University of Connecticut ECE1101 Spring 2021 Homework – Matrix Multiplication Due April 28, 2021 End of Day Matrix multiplication is a common operation in electrical engineering whether it’s solving...

The primary objective is to write four methods that will write in to my text-c file. I can't use data[i] or data[j] because the array is variable sized.Since we want the element at row i and column j, I will use instead use data[i*m+j].


University of Connecticut ECE1101 Spring 2021 Homework – Matrix Multiplication Due April 28, 2021 End of Day Matrix multiplication is a common operation in electrical engineering whether it’s solving linear circuits or decoding communications schemes. Your task for this homework is to write a program that reads data from two files (having matrix data), performing the matrix multiplication, and then writing out the result. If you haven’t seen matrices before, let’s do a quick overview. A matrix is a two- dimensional array of numbers, as shown below: ? = [ 1 0 2 −1 4 3 5 2 1 ] Matrix multiplication takes two matrices and multiplies them, but instead of multiplying element by element, the multiplication is done row by column. The row/column multiplication is done using dot products. Dot product multiplication takes two arrays or vectors of numbers - [?0 ?1 ?2] and [?0 ?1 ?2], and multiplies each pair of numbers as follows: ?0?0 + ?1?1 + ?2?2. In matrix multiplication, if we have two matrices, A and B, we multiply each row of A with each column of B in a dot product multiplication. For example, take the two matrices below: ? = [ 1 0 2 −1 4 3 5 2 1 ] ? = [ 2 −2 5 2 3 1 0 3 −1 ] The multiplication of matrices C=A•B will be as follows – the element at row 0 and column 0 of matrix C will be the dot product of row 0 of A and column 0 of B, the element at row 0 and column 1 of matrix C will be the dot product of row 0 of A and column 1 of B, and more generally the element at row i and column j of matrix C will be the dot product of row i of A and column j of B. ? = [ 1 ∙ 2 + 0 ∙ 2 + 2 ∙ 0 1 ∙ −2 + 0 ∙ 3 + 2 ∙ 3 1 ∙ 5 + 0 ∙ 1 + 2 ∙ −1 −1 ∙ 2 + 4 ∙ 2 + 3 ∙ 0 −1 ∙ −2 + 4 ∙ 3 + 3 ∙ 3 −1 ∙ 5 + 4 ∙ 1 + 3 ∙ −1 5 ∙ 2 + 2 ∙ 2 + 1 ∙ 0 5 ∙ −2 + 2 ∙ 3 + 1 ∙ 3 5 ∙ 5 + 2 ∙ 1 + 1 ∙ −1 ] ? = [ 2 4 3 6 23 −4 14 −1 26 ] You should run the program as follows: ./hw5 3 hw5-a-matrix.txt hw5-b-matrix.txt hw-c-matrix.txt where, in this case, 3 is the size of the matrix, and hw5-a-matrix.txt and hw5-b- matrix.txt are the names of files that contain the input A and B matrices. Two sample A and B files are provided on HuskyCT. You will write the output matrix C to the file named hw5-c-matrix.txt. The matrix files are written with each line containing one row of the matrix with each number separated by a space. Writing the code This code must be written in C++. You are given a main function that looks as follows: #include #include "Matrix.h" int main(int argc, char **argv) { int m = atoi(argv[1]); Matrix A(m, argv[2]); Matrix B(m, argv[3]); Matrix C = A * B; C.write(argv[4]); } m is the size of the matrix, and argv[2], argv[3], and argv[4] are the file names for the two input files and the output file respectively. Matrix A and Matrix B are initialized using a constructor that takes in the size and the filename. Matrix C is created using an overloaded * operator. The Matrix class is defined in Matrix.h as follows: class Matrix { public: Matrix(int); Matrix(int, char *); Matrix(const Matrix &); ~Matrix(); Matrix operator * (Matrix&) const; void write(char *); private: int size; double *data; }; You will need to complete the code for the Matrix(int, char *) constructor, the Matrix(const Matrix &) copy constructor, Matrix * operator, and the write method. The data field is an array that stores the two-dimensional data for the matrix. Since we don't know the size of the array until we run the program and the user tells us, we can’t predefine the matrix as a 2D array. C/C++ does not support variable-sized two- dimensional arrays, so the array has been created in the constructors using new as follows: double *data = new double [size*size]; Unfortunately, we can’t use two-dimensional array syntax like data[i][j] because the array is variable sized. So, instead we map the 2D matrix into a 1D array row by row as shown below: [ ?00 ?01 ?02 ?10 ?11 ?12 ?20 ?21 ?22 ] → [?00 ?01 ?02 ?10 ?11 ?12 ?20 ?21 ?22] Thus, if we want the element at row i and column j, we do the following: data[i*m+j] The methods that you need to write are described below. Matrix(int m, char *filename) constructor Use the fscanf function to read the file. Here is an example of using fscanf to read a number from a file: double value; FILE *file = fopen(filename, “r”); fscanf(file, "%lf ", &value); This will read one number as a double from the file into the variable value. You will need to use this call within two nested loops that iterate over the matrix array going through the rows in the outer loop and the columns in the inner loop to read the data from the file into the data array. Matrix(Matrix &original) copy constructor Iterate through the original data and copy the values into the new object data operator *(Matrix &b) This method will do the multiply of the current Matrix object with the b Matrix. You will need a set of nested loops – this time 3 nested loops. The first two nested loops i and j will iterate over the rows and columns of the output matrix out. The third and innermost loop will iterate over the i-th row of the current data and the j-th column of b data to do the dot product. This innermost loop will do an accumulation of the multiplications to calculate the dot product and the accumulated sum will go into the out.data element at row i and column j. write(char *filename) This method should write to the output file in the same format as the input matrix files. You can use the fprintf function to print the data to the file fprintf(file, "%f ", value); You will need to iterate over the rows and columns of data to print each element of the matrix to the file. Make sure you put a newline at the end of each row. The code will be compiled as follows: g++ -o hw5 hw5-matrix-main.cpp hw5-matrix.cpp Submission Submit your .cpp file on HuskyCT. Use comments to explain what your code does. 2.3 1.9 0.5 1.5 1.3 3.1 3.3 1.2 2.5