SRC/dgehd2.f(3)

NAME
SRC/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 (integer n, integer ilo, integer ihi, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) tau, double precision, dimension( * ) work, integer info)

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.

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 148 of file dgehd2.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.