Cucheb: A GPU implementation of the filtered Lanczos procedure
Cucheb: A GPU implementation of the filtered Lanczos procedure
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Cucheb：过滤 Lanczos 过程的 GPU 实现
DOI：
10.1016/j.cpc.2017.06.016
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发表时间：
2017
期刊：
影响因子：
--
通讯作者：
Y. Saad
中科院分区：
文献类型：
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作者：
J. L. Aurentz;V. Kalantzis;Y. Saad
本文介绍了软件包Cucheb，一个GPU实现的过滤Lanczos程序的解决方案的大型稀疏对称特征值问题。过滤Lanczos程序使用一个精心选择的多项式谱变换，以加速收敛的Lanczos方法计算特征值时，在所需的时间间隔。这种方法已被证明是特别有效的电子结构计算和密度泛函理论中出现的本征值问题。我们将我们的实现与等效的CPU实现进行比较，并表明使用GPU可以将计算时间减少10倍以上。程序摘要程序标题：Cucheb程序文件doi：http://dx.doi.org/10.17632/rjr9tzchmh.1Licensing规定：MIT编程语言：CUDA C/C++问题性质：电子结构计算需要计算位于用户定义的真实的区间内的对称矩阵的所有特征值-特征向量对。为了计算给定区间内的所有特征值，构造多项式谱变换，其映射原始特征值的期望特征值。将矩阵变换到变换矩阵的谱的外部。然后使用Lanczos方法来计算变换矩阵的期望特征向量，然后使用该特征向量来恢复原始矩阵的期望特征值。大部分操作都是使用图形处理单元（GPU）并行执行的。CUcheb：变量，取决于所寻求的特征值的数量以及矩阵的大小和稀疏性。其他注释：Cucheb与CUDA Toolkit v7. 0或更高版本兼容。
This paper describes the software package Cucheb, a GPU implementation of the filtered Lanczos procedure for the solution of large sparse symmetric eigenvalue problems. The filtered Lanczos procedure uses a carefully chosen polynomial spectral transformation to accelerate convergence of the Lanczos method when computing eigenvalues within a desired interval. This method has proven particularly effective for eigenvalue problems that arise in electronic structure calculations and density functional theory. We compare our implementation against an equivalent CPU implementation and show that using the GPU can reduce the computation time by more than a factor of 10.Program SummaryProgram title:CuchebProgram Files doi:http://dx.doi.org/10.17632/rjr9tzchmh.1Licensing provisions:MITProgramming language:CUDA C/C++Nature of problem:Electronic structure calculations require the computation of all eigenvalue–eigenvector pairs of a symmetric matrix that lie inside a user-defined real interval.Solution method:To compute all the eigenvalues within a given interval a polynomial spectral transformation is constructed that maps the desired eigenvalues of the original matrix to the exterior of the spectrum of the transformed matrix. The Lanczos method is then used to compute the desired eigenvectors of the transformed matrix, which are then used to recover the desired eigenvalues of the original matrix. The bulk of the operations are executed in parallel using a graphics processing unit (GPU).Runtime:Variable, depending on the number of eigenvalues sought and the size and sparsity of the matrix.Additional comments:Cucheb is compatible with CUDA Toolkit v7.0 or greater.