CLAGS2(1) LAPACK auxiliary routine (version 3.2) CLAGS2(1)NAMECLAGS2 - 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
PURPOSECLAGS2 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) triangu‐
lar 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) triangu‐
lar 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.
LAPACK auxiliary routine (versioNovember 2008 CLAGS2(1)