Title: Eigensystems

1 Modules and classes

2 Real Symmetric Matrices, GSL::Eigen::Symm module

2.1 Workspace classes

GSL::Eigen::Symm::Workspace::alloc(n)
GSL::Eigen::Symm::Workspace::new(n)
GSL::Eigen::Symmv::Workspace::alloc(n)
GSL::Eigen::Symmv::Workspace::new(n)
GSL::Eigen::Herm::Workspace::alloc(n)
GSL::Eigen::Herm::Workspace::new(n)
GSL::Eigen::Hermv::Workspace::alloc(n)
GSL::Eigen::Hermv::Workspace::new(n)

2.2 Methods to solve eigensystems

GSL::Eigen::symm(A)
GSL::Eigen::symm(A, workspace)
GSL::Matrix#eigen_symm
GSL::Matrix#eigen_symm(workspace)
These methods compute the eigenvalues of the real symmetric matrix. The workspace object workspace can be omitted.
GSL::Eigen::symmv(A)
GSL::Matrix#eigen_symmv
These methods compute the eigenvalues and eigenvectors of the real symmetric matrix, and return an array of two elements: The first is a GSL::Vector object which stores all the eigenvalues. The second is a GSL::Matrix object, whose columns contain eigenvectors.
  1. Singleton method of the GSL::Eigen module, GSL::Eigen::symm

    m = GSL::Matrix.new([1.0, 1/2.0, 1/3.0, 1/4.0], [1/2.0, 1/3.0, 1/4.0, 1/5.0],
                       [1/3.0, 1/4.0, 1/5.0, 1/6.0], [1/4.0, 1/5.0, 1/6.0, 1/7.0])
    eigval, eigvec = Eigen::symmv(m)
  2. Instance method of GSL::Matrix class

    eigval, eigvec = m.eigen_symmv

3 Complex Hermitian Matrices

GSL::Eigen::herm(A)
GSL::Eigen::herm(A, workspace)
GSL::Matrix::Complex#eigen_herm
GSL::Matrix::Complex#eigen_herm(workspace)
These methods compute the eigenvalues of the complex hermitian matrix.
GSL::Eigen::hermv(A)
GSL::Eigen::hermv(A, workspace)
GSL::Matrix::Complex#eigen_hermv
GSL::Matrix::Complex#eigen_hermv(workspace

4 Sorting Eigenvalues and Eigenvectors

GSL::Eigen::symmv_sort(eval, evec, type = GSL::Eigen::SORT_VAL_ASC)
GSL::Eigen::Symmv::sort(eval, evec, type = GSL::Eigen::SORT_VAL_ASC)

These methods simultaneously sort the eigenvalues stored in the vector eval and the corresponding real eigenvectors stored in the columns of the matrix evec into ascending or descending order according to the value of the parameter type,

The sorting is carried out in-place.

GSL::Eigen::hermv_sort(eval, evec, type = GSL::Eigen::SORT_VAL_ASC)
GSL::Eigen::Hermv::sort(eval, evec, type = GSL::Eigen::SORT_VAL_ASC)
These methods simultaneously sort the eigenvalues stored in the vector eval and the corresponding complex eigenvectors stored in the columns of the matrix evec into ascending or descending order according to the value of the parameter type as shown above.

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