# clags2 (l) - Linux Man Pages

## NAME

CLAGS2 - computes 2-by-2 unitary matrices U, V and Q, such that if ( UPPER ) then Uaq*A*Q = Uaq*( A1 A2 )*Q = ( x 0 ) ( 0 A3 ) ( x x ) and Vaq*B*Q = Vaq*( B1 B2 )*Q = ( x 0 ) ( 0 B3 ) ( x x ) or if ( .NOT.UPPER ) then Uaq*A*Q = Uaq*( A1 0 )*Q = ( x x ) ( A2 A3 ) ( 0 x ) and Vaq*B*Q = Vaq*( 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
-CONJG(SNU)  CSU      -CONJG(SNV) CSV )

CSQ      SNQ )

-CONJG(SNQ)  CSQ )
Zaq 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.