Flow Control. Statements We Will Use in Flow Control. Statements We Will Use in Flow Control Relational Operators

Transcription

1 Flow Control We can control when how and the number of times calculations are made based on values of input data and/or data calculations in the program. Statements We Will Use in Flow Control for loops repeat a set of commands for a specified number of times while loops repeat a set of commands while a specified condition is true if, else, elseif execute a set of commands if a specified condition is true ( if ) or execute an alternative set of commands if the specified condition is false ( else, elseif ) 1 2 Statements We Will Use in Flow Control Relational Operators Used in if, elseif and while loops == equal ~= not equal < less than <= less than or equal > greater than >= greater than or equal Statements We Will Use in Flow Control Logical Operators May be used with relational operators & AND OR ~ NOT xor EXCLUSIVE OR 3 4

2 Syntax: for loop for Index = StartValue:Increment:EndValue Matlab commands This may be several lines Index must be a legal Matlab variable name (do not use i or j) StartValue, Increment, and EndValue may be numbers, legal Matlab commands or variable names 5 for loop example 1 Start a new m.file. Name as5_2.m The starter file is on the web site. Look at lines 8-10 in the m.file: for 1:1:5 ii Remove the semicolon from line 9. Save and run the file. What do you expect? 6 for loop example 1 continued Did you get: for loop example 2 Look at lines 13-15: for 1:2:5 ii 4 5 Is it what you expected? The value of ii changes for each cycle of the loop. 7 Remove the semicolon from line 14. Save and run the file. What do you expect? 8

3 for loop example 2 continued Did you get: Is it what you expected? The value of ii again changes for each cycle of the loop. 9 for loop example 3 Sum all the integers from 1 to 10, that is find the sum of Look at lines 18-21: int_sum = 0 for 1:1:10 int_sum = int_sum + ii Remove the semicolon from lines 18 & 20. Save and run the file. What do you expect? 10 for loop example 3 continued Explanation: Initialize the summation variable. int_sum = 0 Loop over the first 10 integers one at a time. for 1:1:10 Add the value of current integer (ii) to the sum. int_sum = int_sum + ii End the loop. Whenever you do a "summation" with a for loop, you must always for loop example 3 continued Explanation continued: Cycle Value of ii Value of int_sum = = = 6... students fill in your notes = 55 "initialize" the summation variable before you start the for loop

4 for loop example 4 Sum all the ODD integers from 1 to 10, that is find the sum of A solution, look at lines 24-27: sum_odd = 0 % Initialize summation % variable for 1:2:9 % Loop over first 5 odd % integers sum_odd = sum_odd + ii % Add current integer % to previous sum % End Loop Remove the semicolon from lines 24 & for loop example 4 continued Cycle Value of ii Value of sum_odd = = = = = 25 Note that the value of ii does not match the cycle number. 14 for loop example 5 Make a list of the squares of the integers from 1 to 10. That is, create the following list: int_sq = [ ] A solution, look at lines 30-32: for 1:1:10 int_sq(ii) = ii.^2 % loop over the first % 10 integers % Calculate square of % current integer, % store in correct % location of int_sq % End the loop Remove the semicolon from line 31. for loop example 5 continued Cycle Value of ii Value of int_sq(ii) 1 1 int_sq(1) = 1.^2 = int_sq(2) = 2.^2 = int_sq(3) = 3.^2 = 9... students fill in your notes int_sq(10) = 10.^2 =

5 for loop example 6 Make a list of the squares of the odd integers from 1 to 10. That is create the following list: int_sq = [ ] We have a problem, the value if the integer that is squared DOES NOT match its location in the list. That is 3 2 is in the 2 nd location, 5 2 is in the 3 rd location, etc. 17 for loop example 6 continued A solution, look at lines 35-39: 1 % Initialize an index for % the list for jj = 1:2:9 % Loop over first 5 odd % integers od_sq(ii) = jj.^2 % Calculate square of current % integer and store in % correct list location ii + 1 % Increment index of the list % End the loop Remove the semicolon from lines 35, 37, & for loop example 6 continued Cycle jj ii Value of od_sq(ii) od_sq(1) = 1.^2 = od_sq(2) = 3.^2 = od_sq(3) = 5.^2 = od_sq(4) = 7.^2 = od_sq(5) = 9.^2 = Some Comments for loop examples 3-6 can all be performed more efficiently using the colon operator and various Matlab vector operations. See the next slide for examples. That is NOT the point. We used these simple examples to illustrate the logic, formulation, and execution of for loops. Most other programming languages will NOT have the matrix/vector capabilities of Matlab and methods similar to those shown in examples 3-6 would have to be used. 20

