Annotation of rpl/lapack/lapack/dlae2.f, revision 1.8
1.8 ! bertrand 1: *> \brief \b DLAE2
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 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">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE DLAE2( A, B, C, RT1, RT2 )
! 22: *
! 23: * .. Scalar Arguments ..
! 24: * DOUBLE PRECISION A, B, C, RT1, RT2
! 25: * ..
! 26: *
! 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: *
! 76: *> \author Univ. of Tennessee
! 77: *> \author Univ. of California Berkeley
! 78: *> \author Univ. of Colorado Denver
! 79: *> \author NAG Ltd.
! 80: *
! 81: *> \date November 2011
! 82: *
! 83: *> \ingroup auxOTHERauxiliary
! 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: *
1.8 ! bertrand 105: * -- LAPACK auxiliary routine (version 3.4.0) --
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..--
1.8 ! bertrand 108: * November 2011
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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