gesvd

cuSOLVER Singular Value Decomposition with singular vectors example

Description

This code demonstrates a usage of cuSOLVER gesvd function to compute a singular value decomposition

A = U * Σ * V^H

A is a 3x2 dense matrix,

A = | 1.0 | 2.0 |
    | 4.0 | 5.0 |
    | 2.0 | 1.0 |

The following code uses three steps:

Step 1: compute A = U * S * VT

Step 2: check accuracy of singular value

Step 3: measure residual A - U * S * VT

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

• cusolverDnDgesvd_bufferSize API
• cusolverDnDgesvd API

Building (make)

Prerequisites

• A Linux/Windows system with recent NVIDIA drivers.
• CMake version 3.18 minimum
• Minimum CUDA 10.1 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_gesvd_example

Sample example output:

A = (matlab base-1)
1.00 2.00
4.00 5.00
2.00 1.00
=====
after gesvd: info_gpu = 0
gesvd converges
S = singular values (matlab base-1)
7.07
1.04
=====
U = left singular vectors (matlab base-1)
-0.31 0.49 0.82
-0.91 0.11 -0.41
-0.29 -0.87 0.41
=====
VT = right singular vectors (matlab base-1)
-0.64 -0.77
-0.77 0.64
=====
|S - S_exact| = 8.881784E-16
|A - U*S*VT| = 1.790181E-15