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

.in +1c
.ti -1c
.RI "subroutine \fBztrevc\fP (side, howmny, select, n, t, ldt, vl, ldvl, vr, ldvr, mm, m, work, rwork, info)"
.br
.RI "\fBZTREVC\fP "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine ztrevc (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, double precision, dimension( * ) rwork, integer info)"

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

.PP
.nf
 ZTREVC 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\&.
.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 (2*N)
.fi
.PP
.br
\fIRWORK\fP 
.PP
.nf
          RWORK is DOUBLE PRECISION array, dimension (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
.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 \fB216\fP of file \fBztrevc\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.