Assignment 7

Corresponds to: Session 7

Quiz: NumPy Arrays - Creation, Basic Operations

Time Allotted: 45 Minutes

1. You have a list of material Young's Moduli: E_values = [210e9, 70e9, 200e9]. To convert this list into a NumPy array for performing calculations, which command is correct?

A. np.create_array(E_values)
B. np.array(E_values)
C. np.convert(E_values)
D. np.list_to_array(E_values)

2. You are initializing a 4x4 global stiffness matrix and want the matrix to be pre-filled with zeros. Which command is the correct syntax?

A. np.zeros(4, 4)
B. np.zeros_matrix(4, 4)
C. np.zeros((4, 4))
D. np.empty_zeros(4, 4)

3. You use the command stress_tensor = np.empty((3, 3)) to allocate memory for a 3x3 stress tensor. What can you expect regarding the initial values within this array?

A. All values will be 0.0
B. All values will be 1.0
C. The values will be arbitrary values remaining in the memory location
D. All values will be NaN

4. You have a 1D array containing the stiffnesses of three springs: k = np.array([500, 1200, 800]). Which function will create a 3x3 diagonal matrix with these specific values on the main diagonal?

A. np.diag(k)
B. np.diagonal(k)
C. np.matrix_diag(k)
D. np.create_diag(k)

5. You need to create a 1D array of length 6 where every element is exactly 1.0. Which command is the most efficient way to achieve this?

A. np.all_ones(6)
B. np.ones(6)
C. np.identity(6)
D. np.array(1, 6)

6. You want to create a 1D array that starts at 0 and increments by 5, up to but NOT including 20. Which command is correct?

A. np.arange(0, 20, 5)
B. np.arange(0, 25, 5)
C. np.linspace(0, 20, 5)
D. np.arange(5, 20, 5)

7. A structural engineer needs to create exactly 11 equally spaced points between 0 and 10 meters to represent nodes on a beam. Which command is most appropriate?

A. np.arange(0, 10, 11)
B. np.linspace(0, 10, 11)
C. np.linspace(0, 11, 10)
D. np.arange(0, 11, 10)

8. You have a 1D array of 12 load values. You want to convert this into a matrix with 3 rows and 4 columns, without altering the original 1D array. Which command performs this transformation?

A. loads.reshape(4, 3)
B. loads.reshape(3, 4)
C. loads.resize(3, 4)
D. loads.reshape(12, 1)

9. What is a primary difference between np.reshape() and np.resize() when the new dimensions do not contain the same number of elements as the original array?

A. reshape() will change the original array, while resize() will not.
B. reshape() will raise an error, while resize() will pad the array or repeat elements to fill the new shape.
C. resize() only works on 1D arrays, while reshape() works on any dimension.
D. There is no difference; they are aliases for the same function.

10. Which code sequence correctly creates a 2x2 matrix where the elements are [1.0, 2.0, 3.0, 4.0]?

A. np.linspace(1, 4, 4).reshape(2, 2)
B. np.arange(1, 4, 4).reshape(2, 2)
C. np.linspace(1, 4, 2).reshape(2, 2)
D. np.arange(1, 5, 2).reshape(2, 2)

11. You have a 1D array representing a load vector: load = np.array([10, 20, 30]). You need to apply a load factor of 1.5 to all loads. Which command is correct?

A. load @ 1.5
B. load * 1.5
C. load . 1.5
D. np.scalar(load, 1.5)

12. You are given two load vectors: P1 = np.array([100, 50]) and P2 = np.array([20, 30]). To find the total resultant load vector, which command should you use?

A. P1 * P2
B. P1 @ P2
C. P1 + P2
D. np.combine(P1, P2)

13. You have two arrays of stress values: stress_initial = np.array([250, 300]) and stress_final = np.array([270, 310]). To find the change in stress (final - initial), which command is correct?

A. stress_final - stress_initial
B. stress_final / stress_initial
C. stress_final @ stress_initial
D. np.diff(stress_final, stress_initial)

14. You have an array of material stiffnesses k = np.array([100, 200, 300]) and an array of reduction factors f = np.array([0.9, 0.8, 0.7]). To find the reduced stiffnesses by multiplying each stiffness by its corresponding factor, which command is correct?

A. k @ f
B. k * f
C. np.matrix_mult(k, f)
D. k . f

15. In structural analysis, you often need to solve the equation F = K @ u, where K is a stiffness matrix and u is a displacement vector. Which operator is used to perform this matrix-vector multiplication?

A. *
B. ^
C. @
D. &

16. If A and B are two NumPy arrays of the same shape, what is the primary difference between the results of A * B and A @ B?

A. A * B performs matrix multiplication, while A @ B performs element-wise multiplication.
B. A * B performs element-wise multiplication, while A @ B performs matrix multiplication.
C. A * B results in a scalar, while A @ B results in an array.
D. There is no difference; both operators perform the same operation.

17. You have a \(3 \times 3\) stiffness matrix K and you want to add a constant offset (increase in value) of 5.0 to every single element in the matrix. Which command achieves this?

