NAME

       clags2.f -

SYNOPSIS

   Functions/Subroutines
       subroutine clags2 (UPPER, A1, A2, A3, B1, B2, B3, CSU, SNU, CSV, SNV, CSQ, SNQ)
           CLAGS2

Function/Subroutine Documentation

   subroutine clags2 (logical UPPER, real A1, complex A2, real A3, real B1, complex B2, real B3,
       real CSU, complex SNU, real CSV, complex SNV, real CSQ, complex SNQ)
       CLAGS2

       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.

       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 REAL

           A2

                     A2 is COMPLEX

           A3

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

           B1

                     B1 is REAL

           B2

                     B2 is COMPLEX

           B3

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

           CSU

                     CSU is REAL

           SNU

                     SNU is COMPLEX
                     The desired unitary matrix U.

           CSV

                     CSV is REAL

           SNV

                     SNV is COMPLEX
                     The desired unitary matrix V.

           CSQ

                     CSQ is REAL

           SNQ

                     SNQ is COMPLEX
                     The desired unitary matrix Q.

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           November 2011

Author

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