7 Control Structures, Logical Statements

Transcription

1 7 Control Structures, Logical Statements 7.1 Logical Statements 1. Logical (true or false) statements comparing scalars or matrices can be evaluated in MATLAB. Two matrices of the same size may be compared, and another matrix of the same size is returned. Elementwise comparisons of the input matrices are computed and a 1 is placed in the output matrix for a true statement and a 0 is returned for a false statement. The following table describes six relational operators, Operator Meaning == is equal to = is not equal to < is less than > is greater than <= is less than or equal to >= is greater than or equal to For example, the following code: >> a = 5<6; >> b = 5<2; >> c = 3 =3; >> d = 3==(5 2); >> e = 10>=10; >> f = ( 1 : 1 0 ) < 2 ( 1 : 1 0 ) ; >> g = ( 1 : 1 0 ) < ( 1 : 1 0 ). ˆ 2 ; >> h = f =g ; will result in, a = 1 b = 0 c = 0 d = 1 e = 1 f = [ ] g = [ ] h = [ ]. 2. Two logical statement can be combined using the first three of the following operators: 1

2 Operator Name Meaning 0 1 & AND OR xor Exclusive OR NOT The last operator in this table can be used to negate a logical statement. Parenthesis can be used to define precedence. For example, >> a = 1&1; >> b = (3 <4) (8 >11); >> c = xor ((4 >=4),(12 <13)); >> d = ((3 >=5) (5 <10) (6 >3)); >> e = (( 4:4) >=0)&(( 2:6) >=0); >> f = (1:9) >=(4 ones ( 1, 9 ) ) ; >> g = xor ( e, f ) ; will result in, 7.2 Control Structures - IF a = 1 b = 1 c = 0 d = 0 e = [ ] f = [ ] g = [ ]. 1. The basic IF structure in MATLAB has the following syntax: i f ( c o n d i t i o n ) command 1 command 2 The condition is replaced with a logical statement. If that statement evaluates to true (1), then the commands are executed; otherwise nothing happens. For example, consider the function: 1 % Example f u n c t i o n y = fun1 ( x ) 3 function [ y ] = fun1 ( x ) 4 y = x ; 5 i f ( x >= 10) 6 y = 2 x ; 7 2

3 This function returns double the input, if it is greater than or equal to 10, otherwise the input is returned. 2. IF structures can include an else statement: i f ( c o n d i t i o n ) command A1 command A2 else command B1 command B2 The condition is replaced with a logical statement. If that statement evaluates to true (1), then the A commands are executed; otherwise the B commands are executed. For example, consider the function: 1 % Example f u n c t i o n y = fun2 ( x ) 3 function [ y ] = fun2 ( x ) 4 i f ( x >= 10) 5 y = 2 x ; 6 else 7 y = x ; 8 This function is effectively the same as the previous one. 3. IF structures can also be made hierarchical with the elseif statement: i f ( c o n d i t i o n 1) command A1 command A2 e l s e i f ( c o n d i t i o n 2) command B1 command B2 else command Z1 command Z2 Any number of elseif statements can be made, and the final else is optional. The conditions are replaced with logical statements. If condition 1 is true, then only the A commands are executed. If condition 1 is false and condition 2 is true, then only the B commands are executed, and so on. In other words, the commands associated with the first true condition are executed. If none of the conditions are true, then the Z commands are executed. For example, consider the function: 1 % Example f u n c t i o n y = fun3 ( x ) 3 function [ y ] = fun3 ( x ) 4 i f ( x >= 10) 5 y = 2 x ; 6 e l s e i f ( x >= 8) 3

4 7 y = 3 x ; 8 else 9 y = x ; 10 This function will output, 2x if x 10 y = 3x if 8 x < 10 x otherwise. 7.3 Control Structures - FOR 1. In MATLAB, a FOR loop can be used for iterative computations. However, since MATLAB is a scripting language, these structures are very slow. The syntax is, for var = v e c t o r command 1 command 2 In this description, var is replaced with a variable name, and vector is replaced with a vector. MATLAB will set var to the first element of the vector and run the commands. Then var is set to the second element of the vector and the commands are run again. This is continued until all elements of the vector have been used. For example, consider the function: 1 % Example f u n c t i o n y = fun4 ( x ) 3 function [ y ] = fun4 ( x ) 4 y = zeros ( 1 0 0, 1 ) ; 5 for i = 1:100 6 i f ( x >= 10) 7 y ( i ) = i x ; 8 e l s e i f ( x >= 8) 9 y ( i ) = ( i +1) x ; 10 else 11 y ( i ) = x ; This function will output a vector y such that, ix if x 10 y (i) = x + ix if 8 x < 10 x otherwise, however it is very inefficient. Whenever possible, FOR loops should be avoided in place of matrix operations. This is a more efficient function that produces the same output: 1 % Example f u n c t i o n y = fun5 ( x ) 3 function [ y ] = fun5 ( x ) 4 i = 1 : ; 5 i f ( x >= 10) 6 y = i x ; 4

5 7 e l s e i f ( x >= 8) 8 y = ( i +1) x ; 9 else 10 y = x ; Exercises These functions may be of help: nthroot, length, find, disp. 1. How many integers in the range [4, 400] have cube roots less than 4? 2. How many integers in the range [4, 400] have cube roots less than 4 or square roots greater than 10? Replicate the following figure: Cube Root Square Root x 3. Write a function with two inputs: a vector and a scalar; and outputs a vector of the same size as the input vector. Deping of the value of the scalar, different operations are performed on the vector as follows (use an IF structure): If the scalar is equal to... Then do the following... 1 add 2 to the vector 2 multiply the vector by 2 3 reverse the order of the vector 4. Modify the function created above to have two output vectors of the same size. The function performs the following: If the scalar is equal to... Then for output 1 do the following to the vector... And for output add 2 to the vector nothing 2 multiply the vector by 2 nothing 3 reverse the order of the vector nothing anything else nothing reverse the order of the vector 5. Use a SWITCH structure for the previous exercise. 6. Write a function (use a FOR structure) that displays the following 20 lines of text: 5

6 The c u r r e n t index i s 1. The c u r r e n t index i s 2. The c u r r e n t index i s Use a WHILE structure for the previous exercise. 6