Question

Write a function that uses function randomo to generate a random value in the range [low, high), where low and high are passed as calling arguments. Make random0 a private function called by your new function.

Short answer

The function `random_in_range` is created to generate a random number within a range [low, high) using a private function called 'random0'. The random0 function generates a random number in the range [0, 1) using Python's standard library random module. The random number within the range [low, high) is generated by transforming the value produced by random0 (which is in the range [0,1)) using the formula `low + (high - low) * random0()`. Here's the implementation: ```python def random_in_range(low, high): import random def random0(): return random.random() return low + (high - low) * random0() ``` This function, when tested with inputs, will generate random numbers within the desired range, calling the private function random0.

Step-by-step solution

Understanding the requirements

First, we need to understand the problem statement and requirements. We are asked to create a high-level function that generates a random number in the range [low, high). In addition, random0 will be a private function (i.e., not accessible in the global scope) that will be called by our high-level function.

Create the high-level function

Let's create a function named "random_in_range" with two parameters: "low" and "high". This function will call the private "random0" function to generate the random number in the desired range. ```python def random_in_range(low, high): # The implementation will be added in the next step pass ```

Implement the random0 function

Now, we need to implement the "random0" function. It should be a private function that generates a random number in the range [0, 1). We'll use the "random" module from Python's standard library for this purpose. ```python def random_in_range(low, high): import random def random0(): return random.random() # The next step will involve using random0 to generate the random number in the desired range ```

Generate the random number in the specified range

With random0 implemented, we can now use it in our high-level function "random_in_range" to generate a random number within the range [low, high). To do this, we will multiply the value generated by random0 with the difference of 'high' and 'low', and then add the 'low'. This will help us transform the value produced by random0, which is in the range [0, 1), to our desired range [low, high). ```python def random_in_range(low, high): import random def random0(): return random.random() return low + (high - low) * random0() ```

Test the function

Finally, we'll test our random_in_range function with different inputs to verify that it works as expected. ```python print(random_in_range(10, 20)) # Generates a random number between 10 (inclusive) and 20 (exclusive) print(random_in_range(-5, 5)) # Generates a random number between -5 (inclusive) and 5 (exclusive) ``` The "random_in_range" function should now work correctly and generate random numbers within the specified range using the private "random0" function.

Key concepts

Programming for Engineers

Programming is a powerful tool for engineers, providing a strong foundation for problem solving and automation in various fields of engineering. For engineers, programming is less about developing software products and more about using programming languages to solve complex engineering problems, analyze data, and simulate real-world systems.

One of the most popular programming languages in this context is MATLAB. It stands out due to its high-level syntax and built-in support for matrix operations, which makes it particularly suitable for numerical computation tasks common in engineering. For example, MATLAB can be used for analyzing data, developing algorithms, and creating models and simulations.

To become proficient in programming for engineering tasks, it is essential to understand the core concepts of algorithm design, function creation, and data manipulation. Learning how to create user-defined functions in MATLAB, such as the 'random_in_range' function from the exercise, is a fundamental skill. It allows engineers to wrap specific functionalities into reusable and modular pieces of code that can be tested and maintained more easily. This modularity also enables better collaboration among team members and aligns well with engineering principles.

MATLAB Random Number Generation

Random number generation is a critical concept in Matlab programming, especially for tasks like simulations, modeling stochastic processes, or any probabilistic algorithm. MATLAB has built-in functions for generating random numbers, like 'rand', 'randi', and 'randn', each serving different purposes.

The 'rand' function, for example, generates uniformly distributed numbers in the interval $0,1$, which is exactly the functionality required for the 'random0' function in the exercise. By scaling and translating the output of 'rand', it is possible to obtain random numbers within any desired range, as done in the 'random_in_range' function where the range [low, high) is specified.

Understanding how random numbers are generated and manipulated is critical for ensuring that the performance of an algorithm is both random and within expected constraints. In the case study provided, the use of multiplication and addition allows for customization of the range while ensuring the distribution remains uniform, which is vital for many engineering applications.

Private Function Implementation

In many programming environments, 'private' functions are those that are localized to a given file or module and are not accessible from outside that specific scope. Creating private functions is crucial for encapsulation, a principle of software engineering that restricts access to certain parts of the code, thereby creating a 'black box' and preventing unintended interference with internal processing.

In MATLAB, while there is no explicit 'private' keyword, similar functionality is achieved by placing functions in a subfolder named 'private'. These functions are only accessible by functions within the same folder or parent directory. However, in Python, as used in the exercise, private functions are typically denoted by a preceding underscore in their name. Nevertheless, this is only a naming convention and does not enforce privacy.

The 'random0' function created in the given exercise simulates a private function within the 'random_in_range' function's scope. By defining 'random0' within 'random_in_range', it is made inaccessible from outside, hence embodying the concept of a private function. Implementing such private functions helps in simplifying debugging and unit testing, as it isolates a part of the code that performs a specific task separate from the rest of the application.