Loop Statements

1. Loop Statements Chapter 4

2. Repeated Tasks are for Computers • Think back to any very difficult quantitative problem that you had to solve in some science class • How long did it take? • How many times did you solve it? • What if you had millions of data points that had to be processed using the same solution? • Only need to solve it once • Tell the computer to repeat n-times • This is the basis for the programming concept called a loop statement

3. Looping Statements in MATLAB MATLAB provides two types of loops • A counted loop • “for” • Used when you know ahead of time how many times some action will be repeated • Repeat n-times • A conditional loop • “while” • Used when you do not know ahead of time how many times some action will be repeated • Repeat until some logical statement becomes false

4. The For Loop • Used with a pre-defined number of iterations of the loop variable The “for” keyword (“for” is a reserved word in MATLAB) The loop variable, which can be any valid variable name Traditionally, we use i, j, k, or other single letters The range or list of values the loopVar will take on Can be any vector, but typically the colon operator is used The action(s) that will be performed during each iteration The “end” keyword. Signifies that the code should go back to beginning of the loop statement if more iterations remain for loopVar = range action(s) end

5. First For Loop • Lets make a simple for loop to see how everything works • During each iteration • Loop variable i is changed • i is printed using fprintf • Note that the actions must be indented • Makes code easier to read • MATLAB editor does this automatically

6. For Loop Examples • The loop variable can change by any increment • Most commonly the increment is 1

7. For Loop Examples • The loop variable can have positive or negative values • Most commonly values are positive • After loop is complete • Can still use the loop variable • Has the final value of the loop

8. For Loop Examples • The loop iterations can be defined by any vector • This is not typical • Whenever possible, use the colon operator

9. For Loop Examples A common use of a loop: • perform an operation on each and every data point, one by one. • Doesn’t matter how many data points there are* *Obviously, there is some limit based on your computer’s RAM, CPU speed, and operating system

10. For Loop Examples • Lets mimic the behavior of the MATLAB function “sum” • Use a for loop

11. Drawbacks of Loops in MATLAB Because MATLAB code is interpreted on the fly (i.e. not compiled into binary exe files) • Each time the loop restarts, the whole loop must be compiled again • Chapter 5 will cover ways to avoid using loops (vectorization) • For most operations, loops are still fast enough • Each time an entry is added to a matrix, the whole matrix must be recreated

12. Timing CPU Time in Scripts/Functions • To calculate execution times of scripts, MATLAB provides a timer function • “tic” starts the timer • “toc” stops the timer and prints the total execution time to the command window • Makes most sense to use in scripts/functions • Using tic toc, we can determine if code is efficient

13. An Inefficient For Loop Each time the loop iterates... • velKmHr is completely re-allocated and remade each iteration • This is why the editor gives a warning • orange wiggly line

14. An Efficient For Loop Each time the loop iterates... • One entry in velKmHr is overwritten • The whole matrix doesn’t need to be remade

15. The Race is On…Which is Faster? • Numerical results are identical • Second script pre-allocates the velKmHr variable • Runs > 5x faster!!! The Take-Home Message: While most operations are very fast, pre-allocating a matrix is easy, so you should always do it (if possible)

16. Combining Loops With If Statements • A loop to find the maximum of a vector • Can also be accomplished with the command “max” • Which do you think is faster?

17. Combining Loops With If Statements • We can combine loops with Boolean logic to test if each entry meets some criterion • Make sure that all of your indenting is consistent. • MATLAB’s editor should do this automatically

18. Combining Loops With If Statements • We can combine loops with Boolean logic tests • Can we pre-allocate “newData”?

19. Nested For Loops • We can nest “for” loops into inner and outer loops • Can also be done with “while” loops • Often useful for dealing with 2D data The outer loop. “loopVar1” is iterated over “range1” The inner loop. “loopVar2” is iterated over “range2” for loopVar1 = range1 for loopVar2 = range2 action(s) end end

20. Nested For Loops • Lets try a simple nested for loop.

21. Nested For Loops • Lets try another simple nested for loop. • This can be very handy for making a grid of data points • A common task in any quantitative science

22. Grid of XY Points? • This is NOT the way to do it! • Lets try a nested for loop

23. Grid of XY Points • To make a 2D grid we need a nested for loop • Outer loop: x-range; Inner loop: y-range • Could even make spherical grids • (r, θ, ϕ)

24. The While Loop • The “for” loop is a counted loop • You must know the number of iterations beforehand • What if you don’t know how many iterations there will be? • Use a conditional loop: the “while” loop • Loop continues until some condition is no longer met • Often paired with counter variables (to keep track of iterations) • Can be used to error check, or only read part of a dataset. • Most for loops can also be written as while loops • Do whichever one is easiest to understand • Typically for loops require less code

25. The While Loop • Used with a conditional test of the loop variable The “while” keyword (“while” is a reserved word in MATLAB) A conditional statement to be tested at the beginning of each loop iteration. If true, loop continues, if false, loop ends The action(s) performed only if the condition(s) is “true” The “end” keyword. At this point, the computer goes back to the beginning of the while loop and re-tests the condition(s). while condition action(s) end

26. While Loop Example Tests if x < 8 • If true: • Prints out x to command window • If false: • Loop terminates

27. While Loop Example • Can test more than one condition in a while loop • Tests if x < 8 or y < 33

28. A Caution About While Loops • Make sure the condition tested will become false eventually • If condition tested is never false: • An infinite loop • Kill by typing ctrl+c • May take several tries • What should be added?

29. Another Caution About While Loops • If you use a while loop to read though a matrix/vector • The whole matrix/vector may not be read • Sometimes this is desired • To test which data meets some condition for all data • Use a for loop + if statement(s) • Why does a while loop work here?

30. While Loop For Error Checking If we require input from the user • The user may input incorrect/invalid data • A while loop can check this

31. Final Thoughts • Loops allow us to solve a problem once • Tell the computer to repeat n-times • While modern computers are VERY fast… • MATLAB is not efficient with loops* *(not true for most other languages) • The whole loop is recompiled with each iteration • Adding entries to end of a matrix is inefficient* *(overwriting is fast) • You should pre-allocate matrices/vectors whenever possible • Multiple loops can be nested • Can nest a for and while loop • Can nest if-elseif-else statements in a loop(s) • When nesting anything, always consistently indent • If loops are not fast in MATLAB, what can I do? • Vectorize your code!! Anyone up for a game?