H.C. Chen 1/24/2019. Chapter 4. Branching Statements and Program Design. Programming 1: Logical Operators, Logical Functions, and the IF-block

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1 Chapter 4 Branching Statements and Program Design Programming 1: Logical Operators, Logical Functions, and the IF-block Learning objectives: 1. Write simple program modules to implement single numerical methods and algorithms 2. Use variables, operators, and control structure to implement simple sequential algorithms 3. Use MATLAB m-file to create user-defined programs Topics/Outline: 1. Logical variables 2. Relational and logic operators 3. Logical functions 4. IF-block 5. Debugging Chapter 4: Branching Statements 1

2 Structured Programming Modular Design Subroutines (function M-files) called by a main program Top-Down Design a systematic development process that begins with the most general statement of a program s objective and then successively divides it into more detailed segments Structured Programming deals with how the actual code is developed so that it is easy to understand, correct, and modify Top-Down Design 1. Clearly state the problem that you are trying to solve 2. Define the inputs required by the program and the outputs to be produced by the program 3. Design the algorithm that you int to implement in the program Decomposition Stepwise refinement 4. Turn the algorithm into MATLAB statements 5. Test the resulting MATLAB program Chapter 4: Branching Statements 2

3 Algorithm Design The sequence of logical steps required to perform a specific task (solve a problem) Each step must be deterministic The process must always after a finite number of steps An algorithm cannot be open-ed The algorithm must be general enough to deal with any contingency Common Program Structures Sequence Selection Repetition Chapter 4: Branching Statements 3

4 Structured Programming Sequential paths Sequence all instructions (statements) are executed sequentially from top to bottom * A strict sequence is highly limiting Non-sequential paths Decisions (Selection) if, else, elseif Loops (Repetition) for, while, break Logical Data Type A special type of data that can have one of only two special possible values o true or false (when displayed in workspace) o 1 or 0 (when displayed in command window) It is legal to mix logical and numerical values in MATLAB (automatic conversion): 1 = true (and so as any non-zero numbers) 0 = false One program can handle multiple cases help computer make decisions Chapter 4: Branching Statements 4

5 Relational Operators Compare values stored in variables and return logical result MATLAB == ~= < <= > >= Interpretation is equal to is not equal to is less than is less than or equal to is greater than is greater than or equal to Note: Do not confuse the equivalence relational operator (==) with the assignment operator (=) Logic Operators Compare logical values and return logical result MATLAB & && xor ~ Interpretation Logical AND Logical AND with shortcut Logical inclusive OR Logical inclusive OR with shortcut Logical exclusive OR Logical NOT Binary logical operation : l 1 op l 2 Unary logical operation : op l 1 Chapter 4: Branching Statements 5

6 Truth Tables for Logic Operators Inputs and or xor not l 1 l 2 l 1 & l 2 l 1 &&l 2 l 1 l 2 l 1 l 2 xor(l 1,l 2 ) ~l 1 false false false false false false false true false true false false true true true true true false false false true true true false true true true true true true false false && and support short-circuit evaluations (partial evaluations), but only works between scalar values && will evaluate expression l 1 and immediately return a false value if l 1 is false will evaluate expression l 1 and immediately return a true value if l 1 is true xor is true if and only if one operand is true and the other one is false Partial Evaluations Most of the time, & and && produce the same result Partial evaluation is faster if the first operand is false Sometimes it is important to use shortcut expression Example: Evaluate whether cos(2a)/sin(b) is greater than 5 x = cos(2*a)/sin(b) > 5 To avoid the possibility of dividing by zero: x = (sin(b) ~= 0) && (cos(2*a)/sin(b)) > 5 Chapter 4: Branching Statements 6

7 Hierarchy of Operations 1. All arithmetic operations are evaluated first 2. All relational operators (==, ~=, >, >=, <, <=) are evaluated, from left to right 3. All ~ operators are evaluated, from left to right 4. All & and && operators are evaluated, from left to right 5. All,, and xor operators are evaluated, from left to right Relational Operators >> x=5; y=3; >> z1 = x >= y z1 = 1 (return 1 for true) >> z2 = (x - 2*y) == 3 z2 = 0 (return 0 for false) >> z3 = sqrt(x) ~= y^2 z3 = 1 (return 1 for true) >> z4 = 'A' < 'C' z4 = 1 (characters are evaluated in alphabetical order) Chapter 4: Branching Statements 7

8 Relational Operators >> a=[ ]; b = 0; >> c1 = a > b c1 = [ true false false true ] >> a=[3 0; -2 5]; b = 0; >> c2 = a < b c2 = >> a=[2 0; -2 5]; b=[5 1; -4 6]; >> c3 = a < b c3 = false true true false false false true true a a a ~ a a Logic Operators 0-1 matrix 0: false ; 1: True b c b ans b ans b & b c ans b b c ans Chapter 4: Branching Statements 8

9 Logic Operators >> value1 = true; value2 = false; value3 = 1; value4 = 0; >> value5 = 10; value6 = -5; value7 = [3 2; 0-1]; >> ~value1 ans = 0 >> ~value3 (convert 1 to true ) ans = 0 >> value1 value2 ans = 1 >> value6 & value7 (convert -5, 3, 2, -1 to true ans = 1 1 and 0 to false) 0 1 >> value5 && value7??? Operands to the and && operators must be convertible to logical scalar values. >> value1 + value5 ans = 11 Logic Functions Ischar(a) Return true if a is a character array and false otherwise Isempty(a) Return true if a is an empty array and false otherwise Isinf(a) Return true if a is infinite (Inf) and false otherwise Isnan(a) Return true if a is NaN (not a number) and false otherwise Isnumeric(a) Return true if a is a numeric array and false otherwise logical(a) Converts numerical values to logical values: if a is non-zero, it is converted to true. If a = 0, it is converted to false Chapter 4: Branching Statements 9

