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 ),

As shipped in IRIX 6.5.15. Unchanged since IRIX 6.5.

NAME
     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
     ),

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.