Welcome! In today's lesson, we'll learn how to use functions with NumPy arrays, a crucial concept for managing large amounts of data. This ability facilitates efficient data processing — a teacher calculating class averages or a business analyst summarising company sales illustrates the practical use of these skills. Are you ready? Let's get started!

Two arrays of the same shape can undergo basic arithmetic operations. The operations are performed element-wise, meaning they're applied to each pair of corresponding elements. Suppose we have two grade arrays of students from two subjects. By adding these arrays, we can calculate the total grades:

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1subject1_grades = np.array([88, 90, 75, 92, 85])
2subject2_grades = np.array([92, 85, 78, 90, 88])
3
4total_grades = subject1_grades + subject2_grades
5
6print("Total grades:", total_grades)  # Output: Total grades: [180 175 153 182 173]

The two arrays are added element-wise in this code to calculate the total grades.

NumPy's Universal Functions (also called ufuncs) perform element-wise operations on arrays, including mathematical functions like sin, cos, log, and sqrt. Let's look at a use case:

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1angles_degrees = np.array([0, 30, 45, 60, 90])
2angles_radians = np.radians(angles_degrees)
3sin_values = np.sin(angles_radians)
4
5print("Sine of angles:", sin_values)  # Output: Sine of angles: [0. 0.5 0.70710678 0.8660254 1.]

This code applies np.sin universal function to each array element. As np.sin expects its input in radians, we first transform degrees to radians with np.radians, applying it to each array element similarly.

NumPy allows the application of a custom function to each element of the array separately by transforming the target function with np.vectorize. Let's create a function to check the parity of a number:

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1def is_even(n):
2    return n % 2 == 0
3
4vectorized_is_even = np.vectorize(is_even)
5
6numbers = np.array([1, 2, 3, 4, 5])
7results = vectorized_is_even(numbers)
8
9print("Results:", results).  # Output: Results: [False True False True False]

The vectorized_is_even function returns an array indicating whether each value in numbers is even.

Well done! You've learned how to apply functions to NumPy arrays, perform arithmetic operations, apply statistical functions, use ufuncs, and extend NumPy with custom functions. Up next are practice exercises for further learning. Let's proceed!