.TH CLAGS2 1 "November 2006" " LAPACK auxiliary routine (version 3.1) " " LAPACK auxiliary routine (version 3.1) " .SH NAME CLAGS2 - 2-by-2 unitary matrices U, V and Q, such that if ( UPPER ) then U\(aq*A*Q = U\(aq*( A1 A2 )*Q = ( x 0 ) ( 0 A3 ) ( x x ) and V\(aq*B*Q = V\(aq*( B1 B2 )*Q = ( x 0 ) ( 0 B3 ) ( x x ) or if ( .NOT.UPPER ) then U\(aq*A*Q = U\(aq*( A1 0 )*Q = ( x x ) ( A2 A3 ) ( 0 x ) and V\(aq*B*Q = V\(aq*( B1 0 )*Q = ( x x ) ( B2 B3 ) ( 0 x ) where U = ( CSU SNU ), V = ( CSV SNV ), .SH SYNOPSIS .TP 19 SUBROUTINE CLAGS2( UPPER, A1, A2, A3, B1, B2, B3, CSU, SNU, CSV, SNV, CSQ, SNQ ) .TP 19 .ti +4 LOGICAL UPPER .TP 19 .ti +4 REAL A1, A3, B1, B3, CSQ, CSU, CSV .TP 19 .ti +4 COMPLEX A2, B2, SNQ, SNU, SNV .SH PURPOSE CLAGS2 computes 2-by-2 unitary matrices U, V and Q, such that if ( UPPER ) then ( -CONJG(SNU) CSU ) ( -CONJG(SNV) CSV ) .br Q = ( CSQ SNQ ) .br ( -CONJG(SNQ) CSQ ) .br Z\(aq denotes the conjugate transpose of Z. .br 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. .br .SH ARGUMENTS .TP 8 UPPER (input) LOGICAL = .TRUE.: the input matrices A and B are upper triangular. .br = .FALSE.: the input matrices A and B are lower triangular. .TP 8 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. .TP 8 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. .TP 8 CSU (output) REAL SNU (output) COMPLEX The desired unitary matrix U. .TP 8 CSV (output) REAL SNV (output) COMPLEX The desired unitary matrix V. .TP 8 CSQ (output) REAL SNQ (output) COMPLEX The desired unitary matrix Q.