LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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◆ dlaqr1()

subroutine dlaqr1 ( integer  n,
double precision, dimension( ldh, * )  h,
integer  ldh,
double precision  sr1,
double precision  si1,
double precision  sr2,
double precision  si2,
double precision, dimension( * )  v 
)

DLAQR1 sets a scalar multiple of the first column of the product of 2-by-2 or 3-by-3 matrix H and specified shifts.

Download DLAQR1 + dependencies [TGZ] [ZIP] [TXT]

Purpose:
      Given a 2-by-2 or 3-by-3 matrix H, DLAQR1 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 DOUBLE PRECISION 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 DOUBLE PRECISION
[in]SI1
          SI1 is DOUBLE PRECISION
[in]SR2
          SR2 is DOUBLE PRECISION
[in]SI2
          SI2 is DOUBLE PRECISION
              The shifts in (*).
[out]V
          V is DOUBLE PRECISION 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.
Contributors:
Karen Braman and Ralph Byers, Department of Mathematics, University of Kansas, USA

Definition at line 120 of file dlaqr1.f.

121*
122* -- LAPACK auxiliary routine --
123* -- LAPACK is a software package provided by Univ. of Tennessee, --
124* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
125*
126* .. Scalar Arguments ..
127 DOUBLE PRECISION SI1, SI2, SR1, SR2
128 INTEGER LDH, N
129* ..
130* .. Array Arguments ..
131 DOUBLE PRECISION H( LDH, * ), V( * )
132* ..
133*
134* ================================================================
135*
136* .. Parameters ..
137 DOUBLE PRECISION ZERO
138 parameter( zero = 0.0d0 )
139* ..
140* .. Local Scalars ..
141 DOUBLE PRECISION H21S, H31S, S
142* ..
143* .. Intrinsic Functions ..
144 INTRINSIC abs
145* ..
146* .. Executable Statements ..
147*
148* Quick return if possible
149*
150 IF( n.NE.2 .AND. n.NE.3 ) THEN
151 RETURN
152 END IF
153*
154 IF( n.EQ.2 ) THEN
155 s = abs( h( 1, 1 )-sr2 ) + abs( si2 ) + abs( h( 2, 1 ) )
156 IF( s.EQ.zero ) THEN
157 v( 1 ) = zero
158 v( 2 ) = zero
159 ELSE
160 h21s = h( 2, 1 ) / s
161 v( 1 ) = h21s*h( 1, 2 ) + ( h( 1, 1 )-sr1 )*
162 $ ( ( h( 1, 1 )-sr2 ) / s ) - si1*( si2 / s )
163 v( 2 ) = h21s*( h( 1, 1 )+h( 2, 2 )-sr1-sr2 )
164 END IF
165 ELSE
166 s = abs( h( 1, 1 )-sr2 ) + abs( si2 ) + abs( h( 2, 1 ) ) +
167 $ abs( h( 3, 1 ) )
168 IF( s.EQ.zero ) THEN
169 v( 1 ) = zero
170 v( 2 ) = zero
171 v( 3 ) = zero
172 ELSE
173 h21s = h( 2, 1 ) / s
174 h31s = h( 3, 1 ) / s
175 v( 1 ) = ( h( 1, 1 )-sr1 )*( ( h( 1, 1 )-sr2 ) / s ) -
176 $ si1*( si2 / s ) + h( 1, 2 )*h21s + h( 1, 3 )*h31s
177 v( 2 ) = h21s*( h( 1, 1 )+h( 2, 2 )-sr1-sr2 ) +
178 $ h( 2, 3 )*h31s
179 v( 3 ) = h31s*( h( 1, 1 )+h( 3, 3 )-sr1-sr2 ) +
180 $ h21s*h( 3, 2 )
181 END IF
182 END IF
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