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dgehd2.f(3)                         LAPACK                         dgehd2.f(3)

NAME
       dgehd2.f -

SYNOPSIS
   Functions/Subroutines
       subroutine dgehd2 (N, ILO, IHI, A, LDA, TAU, WORK, INFO)
           DGEHD2 reduces a general square matrix to upper Hessenberg form
           using an unblocked algorithm.

Function/Subroutine Documentation
   subroutine dgehd2 (integerN, integerILO, integerIHI, double precision,
       dimension( lda, * )A, integerLDA, double precision, dimension( * )TAU,
       double precision, dimension( * )WORK, integerINFO)
       DGEHD2 reduces a general square matrix to upper Hessenberg form using
       an unblocked algorithm.

       Purpose:

            DGEHD2 reduces a real general matrix A to upper Hessenberg form H by
            an orthogonal similarity transformation:  Q**T * 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 DGEBAL; otherwise they should be
                     set to 1 and N respectively. See Further Details.
                     1 <= ILO <= IHI <= max(1,N).

           A

                     A is 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 overwritten 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

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

           TAU

                     TAU is DOUBLE PRECISION array, dimension (N-1)
                     The scalar factors of the elementary reflectors (see Further
                     Details).

           WORK

                     WORK is DOUBLE PRECISION 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.

       Date:
           September 2012

       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**T

             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
             modified element of the upper Hessenberg matrix H, and vi denotes an
             element of the vector defining H(i).

       Definition at line 150 of file dgehd2.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2                   Sat Nov 16 2013                    dgehd2.f(3)