Coursera Machine Learning 第二周 quiz Octave/Matlab Tutorial 习题答案

1.

Suppose I first execute the following Octave/Matlab commands:

         
         
         
         

          
          
          
          

           
           
           
           

            
            
            
            1
           
           
           
           
           
           
           
           

            
            
            
            2
           
           
           
           
          
          
          
          
          
          
          
          

         
         
         
         
         
         
         
         

          
          
          
          

           
           
           
           

            
            
            
            

           
           
           
           
           
           
           
           

            
            
            
            

           
           
           
           
           
           
           
           

            
            
            
            

             
             
             
             

              
              
              
              A 
              
              
              
              = 
              
              
              
              [
              
              
              
              1 
              
              
              
              2
              
              
              
              ; 
              
              
              
              3 
              
              
              
              4
              
              
              
              ; 
              
              
              
              5 
              
              
              
              6
              
              
              
              ]
              
              
              
              ;
             
             
             
             
            
            
            
            
            
            
            
            

             
             
             
             

              
              
              
              B 
              
              
              
              = 
              
              
              
              [
              
              
              
              1 
              
              
              
              2 
              
              
              
              3
              
              
              
              ; 
              
              
              
              4 
              
              
              
              5 
              
              
              
              6
              
              
              
              ]
              
              
              
              ;
             
             
             
             
            
            
            
            
           
           
           
           
           
           
           
           

           
           
           
           

            
            
            
            

           
           
           
           
          
          
          
          
         
         
         
         
         
         
         
         

          
          
          
          

          
          
          
          

         
         
         
         

Which of the following are then valid commands? Check all that apply. (Hint: A' denotes the transpose of A.) 

答案 AB

C = A * B;

C = B' + A;

C = A' * B;

C = B + A;

Let  A=⎡⎣⎢⎢16594211714310615138121⎤⎦⎥⎥ .

2. Which of the following indexing expressions gives  B=⎡⎣⎢⎢16594211714⎤⎦⎥⎥ ? Check all that apply.

答案AB

B = A(:, 1:2);

B = A(1:4, 1:2);

B = A(0:2, 0:4)

B = A(1:2, 1:4);

Let  A  be a 10x10 matrix and x  be a 10-element vector. Your friend wants to compute the product  Ax  and writes the following code:

                      
                     
                     
                     

                       
                      
                      
                      

                        
                       
                       
                       

                        
                        
                        
                         1
                        
                       
                       
                       
                        
                       
                       
                       

                        
                        
                        
                         2
                        
                       
                       
                       
                        
                       
                       
                       

                        
                        
                        
                         3
                        
                       
                       
                       
                        
                       
                       
                       

                        
                        
                        
                         4
                        
                       
                       
                       
                        
                       
                       
                       

                        
                        
                        
                         5
                        
                       
                       
                       
                        
                       
                       
                       

                        
                        
                        
                         6
                        
                       
                       
                       
                       
                      
                      
                      
                       
                      
                      
                      

                      
                     
                     
                     
                      
                     
                     
                     

                       
                      
                      
                      

                        
                       
                       
                       

                         
                        
                        
                        

                        
                       
                       
                       
                        
                       
                       
                       

                         
                        
                        
                        

                         
                        
                        
                        

                         
                        
                        
                        

                        
                       
                       
                       
                        
                       
                       
                       

                         
                        
                        
                        

                          
                         
                         
                         

                           
                          
                          
                          v 
                           
                          
                          
                          = 
                           
                          
                          
                          zeros
                           
                          
                          
                          (
                           
                          
                          
                          10
                           
                          
                          
                          , 
                           
                          
                          
                          1
                           
                          
                          
                          )
                           
                          
                          
                          ;
                          
                         
                         
                         
                         
                        
                        
                        
                         
                        
                        
                        

                          
                         
                         
                         

                           
                          
                          
                          for 
                           
                          
                          
                          i 
                           
                          
                          
                          = 
                           
                          
                          
                          1
                           
                          
                          
                          :
                           
                          
                          
                          10
                          
                         
                         
                         
                         
                        
                        
                        
                         
                        
                        
                        

                          
                         
                         
                         
  
                           
                          
                          
                          for 
                           
                          
                          
                          j 
                           
                          
                          
                          = 
                           
                          
                          
                          1
                           
                          
                          
                          :
                           
                          
                          
                          10
                          
                         
                         
                         
                         
                        
                        
                        
                         
                        
                        
                        

                          
                         
                         
                         
    
                           
                          
                          
                          v
                           
                          
                          
                          (
                           
                          
                          
                          i
                           
                          
                          
                          ) 
                           
                          
                          
                          = 
                           
                          
                          
                          v
                           
                          
                          
                          (
                           
                          
                          
                          i
                           
                          
                          
                          ) 
                           
                          
                          
                          + 
                           
                          
                          
                          A
                           
                          
                          
                          (
                           
                          
                          
                          i
                           
                          
                          
