University:
Boston University
Course:
MET CS 201 | Introduction to Programming
Academic year:

2023
Views:

167

Pages:

12
Author:

granitt3c2r

Exercises for OpenMP Exercise 1: SAXPY • SAXPY: s = a*x + y adds a scalar multiple of a real vector to another real vector. • Use OpenMP to parallelize the SAXPY codes. int i; #pragma omp parallel for private(i) for (i = 0; i < n; i++){ y[i] = a*x[i] + y[i]; } Exercise 2: Matrix Multiplicatoin • Matrix element • Use OpenMP to parallelize the matrix-multiplication codes. Notes: 1. The three matrices are shared data, meaning that all threads can read and write them. 2. Distribute the works of the most outer loop to minimize overheads. #pragma omp parallel for shared(nra,ncb,nca) private(sum,i,j,k) for (i = 0; i < nra; i++){ for (j = 0; j < ncb; j++){ sum = 0.0; for (k = 0; k < nca; k++){ sum = sum + a[i][k] * b[k][j]; } c[i][j] = sum; } } Exercise 3: Laplacian solver • Two-dimensional Laplace equation: • Discretize the laplacian with first-order differential method and express the solution as • The solution on one point only depends on the four neighbor points: • Jacobi iterative algorithm: 1. Give a trial solution A depending on a provided initial condition. 2. Calculate the new value for every element of the solution, that is A_new(i,j), based on the old values of the four neighbor points. 3. Update the solution, i.e. A=A_new, 4. Iterate steps 2 and 3 until converged, i.e. max(| A_new(i,j)-A(i,j)|) tol && iter < iter_max ) { // iterate until converged error = 0.0; #pragma omp parallel for shared(m, n, Anew, A) private(i,j) for( j = 1; j < n-1; j++) for( i = 1; i < m-1; i++ ) { Anew[j][i] = 0.25 * ( A[j][i+1] + A[j][i-1] + A[j-1][i] + A[j+1][i]); //calculate new value from neighbors error = fmax( error, fabs(Anew[j][i] - A[j][i])); // calculate the maximum error } #pragma omp parallel for shared(m, n, Anew, A) private(i,j) for( j = 1; j < n-1; j++) for( i = 1; i < m-1; i++ ) { A[j][i] = Anew[j][i]; } iter++; } // Update the solution Exercise 4: Calculate the value of Pi • Calculate pi with integration method • Numerically, we can approximate the value of pi as the sum of a number of rectangles. • Use OpenMP to parallelize the program for calculating pi. Notes: Use reduction clause to avoid a data racing condition. #pragma omp parallel for default(shared) private(i,x) reduction(+:sum) { for (i = 0; i < n; i++) { x = (i+0.5)*step; sum += 4.0/(1.0+x*x); } } Exercise 5: Matrix-vector multiplication (in Fortran) • Calculate a=B*c, where a is an m dimension vector, c is an n dimension vector and B is an m*n dimension matrix. • Serial Fortran code do i = 1, m a(i) = b(i,1)*c(1) do j = 2, n a(i) = a(i) + b(i,j)*c(j) end do end do • Use OpenMP to parallelize the code for matrix-vector multiplication (version 1) !$OMP PARALLEL DO DEFAULT(shared) PRIVATE(i,j) do i = 1, m a(i) = b(i,1)*c(1) do j = 2, n a(i) = a(i) + b(i,j)*c(j) end do end do !$OMP END PARALLEL DO • Use OpenMP to parallelize the code for matrix-vector multiplication (version 2, only for Fortran) !$OMP PARALLEL DEFAULT(shared) PRIVATE(i,j) !$OMP WORKSHARE a(1:m) = b(1:m,1)*c(1) !$OMP END WORKSHARE !$OMP DO REDUCTION(+:a) do j = 2, n do i = 1, m a(i) = a(i) + b(i,j)*c(j) end do end do !$OMP END DO !$OMP END PARALLEL