syevj

cuSOLVER Standard Symmetric Dense Eigenvalue solver (via Jacobi method) example

Description

This code demonstrates a usage of cuSOLVER syevj function for using syevj to compute spectrum of a pair of dense symmetric matrices (A,B) by

Ax = λx

where A is a 3x3 dense symmetric matrix

A = | 3.5 | 0.5 | 0.0 |
    | 0.5 | 3.5 | 0.0 |
    | 0.0 | 0.0 | 2.0 |

The following code uses syevj to compute eigenvalues and eigenvectors, then compare to exact eigenvalues {2,3,4}.

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

• cusolverDnDsyevj_bufferSize API
• cusolverDnDsyevj API
• cusolverDnXsyevjSetTolerance API
• cusolverDnXsyevjSetMaxSweeps API

Building (make)

Prerequisites

• A Linux/Windows system with recent NVIDIA drivers.
• CMake version 3.18 minimum
• Minimum CUDA 9.0 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_syevj_example

Sample example output:

tol = 1.000000E-07, default value is machine zero
max. sweeps = 15, default value is 100
A = (matlab base-1)
3.50 0.50 0.00
0.50 3.50 0.00
0.00 0.00 2.00
=====
syevj converges
Eigenvalue = (matlab base-1), ascending order
W[1] = 2.000000E+00
W[2] = 3.000000E+00
W[3] = 4.000000E+00
V = (matlab base-1)
0.00 0.71 0.71
0.00 -0.71 0.71
1.00 0.00 0.00
=====
|lambda - W| = 1.332268E-15
residual |A - V*W*V**H|_F = 3.344748E-17
number of executed sweeps = 1