Supporting files for Ex4, Ex5 and Ex6
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Sheet5/bench_funcs.cpp
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285
Sheet5/bench_funcs.cpp
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// bench_funcs.cpp
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#include "bench_funcs.h"
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#include <omp.h>
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#include <cmath>
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#include <cstddef>
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#include <vector>
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#include <algorithm>
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//EXERCISE 4
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// A: parallel sum
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double sum_basic(const std::vector<double>& x)
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{
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double sum = 0.0;
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#pragma omp parallel for reduction(+:sum)
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for (std::size_t i = 0; i < x.size(); ++i) sum += x[i];
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return sum;
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}
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// A: parallel dot product
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double dot_basic(const std::vector<double>& x, const std::vector<double>& y)
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{
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std::size_t N = x.size();
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double sum = 0.0;
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#pragma omp parallel for reduction(+:sum)
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for (std::size_t i = 0; i < N; ++i) sum += x[i] * y[i];
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return sum;
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}
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// Kahan remains same
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double dot_kahan(const std::vector<double>& x, const std::vector<double>& y)
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{
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double sum = 0.0;
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double c = 0.0;
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for (std::size_t i = 0; i < x.size(); ++i)
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{
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double prod = x[i] * y[i];
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double yk = prod - c;
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double t = sum + yk;
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c = (t - sum) - yk;
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sum = t;
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}
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return sum;
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}
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// Norm (sum of squares)
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double norm_basic(const std::vector<double>& x)
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{
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double sumsq = 0.0;
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#pragma omp parallel for reduction(+:sumsq)
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for (std::size_t i = 0; i < x.size(); ++i) sumsq += x[i]*x[i];
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return sumsq;
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}
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// B: matvec (row-major)
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void matvec_rowmajor(const std::vector<double>& A, std::size_t M, std::size_t N,
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const std::vector<double>& x, std::vector<double>& b)
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{
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b.assign(M, 0.0);
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#pragma omp parallel for
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for (std::size_t i = 0; i < M; ++i) {
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double tmp = 0.0;
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const double* Ai = &A[i*N];
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for (std::size_t j = 0; j < N; ++j) tmp += Ai[j] * x[j];
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b[i] = tmp;
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}
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}
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// C: matmul (row-major)
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void matmul_rowmajor(const std::vector<double>& A, std::size_t M, std::size_t L,
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const std::vector<double>& B, std::size_t N,
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std::vector<double>& C)
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{
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C.assign(M * N, 0.0);
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// Parallelize over output rows (i)
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#pragma omp parallel for
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for (std::size_t i = 0; i < M; ++i) {
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for (std::size_t k = 0; k < L; ++k) {
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double Aik = A[i*L + k];
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const double* Bk = &B[k*N];
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double* Ci = &C[i*N];
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for (std::size_t j = 0; j < N; ++j) {
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Ci[j] += Aik * Bk[j];
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}
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}
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}
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}
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// D: polynomial evaluation (Horner), parallel over x points
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void polyp_horner(const std::vector<double>& a, const std::vector<double>& x, std::vector<double>& y)
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{
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std::size_t p = a.size() - 1;
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std::size_t N = x.size();
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y.assign(N, 0.0);
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#pragma omp parallel for
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for (std::size_t i = 0; i < N; ++i) {
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double xi = x[i];
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double val = a[p];
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for (std::size_t k = p; k-- > 0; ) {
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val = val * xi + a[k];
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}
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y[i] = val;
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}
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}
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//EXERCISE 5
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// Parallel assembly of tridiagonal FEM matrix (CSR)
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void build_fem_system(std::size_t n, CSR& K, std::vector<double>& f)
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{
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K.n = n;
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K.row_ptr.resize(n+1);
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f.assign(n, 1.0);
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K.val.resize(3*n); // Each row has at most 3 non-zero entries: [-1,2,-1]
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K.col.resize(3*n);
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for (std::size_t i = 0; i < n; ++i)
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K.row_ptr[i] = 3*i;
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K.row_ptr[n] = 3*n;
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#pragma omp parallel for // Fill matrix in parallel
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for (std::size_t i = 0; i < n; ++i) {
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std::size_t base = 3*i;
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if (i > 0) {
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K.val[base] = -1.0;
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K.col[base] = i - 1;
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} else {
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K.val[base] = 0.0;
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K.col[base] = 0;
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}
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K.val[base + 1] = 2.0;
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K.col[base + 1] = i;
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if (i + 1 < n) {
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K.val[base + 2] = -1.0;
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K.col[base + 2] = i + 1;
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} else {
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K.val[base + 2] = 0.0;
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K.col[base + 2] = i;
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}
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}
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}
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// Parallel Jacobi iteration
