Activity B.3.1. Check Yourself: Slices.
A = np.array([[1, 2, 3],
[4, 5, 6],
[7, 8, 9]])
-
What is
A[:, 0]? -
What is
A[:2, :]? -
What is
A[:, :2]? -
What is the shape of each result?
Section B.3 Indexing and Slicing
This section helps you read Python indexing and slicing as requests for entries, rows, columns, or blocks of a vector or matrix.
x = np.array([10, 20, 30, 40])
x[0] # first entry
x[1] # second entry
x[-1] # last entry
x[:2] # first two entries
x[2:] # entries from index 2 onward
x[::-1] # reversed order
A = np.array([[1, 2, 3],
[4, 5, 6]])
A[0, 1] # row 0, column 1
A[0, :] # first row
A[:, 0] # first column
A[:, 1] # second column
A[:, :2] # all rows, first two columns
The rank-\(k\) SVD reconstruction uses the same slicing language:
Ak = U[:, :k] @ np.diag(s[:k]) @ Vt[:k, :]
First entry.
x[0]
Read as. The first entry of
x.
Shape/return. A scalar.
Used for. Indexing.
Last entry.
x[-1]
Read as. The last entry of
x.
Shape/return. A scalar.
Used for. Indexing.
Column extraction.
A[:, 0]
Read as. The first column of
A.
Shape/return. A one-dimensional array.
Used for. Column extraction.
First columns.
A[:, :k]
Read as. All rows and the first
k columns.
Shape/return. An array block.
Used for. SVD reconstruction.
First singular values.
s[:k]
Read as. The first
k singular values.
Shape/return. A one-dimensional array.
Used for. SVD reconstruction.
First rows.
Vt[:k, :]
Read as. The first
k rows and all columns.
Shape/return. An array block.
Used for. SVD reconstruction.
Reverse order.
[::-1]
Read as. Reverse the order.
Shape/return. A reordered array.
Used for. Rankings.
Boolean mask indexing selects entries where a Boolean array is true. In the optional attention notebook,
S_masked[mask] = -1e9 changes only the entries where mask is true.
