MATLAB GLOSSARY
(as of September 21)
--------------------

MATLAB "Things":

  integers: 
    1, 2, 3
  real numbers: 
    1.23, -0.004, 5.67e8, 9.12E-4
  complex numbers: 
    mathematically, "a+bi".  
  logical variables: 
    a = true, b = false, c = ( x < 10 )
  strings: 
    'a', 'Baby', 'Cat in a hat.', 'My child''s age is 7.'
  vectors (lists of data): 
    [],
    [ a, b ], 
    [ 1, 3, 5, 7 ], 
    [ 'Mon', 'Tue', 'Wed', 'Thu', 'Fri' ]
  matrices: (coming soon)

Special Names:

  eps        the smallest number you can add to 1; 
  Inf        the result of computations like 1/0
  NaN        the result of computations like 0/0
  pi
  realmax    the largest real number MATLAB can handle
  realmin    the smallest positive real number MATLAB can handle

Arithmetic:

  A + 1     B - 2.3   C * D     E / F    G^2

Math functions:

  y = abs ( x )
  y = acos ( x )          inverse cosine
  y = asin ( x )          inverse sine
  y = atan ( x )          inverse tangent
  y = ceil ( x )          round a real number up to an integer
  y = cos ( x )
  y = exp ( x )           "e to x" function
  y = factorial ( n )     1*2*3*...*n
  y = floor ( x )         round a real number down to an integer
  y = gcd ( m, n )        Greatest common divisor;  gcd(30,24) is 6.
  y = humps ( x )         an example function to plot or minimize
  x = input ( 'Enter a value for x:' )  asks user to input value (for scripts)
  tf = isprime ( n )      true if integer n is a prime number.
  y = lcm ( m, n )        Least common multiple;    lcm(6,20) is 60.
  y = log ( x )
  y = log2 ( x )
  y = log10 ( x )
  z = max ( x, y )
  z = min ( x, y )
  r = mod ( x, y )        remainder from division x/y   mod(32,5) is 2
  m = nchoosek ( n, k )   the binomial coefficient "n choose k"
  y = rand ( )            random real 0 < x < 1.
  n = randi ( [ a, b ] )  random integer a <= i <= b.
  y = round ( x )         round a real number to the nearest integer.
  y = sin ( x )
  y = sqrt ( x )
  y = tan ( x )

Assignment statements:

      sqrt(x)    computes the value, stores it as "ans", displays it.
  y = sqrt(x)    computes the value, stores it as "y", displays it.
  y = sqrt(x);   computes the value, stores it as "y".

Logical operators:

  x <  y
  x <= y
  x >  y
  x >= y
  x == y            x is equal to y       Careful!  TWO equal signs needed!
  x ~= y            x is not equal to y

  x < y && y < z          x is less than y AND y is less than z   
  x < y || y < z          x is less than y OR  y is less than z
  ~ ( x == 0 && y == 0 )  it's NOT the case that both x and y are zero.

Logical control:

  if ( x < y )
    fprintf ( ' X is smaller than Y!\n' );
  end

  if ( x <= y && y <= z )
    disp ( '  Y is between X and Z.' )
  end

  if ( 0 <= x )
    y = sqrt ( x );
  else
    y = sqrt ( -x );
  end

  if ( 0 <= x )
    pos = pos + 1;
  elseif ( x == 0 )
    zero = zero + 1;
  else
    neg = neg + 1;
  end

FOR loops, nested FOR loops, the BREAK statement:

  for i = 1 : n
    commands to repeat
  end

  Variations on the FOR statement include:

    for i = 10 : 9           (does nothing)
    for i = 10 : 10          10
    for i = 10 : 20          10, 11, 12, ..., 19, 20
    for i = 10 : 2 : 20      10, 12, 14, ..., 18, 20
    for i = 20 : -1 : 10     20, 18, 16, ..., 12, 10

  for i = 1 : 100
    x = rand ( );
    if ( 0.95 < x )
      fprintf ( '  Jumping out on step %d\n', i );
      break;              <-- terminates loop early.
    end
  end

  for i = 1 : m
    for j = 1 : n
      fprintf ( ' %d', 10 * i + j );
    end
    fprintf ( '\n' );
  end

