Return to zlaev2.f CVS log

Up to [local] / rpl / lapack / lapack

Mise à jour globale de Lapack 3.2.2.

    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