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Annotation of rpl/lapack/lapack/zlaev2.f, revision 1.18

1.11      bertrand    1: *> \brief \b ZLAEV2 computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian 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 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">
1.8       bertrand   15: *> [TXT]</a>
1.15      bertrand   16: *> \endhtmlonly
1.8       bertrand   17: *
                     18: *  Definition:
                     19: *  ===========
                     20: *
                     21: *       SUBROUTINE ZLAEV2( A, B, C, RT1, RT2, CS1, SN1 )
1.15      bertrand   22: *
1.8       bertrand   23: *       .. Scalar Arguments ..
                     24: *       DOUBLE PRECISION   CS1, RT1, RT2
                     25: *       COMPLEX*16         A, B, C, SN1
                     26: *       ..
1.15      bertrand   27: *
1.8       bertrand   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: *
1.15      bertrand   93: *> \author Univ. of Tennessee
                     94: *> \author Univ. of California Berkeley
                     95: *> \author Univ. of Colorado Denver
                     96: *> \author NAG Ltd.
1.8       bertrand   97: *
                     98: *> \ingroup complex16OTHERauxiliary
                     99: *
                    100: *> \par Further Details:
                    101: *  =====================
                    102: *>
                    103: *> \verbatim
                    104: *>
                    105: *>  RT1 is accurate to a few ulps barring over/underflow.
                    106: *>
                    107: *>  RT2 may be inaccurate if there is massive cancellation in the
                    108: *>  determinant A*C-B*B; higher precision or correctly rounded or
                    109: *>  correctly truncated arithmetic would be needed to compute RT2
                    110: *>  accurately in all cases.
                    111: *>
                    112: *>  CS1 and SN1 are accurate to a few ulps barring over/underflow.
                    113: *>
                    114: *>  Overflow is possible only if RT1 is within a factor of 5 of overflow.
                    115: *>  Underflow is harmless if the input data is 0 or exceeds
                    116: *>     underflow_threshold / macheps.
                    117: *> \endverbatim
                    118: *>
                    119: *  =====================================================================
1.1       bertrand  120:       SUBROUTINE ZLAEV2( A, B, C, RT1, RT2, CS1, SN1 )
                    121: *
1.18    ! bertrand  122: *  -- LAPACK auxiliary routine --
1.1       bertrand  123: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
                    124: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
                    125: *
                    126: *     .. Scalar Arguments ..
                    127:       DOUBLE PRECISION   CS1, RT1, RT2
                    128:       COMPLEX*16         A, B, C, SN1
                    129: *     ..
                    130: *
                    131: * =====================================================================
                    132: *
                    133: *     .. Parameters ..
                    134:       DOUBLE PRECISION   ZERO
                    135:       PARAMETER          ( ZERO = 0.0D0 )
                    136:       DOUBLE PRECISION   ONE
                    137:       PARAMETER          ( ONE = 1.0D0 )
                    138: *     ..
                    139: *     .. Local Scalars ..
                    140:       DOUBLE PRECISION   T
                    141:       COMPLEX*16         W
                    142: *     ..
                    143: *     .. External Subroutines ..
                    144:       EXTERNAL           DLAEV2
                    145: *     ..
                    146: *     .. Intrinsic Functions ..
                    147:       INTRINSIC          ABS, DBLE, DCONJG
                    148: *     ..
                    149: *     .. Executable Statements ..
                    150: *
                    151:       IF( ABS( B ).EQ.ZERO ) THEN
                    152:          W = ONE
                    153:       ELSE
                    154:          W = DCONJG( B ) / ABS( B )
                    155:       END IF
                    156:       CALL DLAEV2( DBLE( A ), ABS( B ), DBLE( C ), RT1, RT2, CS1, T )
                    157:       SN1 = W*T
                    158:       RETURN
                    159: *
                    160: *     End of ZLAEV2
                    161: *
                    162:       END