NAME

       zlags2.f -

SYNOPSIS

   Functions/Subroutines
       subroutine zlags2 (UPPER, A1, A2, A3, B1, B2, B3, CSU, SNU, CSV, SNV, CSQ, SNQ)
           ZLAGS2

Function/Subroutine Documentation

   subroutine zlags2 (logical UPPER, double precision A1, complex*16 A2, double precision A3,
       double precision B1, complex*16 B2, double precision B3, double precision CSU, complex*16
       SNU, double precision CSV, complex*16 SNV, double precision CSQ, complex*16 SNQ)
       ZLAGS2

       Purpose:

            ZLAGS2 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 DOUBLE PRECISION

           A2

                     A2 is COMPLEX*16

           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 COMPLEX*16

           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 COMPLEX*16
                     The desired unitary matrix U.

           CSV

                     CSV is DOUBLE PRECISION

           SNV

                     SNV is COMPLEX*16
                     The desired unitary matrix V.

           CSQ

                     CSQ is DOUBLE PRECISION

           SNQ

                     SNQ is COMPLEX*16
                     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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