GSL::Eigen::Symm::Workspace.alloc(n)
GSL::Eigen::Symmv::Workspace.alloc(n)
GSL::Eigen::Herm::Workspace.alloc(n)
GSL::Eigen::Hermv::Workspace.alloc(n)
GSL::Eigen::symm(A)
GSL::Eigen::symm(A, workspace)
GSL::Matrix#eigen_symm
GSL::Matrix#eigen_symm(workspace)
GSL::Eigen::symmv(A)
GSL::Matrix#eigen_symmv
GSL::Vector
object which stores all the eigenvalues.
The second is a GSL::Matrix object
, whose columns contain
eigenvectors.
Singleton method of the GSL::Eigen
module, GSL::Eigen::symm
m = GSL::Matrix.alloc([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)
Instance method of GSL::Matrix
class
eigval, eigvec = m.eigen_symmv
GSL::Eigen::herm(A)
GSL::Eigen::herm(A, workspace)
GSL::Matrix::Complex#eigen_herm
GSL::Matrix::Complex#eigen_herm(workspace)
GSL::Eigen::hermv(A)
GSL::Eigen::hermv(A, workspace)
GSL::Matrix::Complex#eigen_hermv
GSL::Matrix::Complex#eigen_hermv(workspace
GSL::Eigen::Nonsymm.alloc(n)
GSL::Eigen::Nonsymm::params(compute_t, balance, wspace)
GSL::Eigen::Nonsymm::Workspace#params(compute_t, balance)
This method sets some parameters which determine how the eigenvalue
problem is solved in subsequent calls to GSL::Eigen::nonsymm
.
If compute_t is set to 1, the full Schur form T
will be
computed by gsl_eigen_nonsymm. If it is set to 0, T
will not be
computed (this is the default setting).
Computing the full Schur form T
requires approximately 1.5-2 times
the number of flops.
If balance is set to 1, a balancing transformation is applied to
the matrix prior to computing eigenvalues. This transformation is designed
to make the rows and columns of the matrix have comparable norms, and can
result in more accurate eigenvalues for matrices whose entries vary widely
in magnitude. See section Balancing for more information. Note that the
balancing transformation does not preserve the orthogonality of the Schur
vectors, so if you wish to compute the Schur vectors with
GSL::Eigen::nonsymm_Z
you will obtain the Schur vectors of the
balanced matrix instead of the original matrix. The relationship will be
where Q is the matrix of Schur vectors for the balanced matrix, and D
is the balancing transformation. Then GSL::Eigen::nonsymm_Z
will
compute a matrix Z
which satisfies with Z = D Q
.
Note that Z
will not be orthogonal. For this reason, balancing is
not performed by default.
GSL::Eigen::nonsymm(m, eval, wspace)
GSL::Eigen::nonsymm(m)
GSL::Matrix#eigen_nonsymm()
GSL::Matrix#eigen_nonsymm(wspace)
GSL::Matrix#eigen_nonsymm(eval, wspace)
m
and return them, or store in the vector eval if it given.
If T
is desired, it is stored in m
on output, however the lower
triangular portion will not be zeroed out. Otherwise, on output, the diagonal
of m
will contain the 1-by-1 real eigenvalues and 2-by-2 complex
conjugate eigenvalue systems, and the rest of m
is destroyed. GSL::Eigen::nonsymm_Z(m, eval, Z, wspace)
GSL::Eigen::nonsymm_Z(m)
GSL::Matrix#eigen_nonsymm_Z()
GSL::Matrix#eigen_nonsymm(eval, Z, wspace)
GSL::Eigen::nonsymm
except they also
compute the Schur vectors and return them (or store into Z
).GSL::Eigen::Nonsymmv.alloc(n)
GSL::Eigen::nonsymm(m)
GSL::Eigen::nonsymm(m, wspace)
GSL::Eigen::nonsymm(m, eval, evec)
GSL::Eigen::nonsymm(m, eval, evec, wspace)
GSL::Matrix#eigen_nonsymmv()
GSL::Matrix#eigen_nonsymmv(wspace)
GSL::Matrix#eigen_nonsymmv(eval, evec)
GSL::Matrix#eigen_nonsymmv(eval, evec, wspace)
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,
GSL::Eigen::SORT_VAL_ASC
ascending order in numerical valueGSL::Eigen::SORT_VAL_DESC
escending order in numerical valueGSL::Eigen::SORT_ABS_ASC
scending order in magnitudeGSL::Eigen::SORT_ABS_DESC
descending order in magnitudeThe 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)