LAPACK  3.8.0
LAPACK: Linear Algebra PACKage
slaqr1.f
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1 *> \brief \b 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.
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
7 *
8 *> \htmlonly
9 *> Download SLAQR1 + dependencies
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13 *> [ZIP]</a>
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15 *> [TXT]</a>
16 *> \endhtmlonly
17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE SLAQR1( N, H, LDH, SR1, SI1, SR2, SI2, V )
22 *
23 * .. Scalar Arguments ..
24 * REAL SI1, SI2, SR1, SR2
25 * INTEGER LDH, N
26 * ..
27 * .. Array Arguments ..
28 * REAL 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, SLAQR1 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 REAL 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.GE.N
73 *> \endverbatim
74 *>
75 *> \param[in] SR1
76 *> \verbatim
77 *> SR1 is REAL
78 *> \endverbatim
79 *>
80 *> \param[in] SI1
81 *> \verbatim
82 *> SI1 is REAL
83 *> \endverbatim
84 *>
85 *> \param[in] SR2
86 *> \verbatim
87 *> SR2 is REAL
88 *> \endverbatim
89 *>
90 *> \param[in] SI2
91 *> \verbatim
92 *> SI2 is REAL
93 *> The shifts in (*).
94 *> \endverbatim
95 *>
96 *> \param[out] V
97 *> \verbatim
98 *> V is REAL 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 *> \date June 2017
112 *
113 *> \ingroup realOTHERauxiliary
114 *
115 *> \par Contributors:
116 * ==================
117 *>
118 *> Karen Braman and Ralph Byers, Department of Mathematics,
119 *> University of Kansas, USA
120 *>
121 * =====================================================================
122  SUBROUTINE slaqr1( N, H, LDH, SR1, SI1, SR2, SI2, V )
123 *
124 * -- LAPACK auxiliary routine (version 3.7.1) --
125 * -- LAPACK is a software package provided by Univ. of Tennessee, --
126 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
127 * June 2017
128 *
129 * .. Scalar Arguments ..
130  REAL SI1, SI2, SR1, SR2
131  INTEGER LDH, N
132 * ..
133 * .. Array Arguments ..
134  REAL H( ldh, * ), V( * )
135 * ..
136 *
137 * ================================================================
138 *
139 * .. Parameters ..
140  REAL ZERO
141  parameter( zero = 0.0e0 )
142 * ..
143 * .. Local Scalars ..
144  REAL H21S, H31S, S
145 * ..
146 * .. Intrinsic Functions ..
147  INTRINSIC abs
148 * ..
149 * .. Executable Statements ..
150  IF( n.EQ.2 ) THEN
151  s = abs( h( 1, 1 )-sr2 ) + abs( si2 ) + abs( h( 2, 1 ) )
152  IF( s.EQ.zero ) THEN
153  v( 1 ) = zero
154  v( 2 ) = zero
155  ELSE
156  h21s = h( 2, 1 ) / s
157  v( 1 ) = h21s*h( 1, 2 ) + ( h( 1, 1 )-sr1 )*
158  $ ( ( h( 1, 1 )-sr2 ) / s ) - si1*( si2 / s )
159  v( 2 ) = h21s*( h( 1, 1 )+h( 2, 2 )-sr1-sr2 )
160  END IF
161  ELSE
162  s = abs( h( 1, 1 )-sr2 ) + abs( si2 ) + abs( h( 2, 1 ) ) +
163  $ abs( h( 3, 1 ) )
164  IF( s.EQ.zero ) THEN
165  v( 1 ) = zero
166  v( 2 ) = zero
167  v( 3 ) = zero
168  ELSE
169  h21s = h( 2, 1 ) / s
170  h31s = h( 3, 1 ) / s
171  v( 1 ) = ( h( 1, 1 )-sr1 )*( ( h( 1, 1 )-sr2 ) / s ) -
172  $ si1*( si2 / s ) + h( 1, 2 )*h21s + h( 1, 3 )*h31s
173  v( 2 ) = h21s*( h( 1, 1 )+h( 2, 2 )-sr1-sr2 ) +
174  $ h( 2, 3 )*h31s
175  v( 3 ) = h31s*( h( 1, 1 )+h( 3, 3 )-sr1-sr2 ) +
176  $ h21s*h( 3, 2 )
177  END IF
178  END IF
179  END
subroutine slaqr1(N, H, LDH, SR1, SI1, SR2, SI2, V)
SLAQR1 sets a scalar multiple of the first column of the product of 2-by-2 or 3-by-3 matrix H and spe...
Definition: slaqr1.f:123