Some MATLAB Commands

Timing:
  Tic
    Start timer
  Toc
    Report time in seconds since "toc" command.

Functions:
  Powers:
    x^y; returns the Y-th power of X
  Floor:
    i = floor ( x ): round down to an integer.
  Sign:
    s = sign ( x );  +1 for positive, -1 for negative.  What happens at zero?
  Remainder:
    r = mod ( x, y ); returns the remainder after X is divided by Y.
  Allocate space:
    v = zeros ( m, 1 ); creates a column vector of length M
    w = zeros ( 1, n ); creates a row vector of length N
    A = zeros ( m, n ); creates an array of zeros of size MxN
  Set values:
    v = linspace ( first, last, howmany ); create row vector, evenly spaced values.
    v = [ 1; 2; 3 ]; creates a column vector.
    w = [ 1, 2, 3 ]; creates a row vector;
    A = [ 11, 12, 13; 21, 22, 23 ]; creates a 2x3 matrix.
  Set random values between 0 and 1:
    x = rand ( ); a single random number;
    v = rand ( m, 1 ); random column vector;
    w = rand ( 1, n ); randow row vector;
    A = rand ( m, n ); random matrix;
    B = rand ( m ); actually the same as rand ( m, m ), returns a MATRIX.
  Append a value:
    v = [ v, 1 ]; appends "1" to a row vector
    w = [ w; 1 ]; appends "1" to a column vector;
    This can also be done with matrices, but be careful!
  
Vector/array functions:
  Colon notation:
    1:n; means [ 1, 2, 3, ..., n ]
    1:2:10; means [ 1, 3, 5, ..., 9]
    10:-3:0 means [10, 7, 4, 1]
    v(2:4) means [ v(2), v(3), v(4) ]
    A(2,:) means row 2 of matrix A
    A(:,4) means column 4 of matrix A.
  Sum:
    s = sum ( v ); returns the sum of the entries in a vector;
    s = sum ( A ); returns a vector, the sum of each column of A.
    s = sum ( sum ( A ) ); returns a number, the sum of all entries of A.
  Minimum/Maximum (work similarly to Sum)
    v_min = min ( v )
    a_min = min ( A ); (column minimums)
    a_min = min ( min ( A ) ); (matrix minimum)
  Any:
    any ( v == 0 ) returns "TRUE" (actually, 1) if any entry of V is less than 1.
  All:
    all ( 0 <= w ) returns TRUE if all entries of W are greater than 1.
  "AND" (&) and "OR" (|) and "NOT" (~)
    if ( x < 0.0 & y < 0.0 ) ...
    if ( x == 0.0 | y == x ) ...
    if ( x ~= 0.0 ) ...
  FIND: index all entries for which condition is true
    i = find ( v < 0.0 )
  Transpose: MxN matrix becomes NxM matrix.
    A = A'
  Length: Number of entries in vector or matrix
    l = length ( v );
  Size: Returns number of rows and columns in vector or matrix
    [ m, n ] = size ( A );

Vector formulas:
  Multiplication:
    norm = sqrt ( v' * v ); if v is a column vector
    norm = sqrt ( w * w' ); if w is a row vector;
    v2 = A * v1; if A is MxN and V1 is Nx1 (column vector)
    w2 = A * w1'; if A is MxN and W1 is 1xN (row vector)
  Dotted operators: *, /, ^
    x = v1' * v2; computes a scalar;
    v3 = v1 .* v2; multiplies matching pairs of entries.
    v3 = v1 ./ v2; divides matching pairs of values.
    v3 = v1 .^ 2; squares each entry of v1.
    C = A * B; uses matrix multiplication
    C = A .* B; multiplies matching pairs of entries
    C = A^2; is the same as C = A * A, matrix multiplication.
    C = A.^2; squares each entry of A. 
  Solving linear systems:
    b = A \ x; solves A*x=b for the vector x. 

Loops:
  WHILE: do the loop again, if condition is true
    while ( x < 0.0 )
      x = x + 1;
    end
  IF / ELSEIF / ELSE ("elseif" has to be one word, not two!)
    if ( x < 0.0 )
      sign = -1.0;
    elseif ( x > 0.0 )
      sign = +1.0;
    else
      sign = 0.0;
    end

Printing:
  To print a variable, you can just name it, with no semicolon at the end:
    x
  You can use the "disp" command (which omits the variable name)
    disp x
  You can use the "fprintf(1,'STRING',LIST)" command:
    fprintf ( 1, '%g\n', x );                  one real number
    fprintf ( 1, '  n = %d\n', n );            one integer, with label.
    fprintf ( 1, '  x(%d) = %g\n', i, x(i) );  an integer and a real.

Plotting:
  plot ( x, y );
  plot ( x, y, 'r-' );
  plot ( x, y, 'r-', 'Linewidth', 3 );
  plot ( x, y, 'b*' )
  plot ( x, y, 'b*', 'Markersize', 25 );
  grid on
  title ( 'This is my title' )
  clf;  (clear the current screen, get rid of previous picture)
  hold on (I want to use several plot commands, but make a single plot)
  hold off (I am done with the multiple plots on one image)
  figure ( ); put this plot in a new figure box.
  figure ( 3 ): put this plot in figure box 3.

Read data from a file: (each row of the file must have the same number of values)
  xy = load ( 'filename' )