DLAGS2  -  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 DLAGS2( UPPER,  A1,  A2,  A3,  B1, B2, B3, CSU,
                          SNU, CSV, SNV, CSQ, SNQ )

           LOGICAL        UPPER

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


PURPOSE

       DLAGS2  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) DOUBLE PRECISION
               A2       (input)  DOUBLE PRECISION A3      (input)
               DOUBLE PRECISION On entry, A1, A2 and A3 are  ele­
               ments of the input 2-by-2 upper (lower) triangular
               matrix A.

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

       CSU     (output) DOUBLE PRECISION
               SNU      (output)  DOUBLE  PRECISION  The  desired
               orthogonal matrix U.

               SNV      (output)  DOUBLE  PRECISION  The  desired
               orthogonal matrix V.

       CSQ     (output) DOUBLE PRECISION
               SNQ      (output)  DOUBLE  PRECISION  The  desired
               orthogonal matrix Q.


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