CLAGS2
Purpose
CLAGS2 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.
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.
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.
|