LAPACK  3.9.0 LAPACK: Linear Algebra PACKage
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 *
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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 *> \date June 2017
98 *
99 *> \ingroup complex16OTHERauxiliary
100 *
101 *> \par Contributors:
102 * ==================
103 *>
104 *> Karen Braman and Ralph Byers, Department of Mathematics,
105 *> University of Kansas, USA
106 *>
107 * =====================================================================
108  SUBROUTINE zlaqr1( N, H, LDH, S1, S2, V )
109 *
110 * -- LAPACK auxiliary routine (version 3.7.1) --
111 * -- LAPACK is a software package provided by Univ. of Tennessee, --
112 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
113 * June 2017
114 *
115 * .. Scalar Arguments ..
116  COMPLEX*16 S1, S2
117  INTEGER LDH, N
118 * ..
119 * .. Array Arguments ..
120  COMPLEX*16 H( LDH, * ), V( * )
121 * ..
122 *
123 * ================================================================
124 *
125 * .. Parameters ..
126  COMPLEX*16 ZERO
127  parameter( zero = ( 0.0d0, 0.0d0 ) )
128  DOUBLE PRECISION RZERO
129  parameter( rzero = 0.0d0 )
130 * ..
131 * .. Local Scalars ..
132  COMPLEX*16 CDUM, H21S, H31S
133  DOUBLE PRECISION S
134 * ..
135 * .. Intrinsic Functions ..
136  INTRINSIC abs, dble, dimag
137 * ..
138 * .. Statement Functions ..
139  DOUBLE PRECISION CABS1
140 * ..
141 * .. Statement Function definitions ..
142  cabs1( cdum ) = abs( dble( cdum ) ) + abs( dimag( cdum ) )
143 * ..
144 * .. Executable Statements ..
145 *
146 * Quick return if possible
147 *
148  IF( n.NE.2 .AND. n.NE.3 ) THEN
149  RETURN
150  END IF
151 *
152  IF( n.EQ.2 ) THEN
153  s = cabs1( h( 1, 1 )-s2 ) + cabs1( h( 2, 1 ) )
154  IF( s.EQ.rzero ) THEN
155  v( 1 ) = zero
156  v( 2 ) = zero
157  ELSE
158  h21s = h( 2, 1 ) / s
159  v( 1 ) = h21s*h( 1, 2 ) + ( h( 1, 1 )-s1 )*
160  \$ ( ( h( 1, 1 )-s2 ) / s )
161  v( 2 ) = h21s*( h( 1, 1 )+h( 2, 2 )-s1-s2 )
162  END IF
163  ELSE
164  s = cabs1( h( 1, 1 )-s2 ) + cabs1( h( 2, 1 ) ) +
165  \$ cabs1( h( 3, 1 ) )
166  IF( s.EQ.zero ) THEN
167  v( 1 ) = zero
168  v( 2 ) = zero
169  v( 3 ) = zero
170  ELSE
171  h21s = h( 2, 1 ) / s
172  h31s = h( 3, 1 ) / s
173  v( 1 ) = ( h( 1, 1 )-s1 )*( ( h( 1, 1 )-s2 ) / s ) +
174  \$ h( 1, 2 )*h21s + h( 1, 3 )*h31s
175  v( 2 ) = h21s*( h( 1, 1 )+h( 2, 2 )-s1-s2 ) + h( 2, 3 )*h31s
176  v( 3 ) = h31s*( h( 1, 1 )+h( 3, 3 )-s1-s2 ) + h21s*h( 3, 2 )
177  END IF
178  END IF
179  END
zlaqr1
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:109