SLAGS2  -  compute  2-by-2 orthogonal 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 )  The rows of the  trans­
       formed A and B are parallel, where  U = ( CSU SNU ), V = (
       CSV SNV ), Q = ( CSQ SNQ ) ( -SNU CSU ) (  -SNV  CSV  )  (
       -SNQ CSQ )  Z' denotes the transpose of Z


SYNOPSIS

       SUBROUTINE SLAGS2( UPPER,  A1,  A2,  A3,  B1, B2, B3, CSU,
                          SNU, CSV, SNV, CSQ, SNQ )

           LOGICAL        UPPER

           REAL           A1, A2, A3, B1, B2, B3, CSQ, CSU,  CSV,
                          SNQ, SNU, SNV


PURPOSE

       SLAGS2  computes  2-by-2  orthogonal  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 ) The rows of  the  trans­
       formed  A and B are parallel, where U = ( CSU SNU ), V = (
       CSV SNV ), Q = ( CSQ SNQ ) ( -SNU CSU ) (  -SNV  CSV  )  (
       -SNQ CSQ ) Z' denotes the transpose of Z.


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

       B1      (input) REAL
               B2       (input)  REAL  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)  REAL  The  desired  orthogonal
               matrix U.

               SNV      (output)  REAL  The  desired   orthogonal
               matrix V.

       CSQ     (output) REAL
               SNQ       (output)  REAL  The  desired  orthogonal
               matrix Q.


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