LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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zlaqr1.f
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1*> \brief \b ZLAQR1 sets a scalar multiple of the first column of the product of 2-by-2 or 3-by-3 matrix H and specified shifts.
2*
3* =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6* http://www.netlib.org/lapack/explore-html/
7*
8*> \htmlonly
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13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlaqr1.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18* Definition:
19* ===========
20*
21* SUBROUTINE ZLAQR1( N, H, LDH, S1, S2, V )
22*
23* .. Scalar Arguments ..
24* COMPLEX*16 S1, S2
25* INTEGER LDH, N
26* ..
27* .. Array Arguments ..
28* COMPLEX*16 H( LDH, * ), V( * )
29* ..
30*
31*
32*> \par Purpose:
33* =============
34*>
35*> \verbatim
36*>
37*> Given a 2-by-2 or 3-by-3 matrix H, ZLAQR1 sets v to a
38*> scalar multiple of the first column of the product
39*>
40*> (*) K = (H - s1*I)*(H - s2*I)
41*>
42*> scaling to avoid overflows and most underflows.
43*>
44*> This is useful for starting double implicit shift bulges
45*> in the QR algorithm.
46*> \endverbatim
47*
48* Arguments:
49* ==========
50*
51*> \param[in] N
52*> \verbatim
53*> N is INTEGER
54*> Order of the matrix H. N must be either 2 or 3.
55*> \endverbatim
56*>
57*> \param[in] H
58*> \verbatim
59*> H is COMPLEX*16 array, dimension (LDH,N)
60*> The 2-by-2 or 3-by-3 matrix H in (*).
61*> \endverbatim
62*>
63*> \param[in] LDH
64*> \verbatim
65*> LDH is INTEGER
66*> The leading dimension of H as declared in
67*> the calling procedure. LDH >= N
68*> \endverbatim
69*>
70*> \param[in] S1
71*> \verbatim
72*> S1 is COMPLEX*16
73*> \endverbatim
74*>
75*> \param[in] S2
76*> \verbatim
77*> S2 is COMPLEX*16
78*>
79*> S1 and S2 are the shifts defining K in (*) above.
80*> \endverbatim
81*>
82*> \param[out] V
83*> \verbatim
84*> V is COMPLEX*16 array, dimension (N)
85*> A scalar multiple of the first column of the
86*> matrix K in (*).
87*> \endverbatim
88*
89* Authors:
90* ========
91*
92*> \author Univ. of Tennessee
93*> \author Univ. of California Berkeley
94*> \author Univ. of Colorado Denver
95*> \author NAG Ltd.
96*
97*> \ingroup laqr1
98*
99*> \par Contributors:
100* ==================
101*>
102*> Karen Braman and Ralph Byers, Department of Mathematics,
103*> University of Kansas, USA
104*>
105* =====================================================================
106 SUBROUTINE zlaqr1( N, H, LDH, S1, S2, V )
107*
108* -- LAPACK auxiliary routine --
109* -- LAPACK is a software package provided by Univ. of Tennessee, --
110* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
111*
112* .. Scalar Arguments ..
113 COMPLEX*16 S1, S2
114 INTEGER LDH, N
115* ..
116* .. Array Arguments ..
117 COMPLEX*16 H( LDH, * ), V( * )
118* ..
119*
120* ================================================================
121*
122* .. Parameters ..
123 COMPLEX*16 ZERO
124 parameter( zero = ( 0.0d0, 0.0d0 ) )
125 DOUBLE PRECISION RZERO
126 parameter( rzero = 0.0d0 )
127* ..
128* .. Local Scalars ..
129 COMPLEX*16 CDUM, H21S, H31S
130 DOUBLE PRECISION S
131* ..
132* .. Intrinsic Functions ..
133 INTRINSIC abs, dble, dimag
134* ..
135* .. Statement Functions ..
136 DOUBLE PRECISION CABS1
137* ..
138* .. Statement Function definitions ..
139 cabs1( cdum ) = abs( dble( cdum ) ) + abs( dimag( cdum ) )
140* ..
141* .. Executable Statements ..
142*
143* Quick return if possible
144*
145 IF( n.NE.2 .AND. n.NE.3 ) THEN
146 RETURN
147 END IF
148*
149 IF( n.EQ.2 ) THEN
150 s = cabs1( h( 1, 1 )-s2 ) + cabs1( h( 2, 1 ) )
151 IF( s.EQ.rzero ) THEN
152 v( 1 ) = zero
153 v( 2 ) = zero
154 ELSE
155 h21s = h( 2, 1 ) / s
156 v( 1 ) = h21s*h( 1, 2 ) + ( h( 1, 1 )-s1 )*
157 \$ ( ( h( 1, 1 )-s2 ) / s )
158 v( 2 ) = h21s*( h( 1, 1 )+h( 2, 2 )-s1-s2 )
159 END IF
160 ELSE
161 s = cabs1( h( 1, 1 )-s2 ) + cabs1( h( 2, 1 ) ) +
162 \$ cabs1( h( 3, 1 ) )
163 IF( s.EQ.zero ) THEN
164 v( 1 ) = zero
165 v( 2 ) = zero
166 v( 3 ) = zero
167 ELSE
168 h21s = h( 2, 1 ) / s
169 h31s = h( 3, 1 ) / s
170 v( 1 ) = ( h( 1, 1 )-s1 )*( ( h( 1, 1 )-s2 ) / s ) +
171 \$ h( 1, 2 )*h21s + h( 1, 3 )*h31s
172 v( 2 ) = h21s*( h( 1, 1 )+h( 2, 2 )-s1-s2 ) + h( 2, 3 )*h31s
173 v( 3 ) = h31s*( h( 1, 1 )+h( 3, 3 )-s1-s2 ) + h21s*h( 3, 2 )
174 END IF
175 END IF
176 END
subroutine zlaqr1(n, h, ldh, s1, s2, v)
ZLAQR1 sets a scalar multiple of the first column of the product of 2-by-2 or 3-by-3 matrix H and spe...
Definition zlaqr1.f:107