In this course, we will use C for the OpenMP, GPU and MPI programming. This exercise will refresh your memory about C programming. Please write a serial C program to do the matrix$-$vector multiplication.

Implementation requirements:

$$ Because the input matrix and vector can be very large, you must use dynamic memory allocation $($i$.$e$.,$ malloc and free$)$ to store them in the heap. If your implementation stores the input matrix, the input vector, or the output vector in the stack, we will deduct $10$ points.

$$ There are many ways to store the matrix in a dynamically allocated $2-$dimensional array in C$,$ including $($a$)$ using the row$-$major order or column$-$major order in a $1-$dimentional array or $($b$)$ using an array of pointers to a set of $1-$dimensional arrays. In this exercise, please store the matrix in a dynamically allocated $1-$dimensional array in the row$-$major order $(5$ points$).$

To help you meeting the two implementation requirements, we have provided a toy C program that dynamically allocates a $2$D array stored by row$-$major order. This C program is called array$\_$allocation.c under the Problem$\_2$ sub$-$directory.

Your matrix$-$vector multiplication program should take two input files, one for the input matrix and the other one for the input vector. All the numbers are integers. The two input files are provided in the comma$-$separated values $($CSV$)$ format. To prevent the numbers from running out of range, please declare the type of all variables as long int. The output vector should be saved in a CSV file.

Your program should be run using the following command line:

serial$\_$mult$\_$mat$\_$vec file$\_1.$csv n$\_$row$\_1$ n$\_$col$\_1$ file$\_2.$csv n$\_$row$\_2$ result$\_$vector.csv