CodeExample

CodeExample is a repository for my example codes

Generic Solver of Davidson Algorithm

Dependency: Eigen3, BLAS, CMake
To compile: cmake ., then make eigen_test or make std_vector_test

This Davidson Algorithm solver works for symmetric(symm_davidson_diag.h) and non-symmetric(nonsymm_davidson_diag.h) system with real eigenvalues. The generic design makes it possible to use this solver with eigenvectors from different data structure classes. The user needs to provide the following interface functions, where the Array is the template type which stands for the type of eigenvector

• element_type_traits<Array>::type defines the element_type in Array (for example float or double)
• Array copy_and_zero(const Array& a) make a new Array based on a, while initialize all elements as zero
• element_type dot_product(const Array& a, const Array& b) return dot product of Array a and b
• void scale(Array& y , element_type a) scale Array y by factor a
• void axpy(Array&y , element_tye a, const Array& x) performs y += a*x
• element_type norm2(const Array& a) return the L^2 norm of Array a

Two examples are provided that use Eigen::Matrix(eigen_test.cpp) and std::vector(std_vector_test.cpp) as the type of the eigenvectors. The element_type_traits functions are defined in type_traits.h. All other interface functions are defined in eigen_interface.h and std_vector_interface.h.