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.

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.

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

December 2016