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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



     #include <sunperf.h>

     void clags2(int upper, float  a1,  complex  *a2,  float  a3,
               float  b1, complex *b2, float b3, float *csu, com-
               plex *snu, float *csv, complex *snv,  float  *csq,
               complex *snq);

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.

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