Loading...
Searching...
No Matches

## dlae2()

subroutine dlae2 | ( | double precision | a,
|  | double precision | b,
|  | double precision | c,
|  | double precision | rt1,
|  | double precision | rt2 )

DLAE2 computes the eigenvalues of a 2-by-2 symmetric matrix.

Download DLAE2 + dependencies [TGZ] [ZIP] [TXT]

Purpose:

      !>
      !> DLAE2  computes the eigenvalues of a 2-by-2 symmetric matrix
      !>    [  A   B  ]
      !>    [  B   C  ].
      !> On return, RT1 is the eigenvalue of larger absolute value, and RT2
      !> is the eigenvalue of smaller absolute value.
      !>

Parameters

  [in]

  A

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

  [in]

  B

      !>          B is DOUBLE PRECISION
      !>          The (1,2) and (2,1) elements of the 2-by-2 matrix.
      !>

  [in]

  C

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

  [out]

  RT1

      !>          RT1 is DOUBLE PRECISION
      !>          The eigenvalue of larger absolute value.
      !>

  [out]

  RT2

      !>          RT2 is DOUBLE PRECISION
      !>          The eigenvalue of smaller absolute value.
      !>

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.
      !>
      !>  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.
      !>