3/28a more bonus Matlab material

+ $for$ loops with a 2-D matrix as the loop range
+ $cell$ arrays
+ sieve of eratosthenes (for listing primes up to N), $setxor$, $setdiff$
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$for$ loops, revisited

the loop range of a $for$ loop can be a 2D matrix:
the loop variable is successively assigned each column of the matrix

example:

    z = [3 1 4 ; 2 8 7]
    for i = z
        i
    end
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$cell$ arrays

limitation/restriction of matlab arrays:
+ arrays in matlab are *homogeneous*: 
  each element in an array must be of the same datatype
+ arrays in matlab are rectangular:
  each row is the same size; each column is the same size
+ note: these limitations are *not* necessarily bad:
  + rectangular, homogeneous arrays are often faster and smaller
  + the requirement that all elements be of the same datatype
    can detect if we accidentally try to store the wrong value
    in an array

matlab $cell$ arrays
+ $cell$ arrays are built using braces (${$ and $}$)
  instead of brackets ($[$ and $]$)
+ $cell$ arrays are *inhomogeneous*:
  each element can be of a different datatype, including another cell array
+ a $cell$ array of arrays allows us to simulate/implement arrays
  that are ragged in one dimension.

examples:

    { 'hi', 5, struct('a', 7, 'b', 28) } % ok
    [ 'hi', 5, struct('a', 7, 'b', 28) ] % not ok
    { [3] ; [5 -7] ; [] ; [4 -2 28] } % ok, effectively ragged
    [ [3] ; [5 -7] ; [] ; [4 -2 28] ] % not ok
    { 5, { 5 }, '5', { ' 5' } }
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sieve of eratosthenes
+ given integer $N>=0$, this is an algorithm to list primes up to $N$
+ reminder: 1 is not considered to be prime

algorithm:

    list integers from 1 to $N$
    cross 1 off the list
    for each integer $i$ from 1 to $N$
        if $i$ is not crossed off then
            cross off multiples of $i$ in list starting from $2*i$
    list non-crossed-off numbers

matlab code (given $N$):

    list = logical(ones(1,N)); % list(i) == "i is *not* crossed off?"
    list(1) = 0; % cross 1 off
    for i = 1:N
      if list(i)
          list(2*i:i:N) = 0;
      end
    end
    primes = find(list)

revised algorithm:

    list integers from 2 to $N$
    create empty list $primes$ of primes found so far
    while list is non-empty
        i <-- first (smallest) element of list
        put i on list $primes$
        delete *all* multiples of i from list (including i)
    display list $primes$

matlab code for revised algorithm (given $N$):

    list = 2:N;
    primes2 = [];
    while ~isempty(list)
        i = list(1);
        primes2 = [primes2 i];
        list(rem(list,i) == 0) = [];
    end
    primes2

code to check $primes1$ and $primes2$ agree, ignoring order and duplicates:

    if ~isempty(setxor(primes,primes2))
        fprintf('extra values in $primes$: '); 
        disp(setdiff(primes,primes2));
        fprintf('\nextra values in $primes2$: '); 
        disp(setdiff(primes2,primes));
    end