CLAGS2(3F) CLAGS2(3F)
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
),
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
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.
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.
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CLAGS2(3F) CLAGS2(3F)
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.
CLAGS2(3F) CLAGS2(3F)
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
),
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
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.
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.
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CLAGS2(3F) CLAGS2(3F)
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.
PPPPaaaaggggeeee 2222 [ Back ]
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