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Fast CUDA 3x3 SVD
C++ Cuda CMake
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Fast CUDA 3x3 SVD


This is the part of code of

Ming Gao*, Xinlei Wang*, Kui Wu* (joint first authors), Andre Pradhana, Eftychios Sifakis, Cem Yuksel, Chenfanfu Jiang
GPU Optimization of Material Point Methods
ACM Transactions on Graphics (Proceedings of SIGGRAPH ASIA 2018), 37, 6, 2018.

It will produce the same result as “Computing the Singular Value Decomposition of 3x3 matrices with minimal branching and elementary floating point operations" does.

How to use

Though we only provide Visual Studio 2015 *.sln for Windows and cmakelist.txt for Linux, the code doesn't depend on any external library.

Uncomment to VERIFY_RESULTS to verify the resule with CPU version.

Uncomment/comment to use Structure of Arrays or Array of structures for matrix attributes.

The actual CUDA SVD code can be found in svd3_cuda.h.

Copy Dataset_1M.txt file to executable directory


Our GPU implementation takes 0.37 ns per 3x3 SVD on Nvidia Titan Xp, while a AVX512 SVD implementation of [1] takes 2.3 ns and implicit symmetric QR SVD[2] takes 17.0 ns on an 18-cores Intel(R) Xeon(R) Gold 6140 CPU with multithreading.


Please cite the following paper if it helps.

 author       = {Ming Gao* and Xinlei Wang* and Kui Wu* and Andre Pradhana and Eftychios Sifakis and Cem Yuksel and Chenfanfu Jiang},
 title        = {GPU Optimization of Material Point Methods},
 journal      = {ACM Transactions on Graphics (Proceedings of SIGGRAPH ASIA 2018)},
 volume       = {37},  
 number       = {6},  
 year         = {2018},   
 publisher    = {ACM Press},
 address      = {New York, NY, USA},
 note         = {(*Joint First Authors)},


[1] A. McAdams, A. Selle, R. Tamstorf, J. Teran and E. Sifakis, “Computing the Singular Value Decomposition of 3x3 matrices with minimal branching and elementary floating point operations”, University of Wisconsin - Madison technical report TR1690, May 2011

[2] Implicit-shifted Symmetric QR Singular Value Decomposition of 3x3 Matrices, Theodore Gast, C. Fu, Chenfanfu Jiang, Joseph Teran, UCLA Mathematics Department Technical Report (CAM16-19, 2016)

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