zlaev2(3S)

NAME
     ZLAEV2 - compute the eigendecomposition of a 2-by-2 Hermitian matrix [ A
     B ] [ CONJG(B) C ]

SYNOPSIS
     SUBROUTINE ZLAEV2( A, B, C, RT1, RT2, CS1, SN1 )

         DOUBLE         PRECISION CS1, RT1, RT2

         COMPLEX*16     A, B, C, 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
     ZLAEV2 computes the eigendecomposition of a 2-by-2 Hermitian matrix [ A B
     ] [ CONJG(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  CONJG(SN1) ] [    A     B ] [ CS1 -CONJG(SN1) ] = [ RT1  0  ] [-
     SN1     CS1     ] [ CONJG(B) C ] [ SN1     CS1     ]   [  0  RT2 ].


ARGUMENTS
     A      (input) COMPLEX*16
            The (1,1) element of the 2-by-2 matrix.

     B      (input) COMPLEX*16
            The (1,2) element and the conjugate of the (2,1) element of the
            2-by-2 matrix.

     C      (input) COMPLEX*16
            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) COMPLEX*16 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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