NAME¶

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 ),

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 )
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) 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.