Project description

Your C++ program reads dimensions m and n and a sparse coefficient matrix A and a sparse right side vector b from cin and returns the unique solution vector x with Ax = b to cout. If no such unique vector exists, a message is printed. NEW If you are not familiar with Gaussian elimination, you can program the following alternative functionality: Your C++ program reads dimensions m and n and a sparse coefficient matrix A and a sparse vector b from cin and returns the the sparse vector y with y = Ab to cout. Sparse vectors for both alternatives are sparse matrices with n=1.

The public interface and data structure for the spares matrix is given in sparsemat.h. The header file contains already written members for I/O so that you can test your program easily. A sample file containing the input to the sparse matrix A is sparsemat.dat.

Note that the template class needs a Field. We assume the Field type has constructors from ints, copy constructors, the operators +, -, *, /, =, == and that operator>> and operator<< are appropriately overloaded to provide I/O.

Please submit a file sparsemat.h and several test programs.

Hint: since you have not programmed in C++ at all and this is a sophisticated program, I have made available my implementation of put_value. You may wish to look, or try your solution first.

BONUS EXTENSION: Instantiating the template sparsemat<> for many mathematical fields may cause code bloat, because each of the member functions gets compiled for each of the mathematical fields. The task here is to compute with all of three mathematical fields discussed above while using a single class sparsemat<field_base>, where field_base is an abstract base class for the derived classes that implement the double, modular, and fuzzy arithmetic. All member functions used in sparsemat are virtual (cf. C++Examples/Stacks/).

There is a problem with the constructors, as they cannot be virtual. (In Java, clone(), which is default the copy method, can be declared abstract, i.e., virtual). Remember that operator[] returns a copy of the mathematical field element in the matrix. In addition, STL's make_pair template function uses the copy constructor for initializing the pairs data members. However, the copy constructor of field_base cannot return a clone of the element, that is a copy of the derived class object, because no constructors can be declared virtual.

A solution to this problem is to use a separate class abstract_field as the abstract class and instantiate sparsemat<abstract_field> instead. An instance of the abstract_field class contains a pointer to the field_base object, which actually must be derived class object. Now all constructors and the destructor for abstract_field can be written in terms of the virtual member functions clone, etc. of field_base.

The header file abstract_field.h is a prototype for such a design. Note that the static member default_elem_ptr gets initialized by the function set_default_elem_ptr to point to a derived object before each of the derived classes is used.
Note: you should not have to change anything in your sparsemat template class. The class abstract_field can be thought of as a ``wrapped'' pointer type.

Please submit a file abstract.cpp that contains the missing member function definitions, the derived class declarations and their member definitions and a main program that exercises all derived classes.