Question 1

Spectra vs ARPACK: which is better for C++?

Accepted Answer

Spectra is a modern C++ redesign of ARPACK with a header-only design and tight Eigen integration, making it more suitable for C++ projects. However, ARPACK has broader language bindings and may be preferred in mixed-language environments.

Question 2

How to use Spectra with sparse matrices in C++?

Accepted Answer

Use wrapper classes like SparseGenMatProd to define the matrix operation from an Eigen sparse matrix, then instantiate a solver such as GenEigsSolver, specify the number of eigenvalues, and call compute() with a selection rule like LargestMagn.

Question 3

Does Spectra support complex eigenvalues and matrices?

Accepted Answer

Yes, Spectra provides HermEigsSolver for complex Hermitian matrices and GenEigsSolver for general complex-valued matrices, handling both real and complex eigenvalues as demonstrated in the examples with Eigen::MatrixXcd.

Question 4

What is shift-and-invert mode and when should I use it?

Accepted Answer

Shift-and-invert mode targets eigenvalues near a specific value σ, useful for finding smallest eigenvalues of positive definite matrices. It requires defining a shift-solve operation, and solvers like SymEigsShiftSolver are provided for this purpose.

Question 5

How to install Spectra with CMake if I already have Eigen?

Accepted Answer

Set CMAKE_PREFIX_PATH to Eigen's installation directory or use Eigen3_ROOT, then run cmake with -DCMAKE_INSTALL_PREFIX and -DBUILD_TESTS=TRUE. This creates a Spectra::Spectra target for easy integration into other CMake projects.

Question 6

Spectra performance: how fast is it for large problems?

Accepted Answer

Spectra is efficient for large sparse matrices using iterative methods, but performance depends on sparsity and condition number. It excels when computing a few eigenvalues but may be slower for dense matrices or ill-conditioned cases compared to direct solvers.

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