Annotation of rpl/lapack/lapack/zlaqr1.f, revision 1.10
1.8 bertrand 1: *> \brief \b ZLAQR1
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download ZLAQR1 + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlaqr1.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlaqr1.f">
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 of 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.GE.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 of 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 November 2011
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: * =====================================================================
1.1 bertrand 108: SUBROUTINE ZLAQR1( N, H, LDH, S1, S2, V )
109: *
1.8 bertrand 110: * -- LAPACK auxiliary routine (version 3.4.0) --
111: * -- LAPACK is a software package provided by Univ. of Tennessee, --
112: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
113: * November 2011
1.1 bertrand 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: *
1.8 bertrand 123: * ================================================================
1.1 bertrand 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: IF( N.EQ.2 ) THEN
146: S = CABS1( H( 1, 1 )-S2 ) + CABS1( H( 2, 1 ) )
147: IF( S.EQ.RZERO ) THEN
148: V( 1 ) = ZERO
149: V( 2 ) = ZERO
150: ELSE
151: H21S = H( 2, 1 ) / S
152: V( 1 ) = H21S*H( 1, 2 ) + ( H( 1, 1 )-S1 )*
153: $ ( ( H( 1, 1 )-S2 ) / S )
154: V( 2 ) = H21S*( H( 1, 1 )+H( 2, 2 )-S1-S2 )
155: END IF
156: ELSE
157: S = CABS1( H( 1, 1 )-S2 ) + CABS1( H( 2, 1 ) ) +
158: $ CABS1( H( 3, 1 ) )
159: IF( S.EQ.ZERO ) THEN
160: V( 1 ) = ZERO
161: V( 2 ) = ZERO
162: V( 3 ) = ZERO
163: ELSE
164: H21S = H( 2, 1 ) / S
165: H31S = H( 3, 1 ) / S
166: V( 1 ) = ( H( 1, 1 )-S1 )*( ( H( 1, 1 )-S2 ) / S ) +
167: $ H( 1, 2 )*H21S + H( 1, 3 )*H31S
168: V( 2 ) = H21S*( H( 1, 1 )+H( 2, 2 )-S1-S2 ) + H( 2, 3 )*H31S
169: V( 3 ) = H31S*( H( 1, 1 )+H( 3, 3 )-S1-S2 ) + H21S*H( 3, 2 )
170: END IF
171: END IF
172: END
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