cgegs (3) - Linux Manuals

NAME

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 This routine is deprecated and has been replaced by routine CGGES.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 = Q*S*Z**H,  B = Q*T*Z**H
 
 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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