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LAPACK version 3.0
dlaev2(3)

PURPOSE
  DLAEV2 - compute the eigendecomposition of a 2-by-2 symmetric matrix [ A B
  ] [ B C ]

SYNTAX
  SUBROUTINE DLAEV2( A, B, C, RT1, RT2, CS1, SN1 )

      DOUBLE	     PRECISION A, B, C, CS1, RT1, RT2, SN1

DESCRIPTION
  DLAEV2 computes the eigendecomposition of a 2-by-2 symmetric matrix [ A B ]
  [ B C ]. On return, RT1 is the eigenvalue of larger absolute value, RT2 is
  the eigenvalue of smaller absolute value, and (CS1,SN1) is the unit right
  eigenvector for RT1, giving the decomposition

     [ CS1  SN1 ] [  A	 B  ] [ CS1 -SN1 ]  =  [ RT1  0	 ]
     [-SN1  CS1 ] [  B	 C  ] [ SN1  CS1 ]     [  0  RT2 ].

ARGUMENTS
  A	  (input) DOUBLE PRECISION
	  The (1,1) element of the 2-by-2 matrix.

  B	  (input) DOUBLE PRECISION
	  The (1,2) element and the conjugate of the (2,1) element of the 2-
	  by-2 matrix.

  C	  (input) DOUBLE PRECISION
	  The (2,2) element of the 2-by-2 matrix.

  RT1	  (output) DOUBLE PRECISION
	  The eigenvalue of larger absolute value.

  RT2	  (output) DOUBLE PRECISION
	  The eigenvalue of smaller absolute value.

  CS1	  (output) DOUBLE PRECISION
	  SN1	  (output) DOUBLE PRECISION The vector (CS1, SN1) is a unit
	  right eigenvector for RT1.

FURTHER DETAILS
  RT1 is accurate to a few ulps barring over/underflow.

  RT2 may be inaccurate if there is massive cancellation in the determinant
  A*C-B*B; higher precision or correctly rounded or correctly truncated
  arithmetic would be needed to compute RT2 accurately in all cases.

  CS1 and SN1 are accurate to a few ulps barring over/underflow.

  Overflow is possible only if RT1 is within a factor of 5 of overflow.
  Underflow is harmless if the input data is 0 or exceeds
     underflow_threshold / macheps.