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## claev2()

subroutine claev2 | ( | complex | a,
|  | complex | b,
|  | complex | c,
|  | real | rt1,
|  | real | rt2,
|  | real | cs1,
|  | complex | sn1 )

CLAEV2 computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian matrix.

Download CLAEV2 + dependencies [TGZ] [ZIP] [TXT]

Purpose:

      !>
      !> CLAEV2 computes the eigendecomposition of a 2-by-2 Hermitian matrix
      !>    [  A         B  ]
      !>    [  CONJG(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  CONJG(SN1) ] [    A     B ] [ CS1 -CONJG(SN1) ] = [ RT1  0  ]
      !> [-SN1     CS1     ] [ CONJG(B) C ] [ SN1     CS1     ]   [  0  RT2 ].
      !>

Parameters

  [in]

  A

      !>          A is COMPLEX
      !>         The (1,1) element of the 2-by-2 matrix.
      !>

  [in]

  B

      !>          B is COMPLEX
      !>         The (1,2) element and the conjugate of the (2,1) element of
      !>         the 2-by-2 matrix.
      !>

  [in]

  C

      !>          C is COMPLEX
      !>         The (2,2) element of the 2-by-2 matrix.
      !>

  [out]

  RT1

      !>          RT1 is REAL
      !>         The eigenvalue of larger absolute value.
      !>

  [out]

  RT2

      !>          RT2 is REAL
      !>         The eigenvalue of smaller absolute value.
      !>

  [out]

  CS1

      !>          CS1 is REAL
      !>

  [out]

  SN1

      !>          SN1 is COMPLEX
      !>         The vector (CS1, SN1) is a unit right eigenvector for RT1.
      !>

Author
  Univ. of Tennessee
  Univ. of California Berkeley
  Univ. of Colorado Denver
  NAG Ltd.

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.
      !>