Annotation of rpl/lapack/lapack/dlaed5.f, revision 1.15
1.11 bertrand 1: *> \brief \b DLAED5 used by sstedc. Solves the 2-by-2 secular equation.
1.8 bertrand 2: *
3: * =========== DOCUMENTATION ===========
4: *
1.15 ! bertrand 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
1.8 bertrand 7: *
8: *> \htmlonly
1.15 ! bertrand 9: *> Download DLAED5 + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlaed5.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlaed5.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlaed5.f">
1.8 bertrand 15: *> [TXT]</a>
1.15 ! bertrand 16: *> \endhtmlonly
1.8 bertrand 17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE DLAED5( I, D, Z, DELTA, RHO, DLAM )
1.15 ! bertrand 22: *
1.8 bertrand 23: * .. Scalar Arguments ..
24: * INTEGER I
25: * DOUBLE PRECISION DLAM, RHO
26: * ..
27: * .. Array Arguments ..
28: * DOUBLE PRECISION D( 2 ), DELTA( 2 ), Z( 2 )
29: * ..
1.15 ! bertrand 30: *
1.8 bertrand 31: *
32: *> \par Purpose:
33: * =============
34: *>
35: *> \verbatim
36: *>
37: *> This subroutine computes the I-th eigenvalue of a symmetric rank-one
38: *> modification of a 2-by-2 diagonal matrix
39: *>
40: *> diag( D ) + RHO * Z * transpose(Z) .
41: *>
42: *> The diagonal elements in the array D are assumed to satisfy
43: *>
44: *> D(i) < D(j) for i < j .
45: *>
46: *> We also assume RHO > 0 and that the Euclidean norm of the vector
47: *> Z is one.
48: *> \endverbatim
49: *
50: * Arguments:
51: * ==========
52: *
53: *> \param[in] I
54: *> \verbatim
55: *> I is INTEGER
56: *> The index of the eigenvalue to be computed. I = 1 or I = 2.
57: *> \endverbatim
58: *>
59: *> \param[in] D
60: *> \verbatim
61: *> D is DOUBLE PRECISION array, dimension (2)
62: *> The original eigenvalues. We assume D(1) < D(2).
63: *> \endverbatim
64: *>
65: *> \param[in] Z
66: *> \verbatim
67: *> Z is DOUBLE PRECISION array, dimension (2)
68: *> The components of the updating vector.
69: *> \endverbatim
70: *>
71: *> \param[out] DELTA
72: *> \verbatim
73: *> DELTA is DOUBLE PRECISION array, dimension (2)
74: *> The vector DELTA contains the information necessary
75: *> to construct the eigenvectors.
76: *> \endverbatim
77: *>
78: *> \param[in] RHO
79: *> \verbatim
80: *> RHO is DOUBLE PRECISION
81: *> The scalar in the symmetric updating formula.
82: *> \endverbatim
83: *>
84: *> \param[out] DLAM
85: *> \verbatim
86: *> DLAM is DOUBLE PRECISION
87: *> The computed lambda_I, the I-th updated eigenvalue.
88: *> \endverbatim
89: *
90: * Authors:
91: * ========
92: *
1.15 ! bertrand 93: *> \author Univ. of Tennessee
! 94: *> \author Univ. of California Berkeley
! 95: *> \author Univ. of Colorado Denver
! 96: *> \author NAG Ltd.
1.8 bertrand 97: *
1.15 ! bertrand 98: *> \date December 2016
1.8 bertrand 99: *
100: *> \ingroup auxOTHERcomputational
101: *
102: *> \par Contributors:
103: * ==================
104: *>
105: *> Ren-Cang Li, Computer Science Division, University of California
106: *> at Berkeley, USA
107: *>
108: * =====================================================================
1.1 bertrand 109: SUBROUTINE DLAED5( I, D, Z, DELTA, RHO, DLAM )
110: *
1.15 ! bertrand 111: * -- LAPACK computational routine (version 3.7.0) --
1.1 bertrand 112: * -- LAPACK is a software package provided by Univ. of Tennessee, --
113: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.15 ! bertrand 114: * December 2016
1.1 bertrand 115: *
116: * .. Scalar Arguments ..
