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.