Annotation of rpl/lapack/lapack/dlae2.f, revision 1.15
1.11 bertrand 1: *> \brief \b DLAE2 computes the eigenvalues of a 2-by-2 symmetric matrix.
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 DLAE2 + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlae2.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlae2.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlae2.f">
1.8 bertrand 15: *> [TXT]</a>
1.15 ! bertrand 16: *> \endhtmlonly
1.8 bertrand 17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE DLAE2( A, B, C, RT1, RT2 )
1.15 ! bertrand 22: *
1.8 bertrand 23: * .. Scalar Arguments ..
24: * DOUBLE PRECISION A, B, C, RT1, RT2
25: * ..
1.15 ! bertrand 26: *
1.8 bertrand 27: *
28: *> \par Purpose:
29: * =============
30: *>
31: *> \verbatim
32: *>
33: *> DLAE2 computes the eigenvalues of a 2-by-2 symmetric matrix
34: *> [ A B ]
35: *> [ B C ].
36: *> On return, RT1 is the eigenvalue of larger absolute value, and RT2
37: *> is the eigenvalue of smaller absolute value.
38: *> \endverbatim
39: *
40: * Arguments:
41: * ==========
42: *
43: *> \param[in] A
44: *> \verbatim
45: *> A is DOUBLE PRECISION
46: *> The (1,1) element of the 2-by-2 matrix.
47: *> \endverbatim
48: *>
49: *> \param[in] B
50: *> \verbatim
51: *> B is DOUBLE PRECISION
52: *> The (1,2) and (2,1) elements of the 2-by-2 matrix.
53: *> \endverbatim
54: *>
55: *> \param[in] C
56: *> \verbatim
57: *> C is DOUBLE PRECISION
58: *> The (2,2) element of the 2-by-2 matrix.
59: *> \endverbatim
60: *>
61: *> \param[out] RT1
62: *> \verbatim
63: *> RT1 is DOUBLE PRECISION
64: *> The eigenvalue of larger absolute value.
65: *> \endverbatim
66: *>
67: *> \param[out] RT2
68: *> \verbatim
69: *> RT2 is DOUBLE PRECISION
70: *> The eigenvalue of smaller absolute value.
71: *> \endverbatim
72: *
73: * Authors:
74: * ========
75: *
1.15 ! bertrand 76: *> \author Univ. of Tennessee
! 77: *> \author Univ. of California Berkeley
! 78: *> \author Univ. of Colorado Denver
! 79: *> \author NAG Ltd.
1.8 bertrand 80: *
1.15 ! bertrand 81: *> \date December 2016
1.8 bertrand 82: *
1.15 ! bertrand 83: *> \ingroup OTHERauxiliary
1.8 bertrand 84: *
85: *> \par Further Details:
86: * =====================
87: *>
88: *> \verbatim
89: *>
90: *> RT1 is accurate to a few ulps barring over/underflow.
91: *>
92: *> RT2 may be inaccurate if there is massive cancellation in the
93: *> determinant A*C-B*B; higher precision or correctly rounded or
94: *> correctly truncated arithmetic would be needed to compute RT2
95: *> accurately in all cases.
96: *>
97: *> Overflow is possible only if RT1 is within a factor of 5 of overflow.
98: *> Underflow is harmless if the input data is 0 or exceeds
99: *> underflow_threshold / macheps.
100: *> \endverbatim
101: *>
102: * =====================================================================
1.1 bertrand 103: SUBROUTINE DLAE2( A, B, C, RT1, RT2 )
104: *
1.15 ! bertrand 105: * -- LAPACK auxiliary routine (version 3.7.0) --
1.1 bertrand 106: * -- LAPACK is a software package provided by Univ. of Tennessee, --
107: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.15 ! bertrand 108: * December 2016
1.1 bertrand 109: *
110: * .. Scalar Arguments ..
111: DOUBLE PRECISION A, B, C, RT1, RT2
112: * ..
113: *
114: * =====================================================================
115: *
116: * .. Parameters ..
117: DOUBLE PRECISION ONE
118: PARAMETER ( ONE = 1.0D0 )
119: DOUBLE PRECISION TWO
120: PARAMETER ( TWO = 2.0D0 )
121: DOUBLE PRECISION ZERO
122: PARAMETER ( ZERO = 0.0D0 )
123: DOUBLE PRECISION HALF
124: PARAMETER ( HALF = 0.5D0 )
125: * ..
126: * .. Local Scalars ..
127: DOUBLE PRECISION AB, ACMN, ACMX, ADF, DF, RT, SM, TB
128: * ..
129: * .. Intrinsic Functions ..
130: INTRINSIC ABS, SQRT
131: * ..
132: * .. Executable Statements ..
133: *
134: * Compute the eigenvalues
135: *
136: SM = A + C
137: DF = A - C
138: ADF = ABS( DF )
139: TB = B + B
140: AB = ABS( TB )
141: IF( ABS( A ).GT.ABS( C ) ) THEN
142: ACMX = A
143: ACMN = C
144: ELSE
145: ACMX = C
146: ACMN = A
147: END IF
148: IF( ADF.GT.AB ) THEN
149: RT = ADF*SQRT( ONE+( AB / ADF )**2 )
150: ELSE IF( ADF.LT.AB ) THEN
151: RT = AB*SQRT( ONE+( ADF / AB )**2 )
152: ELSE
153: *
154: * Includes case AB=ADF=0
155: *
156: RT = AB*SQRT( TWO )
157: END IF
158: IF( SM.LT.ZERO ) THEN
159: RT1 = HALF*( SM-RT )
160: *
161: * Order of execution important.
162: * To get fully accurate smaller eigenvalue,
163: * next line needs to be executed in higher precision.
164: *
165: RT2 = ( ACMX / RT1 )*ACMN - ( B / RT1 )*B
166: ELSE IF( SM.GT.ZERO ) THEN
167: RT1 = HALF*( SM+RT )
168: *
169: * Order of execution important.
170: * To get fully accurate smaller eigenvalue,
171: * next line needs to be executed in higher precision.
172: *
173: RT2 = ( ACMX / RT1 )*ACMN - ( B / RT1 )*B
174: ELSE
175: *
176: * Includes case RT1 = RT2 = 0
177: *
178: RT1 = HALF*RT
179: RT2 = -HALF*RT
180: END IF
181: RETURN
182: *
183: * End of DLAE2
184: *
185: END
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