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clags2

CLAGS2(l)								 )								 CLAGS2(l)

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 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) REAL
	       A2	(input)  COMPLEX  A3	   (input)  REAL On entry, A1, A2 and A3 are elements 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 elements 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.

LAPACK version 3.0						   15 June 2000 							 CLAGS2(l)