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 )
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 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. More
over, 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.
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.
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