LAPACK

NAME¶

lae2 - lae2: 2x2 eig, step in steqr, stemr

SYNOPSIS¶

Functions¶

subroutine dlae2 (a, b, c, rt1, rt2)
DLAE2 computes the eigenvalues of a 2-by-2 symmetric matrix. subroutine slae2 (a, b, c, rt1, rt2)
SLAE2 computes the eigenvalues of a 2-by-2 symmetric matrix.

Detailed Description¶

Function Documentation¶

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.

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



          A is DOUBLE PRECISION


          The (1,1) element of the 2-by-2 matrix.



          B is DOUBLE PRECISION


          The (1,2) and (2,1) elements of the 2-by-2 matrix.



          C is DOUBLE PRECISION


          The (2,2) element of the 2-by-2 matrix.

RT1



          RT1 is DOUBLE PRECISION


          The eigenvalue of larger absolute value.

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.

subroutine slae2 (real a, real b, real c, real rt1, real rt2)¶

SLAE2 computes the eigenvalues of a 2-by-2 symmetric matrix.