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zgehd2 (3)
  • >> zgehd2 (3) ( Solaris man: Библиотечные вызовы )
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    NAME
         zgehd2 - reduce a complex general matrix A to upper  Hessen-
         berg form H by a unitary similarity transformation
    
    SYNOPSIS
         SUBROUTINE ZGEHD2( N, ILO, IHI, A, LDA, TAU, WORK, INFO )
    
         INTEGER IHI, ILO, INFO, LDA, N
    
         COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
    
    
    
         #include <sunperf.h>
    
         void zgehd2(int n, int ilo, int ihi, doublecomplex *za,  int
                   lda, doublecomplex *tau, int *info) ;
    
    PURPOSE
         ZGEHD2 reduces a complex general matrix A to  upper  Hessen-
         berg  form H by a unitary similarity transformation:  Q' * A
         * Q = H .
    
    
    ARGUMENTS
         N         (input) INTEGER
                   The order of the matrix A.  N >= 0.
    
         ILO       (input) INTEGER
                   IHI     (input) 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.
    
         A         (input/output) 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 subdiag-
                   onal of A are overwritten with the  upper  Hessen-
                   berg  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      (input)
                   INTEGER The leading dimension of the array A.  LDA
                   >= max(1,N).
    
         TAU       (output) COMPLEX*16 array, dimension (N-1)
                   The scalar factors of  the  elementary  reflectors
                   (see Further Details).
    
         WORK      (workspace) COMPLEX*16 array, dimension (N)
         INFO      (output) INTEGER
                   = 0:  successful exit
                   < 0:  if INFO = -i, the i-th argument had an ille-
                   gal value.
    
    FURTHER DETAILS
         The matrix Q is represented as a product of  (ihi-ilo)  ele-
         mentary reflectors
    
            Q = H(ilo) H(ilo+1) . . . H(ihi-1).
    
         Each H(i) has the form
    
            H(i) = I - tau * v * v'
    
         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).
    
    
    
    


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