A. K + 5.0
B. np.add(K, [5, 5, 5])
C. K @ 5.0
D. K * 5.0

18. To perform matrix multiplication between matrix A and matrix B using the @ operator, what is the requirement regarding their dimensions?

A. A and B must have exactly the same dimensions (e.g., both must be \(3 \times 3\)).
B. The number of columns in A must equal the number of rows in B.
C. The number of rows in A must equal the number of columns in B.
D. Both A and B must be 1D arrays.

19. If you multiply a \(2 \times 3\) matrix by a \(3 \times 2\) matrix using the @ operator, what will be the shape of the resulting matrix?

A. \(3 \times 3\)
B. \(2 \times 2\)
C. \(3 \times 2\)
D. \(2 \times 3\)

20. You have a 1D array v = np.array([1, 2, 3]). What is the result of the operation v * 2?

A. [2, 4, 6]
B. [1, 2, 3, 1, 2, 3]
C. [2, 2, 2]
D. [1, 4, 9]

21. You have a 1D array of nodal displacements: u = np.array([0.01, 0.02, 0.03, 0.04, 0.05]). To access the third displacement (0.03), which index should you use?

A. u[3]
B. u[2]
C. u(2)
D. u[1]

22. You are working with a 2x2 stiffness matrix K = np.array([[10, 20], [30, 40]]). Which command correctly retrieves the value 20?

A. K[0, 1]
B. K[1, 0]
C. K[0, 0]
D. K[1, 1]

23. You have a list of sensor readings: readings = np.array([12, 15, 18, 22, 25]). You want to quickly access the very last reading in the array using negative indexing. Which command is correct?

A. readings[-0]
B. readings[last]
C. readings[-1]
D. readings[0]

24. Given a 3x3 matrix M, you want to extract the entire second row. Which of the following is the correct syntax?

A. M[1, :]
B. M[2, :]
C. M[:, 1]
D. M[1]

25. You have a displacement vector v = np.array([10, 20, 30, 40]). If you want to access the element 40 using its index, which is correct?

A. v[4]
B. v[3]
C. v[-2]
D. v[0]

26. You have an array of temperature readings: temp = np.array([20, 21, 22, 23, 24, 25]). Which slicing command will return the sub-array [21, 22, 23]?

A. temp[1:3]
B. temp[2:4]
C. temp[1:4]
D. temp[0:3]

27. You want to select every second element from an array arr = np.array([10, 20, 30, 40, 50, 60]) to perform a downsampling. Which command should you use?

A. arr[::2]
B. arr[1:2]
C. arr[::1]
D. arr[2::1]

28. You have a 3x3 global stiffness matrix K. You want to extract the top-left 2x2 sub-matrix. Which command is correct?

A. K[0:2, 0:2]
B. K[1:3, 1:3]
C. K[0:1, 0:1]
D. K[:2, :2]

29. Given a matrix M = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]]), how do you extract only the last column?

A. M[2, :]
B. M[:, 2]
C. M[:, -1]
D. Both B and C

30. You need to reverse the order of elements in a 1D array data = np.array([1, 2, 3, 4, 5]). Which slicing technique is the most efficient way to do this?

A. data[5:0:-1]
B. data[::-1]
C. data[1::-1]
D. data[::1]

31. You have an array of stress values: stress = np.array([150, 250, 350, 450]). You want to create a new array containing only the values that exceed the yield strength of 300 MPa. Which command uses a mask to achieve this?

A. stress.filter(stress > 300)
B. stress[stress > 300]
C. np.select(stress > 300)
D. stress[where > 300]

32. You are checking nodal displacements in a structure. You need to find all displacements d that are both greater than 0.01 and less than 0.05. Which syntax correctly applies this double-condition mask?

A. d[d > 0.01 and d < 0.05]
B. d[(d > 0.01) & (d < 0.05)]
C. d[(d > 0.01) and (d < 0.05)]
D. d[d.between(0.01, 0.05)]

33. You have two 1D arrays representing load components: load_x = np.array([10, 20]) and load_y = np.array([30, 40]). To combine them into a single 1D array [10, 20, 30, 40], which command is correct?

A. np.concatenate((load_x, load_y))
B. np.concatenate(load_x, load_y)
C. np.concat([load_x, load_y])
D. np.merge(load_x, load_y)

34. You have two \(2 \times 3\) matrices, A and B. You want to stack them vertically to create a single \(4 \times 3\) matrix. Which command should you use?

A. np.concatenate((A, B), axis=1)
B. np.concatenate((A, B), axis=0)
C. np.concatenate((A, B))
D. Both B and C

35. You have two \(2 \times 2\) matrices, M1 and M2. You want to join them side-by-side (horizontally) to result in a \(2 \times 4\) matrix. Which command is correct?

A. np.concatenate((M1, M2), axis=0)
B. np.concatenate((M1, M2), axis=1)
C. np.concatenate((M1, M2), axis=2)
D. np.concatenate((M1, M2), axis=horizontal)