.TH "SRC/ztrevc3.f" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
SRC/ztrevc3.f
.SH SYNOPSIS
.br
.PP
.SS "Functions/Subroutines"

.in +1c
.ti -1c
.RI "subroutine \fBztrevc3\fP (side, howmny, select, n, t, ldt, vl, ldvl, vr, ldvr, mm, m, work, lwork, rwork, lrwork, info)"
.br
.RI "\fBZTREVC3\fP "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine ztrevc3 (character side, character howmny, logical, dimension( * ) select, integer n, complex*16, dimension( ldt, * ) t, integer ldt, complex*16, dimension( ldvl, * ) vl, integer ldvl, complex*16, dimension( ldvr, * ) vr, integer ldvr, integer mm, integer m, complex*16, dimension( * ) work, integer lwork, double precision, dimension( * ) rwork, integer lrwork, integer info)"

.PP
\fBZTREVC3\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 ZTREVC3 computes some or all of the right and/or left eigenvectors of
 a complex upper triangular matrix T\&.
 Matrices of this type are produced by the Schur factorization of
 a complex general matrix:  A = Q*T*Q**H, as computed by ZHSEQR\&.

 The right eigenvector x and the left eigenvector y of T corresponding
 to an eigenvalue w are defined by:

              T*x = w*x,     (y**H)*T = w*(y**H)

 where y**H denotes the conjugate transpose of the vector y\&.
 The eigenvalues are not input to this routine, but are read directly
 from the diagonal of T\&.

 This routine returns the matrices X and/or Y of right and left
 eigenvectors of T, or the products Q*X and/or Q*Y, where Q is an
 input matrix\&. If Q is the unitary factor that reduces a matrix A to
 Schur form T, then Q*X and Q*Y are the matrices of right and left
 eigenvectors of A\&.

 This uses a Level 3 BLAS version of the back transformation\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fISIDE\fP 
.PP
.nf
          SIDE is CHARACTER*1
          = 'R':  compute right eigenvectors only;
          = 'L':  compute left eigenvectors only;
          = 'B':  compute both right and left eigenvectors\&.
.fi
.PP
.br
\fIHOWMNY\fP 
.PP
.nf
          HOWMNY is CHARACTER*1
          = 'A':  compute all right and/or left eigenvectors;
          = 'B':  compute all right and/or left eigenvectors,
                  backtransformed using the matrices supplied in
                  VR and/or VL;
          = 'S':  compute selected right and/or left eigenvectors,
                  as indicated by the logical array SELECT\&.
.fi
.PP
.br
\fISELECT\fP 
.PP
.nf
          SELECT is LOGICAL array, dimension (N)
          If HOWMNY = 'S', SELECT specifies the eigenvectors to be
          computed\&.
          The eigenvector corresponding to the j-th eigenvalue is
          computed if SELECT(j) = \&.TRUE\&.\&.
          Not referenced if HOWMNY = 'A' or 'B'\&.
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
          The order of the matrix T\&. N >= 0\&.
.fi
.PP
.br
\fIT\fP 
.PP
.nf
          T is COMPLEX*16 array, dimension (LDT,N)
          The upper triangular matrix T\&.  T is modified, but restored
          on exit\&.
.fi
.PP
.br
\fILDT\fP 
.PP
.nf
          LDT is INTEGER
          The leading dimension of the array T\&. LDT >= max(1,N)\&.
.fi
.PP
.br
\fIVL\fP 
.PP
.nf
          VL is COMPLEX*16 array, dimension (LDVL,MM)
          On entry, if SIDE = 'L' or 'B' and HOWMNY = 'B', VL must
          contain an N-by-N matrix Q (usually the unitary matrix Q of
          Schur vectors returned by ZHSEQR)\&.
          On exit, if SIDE = 'L' or 'B', VL contains:
          if HOWMNY = 'A', the matrix Y of left eigenvectors of T;
          if HOWMNY = 'B', the matrix Q*Y;
          if HOWMNY = 'S', the left eigenvectors of T specified by
                           SELECT, stored consecutively in the columns
                           of VL, in the same order as their
                           eigenvalues\&.
          Not referenced if SIDE = 'R'\&.
.fi
.PP
.br
\fILDVL\fP 
.PP
.nf
          LDVL is INTEGER
          The leading dimension of the array VL\&.
          LDVL >= 1, and if SIDE = 'L' or 'B', LDVL >= N\&.
.fi
.PP
.br
\fIVR\fP 
.PP
.nf
          VR is COMPLEX*16 array, dimension (LDVR,MM)
          On entry, if SIDE = 'R' or 'B' and HOWMNY = 'B', VR must
          contain an N-by-N matrix Q (usually the unitary matrix Q of
          Schur vectors returned by ZHSEQR)\&.
          On exit, if SIDE = 'R' or 'B', VR contains:
          if HOWMNY = 'A', the matrix X of right eigenvectors of T;
          if HOWMNY = 'B', the matrix Q*X;
          if HOWMNY = 'S', the right eigenvectors of T specified by
                           SELECT, stored consecutively in the columns
                           of VR, in the same order as their
                           eigenvalues\&.
          Not referenced if SIDE = 'L'\&.
.fi
.PP
.br
\fILDVR\fP 
.PP
.nf
          LDVR is INTEGER
          The leading dimension of the array VR\&.
          LDVR >= 1, and if SIDE = 'R' or 'B', LDVR >= N\&.
.fi
.PP
.br
\fIMM\fP 
.PP
.nf
          MM is INTEGER
          The number of columns in the arrays VL and/or VR\&. MM >= M\&.
.fi
.PP
.br
\fIM\fP 
.PP
.nf
          M is INTEGER
          The number of columns in the arrays VL and/or VR actually
          used to store the eigenvectors\&.
          If HOWMNY = 'A' or 'B', M is set to N\&.
          Each selected eigenvector occupies one column\&.
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
          WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
.fi
.PP
.br
\fILWORK\fP 
.PP
.nf
          LWORK is INTEGER
          The dimension of array WORK\&. LWORK >= max(1,2*N)\&.
          For optimum performance, LWORK >= N + 2*N*NB, where NB is
          the optimal blocksize\&.

          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 DOUBLE PRECISION array, dimension (LRWORK)
.fi
.PP
.br
\fILRWORK\fP 
.PP
.nf
          LRWORK is INTEGER
          The dimension of array RWORK\&. LRWORK >= max(1,N)\&.

          If LRWORK = -1, then a workspace query is assumed; the routine
          only calculates the optimal size of the RWORK array, returns
          this value as the first entry of the RWORK array, and no error
          message related to LRWORK is issued by XERBLA\&.
.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
.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
\fBFurther Details:\fP
.RS 4

.PP
.nf
  The algorithm used in this program is basically backward (forward)
  substitution, with scaling to make the the code robust against
  possible overflow\&.

  Each eigenvector is normalized so that the element of largest
  magnitude has magnitude 1; here the magnitude of a complex number
  (x,y) is taken to be |x| + |y|\&.
.fi
.PP
 
.RE
.PP

.PP
Definition at line \fB242\fP of file \fBztrevc3\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.