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Fri Dec 14 14:22:32 2012 UTC (11 years, 5 months ago) by bertrand
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CVS tags: rpl-4_1_16, rpl-4_1_15, rpl-4_1_14, rpl-4_1_13, rpl-4_1_12, rpl-4_1_11, HEAD

Mise à jour de lapack.

1: *> \brief \b DLAE2 computes the eigenvalues of a 2-by-2 symmetric matrix. 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 September 2012 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: * ===================================================================== 103: SUBROUTINE DLAE2( A, B, C, RT1, RT2 ) 104: * 105: * -- LAPACK auxiliary routine (version 3.4.2) -- 106: * -- LAPACK is a software package provided by Univ. of Tennessee, -- 107: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 108: * September 2012 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