SRC/sgehd2.f(3)

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

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.

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 sgehd2.f.

Author

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