these question from "Introduction to Parallel Computing, Second Edition By Ananth Grama, Anshul Gupta, George Karypis, Vipin Kumar" chapter 6

:please dont use copy and paste from another answer:

6.7 Consider the column-wise implementation of matrix-vector product (Program 6.5). An alternate implementation will be to use MPI_Allreduce to perform the required reduction operation and then have each process copy the locally stored elements of vector x from the vector fx. What will be the cost of this implementation? Another implementation can be to perform p single-node reduction operations using a different process as the root. What will be the cost of this implementation?

Program 6.5 Column-wise Matrix-Vector Multiplication 123"sore 4 5 6 7 8 9 ColMatrixVectorMultiply(int n, double ta, double *b, double **, MPI_Comm comm.) { int i, ji int nlocal; double *px; double *fx; int npes, myrank; MPI_Status status; 10 11 12 13 /* Get identity and size information from the communicator */ MPI_Comm_size (comm, Enpes); MPI_Comm_rank (comm, Smyrank); 14 15 nlocal = npes; 16 17 18 /* Allocate memory for arrays storing intermediate results. */ px = (double *) malloc (n*sizeof(double)); fx = (double *) malloc (n*sizeof(double)); 19 20 21 22 23 /* Compute the partial-dot products that correspond to the local columns of for (i=0; i