CLAGS2(3)      LAPACK routine of NEC Numeric Library Collection      CLAGS2(3)



NAME
       CLAGS2

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



PURPOSE
            CLAGS2 computes 2-by-2 unitary matrices U, V and Q, such
            that if ( UPPER ) then

                      U**H *A*Q = U**H *( A1 A2 )*Q = ( x  0  )
                                        ( 0  A3 )     ( x  x  )
            and
                      V**H*B*Q = V**H *( B1 B2 )*Q = ( x  0  )
                                       ( 0  B3 )     ( x  x  )

            or if ( .NOT.UPPER ) then

                      U**H *A*Q = U**H *( A1 0  )*Q = ( x  x  )
                                        ( A2 A3 )     ( 0  x  )
            and
                      V**H *B*Q = V**H *( B1 0  )*Q = ( x  x  )
                                        ( B2 B3 )     ( 0  x  )
            where

              U = (   CSU    SNU ), V = (  CSV    SNV ),
                  ( -SNU**H  CSU )      ( -SNV**H CSV )

              Q = (   CSQ    SNQ )
                  ( -SNQ**H  CSQ )

            The rows of the transformed A and B are parallel. Moreover, 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)
                     UPPER is LOGICAL
                     = .TRUE.: the input matrices A and B are upper triangular.
                     = .FALSE.: the input matrices A and B are lower triangular.

           A1        (input)
                     A1 is REAL

           A2        (input)
                     A2 is COMPLEX

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

           B1        (input)
                     B1 is REAL

           B2        (input)
                     B2 is COMPLEX

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

           CSU       (output)
                     CSU is REAL

           SNU       (output)
                     SNU is COMPLEX
                     The desired unitary matrix U.

           CSV       (output)
                     CSV is REAL

           SNV       (output)
                     SNV is COMPLEX
                     The desired unitary matrix V.

           CSQ       (output)
                     CSQ is REAL

           SNQ       (output)
                     SNQ is COMPLEX
                     The desired unitary matrix Q.



LAPACK routine                  31 October 2017                      CLAGS2(3)