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Annotation of rpl/lapack/lapack/zlaev2.f, revision 1.4

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