Calculate Generalized Eigenvalues, the Generalized Schur Decomposition and the Generalized Singular Value Decomposition of a Matrix Pair with Lapack

Functions to compute generalized eigenvalues and eigenvectors, the generalized Schur decomposition and the generalized Singular Value Decomposition of a matrix pair, using Lapack routines.



o changed package documentation .Rd to update metadata o updated lapack routines to version 3.8.0; many Fortran routines unchanged from Lapack 3.7.0. Changes are minimal.


o clarification in documentation of geigen about when the second matrix must be positive definite. o corrected documentation of gqz; matrices need not be positive definite.


o register native routines in dll o added NeedsCompilation field to DESCRIPTION o use subroutines from Lapack 3.7.0 (no differences in actual code)


o in all files src/x*.f obsolescent Fortran character* declarations replaced o in all files src/x*.f use instead of <complex16> but Lapack routines using <complex16> have not been changed


o moved zheg* routines to separate file o updated Lapack routines to version 3.6.1 o documentation tweaks


o update to routines from Lapack 3.6.0 and use new gsvd routines o Lapack zzgsvd3 and zzgsvp3 from svn revision 1664 and 1671


o gsvd now also handles complex matrices


o documentation tweaks o gsvd does not handle complex matrices o removed CITATION and let it be auto generated (to get details correct)


o added a Generalized Singular Value Decomposition of a matrix pair o documentation tweaks


o change to titlecase in several places and update CITATION o additional comments in cmplxdiv.R about weird complex division on some systems


o replaced zgetc2 in zggesall.f with Lapack 3.5.0 version o additional tests o fix some ftnchek warning/error messages


o added function for computing generalized eigenvalues from a generalized Schur decomposition o introduced S3 classes and methods for calculating generalized eigenvalues from the generalized Schur decomposition o added Copyright field in DESCRIPTION o documentation tweaks and clarifications


o added Lapack Licence o added alpha and beta to return list of geigen() and gqz() for safe calculation of generalized eigenvalues o improved sorting eigenvalues for singular matrix B o improved calculation of eigenvalues for singular B matrix in geigen() o detailed Lapack error/informative messages o option 'R' in gqz() didn't function correctly. Corrected errors and now uses a tolerance for testing zero imaginary part.


o corrected error message in gqz() o stricter test of sorting for gqz() o modified all intermediate Fortran subroutines to have integer arguments which are transferred to character*1 variables for calling the actual Lapack subroutines since on some platforms the Fortran runtime did not accept character in routines called by R o renamed src/xdgg.f to src/xdggev.f


o initial version

Reference manual

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2.3 by Berend Hasselman, 2 years ago

Browse source code at

Authors: Berend Hasselman [cre, aut] , Lapack authors [aut, cph]

Documentation:   PDF Manual  

Task views: Numerical Mathematics

GPL (>= 2) license

Imported by CovTools, PEIP, influenceAUC, quadmatrix.

Depended on by conicfit.

See at CRAN