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cgegs-f(3)

cgegs.f –

Synopsis

Functions/Subroutines

subroutine cgegs (JOBVSL, JOBVSR, N, A, LDA, B, LDB, ALPHA, BETA, VSL, LDVSL, VSR, LDVSR, WORK, LWORK, RWORK, INFO)
CGEEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matrices

Function/Subroutine Documentation

subroutine cgegs (characterJOBVSL, characterJOBVSR, integerN, complex, dimension( lda, * )A, integerLDA, complex, dimension( ldb, * )B, integerLDB, complex, dimension( * )ALPHA, complex, dimension( * )BETA, complex, dimension( ldvsl, * )VSL, integerLDVSL, complex, dimension( ldvsr, * )VSR, integerLDVSR, complex, dimension( * )WORK, integerLWORK, real, dimension( * )RWORK, integerINFO)

CGEEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matrices

Purpose:

 This routine is deprecated and has been replaced by routine CGGES.
 CGEGS computes the eigenvalues, Schur form, and, optionally, the
 left and or/right Schur vectors of a complex matrix pair (A,B).
 Given two square matrices A and B, the generalized Schur
 factorization has the form

A = QSZH, B = QTZH


where Q and Z are unitary matrices and S and T are upper triangular.
The columns of Q are the left Schur vectors
and the columns of Z are the right Schur vectors.


If only the eigenvalues of (A,B) are needed, the driver routine
CGEGV should be used instead. See CGEGV for a description of the
eigenvalues of the generalized nonsymmetric eigenvalue problem
(GNEP).

 

Parameters:

JOBVSL

 JOBVSL is CHARACTER*1
 = 'N': do not compute the left Schur vectors;
 = 'V': compute the left Schur vectors (returned in VSL).

JOBVSR

 JOBVSR is CHARACTER*1
 = 'N': do not compute the right Schur vectors;
 = 'V': compute the right Schur vectors (returned in VSR).

N

 N is INTEGER
 The order of the matrices A, B, VSL, and VSR. N >= 0.

A

 A is COMPLEX array, dimension (LDA, N)
 On entry, the matrix A.
 On exit, the upper triangular matrix S from the generalized
 Schur factorization.

LDA

 LDA is INTEGER
 The leading dimension of A. LDA >= max(1,N).

B

 B is COMPLEX array, dimension (LDB, N)
 On entry, the matrix B.
 On exit, the upper triangular matrix T from the generalized
 Schur factorization.

LDB

 LDB is INTEGER
 The leading dimension of B. LDB >= max(1,N).

ALPHA

 ALPHA is COMPLEX array, dimension (N)
 The complex scalars alpha that define the eigenvalues of
 GNEP. ALPHA(j) = S(j,j), the diagonal element of the Schur
 form of A.

BETA

 BETA is COMPLEX array, dimension (N)
 The non-negative real scalars beta that define the
 eigenvalues of GNEP. BETA(j) = T(j,j), the diagonal element
 of the triangular factor T.
 Together, the quantities alpha = ALPHA(j) and beta = BETA(j)
 represent the j-th eigenvalue of the matrix pair (A,B), in
 one of the forms lambda = alpha/beta or mu = beta/alpha.
 Since either lambda or mu may overflow, they should not,
 in general, be computed.

VSL

 VSL is COMPLEX array, dimension (LDVSL,N)
 If JOBVSL = 'V', the matrix of left Schur vectors Q.
 Not referenced if JOBVSL = 'N'.

LDVSL

 LDVSL is INTEGER
 The leading dimension of the matrix VSL. LDVSL >= 1, and
 if JOBVSL = 'V', LDVSL >= N.

VSR

 VSR is COMPLEX array, dimension (LDVSR,N)
 If JOBVSR = 'V', the matrix of right Schur vectors Z.
 Not referenced if JOBVSR = 'N'.

LDVSR

 LDVSR is INTEGER
 The leading dimension of the matrix VSR. LDVSR >= 1, and
 if JOBVSR = 'V', LDVSR >= N.

WORK

 WORK is COMPLEX array, dimension (MAX(1,LWORK))
 On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK

 LWORK is INTEGER
 The dimension of the array WORK. LWORK >= max(1,2*N).
 For good performance, LWORK must generally be larger.
 To compute the optimal value of LWORK, call ILAENV to get
 blocksizes (for CGEQRF, CUNMQR, and CUNGQR.) Then compute:
 NB -- MAX of the blocksizes for CGEQRF, CUNMQR, and CUNGQR;
 the optimal LWORK is N*(NB+1).
 If LWORK = -1, then a workspace query is assumed; the routine
 only calculates the optimal size of the WORK array, returns
 this value as the first entry of the WORK array, and no error
 message related to LWORK is issued by XERBLA.

RWORK

 RWORK is REAL array, dimension (3*N)

INFO

 INFO is INTEGER
 = 0: successful exit
 < 0: if INFO = -i, the i-th argument had an illegal value.
 =1,...,N:
 The QZ iteration failed. (A,B) are not in Schur
 form, but ALPHA(j) and BETA(j) should be correct for
 j=INFO+1,...,N.
 > N: errors that usually indicate LAPACK problems:
 =N+1: error return from CGGBAL
 =N+2: error return from CGEQRF
 =N+3: error return from CUNMQR
 =N+4: error return from CUNGQR
 =N+5: error return from CGGHRD
 =N+6: error return from CHGEQZ (other than failed
 iteration)
 =N+7: error return from CGGBAK (computing VSL)
 =N+8: error return from CGGBAK (computing VSR)
 =N+9: error return from CLASCL (various places)

 

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

November 2011

Definition at line 224 of file cgegs.f.

Author

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