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Annotation of rpl/lapack/lapack/zlaev2.f, revision 1.1

1.1     ! bertrand    1:       SUBROUTINE ZLAEV2( A, B, C, RT1, RT2, CS1, SN1 )
        !             2: *
        !             3: *  -- LAPACK auxiliary routine (version 3.2) --
        !             4: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
        !             5: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
        !             6: *     November 2006
        !             7: *
        !             8: *     .. Scalar Arguments ..
        !             9:       DOUBLE PRECISION   CS1, RT1, RT2
        !            10:       COMPLEX*16         A, B, C, SN1
        !            11: *     ..
        !            12: *
        !            13: *  Purpose
        !            14: *  =======
        !            15: *
        !            16: *  ZLAEV2 computes the eigendecomposition of a 2-by-2 Hermitian matrix
        !            17: *     [  A         B  ]
        !            18: *     [  CONJG(B)  C  ].
        !            19: *  On return, RT1 is the eigenvalue of larger absolute value, RT2 is the
        !            20: *  eigenvalue of smaller absolute value, and (CS1,SN1) is the unit right
        !            21: *  eigenvector for RT1, giving the decomposition
        !            22: *
        !            23: *  [ CS1  CONJG(SN1) ] [    A     B ] [ CS1 -CONJG(SN1) ] = [ RT1  0  ]
        !            24: *  [-SN1     CS1     ] [ CONJG(B) C ] [ SN1     CS1     ]   [  0  RT2 ].
        !            25: *
        !            26: *  Arguments
        !            27: *  =========
        !            28: *
        !            29: *  A      (input) COMPLEX*16
        !            30: *         The (1,1) element of the 2-by-2 matrix.
        !            31: *
        !            32: *  B      (input) COMPLEX*16
        !            33: *         The (1,2) element and the conjugate of the (2,1) element of
        !            34: *         the 2-by-2 matrix.
        !            35: *
        !            36: *  C      (input) COMPLEX*16
        !            37: *         The (2,2) element of the 2-by-2 matrix.
        !            38: *
        !            39: *  RT1    (output) DOUBLE PRECISION
        !            40: *         The eigenvalue of larger absolute value.
        !            41: *
        !            42: *  RT2    (output) DOUBLE PRECISION
        !            43: *         The eigenvalue of smaller absolute value.
        !            44: *
        !            45: *  CS1    (output) DOUBLE PRECISION
        !            46: *  SN1    (output) COMPLEX*16
        !            47: *         The vector (CS1, SN1) is a unit right eigenvector for RT1.
        !            48: *
        !            49: *  Further Details
        !            50: *  ===============
        !            51: *
        !            52: *  RT1 is accurate to a few ulps barring over/underflow.
        !            53: *
        !            54: *  RT2 may be inaccurate if there is massive cancellation in the
        !            55: *  determinant A*C-B*B; higher precision or correctly rounded or
        !            56: *  correctly truncated arithmetic would be needed to compute RT2
        !            57: *  accurately in all cases.
        !            58: *
        !            59: *  CS1 and SN1 are accurate to a few ulps barring over/underflow.
        !            60: *
        !            61: *  Overflow is possible only if RT1 is within a factor of 5 of overflow.
        !            62: *  Underflow is harmless if the input data is 0 or exceeds
        !            63: *     underflow_threshold / macheps.
        !            64: *
        !            65: * =====================================================================
        !            66: *
        !            67: *     .. Parameters ..
        !            68:       DOUBLE PRECISION   ZERO
        !            69:       PARAMETER          ( ZERO = 0.0D0 )
        !            70:       DOUBLE PRECISION   ONE
        !            71:       PARAMETER          ( ONE = 1.0D0 )
        !            72: *     ..
        !            73: *     .. Local Scalars ..
        !            74:       DOUBLE PRECISION   T
        !            75:       COMPLEX*16         W
        !            76: *     ..
        !            77: *     .. External Subroutines ..
        !            78:       EXTERNAL           DLAEV2
        !            79: *     ..
        !            80: *     .. Intrinsic Functions ..
        !            81:       INTRINSIC          ABS, DBLE, DCONJG
        !            82: *     ..
        !            83: *     .. Executable Statements ..
        !            84: *
        !            85:       IF( ABS( B ).EQ.ZERO ) THEN
        !            86:          W = ONE
        !            87:       ELSE
        !            88:          W = DCONJG( B ) / ABS( B )
        !            89:       END IF
        !            90:       CALL DLAEV2( DBLE( A ), ABS( B ), DBLE( C ), RT1, RT2, CS1, T )
        !            91:       SN1 = W*T
        !            92:       RETURN
        !            93: *
        !            94: *     End of ZLAEV2
        !            95: *
        !            96:       END