CS99, Fall 2002
Lecture 5, Mon 9/23
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Announcements:
+ updates to website
+ H3 will posted
+ continue reading: Chapter 4
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(0) Topics
    + advice about communication
    + more about boolean things
    + more about selection statements
    + nested selection statements
    + logical arrays
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(1) Logic
    + Boolean: test logical TRUTH or FALSEHOOD
    + Boolean Expressions: expressions with boolean values and operators
    + logical values: 0 (false) and 1 (true)
    + logical operators: & (and), | (or), ~ (not), xor (exclusive or)
    + truth tables:

         AND	            OR	               NOT
        
          &   0   1         |   0   1           ~   
            +---+---+         +---+---+       +---+---+ 
          0 | 0 | 0 |       0 | 0 | 1 |       | 0 | 1 | 
            +---+---+         +---+---+       +---+---+ 
          1 | 0 | 1 |       1 | 1 | 1 |       | 1 | 0 | 
            +---+---+         +---+---+       +---+---+ 
      
    + relational operators: >, >=, <, <=, ==, ~=

    + examples) 
      >> 1 < 2            % less than
      >> 1 == 1           % equal (true)
      >> 1 == 2           % equal (false)
      >> 1==1   &   2==2  % true
      >> 1 > 2  |  1 < 2  % true
      >> xor(1 < 2,1 < 3) % false
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(2) Selection statements

    + General form of the $if$ statement is
 
      IF expression
        statements
      ELSEIF expression
        statements
      ELSE
        statements
      END

    + Must have $if$ and $end$
    + $else$ and $elseif$s are optional
    + see also $switch$
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(3) Nested selection statements

    + Any of the statements portion of the "statements" in the if-syntax
      can be ... you guessed it ... any legal statement!
    + So, you can have more if-statements "inside another if!
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(4) Logical Arrays (see pg 157)
    + an array of logical values
    + operations are applied to each element one at a time
    + MATLAB stores 1 or 0 depending on the truth of the relation for 
      each element
    + example)
      >> x = [1 2 3];
      >> y = x >= 2
      y =
         0 1 1
    + To extract elements that correspond to TRUE relations, use
      array(logicalarray).

    + example)
      >> x(y)
      ans = 
           2 3

    + example) Find even integers from an array.
      >> z = 0:10;         % array from 0 to 10
      >> k = mod(z,2)==0;  % $k$ is a logical array
      >> z(k)              % extract even integers from $k$
      ans = 
            0 2 4 6 8 10

    + WARNING:
      To generate logical array, MUST use relations, not just enter 0 and 1!

    + example)
      >> z=3:5;     % array of ints from 3 to 5
      >> q=[0 1 0]; % array of what appears to be logical values (but isn't!)
      >> z(q)       % attempt to extract elements from $z$ (but won't work)
   
      output is the error mesg: 
        ??? Index into matrix is negative or zero. See release notes on 
        changes to logical indices.

      To fix, use $logical$ function:
      >> z(logical(q))
      ans = 
            4
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