LAPACK  3.10.1 LAPACK: Linear Algebra PACKage
dlaqr1.f
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1 *> \brief \b 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.
2 *
3 * =========== DOCUMENTATION ===========
4 *
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6 * http://www.netlib.org/lapack/explore-html/
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15 *> [TXT]</a>
16 *> \endhtmlonly
17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE DLAQR1( N, H, LDH, SR1, SI1, SR2, SI2, V )
22 *
23 * .. Scalar Arguments ..
24 * DOUBLE PRECISION SI1, SI2, SR1, SR2
25 * INTEGER LDH, N
26 * ..
27 * .. Array Arguments ..
28 * DOUBLE PRECISION 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, DLAQR1 sets v to a
38 *> scalar multiple of the first column of the product
39 *>
40 *> (*) K = (H - (sr1 + i*si1)*I)*(H - (sr2 + i*si2)*I)
41 *>
42 *> scaling to avoid overflows and most underflows. It
43 *> is assumed that either
44 *>
45 *> 1) sr1 = sr2 and si1 = -si2
46 *> or
47 *> 2) si1 = si2 = 0.
48 *>
49 *> This is useful for starting double implicit shift bulges
50 *> in the QR algorithm.
51 *> \endverbatim
52 *
53 * Arguments:
54 * ==========
55 *
56 *> \param[in] N
57 *> \verbatim
58 *> N is INTEGER
59 *> Order of the matrix H. N must be either 2 or 3.
60 *> \endverbatim
61 *>
62 *> \param[in] H
63 *> \verbatim
64 *> H is DOUBLE PRECISION array, dimension (LDH,N)
65 *> The 2-by-2 or 3-by-3 matrix H in (*).
66 *> \endverbatim
67 *>
68 *> \param[in] LDH
69 *> \verbatim
70 *> LDH is INTEGER
71 *> The leading dimension of H as declared in
72 *> the calling procedure. LDH >= N
73 *> \endverbatim
74 *>
75 *> \param[in] SR1
76 *> \verbatim
77 *> SR1 is DOUBLE PRECISION
78 *> \endverbatim
79 *>
80 *> \param[in] SI1
81 *> \verbatim
82 *> SI1 is DOUBLE PRECISION
83 *> \endverbatim
84 *>
85 *> \param[in] SR2
86 *> \verbatim
87 *> SR2 is DOUBLE PRECISION
88 *> \endverbatim
89 *>
90 *> \param[in] SI2
91 *> \verbatim
92 *> SI2 is DOUBLE PRECISION
93 *> The shifts in (*).
94 *> \endverbatim
95 *>
96 *> \param[out] V
97 *> \verbatim
98 *> V is DOUBLE PRECISION array, dimension (N)
99 *> A scalar multiple of the first column of the
100 *> matrix K in (*).
101 *> \endverbatim
102 *
103 * Authors:
104 * ========
105 *
106 *> \author Univ. of Tennessee
107 *> \author Univ. of California Berkeley
108 *> \author Univ. of Colorado Denver
109 *> \author NAG Ltd.
110 *
111 *> \ingroup doubleOTHERauxiliary
112 *
113 *> \par Contributors:
114 * ==================
115 *>
116 *> Karen Braman and Ralph Byers, Department of Mathematics,
117 *> University of Kansas, USA
118 *>
119 * =====================================================================
120  SUBROUTINE dlaqr1( N, H, LDH, SR1, SI1, SR2, SI2, V )
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
183  END
subroutine dlaqr1(N, H, LDH, SR1, SI1, SR2, SI2, V)
DLAQR1 sets a scalar multiple of the first column of the product of 2-by-2 or 3-by-3 matrix H and spe...
Definition: dlaqr1.f:121