Mathlab Tutorial

  Standard Matrices:

   >>rand(3)

   >>rand(3,5)

   >>hilb(3)

   >>magic(3)

   >>eye(3)

   >>zeros(3)

   >>ones(3)

   >>[1, 2, 3; 4, 5, 6; 7, 8, 9]

  Variables:

   >>pi

   >>eps

   >>who             <!--Note: used to display active variables-->

   >>ans              <!--Note: used to display the last output-->

   >>clear x         <!--Note: used to clear variables; x is the variable name-->

  Functions:

   >>a = magic(3)

   >>a'                <!--Note: transpose of a-->

   >>min(a)

   >>max(a)

   >>a.*b             <!--Note: entry by entry multiplication rather than matrix multiplication-->

   >>triu(a)

   >>tril(a)

   >>diag(a)

   >>size(a)

   >>sin(a)

   >>exp(a)

   >>log(a)

   >>abs(a)

   >>round(a)

   >>fix(a)

   >>ceil(a)

   >>floor(a)

   >>sum(a)

   >>prod(a)

  Relations and Logical Operations (1 = true and 0 = false)

   >>a & b           <!--and-->

   >>a | b            <!--or-->

   >>~a                <!--not-->

   >>a==b

   >>a<=b

   >>a>=b

   >>any(a)            <!--Note: determines if the matrix has at least one nonzero entry-->

   >>all(a)             <!--Note: determines if the matrix has all nonzero entries-->

  Uses of the Colon:

   >>y=-2:1            <!--Note: creates a matrix with values from -2 to 1-->

   >>y=-2:.5:1         <!--Note: creates a matrix with values from -2 to 1 with .5 intervals-->

   >>x(2, :)            <!--Note: displays elements in row 2-->

   >>x(:, 3)            <!--Note: displays elements in column 3-->

   >>x(1:2, 2:3)       <!--Note: displays elements in rows 1 and 2 from columns 2 to 3-->

   >>x(:, [1 3])        <!--Note: displays all row elements in columns 1 and 3-->

  Other Features:

   >>casesen         <!--Note: toggles case sensitivity on and off -->

   >>format long    <!--Note: display 16 digits -->

   >>format short   <!--Note: display only 5 digits -->

   >>a;                 <!--Note: semicolon is used to skip the display of the matrix -->

   >>save filename <!--Note: saves variable in a file called filename.mat -->

  Programming in Mathlab:

   1. Create a program file: myfile.m

   2. To run the program file: >>myfile

   3. Assignment program: mod.m

   function r=mod(a,d)

   % r=mod(a,d). If a and d are integers, then

   % r is the integer remainder of a after 

   % division by d. If a and b are integer matrices,

   % then r is the matrix of remainders after division

   % by corresponding entries. Compare with REM.


   r=a-d.*floor(a./d); 


   To use the program: >>mod(a,b)


   4. Branching program:


   function b=even(n)


   % b=even(n). If n is an even integer, then b=1

   % otherwise, b=0.


   if mod(n,2)==0,

      b=1;

      else b=0;

   end


   5. For loop program:


   function c=add(a,b)


   % c=add(a,b). This is the function which adds 

   % the matrices a and b. It duplicates the MATLAB 

   % function a+b.


   [m,n]=size(a);

   [k,l]=size(b);

   if m~=k | n~=l,

      r='ERROR using add: matrices are not the same size';

      return, 

   end

   c=zeros(m,n);

   for i=1:m,

      for j=1:n,

         c(i,j)=a(i,j)+b(i,j);

      end

   end


   6. While loop program:


   function l=twolog(n)


   % l=twolog(n). l is the floor of the base 2

   % logarithm of n.


   l=0;

   m=2;

   while m<=n

      l=l+1;

      m=2*m;

   end


   7. Recursion program:


   function y=twoexp(n)


   % y=twoexp(n). This is a recursive program for computing

   % y=2^n. The program halts only if n is a nonnegative integer.


   if n==0, y=1;

      else y=2*twoexp(n-1);

   end