% ECE 1250 S12 Lecture M8

%-------------------------------------------------------------------------------
% 3-D plots example using meshgrid()
%-------------------------------------------------------------------------------
% Rough notes.  (Cleaner version will be posted later.)
[xx,yy]=meshgrid(1:4,1:5)
xx =
     1     2     3     4
     1     2     3     4
     1     2     3     4
     1     2     3     4
     1     2     3     4
yy =
     1     1     1     1
     2     2     2     2
     3     3     3     3
     4     4     4     4
     5     5     5     5
z = cos(2*pi*(3*xx-4*yy)*0.1)
z =
    0.8090    0.3090   -1.0000    0.3090
   -1.0000    0.3090    0.8090   -0.8090
    0.8090   -0.8090   -0.3090    1.0000
   -0.3090    1.0000   -0.3090   -0.8090
   -0.3090   -0.8090    0.8090    0.3090
surfl(xx,yy,z)

%-------------------------------------------------------------------------------
% Random numbers--a reminder
%-------------------------------------------------------------------------------
A = rand(3,4)  % The rand() function generates numbers uniform between 0 and 1
A =
    0.8147    0.9134    0.2785    0.9649
    0.9058    0.6324    0.5469    0.1576
    0.1270    0.0975    0.9575    0.9706

A = randn(3)  % The randn() function generates normally distributed random #'s
              %  with standard deviation = 1.   (Bell curve)
A =
    0.2730   -0.4319    0.5875
   -0.4326   -0.6097    0.4596
    0.1270    0.0795   -0.5957

% When functions that create matrices have only one argument, they create square
%  matrices.






%-------------------------------------------------------------------------------
% And and Or operators
%-------------------------------------------------------------------------------
% Logical operators.
% > < >= <= == ~=
% We use And and Or operators to create compound logical comparisons.
% scalar logic: and = &&, or = ||  (Will not be discussed further.)
% compound operators: and = &, or = |

% Create some matrices for the examples.
A = [1,2;3,5]
A =
     1     2
     3     5
B = [2,2;1,5]
B =
     2     2
     1     5

% A nonzero value is considered True.  Here is the Or operator in action.
A | B
ans =
     1     1
     1     1

% Here, we find out if a comparison is true in the == case OR in the < case:
A == B | A < B
ans =
     1     1
     0     1
% Note, we have an element-by-element logical OR of the results of the == and <:
A == B
ans =
     0     1
     0     1
A < B
ans =
     1     0
     0     0
% If there is a 1 in a given position of either result, we get a 1 in that
%  position in the A == B | A < B comparison.

% Here is the And operation.  There is no position in the comparison matrices
%  where both matrices have a 1.
A == B & A < B
ans =
     0     0
     0     0




%-------------------------------------------------------------------------------
% Any and All operators
%-------------------------------------------------------------------------------
% Recall that we can use the Any and All functions to determine the outcome of
%  a comparison.  These functions are similar to And and Or operators.
any(A == B)
ans =
     0     1
any(any(A==B))
ans =
     1
all(A == B)
ans =
     0     1
% Processes cols

%-------------------------------------------------------------------------------
% If else control flow
%-------------------------------------------------------------------------------
% If statements allow us to change the instructions we execute based on values
%  of variables.
% In the following example, the display() will only be executed if Every entry
%  of A < 3 is True (equal to 1).
if A < 3
  display('A < 3 was TRUE')
end
% Note that every "if" must be closed by an "end" statement.
% Note that we may have multiple lines of code between the "if" and "end".

% The above construct is equivalent to the following statements.
if any(any(A<3))
  display('A < 3 was TRUE')
end
A < 3 was TRUE
A<3
ans =
     1     1
     0     0

% In the following example, the second display() (in the "else" will be executed
%  if the "if" condition fails.
if A>0
  display('A > 0 was TRUE')
else
  display('not A > 0')
end
% Output:
A > 0 was TRUE




The else is optional.
if A < 3
  display('A < 3 was TRUE')
end
% Output:  (no output since A < 3 did not produce all 1's)


% Can also do if ... elseif ... elseif ... else ... end
%  In such a construct, the successive conditions are checked.  If none of
%  them is true, the final "else" is executed.
if A == eye(2)
  display('A is a 2x2 identity matrix.')  % Indent to show level of if
elseif A == zeros(2)
  display('A is a 2x2 zeros matrix.')
  A = eye(2);   % Put any code you like inside if statements.
else
  display('A is neither zeros nor identity.')
  A = zeros(2);
end