14.7 Sorting Eigenvalues and Eigenvectors

Function: int gsl_eigen_symmv_sort (gsl_vector * eval, gsl_matrix * evec, gsl_eigen_sort_t sort_type)

This function simultaneously sorts 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 sort_type,

GSL_EIGEN_SORT_VAL_ASC

ascending order in numerical value

GSL_EIGEN_SORT_VAL_DESC

descending order in numerical value

GSL_EIGEN_SORT_ABS_ASC

ascending order in magnitude

GSL_EIGEN_SORT_ABS_DESC

descending order in magnitude

Function: int gsl_eigen_hermv_sort (gsl_vector * eval, gsl_matrix_complex * evec, gsl_eigen_sort_t sort_type)

This function simultaneously sorts 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 sort_type as shown above.

Function: int gsl_eigen_nonsymmv_sort (gsl_vector_complex * eval, gsl_matrix_complex * evec, gsl_eigen_sort_t sort_type)

This function simultaneously sorts 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 sort_type as shown above. Only GSL_EIGEN_SORT_ABS_ASC and GSL_EIGEN_SORT_ABS_DESC are supported due to the eigenvalues being complex.

Function: int gsl_eigen_gensymmv_sort (gsl_vector * eval, gsl_matrix * evec, gsl_eigen_sort_t sort_type)

This function simultaneously sorts 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 sort_type as shown above.

Function: int gsl_eigen_genhermv_sort (gsl_vector * eval, gsl_matrix_complex * evec, gsl_eigen_sort_t sort_type)

This function simultaneously sorts 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 sort_type as shown above.

Function: int gsl_eigen_genv_sort (gsl_vector_complex * alpha, gsl_vector * beta, gsl_matrix_complex * evec, gsl_eigen_sort_t sort_type)

This function simultaneously sorts the eigenvalues stored in the vectors (alpha, beta) 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 sort_type as shown above. Only GSL_EIGEN_SORT_ABS_ASC and GSL_EIGEN_SORT_ABS_DESC are supported due to the eigenvalues being complex.