ZLAGS2  - 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 ZLAGS2( UPPER,  A1,  A2,  A3,  B1, B2, B3, CSU,
                          SNU, CSV, SNV, CSQ, SNQ )

           LOGICAL        UPPER

           DOUBLE         PRECISION A1, A3, B1, B3, CSQ, CSU, CSV

           COMPLEX*16     A2, B2, SNQ, SNU, SNV


PURPOSE

       ZLAGS2  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) DOUBLE PRECISION
               A2      (input) COMPLEX*16 A3      (input)  DOUBLE
               PRECISION  On entry, A1, A2 and A3 are elements of
               the input 2-by-2 upper (lower)  triangular  matrix


       B1      (input) DOUBLE PRECISION
               B2       (input) COMPLEX*16 B3      (input) DOUBLE
               PRECISION On entry, B1, B2 and B3 are elements  of
               the  input  2-by-2 upper (lower) triangular matrix
               B.

       CSU     (output) DOUBLE PRECISION
               SNU     (output) COMPLEX*16  The  desired  unitary
               matrix U.

       CSV     (output) DOUBLE PRECISION
               SNV      (output)  COMPLEX*16  The desired unitary
               matrix V.

       CSQ     (output) DOUBLE PRECISION
               SNQ     (output) COMPLEX*16  The  desired  unitary
               matrix Q.


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