Annotation of rpl/lapack/lapack/dlae2.f, revision 1.18
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: *> \ingroup OTHERauxiliary
1.8 bertrand 82: *
83: *> \par Further Details:
84: * =====================
85: *>
86: *> \verbatim
87: *>
88: *> RT1 is accurate to a few ulps barring over/underflow.
89: *>
90: *> RT2 may be inaccurate if there is massive cancellation in the
91: *> determinant A*C-B*B; higher precision or correctly rounded or
92: *> correctly truncated arithmetic would be needed to compute RT2
93: *> accurately in all cases.
94: *>
95: *> Overflow is possible only if RT1 is within a factor of 5 of overflow.
96: *> Underflow is harmless if the input data is 0 or exceeds
97: *> underflow_threshold / macheps.
98: *> \endverbatim
99: *>
100: * =====================================================================
1.1 bertrand 101: SUBROUTINE DLAE2( A, B, C, RT1, RT2 )
102: *
1.18 ! bertrand 103: * -- LAPACK auxiliary routine --
1.1 bertrand 104: * -- LAPACK is a software package provided by Univ. of Tennessee, --
105: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
106: *
107: * .. Scalar Arguments ..
108: DOUBLE PRECISION A, B, C, RT1, RT2
109: * ..
110: *
111: * =====================================================================
112: *
113: * .. Parameters ..
114: DOUBLE PRECISION ONE
115: PARAMETER ( ONE = 1.0D0 )
116: DOUBLE PRECISION TWO
117: PARAMETER ( TWO = 2.0D0 )
118: DOUBLE PRECISION ZERO
119: PARAMETER ( ZERO = 0.0D0 )
120: DOUBLE PRECISION HALF
121: PARAMETER ( HALF = 0.5D0 )
122: * ..
123: * .. Local Scalars ..
124: DOUBLE PRECISION AB, ACMN, ACMX, ADF, DF, RT, SM, TB
125: * ..
126: * .. Intrinsic Functions ..
127: INTRINSIC ABS, SQRT
128: * ..
129: * .. Executable Statements ..
130: *
131: * Compute the eigenvalues
132: *
133: SM = A + C
134: DF = A - C
135: ADF = ABS( DF )
136: TB = B + B
137: AB = ABS( TB )
138: IF( ABS( A ).GT.ABS( C ) ) THEN
139: ACMX = A
140: ACMN = C
141: ELSE
142: ACMX = C
143: ACMN = A
144: END IF
145: IF( ADF.GT.AB ) THEN
146: RT = ADF*SQRT( ONE+( AB / ADF )**2 )
147: ELSE IF( ADF.LT.AB ) THEN
148: RT = AB*SQRT( ONE+( ADF / AB )**2 )
149: ELSE
150: *
151: * Includes case AB=ADF=0
152: *
153: RT = AB*SQRT( TWO )
154: END IF
155: IF( SM.LT.ZERO ) THEN
156: RT1 = HALF*( SM-RT )
157: *
158: * Order of execution important.
159: * To get fully accurate smaller eigenvalue,
160: * next line needs to be executed in higher precision.
161: *
162: RT2 = ( ACMX / RT1 )*ACMN - ( B / RT1 )*B
163: ELSE IF( SM.GT.ZERO ) THEN
164: RT1 = HALF*( SM+RT )
165: *
166: * Order of execution important.
167: * To get fully accurate smaller eigenvalue,
168: * next line needs to be executed in higher precision.
169: *
170: RT2 = ( ACMX / RT1 )*ACMN - ( B / RT1 )*B
171: ELSE
172: *
173: * Includes case RT1 = RT2 = 0
174: *
175: RT1 = HALF*RT
176: RT2 = -HALF*RT
177: END IF
178: RETURN
179: *
180: * End of DLAE2
181: *
182: END
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