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One way to increase the length of a vector by utilizing another vector as a reference through vectorization is by using the repeat function in NumPy.
Suppose we have the following two vectors:
import numpy as np
a = np.array([1, 2, 3])
b = np.array([4, 5])
We want to increase the length of vector a to the same length as vector b by repeating its values. We can do this using the repeat function and the size difference between the two vectors:
a_expanded = np.repeat(a, len(b)//len(a)+1)
a_expanded = a_expanded[:len(b)]
# Output: array([1, 2, 3, 1, 2])
We divide the length of b by the length of a to determine how many times we need to repeat vector a, then we slice the array to match the length of vector b.