6 Alternative Ways to Do Examples 3-6 Try These On Your Own Example 3 int_sum = sum(1:1:10) Example 4 sum_odd = sum(1:2:9) Example 5 int_sq = (1:1:10).^2 Example 6 od_sq = (1:2:9).^2 21 Relational Operator Example Produce a true (1) or false (0) answer. Assume, line 42: a = 1 Then, lines 43-46: a == 1 %--> 1 COMMON MISTAKE: be sure % to use two == signs for % comparisons a ~= 1 %--> 0 a <= 2 %--> 1 a > 2 %--> 0 Remove the semicolon from lines Logical Operator Example Produce a true (1) or false (0) answer. Assume, lines 49 & 50: a = 1 b = 2 Then, lines 51-56: a==1 & b==2 %--> 1 a==1 & b==1 %--> 0 a==1 b==1 %--> 1 ~(a==1 b==1) %--> 0 xor(a==1,b==1) %--> 1 xor(a==1,b==2) %--> 0 Remove the semicolon from lines Relational and Logical Operators Order of evaluation: arithmetic, relational, logical Example: a+b > 1 & b-2 > 0 is equivalent to: ((a+b) > 1) & ((b-2) > 0) but which is clearer? See ops and relop help 24

7 Syntax: while loop while <a specified condition is true> Matlab commands This may be several lines Repeat this set of commands until the condition is no longer true Usually used when you do NOT know how many times you may need to repeat the given Matlab commands. 25 while loop continued Step 1: Identify the specified condition (test) that must be TRUE to STOP the operation. Step 2: Use the OPPOSITE form of the test in Step 1 as the while loop condition statement. Step 3: Set up a way of changing (incrementing) the test condition INSIDE the while loop so that the loop will eventually. Set up calculations. Step 4: BEFORE the while loop, set up (initialize) all necessary variables so the test condition and all calculations will evaluate properly the first time. 26 while loop example 1 Repeat for loop example 1 (summation of the first 10 integers) using a while loop. We want to add so we want to STOP when the value of our index (integer) is 11. Therefore, our test condition is: index variable <= 10 That is, as long as the current integer is while loop example 1 continued A solution, lines 59-64: i_sum = 0 % Initialize summation % variable 1 % Initialize index while ii <= 10 % Check if condition is % true, are we still in % the 1 to 10 range i_sum = i_sum + ii % If condition is true, % add to sum ii + 1 % If condition is true, % increment index % Loop back up and check % condition again Remove the semicolon from lines 59, 60, 62, & 63. less than or equal to 10 keep adding

8 while loop example 1 continued Cycle Initial ii i_sum Updated ii = = = = = = = = = = = = = = = = = = = = 11 while loop example 2 Create a list of the powers of 3 less than or equal to 1000, i.e., create the list: pow_of_3 = [ ] Our STOP condition is when 3 N is greater than Therefore our while loop test condition is 3 N <= while loop example 2 continued A solution, lines 67-71: 1 % Initialize index to 1st % power while 3.^ii <= 1000 % Check to see if 3 to the % current power is % less than 1000 pow_of_3(ii) = 3.^ii % If true, calculate % 3 to the current power % and store in proper % location ii + 1 % If true, increment index % to next power % Loop back up and check % condition again Remove the semicolon from lines 67, 69, & 70. while loop example 2 continued Cycle Ini Test pow_of_3 Updated ii ii = 3 pow_of_3(1) = 3 1 = = = 9 pow_of_3(2) = 3 2 = = = 27 pow_of_3(3) = 3 3 = = = 81 pow_of_3(4) = 3 4 = = = 243 pow_of_3(5) = 3 5 = = = 729 pow_of_3(6) = 3 6 = = = 2187 STOP What is the value of ii after the while loop is finished? Why? What is the highest power (N) that satisfies our condition? Are the values of N and ii equal? Why or why not? 31 32

9 while loop example 3 Assume we have the following lists of time an their associated velocities: t = [ ] v = [ ] Find the time that the velocity first goes from positive to negative and find the associated velocity. By inspection time = 5, velocity = while loop example 3 continued A solution, lines 74-81: t = [ ] % Initialize v = [ ] % t, v, and 1 % an index. while v(ii) >= 0 % Check current v % to see if is % non-negative. ii + 1 % If the test is true, % increment the index. % End while loop. t_neg = t(ii) % Get values of t v_neg = v(ii) % and v. Remove the semicolon from lines 74, 75, 76, 78, 80, & while loop example 3 continued Cycle Initial ii v(ii) Updated ii 1 1 v(1) = = v(2) = = v(3) = = v(4) = = v(5) = = v(6) = -2 STOP What is the value of ii after the while loop is finished? Why? Why do we use the current value of ii after the while loop is finished to find our desired values? 35 Other Flow Control Statements That May Be Useful, But We Will Not Cover switch, together with case and otherwise, executes different groups of statements deping on the value of some logical condition. continue passes control to the next iteration of a for or while loop, skipping any remaining statements in the body of the loop. break terminates execution of a for or while loop. try...catch changes flow control if an error is detected during execution. return causes execution to return to the invoking function. All flow constructs use to indicate the of the flow control block. 36