SRC/zgehd2.f(3)            Library Functions Manual            SRC/zgehd2.f(3)

NAME
       SRC/zgehd2.f

SYNOPSIS
   Functions/Subroutines
       subroutine zgehd2 (n, ilo, ihi, a, lda, tau, work, info)
           ZGEHD2 reduces a general square matrix to upper Hessenberg form
           using an unblocked algorithm.

Function/Subroutine Documentation
   subroutine zgehd2 (integer n, integer ilo, integer ihi, complex*16,
       dimension( lda, * ) a, integer lda, complex*16, dimension( * ) tau,
       complex*16, dimension( * ) work, integer info)
       ZGEHD2 reduces a general square matrix to upper Hessenberg form using
       an unblocked algorithm.

       Purpose:


           !>
           !> ZGEHD2 reduces a complex general matrix A to upper Hessenberg form H
           !> by a unitary similarity transformation:  Q**H * A * Q = H .
           !>

       Parameters
           N

           !>          N is INTEGER
           !>          The order of the matrix A.  N >= 0.
           !>

           ILO

           !>          ILO is INTEGER
           !>

           IHI

           !>          IHI is INTEGER
           !>
           !>          It is assumed that A is already upper triangular in rows
           !>          and columns 1:ILO-1 and IHI+1:N. ILO and IHI are normally
           !>          set by a previous call to ZGEBAL; otherwise they should be
           !>          set to 1 and N respectively. See Further Details.
           !>          1 <= ILO <= IHI <= max(1,N).
           !>

           A

           !>          A is COMPLEX*16 array, dimension (LDA,N)
           !>          On entry, the n by n general matrix to be reduced.
           !>          On exit, the upper triangle and the first subdiagonal of A
           !>          are overwritten with the upper Hessenberg matrix H, and the
           !>          elements below the first subdiagonal, with the array TAU,
           !>          represent the unitary matrix Q as a product of elementary
           !>          reflectors. See Further Details.
           !>

           LDA

           !>          LDA is INTEGER
           !>          The leading dimension of the array A.  LDA >= max(1,N).
           !>

           TAU

           !>          TAU is COMPLEX*16 array, dimension (N-1)
           !>          The scalar factors of the elementary reflectors (see Further
           !>          Details).
           !>

           WORK

           !>          WORK is COMPLEX*16 array, dimension (N)
           !>

           INFO

           !>          INFO is INTEGER
           !>          = 0:  successful exit
           !>          < 0:  if INFO = -i, the i-th argument had an illegal value.
           !>

       Author
           Univ. of Tennessee


           Univ. of California Berkeley


           Univ. of Colorado Denver


           NAG Ltd.

       Further Details:


           !>
           !>  The matrix Q is represented as a product of (ihi-ilo) elementary
           !>  reflectors
           !>
           !>     Q = H(ilo) H(ilo+1) . . . H(ihi-1).
           !>
           !>  Each H(i) has the form
           !>
           !>     H(i) = I - tau * v * v**H
           !>
           !>  where tau is a complex scalar, and v is a complex vector with
           !>  v(1:i) = 0, v(i+1) = 1 and v(ihi+1:n) = 0; v(i+2:ihi) is stored on
           !>  exit in A(i+2:ihi,i), and tau in TAU(i).
           !>
           !>  The contents of A are illustrated by the following example, with
           !>  n = 7, ilo = 2 and ihi = 6:
           !>
           !>  on entry,                        on exit,
           !>
           !>  ( a   a   a   a   a   a   a )    (  a   a   h   h   h   h   a )
           !>  (     a   a   a   a   a   a )    (      a   h   h   h   h   a )
           !>  (     a   a   a   a   a   a )    (      h   h   h   h   h   h )
           !>  (     a   a   a   a   a   a )    (      v2  h   h   h   h   h )
           !>  (     a   a   a   a   a   a )    (      v2  v3  h   h   h   h )
           !>  (     a   a   a   a   a   a )    (      v2  v3  v4  h   h   h )
           !>  (                         a )    (                          a )
           !>
           !>  where a denotes an element of the original matrix A, h denotes a
           !>  modified element of the upper Hessenberg matrix H, and vi denotes an
           !>  element of the vector defining H(i).
           !>

       Definition at line 148 of file zgehd2.f.

Author
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LAPACK                          Version 3.12.0                 SRC/zgehd2.f(3)