Previous: dlaein Up: ../lapack-d.html Next: dlaexc

dlaev2

 NAME
      DLAEV2 - compute the eigendecomposition of a 2-by-2 sym-
      metric matrix  [ A B ]  [ B C ]

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

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

 PURPOSE
      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) entry of the 2-by-2 matrix.

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

      C       (input) DOUBLE PRECISION
              The (2,2) entry 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.