Annotation of rpl/lapack/lapack/dlaqr1.f, revision 1.2
1.1 bertrand 1: SUBROUTINE DLAQR1( N, H, LDH, SR1, SI1, SR2, SI2, V )
2: *
3: * -- LAPACK auxiliary routine (version 3.2) --
4: * Univ. of Tennessee, Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..
5: * November 2006
6: *
7: * .. Scalar Arguments ..
8: DOUBLE PRECISION SI1, SI2, SR1, SR2
9: INTEGER LDH, N
10: * ..
11: * .. Array Arguments ..
12: DOUBLE PRECISION H( LDH, * ), V( * )
13: * ..
14: *
15: * Given a 2-by-2 or 3-by-3 matrix H, DLAQR1 sets v to a
16: * scalar multiple of the first column of the product
17: *
18: * (*) K = (H - (sr1 + i*si1)*I)*(H - (sr2 + i*si2)*I)
19: *
20: * scaling to avoid overflows and most underflows. It
21: * is assumed that either
22: *
23: * 1) sr1 = sr2 and si1 = -si2
24: * or
25: * 2) si1 = si2 = 0.
26: *
27: * This is useful for starting double implicit shift bulges
28: * in the QR algorithm.
29: *
30: *
31: * N (input) integer
32: * Order of the matrix H. N must be either 2 or 3.
33: *
34: * H (input) DOUBLE PRECISION array of dimension (LDH,N)
35: * The 2-by-2 or 3-by-3 matrix H in (*).
36: *
37: * LDH (input) integer
38: * The leading dimension of H as declared in
39: * the calling procedure. LDH.GE.N
40: *
41: * SR1 (input) DOUBLE PRECISION
42: * SI1 The shifts in (*).
43: * SR2
44: * SI2
45: *
46: * V (output) DOUBLE PRECISION array of dimension N
47: * A scalar multiple of the first column of the
48: * matrix K in (*).
49: *
50: * ================================================================
51: * Based on contributions by
52: * Karen Braman and Ralph Byers, Department of Mathematics,
53: * University of Kansas, USA
54: *
55: * ================================================================
56: *
57: * .. Parameters ..
58: DOUBLE PRECISION ZERO
59: PARAMETER ( ZERO = 0.0d0 )
60: * ..
61: * .. Local Scalars ..
62: DOUBLE PRECISION H21S, H31S, S
63: * ..
64: * .. Intrinsic Functions ..
65: INTRINSIC ABS
66: * ..
67: * .. Executable Statements ..
68: IF( N.EQ.2 ) THEN
69: S = ABS( H( 1, 1 )-SR2 ) + ABS( SI2 ) + ABS( H( 2, 1 ) )
70: IF( S.EQ.ZERO ) THEN
71: V( 1 ) = ZERO
72: V( 2 ) = ZERO
73: ELSE
74: H21S = H( 2, 1 ) / S
75: V( 1 ) = H21S*H( 1, 2 ) + ( H( 1, 1 )-SR1 )*
76: $ ( ( H( 1, 1 )-SR2 ) / S ) - SI1*( SI2 / S )
77: V( 2 ) = H21S*( H( 1, 1 )+H( 2, 2 )-SR1-SR2 )
78: END IF
79: ELSE
80: S = ABS( H( 1, 1 )-SR2 ) + ABS( SI2 ) + ABS( H( 2, 1 ) ) +
81: $ ABS( H( 3, 1 ) )
82: IF( S.EQ.ZERO ) THEN
83: V( 1 ) = ZERO
84: V( 2 ) = ZERO
85: V( 3 ) = ZERO
86: ELSE
87: H21S = H( 2, 1 ) / S
88: H31S = H( 3, 1 ) / S
89: V( 1 ) = ( H( 1, 1 )-SR1 )*( ( H( 1, 1 )-SR2 ) / S ) -
90: $ SI1*( SI2 / S ) + H( 1, 2 )*H21S + H( 1, 3 )*H31S
91: V( 2 ) = H21S*( H( 1, 1 )+H( 2, 2 )-SR1-SR2 ) +
92: $ H( 2, 3 )*H31S
93: V( 3 ) = H31S*( H( 1, 1 )+H( 3, 3 )-SR1-SR2 ) +
94: $ H21S*H( 3, 2 )
95: END IF
96: END IF
97: END
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