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# Driver Routines for Generalized Eigenvalue and Singular Value Problems

• CALL LA_SYGV / LA_HEGV ( A, B, W, ITYPE=itype, JOBZ=jobz, &
UPLO=uplo, INFO=info )
Computes all the eigenvalues and, optionally, the eigenvectors of a real generalized symmetric-definite or complex Hermitian-definite eigenproblem
• CALL LA_SPGV / LA_HPGV ( AP, BP, W, ITYPE=itype, UPLO=uplo, Z=z, &
INFO=info )
Computes all the eigenvalues and, optionally, the eigenvectors of a real/complex Hermitian generalized eigenproblem. The matrices are in packed storage.
• CALL LA_SBGV / LA_HBGV ( AB, BB, W, UPLO=uplo, Z=z, INFO=info )
Computes all the eigenvalues and, optionally, all eigenvectors of a real generalized symmetric-definite / complex Hermitian banded eigenproblem.
• CALL LA_GGES ( A, B, <alpha>, BETA, VSL=vsl, VSR=vsr, &
SELECT=select, SDIM=sdim, INFO=info )
Computes for a pair of n by n non-symmetric matrices A, B the generalized eigenvalues 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. <alpha> ::= ALPHAR, ALPHAI | ALPHA
• CALL LA_GEGS ( A, B, <alpha>=alpha, BETA=beta, VSL=vsl, VSR=vsr, INFO=info )
Computes for a pair of n by n non-symmetric matrices A, B the generalized eigenvalues 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. <alpha> ::= ALPHAR, ALPHAI | ALPHA
• CALL LA_GGEV ( A, B, <alpha>, BETA, VL=vl, VR=vr, 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. <alpha> ::= ALPHAR, ALPHAI | ALPHA
• CALL LA_GEGV ( A, B, <alpha>=alpha, BETA=beta, VL=vl, VR=vr, 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. <alpha> ::= ALPHAR, ALPHAI | ALPHA
• CALL LA_GGSVD ( A, B, ALPHA, BETA, K=k, L=l, U=u, V=v, Q=q, IWORK=iwork, INFO=info )
Computes the generalized singular values and, optionally, the transformation matrices from the generalized singular value decomposition (GSVD) of a real or complex matrix pair (A,B), where A is m by n and B is p by n.

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Minka Marinova 2000-09-07