Machine Learning week 2 quiz: Octave Tutorial

Octave Tutorial

5 试题

1. 

Suppose I first execute the following Octave commands:

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

Which of the following are then valid Octave commands? Check all that apply and assume all options are written in an Octave command. (Hint: A' denotes the transpose of A.)

C = A * B;

C = B' + A;

C = A' * B;

C = B + A;

2. 

Question text

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

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

B = A(:, 1:2);

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

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

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

3. 

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:

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.

v = A * x;

v = Ax;

v = A .* x;

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:

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, 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:

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.

C = X + 1;

D = X / 4;

B = X .^ 2;

B = X ^ 2;