USING C++

You need to write a matrix class (Mat) that implements common matrix functionality. You need use the Mat.h and Mat.cpp files to write this class. Your Mat class should meet the following requirements.

Dynamic Matrix Allocation

Mat m(10,2); // Allocates a matrix with 10 rows and 2 columns

Mat m; // creates a null matrix // this is a placeholder

 // with 0 rows and 0 columns  

Read and write from istream and ostream, respectively.

Reading from a istream

Mat m; // creates a null matrix

cin >> m; // 1st entry is number of rows (r) // 2nd entry is number of colums (c)

 // r times c entries for the matrix // // note that >> first allocates // the matrix of the right size and // then reads it in.  

 // the allocation only occurs if // m is a null matrix. // otherwise in case of a mismatch an // error is issued  

Writing to an ostream

Mat m(2, 3); ofstream f("output.mat"); f << m; // 1st entry is 2

 // 2nd entry is 3  

// 6 entries

f.close();

Copy constructor and assignment operator with error checking

Mat a(2,3); Mat b(a); // Using copy constructor Mat c = a; // Using assignment operator

// But the following should give an error  

Mat d(10,10); d = a; // Not the same size

Scalar arithmatic

Overload the following operators for matrix-scalar (double) addition/subtraction/multiplication/division: +, -, *, /, +=, -=, *= and /=.

Matrix arithmatic

Overload the following operators for matrix-matrix addition/subtraction/multiplication: +, -, *, +=, -= and *=. Dont forget to error check. E.g., for addition or subtraction the two matrices must be the same size, and for multiplication the number of columns of the first matrix should be equal to the number of rows of the second matrix.

Hint: checkout matrix operations in your favourite linear algebra text book.

Indexing

Overload [] operator to support the following functionality: Mat m(2,3);

cout << m[0][1] << endl; // prints the 0th row and 1st column entry

Fill up

Develop the following functions:

Destructor to deallocate the memory; Mat::ones() to initialize a matrix to all 1s; Mat::zeros() to initialize a matrix to all 0s; and Mat::rand() to intialize a matrix to random values between 0 and 1.

Your class should be called Mat It should be implemeted in files Mat.h and Mat.cpp.

A user will use your class as follows:

... #include "Mat.h" ... int main() { 

 Mat m(2,2); m.ones(); 

return 0; }

Compilation:

$ g++ main.cpp Mat.cpp -o mat_test