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dgehd2 examples
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Man Page Details
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NAME
       DGEHD2  -  a  real  general  matrix  A to upper Hessenberg form H by an
       orthogonal similarity transformation

SYNOPSIS
       SUBROUTINE DGEHD2( N, ILO, IHI, A, LDA, TAU, WORK, INFO )

           INTEGER        IHI, ILO, INFO, LDA, N

           DOUBLE         PRECISION A( LDA, * ), TAU( * ), WORK( * )

PURPOSE
       DGEHD2 reduces a real general matrix A to upper Hessenberg form H by an
       orthogonal 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 DGEBAL; otherwise they
               should be set to 1 and N respectively. See Further Details.

       A       (input/output) DOUBLE PRECISION 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 overwrit-
               ten with the upper Hessenberg matrix H, and the elements  below
               the  first  subdiagonal,  with  the  array  TAU,  represent the
               orthogonal 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) DOUBLE PRECISION array, dimension (N-1)
               The scalar factors of the elementary  reflectors  (see  Further
               Details).

       WORK    (workspace) DOUBLE PRECISION array, dimension (N)

       INFO    (output) INTEGER
               = 0:  successful exit.
               < 0:  if INFO = -i, the i-th argument had an illegal value.

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'

       where tau is a real scalar, and v is a real 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  modi-
       fied  element  of the upper Hessenberg matrix H, and vi denotes an ele-
       ment of the vector defining H(i).

