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

NAME

       LAPACK-3  -  reduces  a  complex general matrix A to upper Hessenberg form H by an unitary
       similarity transformation

SYNOPSIS

       SUBROUTINE CGEHRD( N, ILO, IHI, A, LDA, TAU, WORK, LWORK, INFO )

           INTEGER        IHI, ILO, INFO, LDA, LWORK, N

           COMPLEX        A( LDA, * ), TAU( * ), WORK( * )

PURPOSE

       CGEHRD reduces a complex general matrix A  to  upper  Hessenberg  form  H  by  an  unitary
       similarity transformation:  Q**H * 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 CGEBAL; otherwise they should be
                set to 1 and N respectively. See Further Details.

        A       (input/output) COMPLEX 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 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 array, dimension (N-1)
                The scalar factors of the elementary reflectors (see Further
                Details). Elements 1:ILO-1 and IHI:N-1 of TAU are set to
                zero.

        WORK    (workspace/output) COMPLEX array, dimension (LWORK)
                On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

        LWORK   (input) INTEGER
                The length of the array WORK.  LWORK >= max(1,N).
                For optimum performance LWORK >= N*NB, where NB is the
                optimal blocksize.
                If LWORK = -1, then a workspace query is assumed; the routine
                only calculates the optimal size of the WORK array, returns
                this value as the first entry of the WORK array, and no error
                message related to LWORK is issued by XERBLA.

        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**H
        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).
        This file is a slight modification of LAPACK-3.0's DGEHRD
        subroutine incorporating improvements proposed by Quintana-Orti and
        Van de Geijn (2006). (See DLAHR2.)

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