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zlags2

 NAME
      ZLAGS2 - 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 ZLAGS2( UPPER, A1, A2, A3, B1, B2, B3, CSU, SNU,
                         CSV, SNV, CSQ, SNQ )

          LOGICAL        UPPER

          DOUBLE         PRECISION A1, A3, B1, B3, CSQ, CSU, CSV

          COMPLEX*16     A2, B2, SNQ, SNU, SNV

 PURPOSE
      ZLAGS2 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) DOUBLE PRECISION
              A2      (input) COMPLEX*16 A3      (input) DOUBLE
              PRECISION On entry, A1, A2 and A3 are entries of the
              input 2-by-2 upper (lower) triangular matrix A.

      B1      (input) DOUBLE PRECISION
              B2      (input) COMPLEX*16 B3      (input) DOUBLE
              PRECISION On entry, B1, B2 and B3 are entries of the

              input 2-by-2 upper (lower) triangular matrix B.

      CSU     (output) DOUBLE PRECISION
              SNU     (output) COMPLEX*16 The desired unitary
              matrix U.

      CSV     (output) DOUBLE PRECISION
              SNV     (output) COMPLEX*16 The desired unitary
              matrix V.

      CSQ     (output) DOUBLE PRECISION
              SNQ     (output) COMPLEX*16 The desired unitary
              matrix Q.