Implment laff_norm2

* Still rounding issues

Homework/Week1/laff_dot.m

@@ -47,7 +47,7 @@ y_out = y;
 
     alpha = 0;
     for i = 1:max(size(x))
-        alpha += y(i) * x(i)
+        alpha += y(i) * x(i);
     end
     
 endfunction

Homework/Week1/laff_norm2.m

@@ -0,0 +1,44 @@
+## Copyright (C) 2018 julien Lengrand-Lambert
+## 
+## This program is free software; you can redistribute it and/or modify it
+## under the terms of the GNU General Public License as published by
+## the Free Software Foundation; either version 3 of the License, or
+## (at your option) any later version.
+## 
+## This program is distributed in the hope that it will be useful,
+## but WITHOUT ANY WARRANTY; without even the implied warranty of
+## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+## GNU General Public License for more details.
+## 
+## You should have received a copy of the GNU General Public License
+## along with this program.  If not, see <http://www.gnu.org/licenses/>.
+
+## Author: julien Lengrand-Lambert <jlengrand@juliens-MacBook-Pro.local>
+## Created: 2018-05-03
+function [ alpha ] = laff_norm2 (x)
+
+    function isVector = isVector(x)
+        isVector = (size(x, 1) == 1 || size(x, 2) == 1);
+    endfunction
+
+    if !isVector(x)
+        disp('Error : x not a vector');
+        alpha = 'FAILED';
+        return 
+    end
+
+    xmax = 0.0
+    for i=1:size(x, 1)
+        if abs( x( i ) > xmax ) 
+            xmax = abs( x( i ) );
+        end
+    end
+
+    x = laff_scal( 1/xmax, x );
+
+    % Use laff_dot to compute the length of x as sqrt( x' * x )
+    alpha = sqrt( laff_dot( x, x ) );
+
+    alpha *= xmax;
+    
+endfunction

Homework/Week1/test_norm2.m

@@ -0,0 +1,47 @@
+% Create a vector
+x = [
+1
+2
+3
+]
+
+% test with x column vector, comparing against matlab's norm function
+disp( 'compute length of column vector' )
+if ( isequal( laff_norm2( x ), norm( x ) ) ) 
+    disp( 'TEST PASSED' )
+else
+    disp( 'TEST FAILED.  But could this be due to roundoff?  Lets check:' )
+    disp( 'laff_norm2( x ):' )
+    disp( laff_norm2( x ) )
+    disp( 'norm( x, 2 ):' )
+    disp( norm( x, 2 ) )
+end
+
+disp( ' ' )
+
+% test with x row vector, comparing against matlab's norm function
+disp( 'compute length of row vector' )
+if ( isequal( laff_norm2( x' ), norm( x ) ) ) 
+    disp( 'TEST PASSED' )
+else
+    disp( 'TEST FAILED  But could this be due to roundoff?  Lets check:' )
+    disp( 'laff_norm2( trans(x) ):' )
+    disp( laff_norm2( x' ) )
+    disp( 'norm( x, 2 ):' )
+    disp( norm( x, 2 ) )
+end
+
+disp( ' ' )
+
+% test with illegal x
+x = [
+    2 3
+    -1 -2
+    ];
+
+disp( 'illegal x' )
+if ( isequal( laff_norm2( x ), 'FAILED' ) ) 
+    disp( 'TEST PASSED' )
+else
+    disp( 'TEST FAILED' )
+end

Programming/laff/vecvec/laff_norm2.m

@@ -17,7 +17,7 @@ if ( m_x ~= 1 & n_x ~= 1 )
     return
 end
 
-xmax = 0.0
+xmax = 0.0;
 for i=1:m_x
     if abs( x( i ) > xmax ) 
         xmax = abs( x( i ) );