np.einsum() for efficient computation in NumPy - Cheat Sheet & Quick Revision

Recall & Review

beginner

What does np.einsum() do in numpy?

np.einsum() lets you write simple formulas to do many math operations on arrays efficiently, like sums, products, and transposes, all in one step.

intermediate

How does np.einsum() improve performance compared to regular numpy operations?

It reduces extra steps and temporary arrays by combining operations, so calculations use less memory and run faster.

beginner

Explain the meaning of the subscripts in np.einsum('ij,jk->ik', A, B).

'ij' means matrix A with rows i and columns j.<br>'jk' means matrix B with rows j and columns k.<br>'ik' means the output matrix with rows i and columns k.<br>This does matrix multiplication.

intermediate

Can np.einsum() be used for operations like dot product, outer product, and trace? Give a simple example.

Yes! For example:<br>Dot product: np.einsum('i,i->', a, b)<br>Outer product: np.einsum('i,j->ij', a, b)<br>Trace: np.einsum('ii', A)

beginner

Why might beginners find np.einsum() tricky at first?

Because it uses a special string notation to describe operations, which can look confusing until you practice reading and writing these formulas.

What does np.einsum('ij,jk->ik', A, B) compute?

A Sum of all elements in A and B

B Matrix multiplication of A and B

C Element-wise multiplication of A and B

D Transpose of matrix A

This is the standard matrix multiplication formula using einsum notation.

Which of these is a benefit of using np.einsum()?

A It can combine multiple operations efficiently

B It replaces Python loops with slower code

C It only works on 1D arrays

D It always uses more memory

np.einsum can combine operations to reduce memory use and speed up calculations.

What does the subscript 'ii' mean in np.einsum('ii', A)?

A Outer product of A with itself

B Sum of all elements in A

C Transpose of A

D Sum of diagonal elements (trace) of A

'ii' selects diagonal elements and sums them, which is the trace.

How would you use np.einsum() to compute the dot product of two vectors a and b?

A <code>np.einsum('i,i->', a, b)</code>

B <code>np.einsum('i,j->ij', a, b)</code>

C <code>np.einsum('ij,jk->ik', a, b)</code>

D <code>np.einsum('ii', a)</code>

'i,i->' sums the product of matching elements, which is the dot product.

Which is NOT true about np.einsum()?

A It can perform tensor contractions

B It requires understanding subscript notation

C It only works with 2D arrays

D It can reduce temporary arrays for speed

np.einsum works with arrays of any dimension, not just 2D.

Describe how np.einsum() can be used to perform matrix multiplication. Include an example with explanation.

Think about how rows and columns match in matrix multiplication.

Explain why np.einsum() can be more efficient than chaining multiple numpy operations.

Consider what happens when you do many steps separately versus all at once.