Return to zlaev2.f CVS log

Up to [local] / rpl / lapack / lapack

Annotation of rpl/lapack/lapack/zlaev2.f, revision 1.8

1.8     ! bertrand    1: *> \brief \b ZLAEV2
        !             2: *
        !             3: *  =========== DOCUMENTATION ===========
        !             4: *
        !             5: * Online html documentation available at 
        !             6: *            http://www.netlib.org/lapack/explore-html/ 
        !             7: *
        !             8: *> \htmlonly
        !             9: *> Download ZLAEV2 + dependencies 
        !            10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlaev2.f"> 
        !            11: *> [TGZ]</a> 
        !            12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlaev2.f"> 
        !            13: *> [ZIP]</a> 
        !            14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlaev2.f"> 
        !            15: *> [TXT]</a>
        !            16: *> \endhtmlonly 
        !            17: *
        !            18: *  Definition:
        !            19: *  ===========
        !            20: *
        !            21: *       SUBROUTINE ZLAEV2( A, B, C, RT1, RT2, CS1, SN1 )
        !            22: * 
        !            23: *       .. Scalar Arguments ..
        !            24: *       DOUBLE PRECISION   CS1, RT1, RT2
        !            25: *       COMPLEX*16         A, B, C, SN1
        !            26: *       ..
        !            27: *  
        !            28: *
        !            29: *> \par Purpose:
        !            30: *  =============
        !            31: *>
        !            32: *> \verbatim
        !            33: *>
        !            34: *> ZLAEV2 computes the eigendecomposition of a 2-by-2 Hermitian matrix
        !            35: *>    [  A         B  ]
        !            36: *>    [  CONJG(B)  C  ].
        !            37: *> On return, RT1 is the eigenvalue of larger absolute value, RT2 is the
        !            38: *> eigenvalue of smaller absolute value, and (CS1,SN1) is the unit right
        !            39: *> eigenvector for RT1, giving the decomposition
        !            40: *>
        !            41: *> [ CS1  CONJG(SN1) ] [    A     B ] [ CS1 -CONJG(SN1) ] = [ RT1  0  ]
        !            42: *> [-SN1     CS1     ] [ CONJG(B) C ] [ SN1     CS1     ]   [  0  RT2 ].
        !            43: *> \endverbatim
        !            44: *
        !            45: *  Arguments:
        !            46: *  ==========
        !            47: *
        !            48: *> \param[in] A
        !            49: *> \verbatim
        !            50: *>          A is COMPLEX*16
        !            51: *>         The (1,1) element of the 2-by-2 matrix.
        !            52: *> \endverbatim
        !            53: *>
        !            54: *> \param[in] B
        !            55: *> \verbatim
        !            56: *>          B is COMPLEX*16
        !            57: *>         The (1,2) element and the conjugate of the (2,1) element of
        !            58: *>         the 2-by-2 matrix.
        !            59: *> \endverbatim
        !            60: *>
        !            61: *> \param[in] C
        !            62: *> \verbatim
        !            63: *>          C is COMPLEX*16
        !            64: *>         The (2,2) element of the 2-by-2 matrix.
        !            65: *> \endverbatim
        !            66: *>
        !            67: *> \param[out] RT1
        !            68: *> \verbatim
        !            69: *>          RT1 is DOUBLE PRECISION
        !            70: *>         The eigenvalue of larger absolute value.
        !            71: *> \endverbatim
        !            72: *>
        !            73: *> \param[out] RT2
        !            74: *> \verbatim
        !            75: *>          RT2 is DOUBLE PRECISION
        !            76: *>         The eigenvalue of smaller absolute value.
        !            77: *> \endverbatim
        !            78: *>
        !            79: *> \param[out] CS1
        !            80: *> \verbatim
        !            81: *>          CS1 is DOUBLE PRECISION
        !            82: *> \endverbatim
        !            83: *>
        !            84: *> \param[out] SN1
        !            85: *> \verbatim
        !            86: *>          SN1 is COMPLEX*16
        !            87: *>         The vector (CS1, SN1) is a unit right eigenvector for RT1.
        !            88: *> \endverbatim
        !            89: *
        !            90: *  Authors:
        !            91: *  ========
        !            92: *
        !            93: *> \author Univ. of Tennessee 
        !            94: *> \author Univ. of California Berkeley 
        !            95: *> \author Univ. of Colorado Denver 
        !            96: *> \author NAG Ltd. 
        !            97: *
        !            98: *> \date November 2011
        !            99: *
        !           100: *> \ingroup complex16OTHERauxiliary
        !           101: *
        !           102: *> \par Further Details:
        !           103: *  =====================
        !           104: *>
        !           105: *> \verbatim
        !           106: *>
        !           107: *>  RT1 is accurate to a few ulps barring over/underflow.
        !           108: *>
        !           109: *>  RT2 may be inaccurate if there is massive cancellation in the
        !           110: *>  determinant A*C-B*B; higher precision or correctly rounded or
        !           111: *>  correctly truncated arithmetic would be needed to compute RT2
        !           112: *>  accurately in all cases.
        !           113: *>
        !           114: *>  CS1 and SN1 are accurate to a few ulps barring over/underflow.
        !           115: *>
        !           116: *>  Overflow is possible only if RT1 is within a factor of 5 of overflow.
        !           117: *>  Underflow is harmless if the input data is 0 or exceeds
        !           118: *>     underflow_threshold / macheps.
        !           119: *> \endverbatim
        !           120: *>
        !           121: *  =====================================================================
1.1       bertrand  122:       SUBROUTINE ZLAEV2( A, B, C, RT1, RT2, CS1, SN1 )
                    123: *
1.8     ! bertrand  124: *  -- LAPACK auxiliary routine (version 3.4.0) --
1.1       bertrand  125: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
                    126: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.8     ! bertrand  127: *     November 2011
1.1       bertrand  128: *
                    129: *     .. Scalar Arguments ..
                    130:       DOUBLE PRECISION   CS1, RT1, RT2
                    131:       COMPLEX*16         A, B, C, SN1
                    132: *     ..
                    133: *
                    134: * =====================================================================
                    135: *
                    136: *     .. Parameters ..
                    137:       DOUBLE PRECISION   ZERO
                    138:       PARAMETER          ( ZERO = 0.0D0 )
                    139:       DOUBLE PRECISION   ONE
                    140:       PARAMETER          ( ONE = 1.0D0 )
                    141: *     ..
                    142: *     .. Local Scalars ..
                    143:       DOUBLE PRECISION   T
                    144:       COMPLEX*16         W
                    145: *     ..
                    146: *     .. External Subroutines ..
                    147:       EXTERNAL           DLAEV2
                    148: *     ..
                    149: *     .. Intrinsic Functions ..
                    150:       INTRINSIC          ABS, DBLE, DCONJG
                    151: *     ..
                    152: *     .. Executable Statements ..
                    153: *
                    154:       IF( ABS( B ).EQ.ZERO ) THEN
                    155:          W = ONE
                    156:       ELSE
                    157:          W = DCONJG( B ) / ABS( B )
                    158:       END IF
                    159:       CALL DLAEV2( DBLE( A ), ABS( B ), DBLE( C ), RT1, RT2, CS1, T )
                    160:       SN1 = W*T
                    161:       RETURN
                    162: *
                    163: *     End of ZLAEV2
                    164: *
                    165:       END