dlae2(3S)

NAME
     DLAE2 - compute the eigenvalues of a 2-by-2 symmetric matrix [ A B ] [ B
     C ]

SYNOPSIS
     SUBROUTINE DLAE2( A, B, C, RT1, RT2 )

         DOUBLE        PRECISION A, B, C, RT1, RT2

IMPLEMENTATION
     These routines are part of the SCSL Scientific Library and can be loaded
     using either the -lscs or the -lscs_mp option.  The -lscs_mp option
     directs the linker to use the multi-processor version of the library.

     When linking to SCSL with -lscs or -lscs_mp, the default integer size is
     4 bytes (32 bits). Another version of SCSL is available in which integers
     are 8 bytes (64 bits).  This version allows the user access to larger
     memory sizes and helps when porting legacy Cray codes.  It can be loaded
     by using the -lscs_i8 option or the -lscs_i8_mp option. A program may use
     only one of the two versions; 4-byte integer and 8-byte integer library
     calls cannot be mixed.

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.


ARGUMENTS
     A       (input) DOUBLE PRECISION
             The (1,1) element of the 2-by-2 matrix.

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

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

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.


SEE ALSO
     INTRO_LAPACK(3S), INTRO_SCSL(3S)

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