WHILE loops: repeat "as long as" some condition is true

  while ( condition )
    commands to carry out, because condition is true
  end

  sum = 0;
  k = 0;
  while ( sum < 100 )
    k = k + 1;
    sum = sum + k;
  end

  A "do forever" version of WHILE lets you check conditions any time:

  while ( true )
    commands to carry out;
    if ( condition )
      break
    end
    other commands
  end

Printing:

  x                                           displays x (unformatted)
  x;                                          no display
  y = x + 1                                   sets y, and displays y (unformatted)
  y = x + 1;                                  sets y, no display

  fprintf ( '  The value of x is %f', x );    Prints
  fprintf ( '  The value of x is %f\n', x );  Prints, then starts new line.

  format long                                 16 digit real printout
  format short                                6 digits real printout

  disp ( 'Cannot divide by zero!' )           Displays a string.  
  fprintf ( 'Cannot divide by zero!\n' );     Also displays a string.

  disp ( '' )                                 Prints a blank line.
  fprintf ( '\n' );                           Prints a blank line.

  disp ( 'Can''t divide by zero!' )           Type apostrophe TWICE in strings.
  fprintf ( '  4 %% is a low rate );          Type percent TWICE in strings.

  fprintf() formats:

  %f     print a real number with "fixed point" format.
  %10f   print a real number, using 10 spaces
  %7.2f  print a real number, using 7 spaces, with 2 decimal places
  %.2f   print a real number, using 2 decimal places

  %e     print a real number with "exponential" format (scientific notation).
  %g     print a real number with "general" format (fixed or exponential).

  %d     print the value as an integer
  %10d   print the value as an integer, using 10 spaces

Lists (a simple version of vectors);

  xlist = [];  defines a list with nothing in it;
  xlist = [ xlist, x ]; adds the value x to the end of list xlist
  xlist = [ 1, 2, 3, 4 ]; makes a list with entries 1, 2, 3, and 4.

Plots:

  clf
    clears the current graphics data, leaving a blank plot.

  plot ( xlist, ylist ) 
    where xlist and ylist are lists of x and y data, of the same length.

  plot ( xlist1, ylist1, xlist2, ylist2 )
    plots two sets of data on one graph.

  plot ( ylist )
    plots the data in ylist, using X coordinates 1, 2, 3, ..., N.

  plot ( xlist, ylist, 'LineWidth', 3 )
    plots the graph with a line that is 3 pixels wide (default is 1)

  plot ( xlist, ylist, 'r-' )
    plots the graph using a RED line.
    Color options are 'r', 'g', 'b', 'c', 'm', 'y', 'k', 'w'
    red, green, blue, cyan, magenta, yellow, black, white.

  plot ( xlist, ylist, 'b*' )
    plots the data using BLUE stars, but no lines connect the points.

  plot ( xlist, ylist, 'go-' )
    plots the data using a GREEN line, with circles at data points.

  grid on
    will add grid lines
  title ( 'YOUR TITLE HERE' )
    puts a title above the plot
  xlabel ( 'X Label' )
    puts a label along the X axis
  ylabel ( 'Y Label' )
    puts a label along the Y axis

  hold on
    allows you to issue more plot() commands, whose results will appear on
    the same graph

  hold off
    stops using the current graph for plot output.  The next plot() command
    will appear without any old data.

  axis off
    Don't show the x and y axis and the box, usually surrounding the graph.

  axis equal
    Use the same scale for the x and y axes.  Useful if you want to draw
    a circle, or you want a sine curve plot to look right.

  print ( '-djpeg', 'name.jpg' ) 
    saves a copy of the current plot as a JPEG file.
  print ( '-dpng', 'name.png' )
    saves a copy of the current plot as a PNG file.

