Provided by: liblapack-doc_3.3.1-1_all bug

NAME

       LAPACK-3  -  reduces  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**T * 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 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     (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**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).

 LAPACK routine (version 3.3.1)             April 2011                            DGEHD2(3lapack)