NAME

       sgehd2.f -

SYNOPSIS

   Functions/Subroutines
       subroutine sgehd2 (N, ILO, IHI, A, LDA, TAU, WORK, INFO)
           SGEHD2 reduces a general square matrix to upper Hessenberg form using an unblocked
           algorithm.

Function/Subroutine Documentation

   subroutine sgehd2 (integerN, integerILO, integerIHI, real, dimension( lda, * )A, integerLDA,
       real, dimension( * )TAU, real, dimension( * )WORK, integerINFO)
       SGEHD2 reduces a general square matrix to upper Hessenberg form using an unblocked
       algorithm.

       Purpose:

            SGEHD2 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 SGEBAL; otherwise they should be
                     set to 1 and N respectively. See Further Details.
                     1 <= ILO <= IHI <= max(1,N).

           A

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

           WORK

                     WORK is REAL 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 sgehd2.f.

Author

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