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ZLAGS2(l)					)					ZLAGS2(l)

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 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 ),
       ( -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) element 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 triangular.
	       = .FALSE.: the input matrices A and B are lower triangular.

       A1      (input) DOUBLE PRECISION
	       A2      (input) COMPLEX*16 A3	  (input) DOUBLE PRECISION On entry, A1,  A2  and
	       A3 are elements 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 elements 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.

LAPACK version 3.0			   15 June 2000 				ZLAGS2(l)
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