zlags2()

subroutine zlags2	(	logical	upper,
		double precision	a1,
		complex*16	a2,
		double precision	a3,
		double precision	b1,
		complex*16	b2,
		double precision	b3,
		double precision	csu,
		complex*16	snu,
		double precision	csv,
		complex*16	snv,
		double precision	csq,
		complex*16	snq
	)

ZLAGS2

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Purpose:

 ZLAGS2 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.

Parameters

[in]	UPPER	UPPER is LOGICAL = .TRUE.: the input matrices A and B are upper triangular. = .FALSE.: the input matrices A and B are lower triangular.
[in]	A1	A1 is DOUBLE PRECISION
[in]	A2	A2 is COMPLEX*16
[in]	A3	A3 is DOUBLE PRECISION On entry, A1, A2 and A3 are elements of the input 2-by-2 upper (lower) triangular matrix A.
[in]	B1	B1 is DOUBLE PRECISION
[in]	B2	B2 is COMPLEX*16
[in]	B3	B3 is DOUBLE PRECISION On entry, B1, B2 and B3 are elements of the input 2-by-2 upper (lower) triangular matrix B.
[out]	CSU	CSU is DOUBLE PRECISION
[out]	SNU	SNU is COMPLEX*16 The desired unitary matrix U.
[out]	CSV	CSV is DOUBLE PRECISION
[out]	SNV	SNV is COMPLEX*16 The desired unitary matrix V.
[out]	CSQ	CSQ is DOUBLE PRECISION
[out]	SNQ	SNQ is COMPLEX*16 The desired unitary matrix Q.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.