.TH "SRC/DEPRECATED/cgegv.f" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
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.SH NAME
SRC/DEPRECATED/cgegv.f
.SH SYNOPSIS
.br
.PP
.SS "Functions/Subroutines"

.in +1c
.ti -1c
.RI "subroutine \fBcgegv\fP (jobvl, jobvr, n, a, lda, b, ldb, alpha, beta, vl, ldvl, vr, ldvr, work, lwork, rwork, info)"
.br
.RI "\fB CGEGV computes the eigenvalues and, optionally, the left and/or right eigenvectors of a complex matrix pair (A,B)\&.\fP "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine cgegv (character jobvl, character jobvr, integer n, complex, dimension( lda, * ) a, integer lda, complex, dimension( ldb, * ) b, integer ldb, complex, dimension( * ) alpha, complex, dimension( * ) beta, complex, dimension( ldvl, * ) vl, integer ldvl, complex, dimension( ldvr, * ) vr, integer ldvr, complex, dimension( * ) work, integer lwork, real, dimension( * ) rwork, integer info)"

.PP
\fB CGEGV computes the eigenvalues and, optionally, the left and/or right eigenvectors of a complex matrix pair (A,B)\&.\fP  
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\fBPurpose:\fP
.RS 4

.PP
.nf
!>
!> This routine is deprecated and has been replaced by routine CGGEV\&.
!>
!> CGEGV computes the eigenvalues and, optionally, the left and/or right
!> eigenvectors of a complex matrix pair (A,B)\&.
!> Given two square matrices A and B,
!> the generalized nonsymmetric eigenvalue problem (GNEP) is to find the
!> eigenvalues lambda and corresponding (non-zero) eigenvectors x such
!> that
!>    A*x = lambda*B*x\&.
!>
!> An alternate form is to find the eigenvalues mu and corresponding
!> eigenvectors y such that
!>    mu*A*y = B*y\&.
!>
!> These two forms are equivalent with mu = 1/lambda and x = y if
!> neither lambda nor mu is zero\&.  In order to deal with the case that
!> lambda or mu is zero or small, two values alpha and beta are returned
!> for each eigenvalue, such that lambda = alpha/beta and
!> mu = beta/alpha\&.
!>
!> The vectors x and y in the above equations are right eigenvectors of
!> the matrix pair (A,B)\&.  Vectors u and v satisfying
!>    u**H*A = lambda*u**H*B  or  mu*v**H*A = v**H*B
!> are left eigenvectors of (A,B)\&.
!>
!> Note: this routine performs  on A and B
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIJOBVL\fP 
.PP
.nf
!>          JOBVL is CHARACTER*1
!>          = 'N':  do not compute the left generalized eigenvectors;
!>          = 'V':  compute the left generalized eigenvectors (returned
!>                  in VL)\&.
!> 
.fi
.PP
.br
\fIJOBVR\fP 
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!>          JOBVR is CHARACTER*1
!>          = 'N':  do not compute the right generalized eigenvectors;
!>          = 'V':  compute the right generalized eigenvectors (returned
!>                  in VR)\&.
!> 
.fi
.PP
.br
\fIN\fP 
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.nf
!>          N is INTEGER
!>          The order of the matrices A, B, VL, and VR\&.  N >= 0\&.
!> 
.fi
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.br
\fIA\fP 
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.nf
!>          A is COMPLEX array, dimension (LDA, N)
!>          On entry, the matrix A\&.
!>          If JOBVL = 'V' or JOBVR = 'V', then on exit A
!>          contains the Schur form of A from the generalized Schur
!>          factorization of the pair (A,B) after balancing\&.  If no
!>          eigenvectors were computed, then only the diagonal elements
!>          of the Schur form will be correct\&.  See CGGHRD and CHGEQZ
!>          for details\&.
!> 
.fi
.PP
.br
\fILDA\fP 
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.nf
!>          LDA is INTEGER
!>          The leading dimension of A\&.  LDA >= max(1,N)\&.
!> 
.fi
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.br
\fIB\fP 
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.nf
!>          B is COMPLEX array, dimension (LDB, N)
!>          On entry, the matrix B\&.
!>          If JOBVL = 'V' or JOBVR = 'V', then on exit B contains the
!>          upper triangular matrix obtained from B in the generalized
!>          Schur factorization of the pair (A,B) after balancing\&.
!>          If no eigenvectors were computed, then only the diagonal
!>          elements of B will be correct\&.  See CGGHRD and CHGEQZ for
!>          details\&.
!> 
.fi
.PP
.br
\fILDB\fP 
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!>          LDB is INTEGER
!>          The leading dimension of B\&.  LDB >= max(1,N)\&.
!> 
.fi
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.br
\fIALPHA\fP 
.PP
.nf
!>          ALPHA is COMPLEX array, dimension (N)
!>          The complex scalars alpha that define the eigenvalues of
!>          GNEP\&.
!> 
.fi
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.br
\fIBETA\fP 
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.nf
!>          BETA is COMPLEX array, dimension (N)
!>          The complex scalars beta that define the eigenvalues of GNEP\&.
!>
!>          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\&.
!> 
.fi
.PP
.br
\fIVL\fP 
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.nf
!>          VL is COMPLEX array, dimension (LDVL,N)
!>          If JOBVL = 'V', the left eigenvectors u(j) are stored
!>          in the columns of VL, in the same order as their eigenvalues\&.
!>          Each eigenvector is scaled so that its largest component has
!>          abs(real part) + abs(imag\&. part) = 1, except for eigenvectors
!>          corresponding to an eigenvalue with alpha = beta = 0, which
!>          are set to zero\&.
!>          Not referenced if JOBVL = 'N'\&.
!> 
.fi
.PP
.br
\fILDVL\fP 
.PP
.nf
!>          LDVL is INTEGER
!>          The leading dimension of the matrix VL\&. LDVL >= 1, and
!>          if JOBVL = 'V', LDVL >= N\&.
!> 
.fi
.PP
.br
\fIVR\fP 
.PP
.nf
!>          VR is COMPLEX array, dimension (LDVR,N)
!>          If JOBVR = 'V', the right eigenvectors x(j) are stored
!>          in the columns of VR, in the same order as their eigenvalues\&.
!>          Each eigenvector is scaled so that its largest component has
!>          abs(real part) + abs(imag\&. part) = 1, except for eigenvectors
!>          corresponding to an eigenvalue with alpha = beta = 0, which
!>          are set to zero\&.
!>          Not referenced if JOBVR = 'N'\&.
!> 
.fi
.PP
.br
\fILDVR\fP 
.PP
.nf
!>          LDVR is INTEGER
!>          The leading dimension of the matrix VR\&. LDVR >= 1, and
!>          if JOBVR = 'V', LDVR >= N\&.
!> 
.fi
.PP
.br
\fIWORK\fP 
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.nf
!>          WORK is COMPLEX array, dimension (MAX(1,LWORK))
!>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK\&.
!> 
.fi
.PP
.br
\fILWORK\fP 
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.nf
!>          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  MAX( 2*N, 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\&.
!> 
.fi
.PP
.br
\fIRWORK\fP 
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.nf
!>          RWORK is REAL array, dimension (8*N)
!> 
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
!>          INFO is INTEGER
!>          = 0:  successful exit
!>          < 0:  if INFO = -i, the i-th argument had an illegal value\&.
!>          =1,\&.\&.\&.,N:
!>                The QZ iteration failed\&.  No eigenvectors have been
!>                calculated, 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 CTGEVC
!>                =N+8: error return from CGGBAK (computing VL)
!>                =N+9: error return from CGGBAK (computing VR)
!>                =N+10: error return from CLASCL (various calls)
!> 
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 

