clags2 (l) - Linux Manuals
clags2: computes 2-by-2 unitary matrices U, V and Q, such that if ( UPPER ) then Uaq*A*Q = Uaq*( A1 A2 )*Q = ( x 0 ) ( 0 A3 ) ( x x ) and Vaq*B*Q = Vaq*( B1 B2 )*Q = ( x 0 ) ( 0 B3 ) ( x x ) or if ( .NOT.UPPER ) then Uaq*A*Q = Uaq*( A1 0 )*Q = ( x x ) ( A2 A3 ) ( 0 x ) and Vaq*B*Q = Vaq*( B1 0 )*Q = ( x x ) ( B2 B3 ) ( 0 x ) where U = ( CSU SNU ), V = ( CSV SNV ),
NAME
CLAGS2 - computes 2-by-2 unitary matrices U, V and Q, such that if ( UPPER ) then Uaq*A*Q = Uaq*( A1 A2 )*Q = ( x 0 ) ( 0 A3 ) ( x x ) and Vaq*B*Q = Vaq*( B1 B2 )*Q = ( x 0 ) ( 0 B3 ) ( x x ) or if ( .NOT.UPPER ) then Uaq*A*Q = Uaq*( A1 0 )*Q = ( x x ) ( A2 A3 ) ( 0 x ) and Vaq*B*Q = Vaq*( 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(
(
Zaq 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.