CLAGS2(1) | LAPACK auxiliary routine (version 3.2) | CLAGS2(1) |
NAME¶
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 ),
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
( -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.
November 2008 | LAPACK auxiliary routine (version 3.2) |