Part F: Objects, Classes, and Error Handling

Exercises

1. Write a class MyMatrix that represents a matrix. Passed the number of rows and columns, a MyMatrix matrix is constructed from a two-dimensional array of floats. These matrices should support the following operations:
   • Addition and subtraction (element-by-element),
   • Multiplication (matrix product), and
   • Generalized inverse (returning another matrix object).
   • (Feel free to use the numpy package inside your methods for these operations.)
2. Write a specialized subclass SqMatrix that represents a square matrix.
   • Implement SqMatrix by inheriting from the MyMatrix class.
   • SqMatrix should verify that it is constructed from a square array.
   • If it is not square, it should raise a ValueError and print an informative error message.
   • In addition to the inherited matrix operations, the class should provide:
     • Inversion (returning another matrix object) and
     • Eigenvalues (returning an array).
     • (Feel free to use the numpy package inside your methods for these operations.)
3. Rewrite the one-dimensional map tool that we've been developing in an object-oriented fashion:
   • Define a class OneDimMap representing a one-dimensional map, with attributes consisting of an initial condition, current state, and parameter list.
   • As part of the class, define an iteration method that iterates the current state some number (passed in as an argument) of time steps, returning the final state reached.
4. Recall the MatrixIO.py module that reads in and writes out a matrix. The function that reads in a matrix does not catch the error when the file to be opened does not exist. Modify that module to catch this error and respond gracefully: The program should not terminate with Python error messages! Instead, it should print an informative error message, giving the file's name, saying that it could not be opened because it does not exist, and then exit.