NAME

       dlags2.f -

SYNOPSIS

   Functions/Subroutines
       subroutine dlags2 (UPPER, A1, A2, A3, B1, B2, B3, CSU, SNU, CSV, SNV, CSQ, SNQ)
           DLAGS2 computes 2-by-2 orthogonal matrices U, V, and Q, and applies them to matrices A
           and B such that the rows of the transformed A and B are parallel.

Function/Subroutine Documentation

   subroutine dlags2 (logical UPPER, double precision A1, double precision A2, double precision
       A3, double precision B1, double precision B2, double precision B3, double precision CSU,
       double precision SNU, double precision CSV, double precision SNV, double precision CSQ,
       double precision SNQ)
       DLAGS2 computes 2-by-2 orthogonal matrices U, V, and Q, and applies them to matrices A and
       B such that the rows of the transformed A and B are parallel.

       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.

       Parameters:
           UPPER

                     UPPER is LOGICAL
                     = .TRUE.: the input matrices A and B are upper triangular.
                     = .FALSE.: the input matrices A and B are lower triangular.

           A1

                     A1 is DOUBLE PRECISION

           A2

                     A2 is DOUBLE PRECISION

           A3

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

           B1

                     B1 is DOUBLE PRECISION

           B2

                     B2 is DOUBLE PRECISION

           B3

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

           CSU

                     CSU is DOUBLE PRECISION

           SNU

                     SNU is DOUBLE PRECISION
                     The desired orthogonal matrix U.

           CSV

                     CSV is DOUBLE PRECISION

           SNV

                     SNV is DOUBLE PRECISION
                     The desired orthogonal matrix V.

           CSQ

                     CSQ is DOUBLE PRECISION

           SNQ

                     SNQ is DOUBLE PRECISION
                     The desired orthogonal matrix Q.

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           September 2012

Author

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