Mvmult_n_unb_var2B.m

% Copyright 2023 The University of Texas at Austin
%
% For licensing information see
%                http://www.cs.utexas.edu/users/flame/license.html 
%                                                                                 
% Programmed by: Anni Liu

% Interpret the function: http://edx-org-utaustinx.s3.amazonaws.com/UT501x/PictureFLAME/PictureFLAME.html

function [ y_out ] = Mvmult_n_unb_var2B( A, x, y )

  [ ATL, ATR, ...
    ABL, ABR ] = FLA_Part_2x2( A, ...
                               0, 0, 'FLA_TL' );

  [ xT, ...
    xB ] = FLA_Part_2x1( x, ...
                         0, 'FLA_TOP' );

  [ yT, ...
    yB ] = FLA_Part_2x1( y, ...
                         0, 'FLA_TOP' );

  while ( size( ATL, 1 ) < size( A, 1 ) )

    [ A00,  a01,     A02,  ...
      a10t, alpha11, a12t, ...
      A20,  a21,     A22 ] = FLA_Repart_2x2_to_3x3( ATL, ATR, ...
                                                    ABL, ABR, ...
                                                    1, 1, 'FLA_BR' );

    [ x0, ...
      chi1, ...
      x2 ] = FLA_Repart_2x1_to_3x1( xT, ...
                                    xB, ...
                                    1, 'FLA_BOTTOM' );

    [ y0, ...
      psi1, ...
      y2 ] = FLA_Repart_2x1_to_3x1( yT, ...
                                    yB, ...
                                    1, 'FLA_BOTTOM' );

    %------------------------------------------------------------%

    y0 = chi1 * alpha01 + y0;
    psi1 = chi1 * alpha11 + psi1;
    y2 = chi1 * a21 + y2; 

    %------------------------------------------------------------%

    [ ATL, ATR, ...
      ABL, ABR ] = FLA_Cont_with_3x3_to_2x2( A00,  a01,     A02,  ...
                                             a10t, alpha11, a12t, ...
                                             A20,  a21,     A22, ...
                                             'FLA_TL' );

    [ xT, ...
      xB ] = FLA_Cont_with_3x1_to_2x1( x0, ...
                                       chi1, ...
                                       x2, ...
                                       'FLA_TOP' );

    [ yT, ...
      yB ] = FLA_Cont_with_3x1_to_2x1( y0, ...
                                       psi1, ...
                                       y2, ...
                                       'FLA_TOP' );

  end

  y_out = [ yT
            yB ];

return

% Test the function
% A = randi( [ -2, 2 ], 4, 4 )
% x = randi( [ -2, 2 ], 4, 1 )
% y = randi( [ -2, 2 ], 4, 1 )

% if ( isequal( Mvmult_n_unb_var2B( A, x, y ), A * x + y ) )
%     disp( 'Mvmult_unb_var2B appears to be correct' )
% else
%     disp( 'Mvmult_unb_var2B has a problem' )
% end