SGEHD2 reduces a real general matrix A to upper Hessenberg form H by


 an orthogonal similarity transformation:  Q**T * A * Q = H .

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.

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

September 2012

  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).