dlaev2(3S)

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

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

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

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
     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) element of the 2-by-2 matrix.

     B       (input) DOUBLE PRECISION
             The (1,2) element and the conjugate of the (2,1) element 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.

     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.


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

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