Expert Driver Routines for Generalized Eigenvalue Problems

• CALL LA_SYGVX / LA_HEGVX ( A, B, W, ITYPE=itype, JOBZ=jobz, UPLO=uplo, VL=vl, VU=vu, &
                                       IL=il, IU=iu, M=m, IFAIL=ifail, ABSTOL=abstol, INFO=info )
  Compute selected eigenvalues and, optionally, the eigenvectors of a real generalized symmetric-definite or complex Hermitian-definite eigenproblem. Eigenvalues and eigenvectors can be selected by specifying either a range of values or a range of indices for the desired eigenvalues.
• CALL LA_SPGVX / LA_HPGVX ( AP, BP, W, ITYPE=itype, UPLO=uplo, Z=z, VL= vl, VU= vu, &
                                       IL= il, IU= iu, M= m, IFAIL= ifail, ABSTOL= abstol, INFO=info )
  Compute selected eigenvalues and, optionally, the eigenvectors of a real generalized symmetric-definite or complex Hermitian-definite eigenproblem. Eigenvalues and eigenvectors can be selected by specifying either a range of values or a range of indices for the desired eigenvalues. The matrices are in packed storage.
• CALL LA_SBGVX / LA_HBGVX ( AB, BB, W, UPLO=uplo, Z=z, VL=vl, VU=vu, IL=il, IU=iu,
  M=m, IFAIL=ifail, Q=q, ABSTOL=abstol, INFO=info )
  Compute selected eigenvalues and, optionally, the corresponding eigenvectors of a real generalized symmetric-definite or complex Hermitian-definite eigenproblem. Eigenvalues and eigenvectors can be selected by specifying either a range of values or a range of indices for the desired eigenvalues.
• CALL LA_GGESX ( A, B, <alpha>, BETA, VSL=vsl, VSR=vsr, SELECT=select, &
                                       SDIM=sdim, RCONDE=rconde, RCONDV=rcondv,INFO=info )
  Computes for a pair of n by n real or complex matrices (A, B) the (generalized) real or complex Schur form, the generalized eigenvalues in the form of scalar pairs (alpha,beta), and, optionally, the left and/or right Schur vectors. also computes two reciprocal condition numbers for the average of the selected eigenvalues and reciprocal condition numbers for the right and left deflating subspaces corresponding to the selected eigenvalues.
  <alpha> ::= ALPHAR, ALPHAI | ALPHA
• CALL LA_GGEVX ( A, B, <alpha>, BETA, VL=vl, VR=vr, BALANC=balanc, &
                                       ILO=ilo, IHI=ihi, LSCALE=lscale, RSCALE=rscale, ABNRM=abnrm, &
                                       BBNRM=bbnrm, RCONDE=rconde, RCONDV=rcondv, INFO=info )
  Computes for a pair of n-by-n real or complex matrices (A, B) the generalized eigenvalues in the form of scalar pairs (alpha; beta) and, optionally, the left and/or right generalized eigenvectors. Also computes a balancing transformation (to improve the conditioning of the eigenvalues and eigenvectors), reciprocal condition numbers for the eigenvalues, and reciprocal condition numbers for the right eigenvectors.
  <alpha> ::= ALPHAR, ALPHAI | ALPHA