NumPy quiz

Question 1

What is NumPy broadcasting and what are the three rules that govern it?

Accepted Answer

Arrays with size 1 along a dimension are stretched

Answer

Broadcasting always copies data to align shapes

Answer

Both arrays must have the same number of dimensions

Answer

Broadcasting only works for 2D arrays

Question 2

What are NumPy strides and how do they enable zero-copy operations like transposition?

Accepted Answer

Transposing swaps strides without copying data

Answer

Transposing copies the entire array

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Strides are always (1, 1) for 2D arrays

Answer

C-contiguous arrays have Fortran-order strides

Question 3

What is a NumPy universal function (ufunc) and how does it differ from a regular Python function?

Accepted Answer

ufuncs support broadcasting and compiled C execution

Answer

ufuncs are slower than Python loops for small arrays

Answer

np.vectorize creates a true compiled ufunc

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ufuncs cannot operate on multiple arrays simultaneously

Question 4

How does fancy indexing differ from basic slicing in NumPy, and what are the performance implications?

Accepted Answer

Fancy indexing always returns a copy

Answer

Fancy indexing returns a view

Answer

Basic slicing always returns a copy

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Boolean masks return views

Question 5

How does np.linalg.svd work and what are the shapes of its output matrices?

Accepted Answer

Economy SVD gives U shape (m,k) and Vh shape (k,n)

Answer

U is always square, Vh is always rectangular

Answer

Singular values can be negative

Answer

SVD only works for square matrices

Question 6

How does np.random's default_rng differ from the legacy np.random module?

Accepted Answer

default_rng() creates an independent Generator object

Answer

Legacy np.random uses PCG64

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np.random.randn is thread-safe

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default_rng only supports uniform distribution

Question 7

How do you implement a numerically stable softmax using NumPy?

Accepted Answer

Subtract maximum to prevent overflow

Answer

Subtract minimum instead of maximum for stability

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Naive softmax is always numerically stable

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Softmax is undefined for negative inputs

Question 8

How does np.memmap enable processing datasets larger than RAM?

Accepted Answer

np.memmap loads pages on demand using virtual memory

Answer

np.memmap loads the entire file into RAM at once

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np.memmap only supports read-only mode

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np.memmap is slower than reading with np.load

Question 9

How do you compute pairwise Euclidean distances between two sets of vectors efficiently in NumPy?

Accepted Answer

Use the ||a-b||²=||a||²-2a·bᵀ+||b||² identity with matmul

Answer

Use np.linalg.norm in a nested loop

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scipy.spatial.distance is the only correct approach

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Compute element-wise subtraction with broadcasting only

Question 10

What is np.vectorize and when should you avoid it for performance?

Accepted Answer

np.vectorize uses a Python loop internally

Answer

np.vectorize compiles Python code to C

Answer

np.vectorize always outperforms explicit loops

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np.vectorize is equivalent to np.frompyfunc in all ways

Question 11

What does np.argsort return and how is it used for ranking and partial sorting?

Accepted Answer

np.argsort returns indices that sort the array

Answer

np.argsort returns sorted values

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np.argpartition fully sorts the array

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np.argsort(np.argsort(x)) gives the minimum value

Question 12

How does np.linalg.eig differ from np.linalg.eigh for symmetric matrices?

Accepted Answer

eigh guarantees real eigenvalues for symmetric matrices

Answer

eigh works for any square matrix

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eig sorts eigenvalues ascending

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eigh uses the general QR algorithm

Question 13

What is the GIL and how does it affect NumPy multithreading?

Accepted Answer

BLAS operations in NumPy release the GIL

Answer

NumPy never releases the GIL

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threading is better than multiprocessing for NumPy

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np.dot is always single-threaded

Question 14

How do you use np.linalg.norm and what are the common norm types?

Accepted Answer

ord=None gives L2 (Frobenius) norm by default

Answer

ord=None gives L1 norm for vectors

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Matrix L2 norm equals sum of singular values

Answer

np.linalg.norm cannot operate along an axis

Question 15

What are the dtype promotion rules in NumPy and how do they affect precision?

Accepted Answer

int32 + float32 = float64

Answer

int32 + float32 = float32

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float32 + float64 = float32

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uint8 + int8 = uint8

Question 16

How do you implement the Gram matrix efficiently in NumPy for kernel methods?

Accepted Answer

O(n²·d) time for linear kernel via matrix multiply

Answer

O(n³) time for linear kernel

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RBF kernel requires O(n²·d²) computation

Answer

Gram matrix is always diagonal

Question 17

How does np.linalg.cholesky decomposition enable efficient sampling from multivariate Gaussians?

Accepted Answer

Cholesky requires the matrix to be symmetric positive definite

Answer

Cholesky works on any square matrix

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Cholesky is slower than LU decomposition

Answer

Sampling uses L.T @ z, not L @ z

Question 18

Explain the role of BLAS and LAPACK in NumPy's performance for linear algebra operations.

Accepted Answer

BLAS Level 3 handles matrix-matrix operations like DGEMM

Answer

BLAS only handles vector operations

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NumPy implements its own matrix multiply without BLAS

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LAPACK is slower than hand-written NumPy code

Question 19

How does np.gradient compute numerical derivatives and how does it handle boundaries?

Accepted Answer

np.gradient uses central differences at interior, forward/backward at boundaries

Answer

np.gradient uses forward differences at all points

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np.gradient reduces array length by 1

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np.gradient requires uniform spacing

Question 20

What is np.tile vs np.repeat and when would you use each?

Accepted Answer

np.tile([1,2,3], 2) = [1,2,3,1,2,3]

Answer

np.tile([1,2,3], 2) = [1,1,2,2,3,3]

Answer

np.repeat and np.tile are identical

Answer

np.repeat returns a view

Question 21

How does np.linalg.matrix_power work and what are its applications?

Accepted Answer

np.linalg.matrix_power uses repeated squaring, O(d³ log n)

Answer

np.linalg.matrix_power is O(n·d³)

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matrix_power does not support negative exponents

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matrix_power requires A to be symmetric

Question 22

What is np.shares_memory and why does it matter for debugging NumPy code?

Accepted Answer

np.shares_memory detects any memory overlap, stronger than checking base

Answer

np.shares_memory is equivalent to checking a.base is b

Answer

All slices always return copies

Answer

np.shares_memory is only relevant for 2D arrays

Test yourself