LAQR1 - LAQR1 - 5.3 English - 68552

LAQR1 sets a scalar multiple of the first column of the product of 2-by-2 or 3-by-3 matrix H and specified shifts.

Purpose:

    Given a 2-by-2 or 3-by-3 matrix H, SLAQR1 sets v to a
    scalar multiple of the first column of the product

    (*)  K = (H - (sr1 + i*si1)*I)*(H - (sr2 + i*si2)*I)

    scaling to avoid overflows and most underflows. It
    is assumed that either

            1) sr1 = sr2 and si1 = -si2
        or
            2) si1 = si2 = 0.

    This is useful for starting double implicit shift bulges
    in the QR algorithm.

Parameters:

• N – [in]

  N is INTEGER

  Order of the matrix H. N must be either 2 or 3.

• H – [in]

  H is REAL array, dimension (LDH,N)

  The 2-by-2 or 3-by-3 matrix H in (*).

• LDH – [in]

  LDH is INTEGER

  The leading dimension of H as declared in the calling procedure. LDH >= N

• SR1 – [in] SR1 is REAL

• SI1 – [in] SI1 is REAL

• SR2 – [in] SR2 is REAL

• SI2 – [in]

  SI2 is REAL

  The shifts in (*).

• V – [out]

  V is REAL array, dimension (N)

  A scalar multiple of the first column of the matrix K in (*).