BMAN73701 Week 3 Numerical Analysis Quiz

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Questions and Answers

X = np.array([[1,2,3],[4,5,6]]) a = np.array([0,1,0]) What is the output when multiplying the array X by the array a?

array([[1, 0, 3], [0, 5, 6]])
Error: operands could not be broadcast together
array([[1, 2, 3], [4, 5, 6]])
array([[0, 2, 0], [0, 5, 0]]) (correct)

Broadcasting allows mathematical operations between NumPy arrays of the same shape only.

False (B)

X = np.array([[1,2,3],[4,5,6]]) b = np.array([0,1]) What error occurs when trying to multiply the array X with the array b without reshaping?

Error: operands could not be broadcast together

Match the following operations with their type:

sum = Aggregation operation mean = Aggregation operation reshape = Array manipulation broadcasting = Enables operations on different shaped arrays Signup and view all the answers

The calculation of total requires using nested for-loops.

False (B) Signup and view all the answers

What is the shape of vector x?

4 Signup and view all the answers

Match the tasks to their descriptions based on the operations performed:

Reshape = Alters the dimensions of an array Pairwise product = Multiplies corresponding elements from two arrays Sum = Calculates the aggregate of values Total = Final result of all pairwise products Signup and view all the answers

Which of these vectors is being summed?

The products of x and y elements (B) Signup and view all the answers

What are the numerical elements of vector y?

2, 3, 4, 5 Signup and view all the answers

The provided method for calculating the total utilizes broadcasting.

True (A) Signup and view all the answers

What does the expression `x[0:2]` evaluate to?

x[[0, 1]] (A), x[range(2)] (C) Signup and view all the answers

The expression `x[-1, :]` returns the first row of the array x.

False (B) Signup and view all the answers

What would be the output of `x[:, [0,1]]` given the array `x = np.array([[3, 2, 1], [4, 5, 6]])`?

array([[3, 2], [4, 5]]) Signup and view all the answers

The default START value for slicing when STEP is less than 0 is ___.

len(x) - 1 Signup and view all the answers

`x = np.array([[0,1,2], [0,1,2], [0,1,2]])` Which of the following expressions would result in an output shape of (2, 1)?

x[1:, :1] (B) Signup and view all the answers

The expression `x[::-1, [2, 1, 0]]` reverses the order of the rows and selects the columns from right to left.

True (A) Signup and view all the answers

What happens if you use `A[:, :2]` on the array `A` with shape (3, 3)?

Selects the first two columns for all three rows. Signup and view all the answers

`x = np.array([[0,1,2], [0,1,2], [0,1,2]])` Match the following numpy slicing expressions with their expected output shape:

x[:, 1:] = (3, 2) x[0:2, :] = (2, 3) x[:1, :] = (1, 3) x[-1, :] = (3,) Signup and view all the answers

What is the primary purpose of the numpy.random sub-module?

Random number generation (A) Signup and view all the answers

SciPy is primarily designed for data visualization rather than numerical analysis.

False (B) Signup and view all the answers

What function in numpy.random would you use to create an array of uniformly distributed random numbers?

np.random.rand Signup and view all the answers

The ______ function in SciPy is used for optimization tasks such as linear programming.

scipy.optimize Signup and view all the answers

Which of the following functions is used for obtaining the mean value in NumPy?

Both np.mean and np.average (A) Signup and view all the answers

What does the np.random.seed(N) function do?

It initializes the random number generator with a seed value. Signup and view all the answers

Match the following SciPy modules with their functions:

scipy.optimize = Numerical optimization scipy.linalg = Linear algebra operations scipy.stats = Statistical tests numpy.random = Random number functions Signup and view all the answers

It is advisable to mix the numpy.random and the built-in random module in your projects.

False (B) Signup and view all the answers

What does the function `np.min(A, axis = 0)` return?

The minimum along the rows. (D) Signup and view all the answers

p = [p11 .... p1n] [pk1.....pkn] where each row gives n prediction by k ml method obs = [obs1 ... obsn] What does `np.max(np.mean((P-obs)**2, axis = 1))` compute?

The maximum Mean Squared Error (MSE) Signup and view all the answers

The numpy function `np.min(A, axis = 1)` returns the minimum values along the ______.

columns Signup and view all the answers

Match the numpy functions to their descriptions:

np.min(A) = Returns the minimum value of the array np.min(A, axis=0) = Returns minimum along the row (per column) np.min(A, axis=1) = Returns minimum along the columns (per row) np.max(np.mean((P-obs)**2, axis = 1)) = Calculates maximum Mean Squared Error Signup and view all the answers

If `obs` contains the actual observed values, which variable represents the predicted values?

P (D) Signup and view all the answers

The MSE can never be negative.

True (A) Signup and view all the answers

What does the operation `𝑃𝑘𝑖 − 𝑜𝑏𝑠𝑖` represent in the context of MSE?

The difference between predicted values and actual observations Signup and view all the answers

Which method can be used to find the minimum value in a NumPy array?

A.min() (C) Signup and view all the answers

The method np.any() checks if all elements in an array are true.

False (B) Signup and view all the answers

What will the output of np.all(b) be if b is defined as np.array([1, 1, 0, 0])?

false Signup and view all the answers

To check if there are any negative values in an array A, use the function np.any(A < ______).

0 Signup and view all the answers

Match the following NumPy functions with their descriptions:

np.all() = Checks if all elements are true np.any() = Checks if any element is true np.logical_and() = Computes the logical AND operation np.logical_not() = Inverts the truth value of elements Signup and view all the answers

What result does np.all(A < 0, axis=0) return?

1 value per column (C) Signup and view all the answers

Methods in NumPy can be applied to lists in Python.

False (B) Signup and view all the answers

Which function is used to determine if there are negative values in an array A?

np.any(A < 0) Signup and view all the answers

Flashcards

Pairwise Product Calculation

Calculating the sum of all possible products obtained by multiplying corresponding elements from each of the two vectors.

Vector Element Pairwise Product

The product of corresponding elements from the input vectors.

Vector Summation (Total)

Adding up the results of all pairwise products of the elements across the two vectors.

NumPy's Vectorized Operation:

A computational approach that utilizes optimized array operations for efficiency; avoiding explicit loops (iterating through entries one by one).