本征和并行化对共轭梯度没有影响.前提条件也失败 [英] Eigen and parallellization makes no difference for conjugate gradient. Precondition also fails

问题描述

这与此问题.今天，我对共轭梯度进行了一些实验，特别是对max_iterations和tolerance进行了实验.它更快但不够快.根据文档，在编译中添加-fopenmp应该足以启用multi-threading.

This is related to this question. I have today experimented a bit with Conjugate Gradient, in particular I experimented with max_iterations and tolerance. It is faster but not fast enough. According to the documentation it should be enough to add -fopenmp in the compilation to enable multi-threading.

我已经同时使用

`omp_set_num_threads(nbrThreads);
 Eigen::setNbThreads(nbrThreads);`

使用5个线程或1个线程在时间上没有区别，我认为这有点奇怪.

It makes no difference in time if I use 5 threads or 1 thread, and that I think is a bit strange.

第二，使用pre-conditoning加快解决方案的另一种方法.当我尝试做时:

Secondly, another way to speed up the solution using pre-conditoning. When I try to do:

    Eigen::ConjugateGradient<Eigen::SparseMatrix<float>, Eigen::Lower, Eigen::IncompleteCholesky<float>> cg;

我得到了错误:

    void Eigen::IncompleteCholesky<Scalar, _UpLo, _OrderingType>::_solve_impl(const Rhs&, Dest&) const [with Rhs = Eigen::Matr
ix<float, -1, 1>; Dest = Eigen::Matrix<float, -1, 1>; Scalar = float; int _UpLo = 1; _OrderingType = Eigen::AMDOrdering<int>]: Assertion `m_factorizationIsOk && "factorize() should be called first"' failed.

考虑到Eigen::SimplicialLDLT是Cholesky因式分解的，那么不完全也应该起作用?

Given that Eigen::SimplicialLDLT works which is a Cholesky factorization, then the incomplete should also work?

这是我叫cg的方式:

Here is how I call cg:

Eigen::ConjugateGradient<Eigen::SparseMatrix<float>, Eigen::Lower, Eigen::IncompleteCholesky<float>> cg;
cg.setTolerance(0.01);
cg.setMaxIterations(50);
cg.analyzePattern(A_tot);
cg.compute(A_tot);
Eigen::VectorXf opt = cg.solveWithGuess(b_tot, rho_current);

实际上，当您在此处了解有关IterativeSolvers的信息时，则未列出IncompleteCholesky .尽管在此处中定义了.

Actually when you read about IterativeSolvers here, then IncompleteCholesky is not listed. Although IncompleCholesky is defined here.

推荐答案

如文档中所述，您需要存储完整的矩阵(上下三角形部分)，并将Lower|Upper传递给ConjugateGradient以获得与cg多线程.

As explained in the documentation, you need to store the full matrix (both upper and lower triangular part), and pass Lower|Upper to ConjugateGradient to get multi-threading with cg.

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