function []=prob_7_1_22()
%
% Written by:
% -- 
% John L. Weatherwax                2006-11-21
% 
% email: wax@alum.mit.edu
% 
% Please send comments and especially bug reports to the
% above email address.
% 
%-----
  
clc; close all; 

H = [ -6 -6 -7 0 7 6 6 -3 -3 0 0 -6 ;
      -7 2 1 8 1 2 -7 -7 -2 -2 -7 -7 ];

figure; 
x = H(1,:).'; y = H(2,:).'; axis( [ -20 20 -20 20 ] ); axis( 'square' );
plot( x, y, 'o' ); hold on; 
plot( x, y, '-' ); grid on; 
xlim( [ -20 20 ] ); ylim( [ -20 20 ] ); axis( 'square' );
title( 'the original house' ); 

A = [ 2 0 ; 0 1 ]; 
ah = A * H; 

figure; 
x = ah(1,:).'; y = ah(2,:).';
plot( x, y, 'o' ); hold on; 
plot( x, y, '-' ); grid on; 
xlim( [ -20 20 ] ); ylim( [ -20 20 ] ); axis( 'square' );
title( 'first A -- expands the x direction only' ); 

A = [ 0.7 0.7 ; 0.3 0.3 ]; 
ah = A * H; 

figure; 
x = ah(1,:).'; y = ah(2,:).';
plot( x, y, 'o' ); hold on; 
plot( x, y, '-' ); grid on; 
xlim( [ -20 20 ] ); ylim( [ -20 20 ] ); axis( 'square' );
title( 'second A -- collapse along a line');

A = [ 1 1 ; 0 1 ];
ah = A * H; 

figure; 
x = ah(1,:).'; y = ah(2,:).';
plot( x, y, 'o' ); hold on; 
plot( x, y, '-' ); grid on; 
xlim( [ -20 20 ] ); ylim( [ -20 20 ] ); axis( 'square' );
title( 'third A -- y component is constant');