For Loops

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Misc

Colloquium

“Structure and Symmetry: An Introduction to Lie Algebras and Representation Theory”

By Chad Magnum, Niagara University

Friday, April 7, 2:30 PM, Newton 203

Extra credit as usual for writing a paragraph or so about connections you make to the talk

Friday’s Class

I’ll be out of town Friday (April 7)

Class will be led by Prof. Farian

Most likely a lab day for the numeric integration lab

Questions?

For Loops

Example 1. Write a loop that prints “I will not misuse loops” 100 times

Relevant ideas or questions from the reading

• for loops are good for doing a fixed number of iterations
• They require a start value, increment, and end value
  • Although the increment can actually be left out if it is 1

Solution

%% Print "I will not misuse loops" 100 times.
for count = 1 : 100
    fprintf( 'I will not misuse loops\n' )
end

Comments

• One of the important lessons from this is simply the syntax of a for loop: the keyword for, a variable that will step through a sequence of values, statements to execute for each one of those values, and the keyword end.
• The sequence of values that the variable steps through can actually be any vector, which is why the notation looks like the colon constructor for a vector (that’s exactly what it is).

Example 2. Given a natural number n, write a loop that calculates the sum of the first n odd numbers (e.g., if n = 1, the result is 1; if n = 2 the result is 1 + 3; if n = 3 the result is 1 + 3 + 5; etc.)

What is the kth odd number?

• If k = 1, 1st odd number = 1
• If k = 2, 2nd odd number = 3
• If k = 3, 3rd odd number = 5
• In general, kth odd number = 2k - 1

Solutions

• There are two ways to use the kth odd number = 2k - 1 idea. The first is to step through the odd numbers between 1 and the nth, adding them up along the way:

function total = oddSum( n )
%ODDSUM Find the sum of the first n odd numbers.
% e.g., if n = 2, result = 1 + 3
% e.g., if n = 3, result = 1 + 3 + 5
%
% Progamming idiom for keeping an accumulating result:
% total = initial value
% loop
%     update total
% end

total = 0;
for i = 1 : 2 : 2*n - 1
    total = total + i;
end

end

• The second is to step through just the numbers from 1 to n, calculating and adding up the ith odd number for each i:

function total = oddSum( n )
%ODDSUM Find the sum of the first n odd numbers.
% e.g., if n = 2, result = 1 + 3
% e.g., if n = 3, result = 1 + 3 + 5
%
% Progamming idiom for keeping an accumulating result:
% total = initial value
% loop
%     update total
% end

total = 0;
for i = 1 : n
    total = total + (2*i - 1);
end

end

Comments

• This is a more sophisticated loop than the one that printed “I will not misuse loops,” in that this loop uses the loop variable in the loop body.
• Notice the “keep an accumulating result” idiom mentioned in the comments for these functions: programming idioms are patterns in code that appear over and over again to solve common kinds of problem.

Example 3. write a loop that calculates the sum of the numbers in a vector v.

Solution

function y = vecSum( v )
%VECSUM Find the sum of the numbers in vector v

y = 0;
for i = v
    y = y + i;
end

end

Comments

• This example shows most clearly of any example today how the variable in a for loop steps through a vector, and how that fact might be used.

Next

Lab day to start the numeric integration lab.

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