CLAGS2  - compute 2-by-2 unitary matrices U, V and Q, such
       that if ( UPPER ) then  U'*A*Q = U'*( A1 A2 )*Q = ( x 0  )
       ( 0 A3 ) ( x x ) and V'*B*Q = V'*( B1 B2 )*Q = ( x 0 ) ( 0
       B3 ) ( x x )  or if ( .NOT.UPPER ) then  U'*A*Q = U'*(  A1
       0  )*Q  = ( x x ) ( A2 A3 ) ( 0 x ) and V'*B*Q = V'*( B1 0
       )*Q = ( x x ) ( B2 B3 ) ( 0 x ) where  U = ( CSU SNU ),  V
       = ( CSV SNV ),


SYNOPSIS

       SUBROUTINE CLAGS2( UPPER,  A1,  A2,  A3,  B1, B2, B3, CSU,
                          SNU, CSV, SNV, CSQ, SNQ )

           LOGICAL        UPPER

           REAL           A1, A3, B1, B3, CSQ, CSU, CSV

           COMPLEX        A2, B2, SNQ, SNU, SNV


PURPOSE

       CLAGS2 computes 2-by-2 unitary matrices U, V and  Q,  such
       that if ( UPPER ) then U'*A*Q = U'*( A1 A2 )*Q = ( x 0 ) (
       0 A3 ) ( x x ) and V'*B*Q = V'*( B1 B2 )*Q = ( x 0 )  (  0
       B3  ) ( x x ) or if ( .NOT.UPPER ) then U'*A*Q = U'*( A1 0
       )*Q = ( x x ) ( A2 A3 ) ( 0 x ) and V'*B*Q = V'*( B1 0 )*Q
       =  (  x x ) ( B2 B3 ) ( 0 x ) where U = ( CSU SNU ), V = (
       CSV SNV ),       ( -CONJG(SNU)  CSU )       (  -CONJG(SNV)
       CSV )

         Q = (     CSQ      SNQ )
             ( -CONJG(SNQ)  CSQ )

       Z' denotes the conjugate transpose of Z.

       The  rows  of  the transformed A and B are parallel. More­
       over, if the input 2-by-2 matrix A is not zero,  then  the
       transformed  (1,1)  entry  of  A is not zero. If the input
       matrices A and B are both not zero, then  the  transformed
       (2,2) element of B is not zero, except when the first rows
       of input A and B are parallel  and  the  second  rows  are
       zero.


ARGUMENTS

       UPPER   (input) LOGICAL
               =  .TRUE.:  the  input  matrices A and B are upper
               triangular.
               = .FALSE.: the input matrices A and  B  are  lower
               triangular.

       A1      (input) REAL
               A2       (input)  COMPLEX  A3      (input) REAL On
               entry, A1, A2 and A3 are  elements  of  the  input
               2-by-2 upper (lower) triangular matrix A.

               B2       (input)  COMPLEX  B3      (input) REAL On
               entry, B1, B2 and B3 are  elements  of  the  input
               2-by-2 upper (lower) triangular matrix B.

       CSU     (output) REAL
               SNU       (output)  COMPLEX  The  desired  unitary
               matrix U.

       CSV     (output) REAL
               SNV      (output)  COMPLEX  The  desired   unitary
               matrix V.

       CSQ     (output) REAL
               SNQ       (output)  COMPLEX  The  desired  unitary
               matrix Q.


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