Part H: 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.
   • 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 an initial condition, current state, and parameter list.
   • As part of the class, define an iteration method that iterates the current state some number of time steps, returning the final state reached.
4. Recall the one-dimensional map program that calculates the Lyapunov characteristic exponent. That program does not catch the error, which is expected, if not common, of passing a zero derivative to the logarithm. Modify that program to catch this error and respond gracefully (not terminate!).