09-nestedLoops.md

Nested loops

What happens when you nest loops?

1. Given a 2d array (matrix) X, write two nested for loops that traverse it and display the value and indeces on the command prompt

% the details of what X exactly represents are not that important here ;]
h = [1 2 3 9];
X = convmtx(h,6)

Your nested for loops should produce something like:

row=1, column=1, VALUE: 1
row=2, column=1, VALUE: 0
...
row=3, column=4, VALUE: 2
...
row=6, column=6, VALUE: 9

Hint 1 - loop over rows

Step one is to think about how to loop over one dimension of this table... row 1, 2, ..

• How big is X? Hard-code the number of rows

% how big is X?
size(X) % 6 by 6

for iRow = 1:6
   X(iRow, :)  % this picks each row in turn
end

% but better not to hard-code the number 6
nRows = size(X,1);
for iRow = 1:nRows
   X(iRow, :)  % this picks each row in turn
end

Hint 2 - loop over columns

Step two... the natural step is to try out the other way... we now need to put the index in the 2nd position!

nRows = size(X,1);
nColumns = size(X,2);

for iColumn = 1:nColumns
   X(:, iColumn)  % this picks each COLUMN in turn
end

Hint 3 - loop over both

Now, let's put those two things together. Read through the comments in the code and make sure you understand exactly what's happening. Draw a diagram of the matrix / table and indicate in which way the code steps through...

nRows = size(X,1);
nColumns = size(X,2);

% each time we go to a new row...
% we want then go through each column
for iRow = 1:nRows
    % loop over rows (this loop runs 6 times)
    % and each time we go to a new row (including the first)
    % step through each column... that ends up being a single element
    for iColumn = 1:nColumns
        % this loop runs 6 times for each row
        % so 6 x 6 times... 36
        X(iRow, iColumn)  % need to say which ROW and COLUMN
    end
end

2. How can you traverse across first? What changes are required in your code?

3. If you only wanted to have one loop, can you think of a way to traverse the whole matrix?

• by using only one index?
• by calculating the row and column numbers from the one counter?

Hint - linear indexing

Look up / google linear indexing and remind yourself how that can be used to "address" a particular element in the table/matrix.

4. Turn your code into a function that can handle 2D matrices of any size (square or rectangular).

• bonus: add reality / error checks to make sure the input is really 2D
• bonus: your function returns the sum of all elements (and as a second argument, the number of elements in the matrix)

Hint

Use if/else to check the number of dimensions; the command ndims() will help.

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