Annotation of rpl/lapack/lapack/dlaed5.f, revision 1.3
1.1 bertrand 1: SUBROUTINE DLAED5( I, D, Z, DELTA, RHO, DLAM )
2: *
3: * -- LAPACK routine (version 3.2) --
4: * -- LAPACK is a software package provided by Univ. of Tennessee, --
5: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
6: * November 2006
7: *
8: * .. Scalar Arguments ..
9: INTEGER I
10: DOUBLE PRECISION DLAM, RHO
11: * ..
12: * .. Array Arguments ..
13: DOUBLE PRECISION D( 2 ), DELTA( 2 ), Z( 2 )
14: * ..
15: *
16: * Purpose
17: * =======
18: *
19: * This subroutine computes the I-th eigenvalue of a symmetric rank-one
20: * modification of a 2-by-2 diagonal matrix
21: *
22: * diag( D ) + RHO * Z * transpose(Z) .
23: *
24: * The diagonal elements in the array D are assumed to satisfy
25: *
26: * D(i) < D(j) for i < j .
27: *
28: * We also assume RHO > 0 and that the Euclidean norm of the vector
29: * Z is one.
30: *
31: * Arguments
32: * =========
33: *
34: * I (input) INTEGER
35: * The index of the eigenvalue to be computed. I = 1 or I = 2.
36: *
37: * D (input) DOUBLE PRECISION array, dimension (2)
38: * The original eigenvalues. We assume D(1) < D(2).
39: *
40: * Z (input) DOUBLE PRECISION array, dimension (2)
41: * The components of the updating vector.
42: *
43: * DELTA (output) DOUBLE PRECISION array, dimension (2)
44: * The vector DELTA contains the information necessary
45: * to construct the eigenvectors.
46: *
47: * RHO (input) DOUBLE PRECISION
48: * The scalar in the symmetric updating formula.
49: *
50: * DLAM (output) DOUBLE PRECISION
51: * The computed lambda_I, the I-th updated eigenvalue.
52: *
53: * Further Details
54: * ===============
55: *
56: * Based on contributions by
57: * Ren-Cang Li, Computer Science Division, University of California
58: * at Berkeley, USA
59: *
60: * =====================================================================
61: *
62: * .. Parameters ..
63: DOUBLE PRECISION ZERO, ONE, TWO, FOUR
64: PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0, TWO = 2.0D0,
65: $ FOUR = 4.0D0 )
66: * ..
67: * .. Local Scalars ..
68: DOUBLE PRECISION B, C, DEL, TAU, TEMP, W
69: * ..
70: * .. Intrinsic Functions ..
71: INTRINSIC ABS, SQRT
72: * ..
73: * .. Executable Statements ..
74: *
75: DEL = D( 2 ) - D( 1 )
76: IF( I.EQ.1 ) THEN
77: W = ONE + TWO*RHO*( Z( 2 )*Z( 2 )-Z( 1 )*Z( 1 ) ) / DEL
78: IF( W.GT.ZERO ) THEN
79: B = DEL + RHO*( Z( 1 )*Z( 1 )+Z( 2 )*Z( 2 ) )
80: C = RHO*Z( 1 )*Z( 1 )*DEL
81: *
82: * B > ZERO, always
83: *
84: TAU = TWO*C / ( B+SQRT( ABS( B*B-FOUR*C ) ) )
85: DLAM = D( 1 ) + TAU
86: DELTA( 1 ) = -Z( 1 ) / TAU
87: DELTA( 2 ) = Z( 2 ) / ( DEL-TAU )
88: ELSE
89: B = -DEL + RHO*( Z( 1 )*Z( 1 )+Z( 2 )*Z( 2 ) )
90: C = RHO*Z( 2 )*Z( 2 )*DEL
91: IF( B.GT.ZERO ) THEN
92: TAU = -TWO*C / ( B+SQRT( B*B+FOUR*C ) )
93: ELSE
94: TAU = ( B-SQRT( B*B+FOUR*C ) ) / TWO
95: END IF
96: DLAM = D( 2 ) + TAU
97: DELTA( 1 ) = -Z( 1 ) / ( DEL+TAU )
98: DELTA( 2 ) = -Z( 2 ) / TAU
99: END IF
100: TEMP = SQRT( DELTA( 1 )*DELTA( 1 )+DELTA( 2 )*DELTA( 2 ) )
101: DELTA( 1 ) = DELTA( 1 ) / TEMP
102: DELTA( 2 ) = DELTA( 2 ) / TEMP
103: ELSE
104: *
105: * Now I=2
106: *
107: B = -DEL + RHO*( Z( 1 )*Z( 1 )+Z( 2 )*Z( 2 ) )
108: C = RHO*Z( 2 )*Z( 2 )*DEL
109: IF( B.GT.ZERO ) THEN
110: TAU = ( B+SQRT( B*B+FOUR*C ) ) / TWO
111: ELSE
112: TAU = TWO*C / ( -B+SQRT( B*B+FOUR*C ) )
113: END IF
114: DLAM = D( 2 ) + TAU
115: DELTA( 1 ) = -Z( 1 ) / ( DEL+TAU )
116: DELTA( 2 ) = -Z( 2 ) / TAU
117: TEMP = SQRT( DELTA( 1 )*DELTA( 1 )+DELTA( 2 )*DELTA( 2 ) )
118: DELTA( 1 ) = DELTA( 1 ) / TEMP
119: DELTA( 2 ) = DELTA( 2 ) / TEMP
120: END IF
121: RETURN
122: *
123: * End OF DLAED5
124: *
125: END
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