NAME
CLAGS2 - compute 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 )
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 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 ), ( -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.
ČLÁNKY DO MAILU