% Moed 09A bio  MatlabBio 76623   20/7/09 
% solution by Roie Knaanie 
% part A 

clc
clear
format compact

%% 1
C = [1 0 1;0 1 0;1 0 1].*ones(3)
B = 2.5 + rand(3)
D = (C&B') < ~C*2

% D =
%      0     1     0
%      1     0     1
%      0     1     0

%% 2
A = [1 2 3;2 3 4;4 1 3] .* (ones(3).^2)
G = A(2:3,1:2)* A(1:2,2:3)

%  A(2:3,1:2)  * A(1:2,2:3)
%      2     3 *  2   3
%      4     1    3    4
% 
% G =
%     13    18
%     11    16

%% 3
N = rand(6); x = 14:-2:4
L = eye(2) + length( N'\x') 

% x =
%     14    12    10     8     6     4
% L =
%      7     6
%      6     7
     
%% 4
B = [ zeros(3,2) fliplr(rand(3)+1.5) ]
B(1,7) = -5
D = all(B ~= 0)

% B =
%          0         0    2.2513    1.8404    1.6190         0   -5.0000
%          0         0    1.7551    2.0853    1.9984         0         0
%          0         0    2.0060    1.7238    2.4597         0         0
% D =
%      0     0     1     1     1     0     0

%% 5
A = ones(4)-eye(4)*2
m = 1:size(A,2)
A(2,:) = A(2,:)+ mod(m,3)

% m =
%      1     2     3     4
% A =
%     -1     1     1     1
%      2     1     1     2
%      1     1    -1     1
%      1     1     1    -1
%% 6
v = 0:5
e = (v+1)>mean(v-1)
z = mean( find( e>0 ))

% v =
%      0     1     2     3     4     5
% e =
%      0     1     1     1     1     1
% z =
%      4

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% PART B - Q1
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

function [D A]= filter_noise( A ) 
% Moed 09A   MatlabBio part B - q1)
if nargin<1  
    clear, clc
    format compact
%     A = fix( rand(12,7)*10 )  - 1; 
A = [0     5     6     2    -1     0
       5     6     5     3     8    -3
       6    -1     2     1     8     2
       5     8     7     7    -2     3
       3     6     4    -4     0     3 ]

end

[N,M] = size(A) ;
D = A;  % initialization

for i= 1:N
    for j= 1:M
        if A(i,j) < 0
            if i==1 || i==N || j==1 || j==M   % found a negative cell on the frame
                D(i,j)  = 0 ;
            else
                S = sum( sum( A(i-1:i+1, j-1:j+1) )) - A(i,j) ; % sum of the 8 neighbours of A(i,j) 
                D(i,j) = S / 8;   % store the average in D(i,j)
            end     
        end
    end
end

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% PART B - Q2
%%%%%%%%%% 
function R = isSymmetric(A)
% Moed 09A   MatlabBio part B - q2)
% check with: M = magic(4); A = M + M'    
R = true;   % initialization

[N, M] = size(A);
if N ~= M    % check if A is square
    R = false;
    return;  % or: error('A is not square!');
                        % the return statement is optional here
end

for i = 1:N
    for j = i:N
        if( A(i,j) ~= A(j,i) )
            R = false;
        end
    end
end

%{
function R = isSymmetric(A) 
% much shorter version:
[N, M] = size(A);
R = all(all(A==A'))  & N==M
%}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% PART C - Q3
%%%%%%%%%%

function v = f3(A)
% Moed 09A   MatlabBio part C - q3)
% f3 gets a matrix of integers A as input,
% and returns v. What is v?   
% try  A = [ 1 8 0 3 ;2 0 0 -4]    
[m,n] = size(A);
v = zeros(1,n);

for k = 1:n
    c= A(:,k) ~=0 ;
    sc = sum( c );
    v(k) = sc > 0;
end

%{A = [ 1 8 0 3 ;2 0 0 -4]  
% A =
%      1     8     0     3
%      2     0     0    -4
% v = f3(A)
% v =
%      1     1     0     1
%}

%{
 The solution: 
a) The output v is a vector
v = [  1     1     0     1 ]

b) f3 gets a matrix of integers A
and returns a vector v of  1/0 .
the elment
v(k) = 1 if the k column of A contains a nonzero number,
v(k) = 0 if the k column of A is all zeros.
Similar to the operation of: v = any(A)
%}