.TH "cgges3.f" 3 "Tue Nov 14 2017" "Version 3.8.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
cgges3.f
.SH SYNOPSIS
.br
.PP
.SS "Functions/Subroutines"

.in +1c
.ti -1c
.RI "subroutine \fBcgges3\fP (JOBVSL, JOBVSR, SORT, SELCTG, \fBN\fP, A, \fBLDA\fP, B, \fBLDB\fP, SDIM, ALPHA, BETA, VSL, LDVSL, VSR, LDVSR, WORK, LWORK, RWORK, BWORK, INFO)"
.br
.RI "\fB CGGES3 computes the eigenvalues, the Schur form, and, optionally, the matrix of Schur vectors for GE matrices (blocked algorithm)\fP "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine cgges3 (character JOBVSL, character JOBVSR, character SORT, external SELCTG, integer N, complex, dimension( lda, * ) A, integer LDA, complex, dimension( ldb, * ) B, integer LDB, integer SDIM, complex, dimension( * ) ALPHA, complex, dimension( * ) BETA, complex, dimension( ldvsl, * ) VSL, integer LDVSL, complex, dimension( ldvsr, * ) VSR, integer LDVSR, complex, dimension( * ) WORK, integer LWORK, real, dimension( * ) RWORK, logical, dimension( * ) BWORK, integer INFO)"

.PP
\fB CGGES3 computes the eigenvalues, the Schur form, and, optionally, the matrix of Schur vectors for GE matrices (blocked algorithm)\fP  
.PP
\fBPurpose: \fP
.RS 4

.PP
.nf
 CGGES3 computes for a pair of N-by-N complex nonsymmetric matrices
 (A,B), the generalized eigenvalues, the generalized complex Schur
 form (S, T), and optionally left and/or right Schur vectors (VSL
 and VSR). This gives the generalized Schur factorization

         (A,B) = ( (VSL)*S*(VSR)**H, (VSL)*T*(VSR)**H )

 where (VSR)**H is the conjugate-transpose of VSR.

 Optionally, it also orders the eigenvalues so that a selected cluster
 of eigenvalues appears in the leading diagonal blocks of the upper
 triangular matrix S and the upper triangular matrix T. The leading
 columns of VSL and VSR then form an unitary basis for the
 corresponding left and right eigenspaces (deflating subspaces).

 (If only the generalized eigenvalues are needed, use the driver
 CGGEV instead, which is faster.)

 A generalized eigenvalue for a pair of matrices (A,B) is a scalar w
 or a ratio alpha/beta = w, such that  A - w*B is singular.  It is
 usually represented as the pair (alpha,beta), as there is a
 reasonable interpretation for beta=0, and even for both being zero.

 A pair of matrices (S,T) is in generalized complex Schur form if S
 and T are upper triangular and, in addition, the diagonal elements
 of T are non-negative real numbers.
.fi
.PP
 
.RE
.PP
\fBParameters:\fP
.RS 4
\fIJOBVSL\fP 
.PP
.nf
          JOBVSL is CHARACTER*1
          = 'N':  do not compute the left Schur vectors;
          = 'V':  compute the left Schur vectors.
.fi
.PP
.br
\fIJOBVSR\fP 
.PP
.nf
          JOBVSR is CHARACTER*1
          = 'N':  do not compute the right Schur vectors;
          = 'V':  compute the right Schur vectors.
.fi
.PP
.br
\fISORT\fP 
.PP
.nf
          SORT is CHARACTER*1
          Specifies whether or not to order the eigenvalues on the
          diagonal of the generalized Schur form.
          = 'N':  Eigenvalues are not ordered;
          = 'S':  Eigenvalues are ordered (see SELCTG).
.fi
.PP
.br
\fISELCTG\fP 
.PP
.nf
          SELCTG is a LOGICAL FUNCTION of two COMPLEX arguments
          SELCTG must be declared EXTERNAL in the calling subroutine.
          If SORT = 'N', SELCTG is not referenced.
          If SORT = 'S', SELCTG is used to select eigenvalues to sort
          to the top left of the Schur form.
          An eigenvalue ALPHA(j)/BETA(j) is selected if
          SELCTG(ALPHA(j),BETA(j)) is true.

