1i* WI[3] = 3.460466E+00 + 1i*-2.323549E+00
=====
VR = (matlab base -1)
0.52 0.10 0.19
-0.83 0.76 0.00
-0.22 0.57 -0.23
=====
|A*VR - VR*diag(W)| = 4.055924E-15

Example 2

$  ./cusolver_geev_example2

Sample example output:

A = (matlab base -1)
1.00 2.00 -3.00
7.00 4.00 -2.00
4.00 2.00 1.00
=====
info = 0 : Xgeev converged
eigenvalues = (matlab base -1)
-0.92 + 0.00j
3.46 + 2.32j
3.46 + -2.32j
=====
VR =
0.52 0.10 0.19
-0.83 0.76 0.00
-0.22 0.57 -0.23
=====

Example 3

$  ./cusolver_geev_example3

Sample example output:

A = (matlab base -1)
2.00 + 1.00j -1.00 + 0.00j 1.00 + 2.00j
2.00 + 1.00j -3.00 + 1.00j 2.00 + 3.00j
1.00 + 2.00j -1.00 + 2.00j 0.00 + 1.00j
=====
info = 0 : Xgeev converged
eigenvalues = (matlab base -1)
0.14 + 3.80j
0.22 + 0.85j
-1.37 + -1.66j
=====
VR =
0.33 + -0.20j -0.13 + -0.57j -0.33 + -0.01j
0.67 + 0.00j 0.47 + 0.20j -0.36 + 0.51j
0.64 + 0.01j 0.62 + 0.00j 0.71 + 0.00j
=====
|A*VR - VR*diag(W)| = 2.970989E-15