117: INTEGER I
118: DOUBLE PRECISION DLAM, RHO
119: * ..
120: * .. Array Arguments ..
121: DOUBLE PRECISION D( 2 ), DELTA( 2 ), Z( 2 )
122: * ..
123: *
124: * =====================================================================
125: *
126: * .. Parameters ..
127: DOUBLE PRECISION ZERO, ONE, TWO, FOUR
128: PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0, TWO = 2.0D0,
129: $ FOUR = 4.0D0 )
130: * ..
131: * .. Local Scalars ..
132: DOUBLE PRECISION B, C, DEL, TAU, TEMP, W
133: * ..
134: * .. Intrinsic Functions ..
135: INTRINSIC ABS, SQRT
136: * ..
137: * .. Executable Statements ..
138: *
139: DEL = D( 2 ) - D( 1 )
140: IF( I.EQ.1 ) THEN
141: W = ONE + TWO*RHO*( Z( 2 )*Z( 2 )-Z( 1 )*Z( 1 ) ) / DEL
142: IF( W.GT.ZERO ) THEN
143: B = DEL + RHO*( Z( 1 )*Z( 1 )+Z( 2 )*Z( 2 ) )
144: C = RHO*Z( 1 )*Z( 1 )*DEL
145: *
146: * B > ZERO, always
147: *
148: TAU = TWO*C / ( B+SQRT( ABS( B*B-FOUR*C ) ) )
149: DLAM = D( 1 ) + TAU
150: DELTA( 1 ) = -Z( 1 ) / TAU
151: DELTA( 2 ) = Z( 2 ) / ( DEL-TAU )
152: ELSE
153: B = -DEL + RHO*( Z( 1 )*Z( 1 )+Z( 2 )*Z( 2 ) )
154: C = RHO*Z( 2 )*Z( 2 )*DEL
155: IF( B.GT.ZERO ) THEN
156: TAU = -TWO*C / ( B+SQRT( B*B+FOUR*C ) )
157: ELSE
158: TAU = ( B-SQRT( B*B+FOUR*C ) ) / TWO
159: END IF
160: DLAM = D( 2 ) + TAU
161: DELTA( 1 ) = -Z( 1 ) / ( DEL+TAU )
162: DELTA( 2 ) = -Z( 2 ) / TAU
163: END IF
164: TEMP = SQRT( DELTA( 1 )*DELTA( 1 )+DELTA( 2 )*DELTA( 2 ) )
165: DELTA( 1 ) = DELTA( 1 ) / TEMP
166: DELTA( 2 ) = DELTA( 2 ) / TEMP
167: ELSE
168: *
169: * Now I=2
170: *
171: B = -DEL + RHO*( Z( 1 )*Z( 1 )+Z( 2 )*Z( 2 ) )
172: C = RHO*Z( 2 )*Z( 2 )*DEL
173: IF( B.GT.ZERO ) THEN
174: TAU = ( B+SQRT( B*B+FOUR*C ) ) / TWO
175: ELSE
176: TAU = TWO*C / ( -B+SQRT( B*B+FOUR*C ) )
177: END IF
178: DLAM = D( 2 ) + TAU
179: DELTA( 1 ) = -Z( 1 ) / ( DEL+TAU )
180: DELTA( 2 ) = -Z( 2 ) / TAU
181: TEMP = SQRT( DELTA( 1 )*DELTA( 1 )+DELTA( 2 )*DELTA( 2 ) )
182: DELTA( 1 ) = DELTA( 1 ) / TEMP
183: DELTA( 2 ) = DELTA( 2 ) / TEMP
184: END IF
185: RETURN
186: *
187: * End OF DLAED5
188: *
189: END
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