lae2(3)                    Library Functions Manual                    lae2(3)

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

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

           B

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

           C

           !>          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.
           !>

       Definition at line 101 of file dlae2.f.

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

       Purpose:


           !>
           !> SLAE2  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

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

           B

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

           C

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

           RT1

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

           RT2

           !>          RT2 is REAL
           !>          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.
           !>

       Definition at line 101 of file slae2.f.

Author
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LAPACK                          Version 3.12.0                         lae2(3)