  Polygons:

    fill ( xlist, ylist, color )
      draws the shape outlined by the points in xlist and ylist, and
      fills it with the given color.  
      COLOR can be 'r', 'g', 'b', 'c', 'm', 'y', 'k', 'w'.
      COLOR can be a list of three RGB values, each between 0 and 1.
      orange = [ 1.0, 0.4, 0.0 ];
      maroon = [ 0.4, 0.0, 0.0 ];

    plot ( xlist, ylist )
      can be used to draw a polygon.  However, you have to add a copy of the
      first x value to the end of the xlist, and the first y value to the end of
      the y list, in order for the polygon to be drawn completely.  

  Bar plota:

  bar ( ylist ) 
    will create a bar graph of the y values in ylist.
    The y values will have x "coordinates" 1, 2, 3, ...

  bar ( xlist, ylist )
    will create a bar graph where a bar of height y is drawn
    at coordinate x, for each pair if x and y values in xlist and ylist.

Sequences defined by a formula:

  * Sequences are represented as a(i), where i is an index (an integer)

  * Mathematical sequences might start at a(0) or a(1).

  * Print sequence elements 0 through n:

    for i = 0 : n
      value = FORMULA based on i;
      fprintf ( ' %d', value );
    end
    fprintf ( '\n' );

  * Find first element for which CONDITION is true:

    i = 0;
    while ( true )
      value = FORMULA based on i;
      if ( CONDITION )
        break;
      end
      i = i + 1;
    end

Sequences define by "stepping stones" (recurrence):

  * Print sequence elements 0 through n:

    for i = 0 : n
      if ( i == 0 )
        value = INITIAL VALUE
      else
        value_old = value;
        value = FORMULA based on value_old;
      end
      fprintf ( ' %d', value );
    end
    fprintf ( '\n' );
  
  * Find first element for which CONDITION is true:

    i = 0;
    while ( true )
      if ( i == 0 )
        value = INITIAL VALUE
      else
        value_old = value;
        value = FORMULA based on value_old;
      end
      if ( CONDITION )
        break;
      end
      i = i + 1;
    end

Sequences define by TWO "stepping stones":

  * Print sequence elements 0 through n:

    for i = 0 : n
      if ( i == 0 )
        value = INITIAL VALUE #1
      elseif ( i == 1 )
        value_old = value
        value = INITIAL VALUE #2
      else
        value_oldest = value_old
        value_old = value;
        value = FORMULA based on value_old and value_oldest;
      end
      fprintf ( ' %d', value );
    end
    fprintf ( '\n' );
  
  * Find first element for which CONDITION is true:

    i = 0;
    while ( true )
      if ( i == 0 )
        value = INITIAL VALUE #1
      elseif ( i == 1 )
        value_old = value
        value = INITIAL VALUE #2
      else
        value_oldest = value_old
        value_old = value;
        value = FORMULA based on value_old and value_oldest;
      end
      if ( CONDITION )
        break;
      end
      i = i + 1;
    end

Miscellaneous:

  error ( 'Message' )                   print message, terminate script.

  cd ..          move MATLAB's current directory up one level
  cd dirname     move MATLAB's current directory to "dirname"
  clear          clears MATLAB's memory; all variable values are lost.
  clc            clear the command window.
  dir            list the files in the current directory
  doc sin        extensive help on "sin" function
  exit           exit MATLAB completely (lose unsaved work!)
  help sin       brief help on "sin" function
  ls             list the files in the current directory
  pause          MATLAB will wait until you hit RETURN before carrying out
                 the next command.
  pwd            what is the full name of MATLAB's current directory?
  quit           exit MATLAB completely (lose unsaved work!)
  type filename  type the contents of the file "filename"
  %              begin a comment
  ...            continue this text on a new line
  Ctrl-C         force MATLAB to stop the current computation.

Parentheses:

  A + B * C
  ----------  must be written ( a + b * c ) / ( d + e )
  D + E

  F + G
  -----       must be written ( f + g ) / ( 2 * h )
  2 H

                  2
 1     - ( x - y )
 -   e              must be written ( 1 / 2 ) * exp ( - ( ( x - y )^2 ) )
 2 

     2 
  sin  pi x         must be written ( sin ( pi * x ) ) ^ 2