                          , 
                           
                          
                          
                          j
                           
                          
                          
                          ) * 
                           
                          
                          
                          x
                           
                          
                          
                          (
                           
                          
                          
                          j
                           
                          
                          
                          )
                           
                          
                          
                          ;
                          
                         
                         
                         
                         
                        
                        
                        
                         
                        
                        
                        

                          
                         
                         
                         
  
                           
                          
                          
                          end
                          
                         
                         
                         
                         
                        
                        
                        
                         
                        
                        
                        

                          
                         
                         
                         

                           
                          
                          
                          end
                          
                         
                         
                         
                         
                        
                        
                        
                        
                       
                       
                       
                        
                       
                       
                       

                        
                       
                       
                       

                         
                        
                        
                        

                        
                       
                       
                       
                       
                      
                      
                      
                      
                     
                     
                     
                      
                     
                     
                     

                       
                      
                      
                      

                       
                      
                      
                      

                      
                     
                     
                     

How would you vectorize this code to run without any for loops? Check all that apply.

答案A

v = A * x;

v = Ax;

v = x' * A;

v = sum (A * x);

 

4.Say you have two column vectors  v  and  w , each with 7 elements (i.e., they have dimensions 7x1). Consider the following code:

答案AB

                           
                           
                           
                           

                            
                            
                            
                            

                             
                             
                             
                             

                              
                              
                              
                              1
                             
                             
                             
                             
                             
                             
                             
                             

                              
                              
                              
                              2
                             
                             
                             
                             
                             
                             
                             
                             

                              
                              
                              
                              3
                             
                             
                             
                             
                             
                             
                             
                             

                              
                              
                              
                              4
                             
                             
                             
                             
                            
                            
                            
                            
                            
                            
                            
                            

                           
                           
                           
                           
                           
                           
                           
                           

                            
                            
                            
                            

                             
                             
                             
                             

                              
                              
                              
                              

                             
                             
                             
                             
                             
                             
                             
                             

                              
                              
                              
                              

                              
                              
                              
                              

                              
                              
                              
                              

                             
                             
                             
                             
                             
                             
                             
                             

                              
                              
                              
                              

                               
                               
                               
                               

                                
                                
                                
                                z 
                                
                                
                                
                                = 
                                
                                
                                
                                0
                                
                                
                                
                                ;
                               
                               
                               
                               
                              
                              
                              
                              
                              
                              
                              
                              

                               
                               
                               
                               

                                
                                
                                
                                for 
                                
                                
                                
                                i 
                                
                                
                                
                                = 
                                
                                
                                
                                1
                                
                                
                                
                                :
                                
                                
                                
                                7
                               
                               
                               
                               
                              
                              
                              
                              
                              
                              
                              
                              

                               
                               
                               
                               
  
                                
                                
                                
                                z 
                                
                                
                                
                                = 
                                
                                
                                
                                z 
                                
                                
                                
                                + 
                                
                                
                                
                                v
                                
                                
                                
                                (
                                
                                
                                
                                i
                                
                                
                                
                                ) * 
                                
                                
                                
                                w
                                
                                
                                
                                (
                                
                                
                                
                                i
                                
                                
                                
                                )
                               
                               
                               
                               
                              
                              
                              
                              
                              
                              
                              
                              

                               
                               
                               
                               

                                
                                
                                
                                end
                               
                               
                               
                               
                              
                              
                              
                              
                             
                             
                             
                             
                             
                             
                             
                             

                             
                             
                             
                             

                              
                              
                              
                              

                             
                             
                             
                             
                            
                            
                            
                            
                           
                           
                           
                           
                           
                           
                           
                           

                            
                            
                            
                            

                            
                            
                            
                            

                           
                           
                           
                           

Which of the following vectorizations correctly compute z? Check all that apply.

z = sum (v .* w);

z = w' * v;

z = v * w';

z = w * v';

5.In Octave/Matlab, many functions work on single numbers, vectors, and matrices. For example, the sin function when applied to a matrix will return a new matrix with the sin of each element. But you have to be careful, as certain functions have different behavior. Suppose you have an 7x7 matrix  X . You want to compute the log of every element, the square of every element, add 1 to every element, and divide every element by 4. You will store the results in four matrices,  A,B,C,D . One way to do so is the following code:

                            
                           
                           
                           

                             
                            
                            
                            

                              
                             
                             
                             

                              
                              
                              
                               1
                              
                             
                             
                             
                              
                             
                             
                             

                              
                              
                              
                               2
                              
                             
                             
                             
                              
                             
                             
                             

                              
                              
                              
                               3
                              
                             
                             
                             
                              
                             
                             
                             

                              
                              
                              
                               4
                              
                             
                             
                             
                              
                             
                             
                             

                              
                              
                              
                               5
                              
                             
                             
                             
                              
                             
                             
                             

                              
                              
                              
                               6
                              
                             
                             
                             
                              
                             
                             
                             

