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clags2

 NAME
      CLAGS2 - compute 2-by-2 unitary matrices U, V and Q, such
      that if ( UPPER ) then   U'*A*Q = U'*( A1 A2 )*Q = ( x 0 )
      ( 0 A3 ) ( x x ) and  V'*B*Q = V'*( B1 B2 )*Q = ( x 0 )  ( 0
      B3 ) ( x x )  or if ( .NOT.UPPER ) then   U'*A*Q = U'*( A1 0
      )*Q = ( x x )  ( A2 A3 ) ( 0 x ) and  V'*B*Q = V'*( B1 0 )*Q
      = ( x x )  ( B2 B3 ) ( 0 x ) where   U = ( CSU SNU ), V = (
      CSV SNV ),

 SYNOPSIS
      SUBROUTINE CLAGS2( UPPER, A1, A2, A3, B1, B2, B3, CSU, SNU,
                         CSV, SNV, CSQ, SNQ )

          LOGICAL        UPPER

          REAL           A1, A3, B1, B3, CSQ, CSU, CSV

          COMPLEX        A2, B2, SNQ, SNU, SNV

 PURPOSE
      CLAGS2 computes 2-by-2 unitary matrices U, V and Q, such
      that if ( UPPER ) then
            ( -CONJG(SNU)  CSU )      ( -CONJG(SNV) CSV )

        Q = (     CSQ      SNQ )
            ( -CONJG(SNQ)  CSQ )

      Z' denotes the conjugate transpose of Z.

      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) entry of B is not zero, except when the first rows of
      input A and B are parallel and the second rows are zero.

 ARGUMENTS
      UPPER   (input) LOGICAL
              = .TRUE.: the input matrices A and B are upper tri-
              angular.
              = .FALSE.: the input matrices A and B are lower tri-
              angular.

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

      B1      (input) REAL
              B2      (input) COMPLEX B3      (input) REAL On
              entry, B1, B2 and B3 are entries of the input 2-by-2

              upper (lower) triangular matrix B.

      CSU     (output) REAL
              SNU     (output) COMPLEX The desired unitary matrix
              U.

      CSV     (output) REAL
              SNV     (output) COMPLEX The desired unitary matrix
              V.

      CSQ     (output) REAL
              SNQ     (output) COMPLEX The desired unitary matrix
              Q.