DLAGS2(3)      LAPACK routine of NEC Numeric Library Collection      DLAGS2(3)



NAME
       DLAGS2

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



PURPOSE
            DLAGS2 computes 2-by-2 orthogonal matrices U, V and Q, such
            that if ( UPPER ) then

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

            or if ( .NOT.UPPER ) then

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

            The rows of the transformed A and B are parallel, where

              U = (  CSU  SNU ), V = (  CSV SNV ), Q = (  CSQ   SNQ )
                  ( -SNU  CSU )      ( -SNV CSV )      ( -SNQ   CSQ )

            Z**T denotes the transpose of Z.




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 DOUBLE PRECISION

           A2        (input)
                     A2 is DOUBLE PRECISION

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

           B1        (input)
                     B1 is DOUBLE PRECISION

           B2        (input)
                     B2 is DOUBLE PRECISION

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

           CSU       (output)
                     CSU is DOUBLE PRECISION

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

           CSV       (output)
                     CSV is DOUBLE PRECISION

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

           CSQ       (output)
                     CSQ is DOUBLE PRECISION

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



LAPACK routine                  31 October 2017                      DLAGS2(3)