10 Logical Functions >> choice = input('continue? (y/n): ','s'); continue? (y/n): y >> strcmp(choice,'y') ans = 1 >> strcmp(choice,'n') ans = 0 strcmp: string comparison. Returns true(1) if choice stores y. Returns false(0)if choice stores n. Branches Branches are MATLAB statements that permit us to select and execute specific sections (blocks) of code while skipping other sections. if switch try/catch Chapter 4: Branching Statements 10

11 Selection (IF) Statements The most common form of selection structure is simple if statement The if statement will have a condition associated with it The condition is typically a logical expression that must be evaluated as either true or false The outcome of the evaluation will determine the next step performed Logical IF Statements If (condition) executable_statements if (x <= -1.0 x >= 1.0) y = 0. if (x > -1.0 & x < 0.) y = 1. + x if (x >= 0. & x < 1.0) y = 1.- x y x Chapter 4: Branching Statements 11

12 Nested IF Statement Structures can be nested within each other if (condition) statement block elseif (condition) another statement block else another statement block Can have any number of elseif, but at most one else How to use Nested IF If the condition is true the statements following the statement block are executed. If the condition is not true, then the control is transferred to the next else, elseif, or statement at the same if level. There can be any number of elseif clauses (0 or more) in an if construct, but there can be at most one else clause. Chapter 4: Branching Statements 12

13 else and elseif if temperature > 100 disp( Too hot - equipment malfunctioning. ) elseif temperature > 75 disp( Normal operating range. ) elseif temperature > 60 disp( Temperature below desired operating range. ) else disp( Too Cold - turn off equipment. ) Nested IF Statements Nested if (if, if else, if elseif) if (x <= -1.0) y = 0. elseif (x <= 0.) y = 1. + x elseif (x <= 1.0) y = 1. - x else y=0. y x Chapter 4: Branching Statements 13

14 Bungee Jumper Bungee chord length = L Initial height of bungee jumper = H > L Water depth = h if y <= L solve with free-fall equation elseif (y > L) & (y <= H) solve with spring tension elseif (y > H) & (y < H+h) solve with spring tension and water resistance else disp('hit Lake Bottom! Ouch!') Only the first true block will execute elseif, else are optional Always indent ( for clarity, does not change result) Chapter 4: Branching Statements 14

15 Nested IF Statements Nesting: the block inside one IF block may have additional IF blocks if (condition) statement block if (condition) another statement block else another statement block else another statement block keep indenting each block needs its own Nesting and Indentation Example: Roots of a Quadratic Equation x ax 2 bx c 0 2 b b 4ac 2a If a=0, b=0, no solution (or trivial sol. c=0) If a=0, b 0, one real root: x=-c/b If a 0, d=b 2 4ac 0, two real roots If a 0, d=b 2 4ac <0, two complex roots Chapter 4: Branching Statements 15

16 Nesting and Indentation function quadroots(a,b,c) % Computes real and complex roots of quadratic equation % a*x^2 + b*x + c = 0 % Output: (r1,i1,r2,i2) - real and imaginary parts of the % first and second root if a == 0 % weird cases if b ~= 0 % single root r1 = -c/b else % trivial solution error('trivial or No Solution. Try again') % quadratic formula else d = b^2-4*a*c; % discriminant if d >= 0 % real roots r1 = (-b + sqrt(d)) / (2*a) r2 = (-b - sqrt(d)) / (2*a) else % complex roots r1 = -b / (2*a) r2 = r1 i1 = sqrt(abs(d)) / (2*a) i2 = -i1 Roots of Quadratic Equation >> quadroots(5,3,-4) r1 = r2 = (two real roots) >> quad = quadroots(5,3,4) r1 = r2 = i1 = i2 = (two complex roots) >> quadroots(0,0,5)??? Error using ==> quadroots Trivial or No Solution. Try again (no root) Chapter 4: Branching Statements 16

17 Switch Structure Similar to if elseif, but the branching is based on the value of a single test expression switch testexpression case value statement block case value another statement block otherwise another statement block Switch Example: Determine the number of days in a month (Apr, Jun, Sept, Nov.) (February) Chapter 4: Branching Statements 17

18 Switch Example: Determine the number of days in a month >> ndays_in_month Enter the year = 2011 Enter the month (1-12) = 2 number of days in this month = 28 >> ndays_in_month Enter the year = 3680 Enter the month (1-12) = 2 number of days in this month = 29 >> ndays_in_month Enter the year = 2500 Enter the month (1-12) = 10 number of days in this month = 31 Try/Catch Statements A special branching construct designed to trap errors when debugging the MATLAB code try statement block catch another statement block 1. Execute the statements in the try block first 2. If no error occurs, skip the catch block and continue to the first statement following the 3. If an error does occur in the try block, the program will immediately execute the statements in catch block Chapter 4: Branching Statements 18

19 The try/catch Construct Using trap/catch in debugging to trap error Execute the catch block only if error is detected in the try block Trap error using trap/catch construct >> try_catch Enter array A = [ ]; Enter index of element to display: 8 A(8) = -3 >> try_catch Enter array A = [ ]; Enter index of element to display: 12 Illegal array index: 12 Exceeding matrix dimension: size(a) = 10 >> try_catch Enter array A = 0:0.1:10; Enter index of element to display: 95 A(95) = 9.4 >> try_catch Enter array A = 0:0.1:10; Enter index of element to display: 200 Illegal array index: 200 Exceeding matrix dimension: size(a) = 101 Chapter 4: Branching Statements 19