                              
                              
                              
                               7
                              
                             
                             
                             
                              
                             
                             
                             

                              
                              
                              
                               8
                              
                             
                             
                             
                             
                            
                            
                            
                             
                            
                            
                            

                            
                           
                           
                           
                            
                           
                           
                           

                             
                            
                            
                            

                              
                             
                             
                             

                               
                              
                              
                              

                              
                             
                             
                             
                              
                             
                             
                             

                               
                              
                              
                              

                               
                              
                              
                              

                               
                              
                              
                              

                              
                             
                             
                             
                              
                             
                             
                             

                               
                              
                              
                              

                                
                               
                               
                               

                                 
                                
                                
                                for 
                                 
                                
                                
                                i 
                                 
                                
                                
                                = 
                                 
                                
                                
                                1
                                 
                                
                                
                                :
                                 
                                
                                
                                7
                                
                               
                               
                               
                               
                              
                              
                              
                               
                              
                              
                              

                                
                               
                               
                               
  
                                 
                                
                                
                                for 
                                 
                                
                                
                                j 
                                 
                                
                                
                                = 
                                 
                                
                                
                                1
                                 
                                
                                
                                :
                                 
                                
                                
                                7
                                
                               
                               
                               
                               
                              
                              
                              
                               
                              
                              
                              

                                
                               
                               
                               
    
                                 
                                
                                
                                A
                                 
                                
                                
                                (
                                 
                                
                                
                                i
                                 
                                
                                
                                , 
                                 
                                
                                
                                j
                                 
                                
                                
                                ) 
                                 
                                
                                
                                = 
                                 
                                
                                
                                log
                                 
                                
                                
                                (
                                 
                                
                                
                                X
                                 
                                
                                
                                (
                                 
                                
                                
                                i
                                 
                                
                                
                                , 
                                 
                                
                                
                                j
                                 
                                
                                
                                ))
                                 
                                
                                
                                ;
                                
                               
                               
                               
                               
                              
                              
                              
                               
                              
                              
                              

                                
                               
                               
                               
    
                                 
                                
                                
                                B
                                 
                                
                                
                                (
                                 
                                
                                
                                i
                                 
                                
                                
                                , 
                                 
                                
                                
                                j
                                 
                                
                                
                                ) 
                                 
                                
                                
                                = 
                                 
                                
                                
                                X
                                 
                                
                                
                                (
                                 
                                
                                
                                i
                                 
                                
                                
                                , 
                                 
                                
                                
                                j
                                 
                                
                                
                                ) 
                                 
                                
                                
                                ^ 
                                 
                                
                                
                                2
                                 
                                
                                
                                ;
                                
                               
                               
                               
                               
                              
                              
                              
                               
                              
                              
                              

                                
                               
                               
                               
    
                                 
                                
                                
                                C
                                 
                                
                                
                                (
                                 
                                
                                
                                i
                                 
                                
                                
                                , 
                                 
                                
                                
                                j
                                 
                                
                                
                                ) 
                                 
                                
                                
                                = 
                                 
                                
                                
                                X
                                 
                                
                                
                                (
                                 
                                
                                
                                i
                                 
                                
                                
                                , 
                                 
                                
                                
                                j
                                 
                                
                                
                                ) 
                                 
                                
                                
                                + 
                                 
                                
                                
                                1
                                 
                                
                                
                                ;
                                
                               
                               
                               
                               
                              
                              
                              
                               
                              
                              
                              

                                
                               
                               
                               
    
                                 
                                
                                
                                D
                                 
                                
                                
                                (
                                 
                                
                                
                                i
                                 
                                
                                
                                , 
                                 
                                
                                
                                j
                                 
                                
                                
                                ) 
                                 
                                
                                
                                = 
                                 
                                
                                
                                X
                                 
                                
                                
                                (
                                 
                                
                                
                                i
                                 
                                
                                
                                , 
                                 
                                
                                
                                j
                                 
                                
                                
                                ) 
                                 
                                
                                
                                / 
                                 
                                
                                
                                4
                                 
                                
                                
                                ;
                                
                               
                               
                               
                               
                              
                              
                              
                               
                              
                              
                              

                                
                               
                               
                               
  
                                 
                                
                                
                                end
                                
                               
                               
                               
                               
                              
                              
                              
                               
                              
                              
                              

                                
                               
                               
                               

                                 
                                
                                
                                end
                                
                               
                               
                               
                               
                              
                              
                              
                              
                             
                             
                             
                              
                             
                             
                             

                              
                             
                             
                             

                               
                              
                              
                              

                              
                             
                             
                             
                             
                            
                            
                            
                            
                           
                           
                           
                            
                           
                           
                           

                             
                            
                            
                            

                             
                            
                            
                            

                            
                           
                           
                           

Which of the following correctly compute  A,B,C,  or  D ? Check all that apply.

答案ABC

C = X + 1;

D = X / 4;

A = log (X);

B = X ^ 2;