CS2141 Program Three

Matrices are used in a wide variety of applications in mathematics, physics, and a plethora of other fields. Though widely used, matrices provide a number of interesting implementational challenges, including the need to deal with dynamic memory allocation and mis-matched matrix sized. (Operations on large or distributed matrices present efficiency challenges as well, though these are rather beyond the scope of this course.) Matrices also have the rather nice feature of supporting a wide variety of mathematical operations. This makes them ideal as an introduction to operator overloading.

For this assignment, you will be implementing a matrix class capable of dealing with matrices of doubles.

Goals

• To become comfortable with building more complex classes.
• To practice Operator Overloading, involving friends and const references.
• To work more with pointers, references, and memory management.
• To practice error handling.

Problem Description

Your task for this program is to build a Matrix class to represent a matrix of doubles. Your class will need to provide overloaded operators to make using the class easier.

Unlike previous projects, main() will be provided for you. You need only provide an implemenation of the Matrix class to power the pre-written code.

Input

There is no need for you to implement input as part of your matrix class.

Ouput

You should overload the << operator to output Matrices:

Matrices should be output as bracketed matrices with bracketed rows. Each row should have have values printed with one space between them. The matrix should start on a new line, and each row should be on a seperate line. All lines but the first should have a single space prior to the first bracket on the line.

This statement

should print something formatted like:

The first Matrix is:
[[4.2 5.6 3.2 6.7 1.221 6 1000000]
 [4.6 1.1 0.9999 3.1 1 100000 0]
 [0 0 0 0 0 0 0]
 [4 5 6 7 0 0 0]]
 
The second Matrix is:
[[5.5 1000.1 0 0 0 0]
 [4.6 1.1 0.9999 3.1 1 100000]
 [0 0 0 0 0 0]
 [4.5 5.5 6.5 0 0 0]
 [0 0 0 0 0 0]]

Code Requirements

Matrix Class

This class should create a Matrix which can store doubles.

The Matrix class should have the following functionality:

• You should be able to create a Matrix from a 2D array of doubles, given the array, and the dimensions.
• You should be able to create a Matrix comprized of all zeros by providing only the dimensions.
• You should be able to create an empty Matrix by providing no arguments to the constructor.
• You should be able to create a new Matrix which is functionally a duplicate of another Matrix, but without using the same memory. (ie you need a copy constructor)
• You should be able to assign a Matrix the value of another Matrix, making it functionally equivalent. (ie you need an assignment operator)
• You should have accessor methods to get the dimensions of the Matrix (however, you shouldn't be able to resize the matrix in this way).
• In the event that an operation should fail for whatever reason, you should return an empty Matrix rather than crashing the program.

• Operator Overloading

  You should overload operators to do the following:

  • Output Matrices (see above).
  • Access a location in a Matrix using () ( both matrix(1,2) = a; and a = matrix(1,2); should work).
  • Multiply two Matrixes of the appropriate size (remember: order is important).
  • Add / subtract two Matrices of the same size.
  • Multiple / divide a Matrix by an int or double.
  • Check for equality or inequality (== and !=). You need not overload other comparison operators.

  You should implement both the common (eg +) and assignment (eg +=) forms of the mathematical operations. Remember that multiplication may change the size of the matrix!

  Main

  int main() is provided for you in the file main.cpp. You should not make any changes to this file. It should, in fact, be possible for the grader to compile your program with a different version of main.cpp and have the new program compile and run.

  Makefile

  You will provide a Makefile that we can use to compile and run your program. It needs to include the rules for default, clean, and run (see the example here for details). Note that you will need to include main.cpp in the Makefile.

  Source Files and Headers

  The main function is, of course, implemented in main.cpp. Your class should be implemented in Matrix.h and Matrix.cpp. Other classes or functions should have appropriate header and source files.

  Other Guidelines

  • No global variables. Global constants are okay though, so long as they're declared const.
  • No memory leaks (that means 0 bytes leaked!) Clean up everything you allocate.
  • You should handle errors appropriately. Don't just kill the program.
  • Here are the gradesheet and guidelines for this program.

  Only the following functions and classes may be used (remember to add using namespace std;):

  • The classes and functions you write yourself.
  • Those from iostream
  • Those from iomanip
  • Those from string
  • Those from sstream

  Note, however, that while you may include these libraries it is not required that you do so.

  Hopefully Helpful Hints

  • Start Early! It's okay to finish early.
  • Make sure you comment your code! Proper documentation and formatting is an important part of your grade.
  • If you need help, you can ask your instructor.

  Have fun, and remember that all the usual rules regarding cheating and cooperation are in full effect for this program.