Exercise 1: automatic differentiation (1/2)

Implement a C++ framework for computing derivatives of arbitrary functions using a polymorphic approach. The goal is to create a structure that can handle common arithmetic operations, such as addition, subtraction, multiplication, division, and exponentiation, on values and their derivatives.

Test the program to compute the value and the derivative of the polynomial and of the function at .

Exercise 1: automatic differentiation (2/2)

1. Define an abstract base class ADExpression with two pure virtual functions:
   • double evaluate(): This function returns the value of the variable.
   • double derivative(): This function returns the derivative of the variable.
2. Implement a concrete class Scalar that inherits from ADExpression. This class represents a scalar variable and its derivative.
3. Implement the following operation classes that also inherit from ADExpression:
   • Sum: Represents the addition of two ADExpression objects.
   • Difference: Represents the subtraction of two ADExpression objects.
   • Product: Represents the multiplication of two ADExpression objects.
   • Division: Represents the division of two ADExpression objects.
   • Power: Represents raising an ADExpression object to a constant exponent.
4. In the main function, demonstrate the usage of these classes.

Exercise 2: inheritance and polymorphism for data analysis

In the context of data analysis, create a C++ program that models different types of data sources and transformation objects.

1. Define an abstract class DataSource with attributes and methods that represent common properties of data sources. Create derived classes such as FileDataSource and ConsoleDataSource.
2. Define an abstract class DataTransformer with a virtual method for data transformation. Create derived classes such as LinearScaler, LogTransformer, and StandardScaler that implement specific data transformation methods.
3. Test all functionalities by prompting the user with proper questions.

Exercise 2 (1/5)

1. Define an abstract class DataSource with a string attribute name, a vector data, a method display_info() and a pure virtual method read_data().
2. Implement a constructor and a virtual destructor in the DataSource class with.
3. Create derived classes FileDataSource and ConsoleDataSource that inherit from DataSource.
4. Implement constructors for all classes to model different data source types. For example, FileDataSource should initialize a filename and an input file, ConsoleDataSource should have a default constructor.
5. Implement destructors for the derived classes. For example, the FileDataSource constructor should open the file, and its destructor should close it.

Exercise 2 (2/5)

1. Implement the read_data() methods. FileDataSource::read_data() should import values from a file (see data.txt as an example), whereas ConsoleDataSource::read_data() should read a list of values from the standard input.
2. Create objects of these classes and demonstrate inheritance. For example, create a FileDataSource object and call display_info() and read_data() methods to read and display data from a file.
3. Ensure that resources associated with data sources are properly managed during construction and destruction.

Exercise 2 (3/5)

1. Define a base class DataTransformer, bound to DataSource by polymorphic composition. DataTransformer should have a pure virtual method transform() that transforms the data vector in the corresponding DataSource.
2. Create derived classes LinearScaler, LogTransformer, and StandardScaler that inherit from DataTransformer.
3. Override the transform() method in each derived class to provide specific data transformation. For example, LinearScaler scales the data by multiplying them by a given scaling factor, LogTransformer applies a logarithmic transformation and sets negative entries to 0, and StandardScaler performs standardization to the interval.
4. Create objects of these classes and demonstrate their use to transform the previously defined DataSource object.

Exercise 2 (4/5)

1. Use the DataSource and the DataTransformer hierarchy polymorphically. In particular, the program should prompt the user to import data either from a file or from console, and to select the transformation method.
2. Display the original and the transformed data.

Exercise 2 (5/5)

Possibilities for extensions

1. In case a FileDataSource is selected, prompt the user to specify the filename from the console.
2. In case a LinearScaler is selected, prompt the user to specify the scaling factor from the console.
3. Add a new class to the DataSource hierarchy to import a given field from an input CSV file (see data.csv as an example).
4. Write a class or method to overwrite the original data from the text or CSV file with the transformed ones.