JuliaGPU/CUDA.jl

ComplexF32 eigen can return `NaN` unexpectedly

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#2,186 opened on Nov 30, 2023

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bughelp wanted

Description

Describe the bug

There seems to be an issue with the stability of the eigen function with ComplexF32. Occasionally the eigen code will return NaN which is inconsistent with the CPU decomposition.

To reproduce

The Minimal Working Example (MWE) for this bug:

using CUDA, HDF5, LinearAlgebra
fid = h5open("broken_eigen.h5", "r")
m = read(fid, "matrix")
m = Hermitian(m)
cm = Hermitian(cu(m))
D, V = eigen(m)
cuD, cuV, eigen(cm)
close(fid)

broken_eigen.h5.txt ** Please note that this file is a .h5 file but I saved it as a txt because it would not let me post here just remove the .txt extension.

Status `~/.julia/environments/v1.9/Project.toml`
  [052768ef] CUDA v5.1.1
  [34da2185] Compat v4.10.0
  [f67ccb44] HDF5 v0.17.1
  [33e6dc65] MKL v0.6.1

Expected behavior

I would expect cuD and cuV to be the eigen values and eigen vectors of the CuMatrix cm which has values between [-4.6161222f-8, 0.8686561f0] with an absolute minimum value of 1.3966348f-25

Version info

Details on Julia:

Julia Version 1.9.4
Commit 8e5136fa297 (2023-11-14 08:46 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: Linux (x86_64-linux-gnu)
  CPU: 32 × Intel(R) Xeon(R) Gold 6244 CPU @ 3.60GHz
  WORD_SIZE: 64
  LIBM: libopenlibm
  LLVM: libLLVM-14.0.6 (ORCJIT, cascadelake)
  Threads: 1 on 32 virtual cores

Details on CUDA:

CUDA runtime 12.3, artifact installation
CUDA driver 12.3
NVIDIA driver 535.113.1, originally for CUDA 12.2

CUDA libraries: 
- CUBLAS: 12.3.2
- CURAND: 10.3.4
- CUFFT: 11.0.11
- CUSOLVER: 11.5.3
- CUSPARSE: 12.1.3
- CUPTI: 21.0.0
- NVML: 12.0.0+535.113.1

Julia packages: 
- CUDA: 5.1.0
- CUDA_Driver_jll: 0.7.0+0
- CUDA_Runtime_jll: 0.10.0+1

Toolchain:
- Julia: 1.9.4
- LLVM: 14.0.6

1 device:
  0: NVIDIA RTX A6000 (sm_86, 45.964 GiB / 47.988 GiB available)

Contributor guide

Tech stack
None
Domain
performancedata
Issue type
bug
DifficultyEstimated implementation difficulty for a new contributor, from 1 for very small changes to 5 for expert-level work.
5
Estimated timeA rough time range for an experienced contributor to investigate, implement, test, and prepare a pull request.
3-5 days
Activity statusHow available the issue appears right now: fresh, active, stale, blocked, or waiting on maintainer input.
fresh
ClarityHow clearly the issue explains the expected change, acceptance criteria, and next step.
clear
Prerequisites
knowledge of CUDAfamiliarity with Juliaunderstanding of eigen decomposition
Newbie friendlinessA 1-100 score estimating how approachable this issue is for first-time contributors.
10
Research direction
The issue involves unexpected NaN from the eigen decomposition for ComplexF32 on GPU. The bug is likely in the cuSOLVER wrapper within CUDA.jl. Investigate the implementation in src/linalg/eigen.jl and compare with CPU eigen results. Check for any known numerical instability in cuSOLVER for single precision complex. Consider testing with different matrix sizes or adding a workaround.