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Univ\&. of California Berkeley 

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Univ\&. of Colorado Denver 

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NAG Ltd\&. 
.RE
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\fBFurther Details:\fP
.RS 4

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.nf
!>
!>  Balancing
!>  ---------
!>
!>  This driver calls CGGBAL to both permute and scale rows and columns
!>  of A and B\&.  The permutations PL and PR are chosen so that PL*A*PR
!>  and PL*B*R will be upper triangular except for the diagonal blocks
!>  A(i:j,i:j) and B(i:j,i:j), with i and j as close together as
!>  possible\&.  The diagonal scaling matrices DL and DR are chosen so
!>  that the pair  DL*PL*A*PR*DR, DL*PL*B*PR*DR have elements close to
!>  one (except for the elements that start out zero\&.)
!>
!>  After the eigenvalues and eigenvectors of the balanced matrices
!>  have been computed, CGGBAK transforms the eigenvectors back to what
!>  they would have been (in perfect arithmetic) if they had not been
!>  balanced\&.
!>
!>  Contents of A and B on Exit
!>  -------- -- - --- - -- ----
!>
!>  If any eigenvectors are computed (either JOBVL='V' or JOBVR='V' or
!>  both), then on exit the arrays A and B will contain the complex Schur
!>  form[*] of the  versions of A and B\&.  If no eigenvectors
!>  are computed, then only the diagonal blocks will be correct\&.
!>
!>  [*] In other words, upper triangular form\&.
!> 
.fi
.PP
 
.RE
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Definition at line \fB280\fP of file \fBcgegv\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.