slaqr1()

subroutine slaqr1	(	integer	N,
		real, dimension( ldh, * )	H,
		integer	LDH,
		real	SR1,
		real	SI1,
		real	SR2,
		real	SI2,
		real, dimension( * )	V
	)

SLAQR1 sets a scalar multiple of the first column of the product of 2-by-2 or 3-by-3 matrix H and specified shifts.

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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

[in]	N	N is INTEGER Order of the matrix H. N must be either 2 or 3.
[in]	H	H is REAL array, dimension (LDH,N) The 2-by-2 or 3-by-3 matrix H in (*).
[in]	LDH	LDH is INTEGER The leading dimension of H as declared in the calling procedure. LDH >= N
[in]	SR1	SR1 is REAL
[in]	SI1	SI1 is REAL
[in]	SR2	SR2 is REAL
[in]	SI2	SI2 is REAL The shifts in (*).
[out]	V	V is REAL array, dimension (N) A scalar multiple of the first column of the matrix K in (*).

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date

June 2017

Contributors:

Karen Braman and Ralph Byers, Department of Mathematics, University of Kansas, USA

Definition at line 123 of file slaqr1.f.

*
*  -- LAPACK auxiliary routine (version 3.7.1) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     June 2017
*
*     .. Scalar Arguments ..
      REAL               SI1, SI2, SR1, SR2
      INTEGER            LDH, N
*     ..
*     .. Array Arguments ..
      REAL               H( LDH, * ), V( * )
*     ..
*
*  ================================================================
*
*     .. Parameters ..
      REAL               ZERO
      parameter( zero = 0.0e0 )
*     ..
*     .. Local Scalars ..
      REAL               H21S, H31S, S
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          abs
*     ..
*     .. Executable Statements ..
*
*     Quick return if possible
*
      IF( n.NE.2 .AND. n.NE.3 ) THEN
         RETURN
      END IF
*
      IF( n.EQ.2 ) THEN
         s = abs( h( 1, 1 )-sr2 ) + abs( si2 ) + abs( h( 2, 1 ) )
         IF( s.EQ.zero ) THEN
            v( 1 ) = zero
            v( 2 ) = zero
         ELSE
            h21s = h( 2, 1 ) / s
            v( 1 ) = h21s*h( 1, 2 ) + ( h( 1, 1 )-sr1 )*
     $               ( ( h( 1, 1 )-sr2 ) / s ) - si1*( si2 / s )
            v( 2 ) = h21s*( h( 1, 1 )+h( 2, 2 )-sr1-sr2 )
         END IF
      ELSE
         s = abs( h( 1, 1 )-sr2 ) + abs( si2 ) + abs( h( 2, 1 ) ) +
     $       abs( h( 3, 1 ) )
         IF( s.EQ.zero ) THEN
            v( 1 ) = zero
            v( 2 ) = zero
            v( 3 ) = zero
         ELSE
            h21s = h( 2, 1 ) / s
            h31s = h( 3, 1 ) / s
            v( 1 ) = ( h( 1, 1 )-sr1 )*( ( h( 1, 1 )-sr2 ) / s ) -
     $               si1*( si2 / s ) + h( 1, 2 )*h21s + h( 1, 3 )*h31s
            v( 2 ) = h21s*( h( 1, 1 )+h( 2, 2 )-sr1-sr2 ) +
     $               h( 2, 3 )*h31s
            v( 3 ) = h31s*( h( 1, 1 )+h( 3, 3 )-sr1-sr2 ) +
     $               h21s*h( 3, 2 )
         END IF
      END IF

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