          Note that a selected complex eigenvalue may no longer satisfy
          SELCTG(ALPHA(j),BETA(j)) = .TRUE. after ordering, since
          ordering may change the value of complex eigenvalues
          (especially if the eigenvalue is ill-conditioned), in this
          case INFO is set to N+2 (See INFO below).
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
          The order of the matrices A, B, VSL, and VSR.  N >= 0.
.fi
.PP
.br
\fIA\fP 
.PP
.nf
          A is COMPLEX array, dimension (LDA, N)
          On entry, the first of the pair of matrices.
          On exit, A has been overwritten by its generalized Schur
          form S.
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
          LDA is INTEGER
          The leading dimension of A.  LDA >= max(1,N).
.fi
.PP
.br
\fIB\fP 
.PP
.nf
          B is COMPLEX array, dimension (LDB, N)
          On entry, the second of the pair of matrices.
          On exit, B has been overwritten by its generalized Schur
          form T.
.fi
.PP
.br
\fILDB\fP 
.PP
.nf
          LDB is INTEGER
          The leading dimension of B.  LDB >= max(1,N).
.fi
.PP
.br
\fISDIM\fP 
.PP
.nf
          SDIM is INTEGER
          If SORT = 'N', SDIM = 0.
          If SORT = 'S', SDIM = number of eigenvalues (after sorting)
          for which SELCTG is true.
.fi
.PP
.br
\fIALPHA\fP 
.PP
.nf
          ALPHA is COMPLEX array, dimension (N)
.fi
.PP
.br
\fIBETA\fP 
.PP
.nf
          BETA is COMPLEX array, dimension (N)
          On exit,  ALPHA(j)/BETA(j), j=1,...,N, will be the
          generalized eigenvalues.  ALPHA(j), j=1,...,N  and  BETA(j),
          j=1,...,N  are the diagonals of the complex Schur form (A,B)
          output by CGGES3. The  BETA(j) will be non-negative real.

          Note: the quotients ALPHA(j)/BETA(j) may easily over- or
          underflow, and BETA(j) may even be zero.  Thus, the user
          should avoid naively computing the ratio alpha/beta.
          However, ALPHA will be always less than and usually
          comparable with norm(A) in magnitude, and BETA always less
          than and usually comparable with norm(B).
.fi
.PP
.br
\fIVSL\fP 
.PP
.nf
          VSL is COMPLEX array, dimension (LDVSL,N)
          If JOBVSL = 'V', VSL will contain the left Schur vectors.
          Not referenced if JOBVSL = 'N'.
.fi
.PP
.br
\fILDVSL\fP 
.PP
.nf
          LDVSL is INTEGER
          The leading dimension of the matrix VSL. LDVSL >= 1, and
          if JOBVSL = 'V', LDVSL >= N.
.fi
.PP
.br
\fIVSR\fP 
.PP
.nf
          VSR is COMPLEX array, dimension (LDVSR,N)
          If JOBVSR = 'V', VSR will contain the right Schur vectors.
          Not referenced if JOBVSR = 'N'.
.fi
.PP
.br
\fILDVSR\fP 
.PP
.nf
          LDVSR is INTEGER
          The leading dimension of the matrix VSR. LDVSR >= 1, and
          if JOBVSR = 'V', LDVSR >= N.
.fi
.PP
.br
\fIWORK\fP 
.PP
.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 
.PP
.nf
          LWORK is INTEGER
          The dimension of the array WORK.

          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 
.PP
.nf
          RWORK is REAL array, dimension (8*N)
.fi
.PP
.br
\fIBWORK\fP 
.PP
.nf
          BWORK is LOGICAL array, dimension (N)
          Not referenced if SORT = '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.  (A,B) are not in Schur
                form, but ALPHA(j) and BETA(j) should be correct for
                j=INFO+1,...,N.
          > N:  =N+1: other than QZ iteration failed in CHGEQZ
                =N+2: after reordering, roundoff changed values of
                      some complex eigenvalues so that leading
                      eigenvalues in the Generalized Schur form no
                      longer satisfy SELCTG=.TRUE.  This could also
                      be caused due to scaling.
                =N+3: reordering failed in CTGSEN.
.fi
.PP
 
.RE
.PP
\fBAuthor:\fP
.RS 4
Univ\&. of Tennessee 
.PP
Univ\&. of California Berkeley 
.PP
Univ\&. of Colorado Denver 
.PP
NAG Ltd\&. 
.RE
.PP
\fBDate:\fP
.RS 4
January 2015 
.RE
.PP

.PP
Definition at line 271 of file cgges3\&.f\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.
