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First attempt at single precision tyeps * * * corrections to qrupdate single precision routines * * * prefer demotion to single over promotion to double * * * Add single precision support to log2 function * * * Trivial PROJECT file update * * * Cache optimized hermitian/transpose methods * * * Add tests for tranpose/hermitian and ChangeLog entry for new transpose code
author David Bateman <dbateman@free.fr>
date Sun, 27 Apr 2008 22:34:17 +0200
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7788:45f5faba05a2 7789:82be108cc558
1 SUBROUTINE CLAQR1( N, H, LDH, S1, S2, V )
2 *
3 * -- LAPACK auxiliary routine (version 3.1) --
4 * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
5 * November 2006
6 *
7 * .. Scalar Arguments ..
8 COMPLEX S1, S2
9 INTEGER LDH, N
10 * ..
11 * .. Array Arguments ..
12 COMPLEX H( LDH, * ), V( * )
13 * ..
14 *
15 * Given a 2-by-2 or 3-by-3 matrix H, CLAQR1 sets v to a
16 * scalar multiple of the first column of the product
17 *
18 * (*) K = (H - s1*I)*(H - s2*I)
19 *
20 * scaling to avoid overflows and most underflows.
21 *
22 * This is useful for starting double implicit shift bulges
23 * in the QR algorithm.
24 *
25 *
26 * N (input) integer
27 * Order of the matrix H. N must be either 2 or 3.
28 *
29 * H (input) COMPLEX array of dimension (LDH,N)
30 * The 2-by-2 or 3-by-3 matrix H in (*).
31 *
32 * LDH (input) integer
33 * The leading dimension of H as declared in
34 * the calling procedure. LDH.GE.N
35 *
36 * S1 (input) COMPLEX
37 * S2 S1 and S2 are the shifts defining K in (*) above.
38 *
39 * V (output) COMPLEX array of dimension N
40 * A scalar multiple of the first column of the
41 * matrix K in (*).
42 *
43 * ================================================================
44 * Based on contributions by
45 * Karen Braman and Ralph Byers, Department of Mathematics,
46 * University of Kansas, USA
47 *
48 * ================================================================
49 *
50 * .. Parameters ..
51 COMPLEX ZERO
52 PARAMETER ( ZERO = ( 0.0e0, 0.0e0 ) )
53 REAL RZERO
54 PARAMETER ( RZERO = 0.0e0 )
55 * ..
56 * .. Local Scalars ..
57 COMPLEX CDUM
58 REAL H21S, H31S, S
59 * ..
60 * .. Intrinsic Functions ..
61 INTRINSIC ABS, AIMAG, REAL
62 * ..
63 * .. Statement Functions ..
64 REAL CABS1
65 * ..
66 * .. Statement Function definitions ..
67 CABS1( CDUM ) = ABS( REAL( CDUM ) ) + ABS( AIMAG( CDUM ) )
68 * ..
69 * .. Executable Statements ..
70 IF( N.EQ.2 ) THEN
71 S = CABS1( H( 1, 1 )-S2 ) + CABS1( H( 2, 1 ) )
72 IF( S.EQ.RZERO ) THEN
73 V( 1 ) = ZERO
74 V( 2 ) = ZERO
75 ELSE
76 H21S = H( 2, 1 ) / S
77 V( 1 ) = H21S*H( 1, 2 ) + ( H( 1, 1 )-S1 )*
78 $ ( ( H( 1, 1 )-S2 ) / S )
79 V( 2 ) = H21S*( H( 1, 1 )+H( 2, 2 )-S1-S2 )
80 END IF
81 ELSE
82 S = CABS1( H( 1, 1 )-S2 ) + CABS1( H( 2, 1 ) ) +
83 $ CABS1( H( 3, 1 ) )
84 IF( S.EQ.ZERO ) THEN
85 V( 1 ) = ZERO
86 V( 2 ) = ZERO
87 V( 3 ) = ZERO
88 ELSE
89 H21S = H( 2, 1 ) / S
90 H31S = H( 3, 1 ) / S
91 V( 1 ) = ( H( 1, 1 )-S1 )*( ( H( 1, 1 )-S2 ) / S ) +
92 $ H( 1, 2 )*H21S + H( 1, 3 )*H31S
93 V( 2 ) = H21S*( H( 1, 1 )+H( 2, 2 )-S1-S2 ) + H( 2, 3 )*H31S
94 V( 3 ) = H31S*( H( 1, 1 )+H( 3, 3 )-S1-S2 ) + H21S*H( 3, 2 )
95 END IF
96 END IF
97 END