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void jacobi_csr_parallel(const CSR& K, const std::vector<double>& f,
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std::vector<double>& u,
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std::size_t max_iter, double omega, double tol)
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{
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std::size_t n = K.n;
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u.assign(n, 0.0);
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std::vector<double> u_new(n, 0.0);
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for (std::size_t iter = 0; iter < max_iter; ++iter) {
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double max_err = 0.0;
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#pragma omp parallel for reduction(max:max_err)
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for (std::size_t i = 0; i < n; ++i) {
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double diag = 0.0;
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double sum = 0.0;
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for (std::size_t idx = K.row_ptr[i]; idx < K.row_ptr[i+1]; ++idx) {
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std::size_t j = K.col[idx];
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double v = K.val[idx];
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if (j == i) diag = v;
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else sum += v * u[j];
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}
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double ui_new = u[i] + omega * (f[i] - sum - diag*u[i]) / diag;
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u_new[i] = ui_new;
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double err = std::fabs(ui_new - u[i]);
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if (err > max_err) max_err = err;
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}
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u.swap(u_new);
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if (max_err < tol) break;
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}
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}
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//EXERCISE 6
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// Helper: build empty CSR structure (3 entries per row)
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static void prepare_tridiag_csr(std::size_t n, CSR &K)
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{
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K.n = n;
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K.row_ptr.resize(n + 1);
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// Each row has 3 slots (left, diag, right)
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for (std::size_t i = 0; i < n; ++i) K.row_ptr[i] = 3 * i;
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K.row_ptr[n] = 3 * n;
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K.val.assign(3 * n, 0.0);
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K.col.resize(3 * n);
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// fill col indices
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for (std::size_t i = 0; i < n; ++i) {
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std::size_t base = 3 * i;
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// left column index
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if (i > 0) K.col[base + 0] = i - 1;
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else K.col[base + 0] = i; // dummy (no entry)
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// diagonal
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K.col[base + 1] = i;
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// right
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if (i + 1 < n) K.col[base + 2] = i + 1;
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else K.col[base + 2] = i; // dummy
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}
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}
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// Element-level element matrix (1D linear element on uniform mesh)
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// local ordering: node 0 = left, node 1 = right
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// element matrix (unscaled) = [ 1 -1; -1 1 ]
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// For a uniform mesh with h=1/(n-1) stiffness would be 1/h. For simplicity we use 1.0 scaling.
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inline void element_matrix_vals(double out[4])
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{
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// ordering out = [K00, K01, K10, K11]
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out[0] = 1.0; out[1] = -1.0; out[2] = -1.0; out[3] = 1.0;
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}
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// Atomic assembly: parallel over elements, atomic adds to K.val
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void build_fem_system_atomic(std::size_t n, CSR &K, std::vector<double> &f)
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{
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prepare_tridiag_csr(n, K);
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f.assign(n, 1.0); // RHS = 1
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std::size_t nel = (n >= 2) ? (n - 1) : 0;
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// Parallel over elements
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#pragma omp parallel for
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for (std::size_t e = 0; e < nel; ++e) {
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// global node indices for element e: i = e, j = e+1
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std::size_t i = e;
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std::size_t j = e + 1;
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double Em[4];
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element_matrix_vals(Em);
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// contributions:
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// K(i,i) += Em[0]
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// K(i,j) += Em[1]
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// K(j,i) += Em[2]
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// K(j,j) += Em[3]
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std::size_t idx_ii = 3 * i + 1; // diag of row i
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std::size_t idx_ij = 3 * i + 2; // right of row i
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std::size_t idx_ji = 3 * j + 0; // left of row j
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std::size_t idx_jj = 3 * j + 1; // diag of row j
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#pragma omp atomic
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K.val[idx_ii] += Em[0];
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#pragma omp atomic
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K.val[idx_ij] += Em[1];
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#pragma omp atomic
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K.val[idx_ji] += Em[2];
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#pragma omp atomic
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K.val[idx_jj] += Em[3];
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}
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}
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// No-atomic grouped assembly (method (a))
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// We compute each row i's three entries by summing the (<=2) contributing elements.
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// Parallel over rows; no atomics.
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void build_fem_system_no_atomic(std::size_t n, CSR &K, std::vector<double> &f)
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{
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prepare_tridiag_csr(n, K);
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f.assign(n, 1.0);
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// element matrix values (same for all elements here)
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double Em00 = 1.0, Em01 = -1.0, Em10 = -1.0, Em11 = 1.0;
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#pragma omp parallel for // parallel over rows (global entries)
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for (std::size_t i = 0; i < n; ++i) {
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std::size_t base = 3 * i;
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// left entry (K[i, i-1]) gets contribution only from element e = i-1
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if (i > 0) K.val[base + 0] = Em10; // from element e=i-1 local(1,0)
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else K.val[base + 0] = 0.0;
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// diagonal K[i,i] gets contributions from element e=i-1 (local(1,1)) and e=i (local(0,0))
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double diag = 0.0;
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if (i > 0) diag += Em11; // e = i-1 local(1,1)
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if (i + 1 < n) diag += Em00; // e = i local(0,0)
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K.val[base + 1] = diag;
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// right entry (K[i,i+1]) gets contribution only from element e = i
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if (i + 1 < n) K.val[base + 2] = Em01; // e=i local(0,1)
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else K.val[base + 2] = 0.0;
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}
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}
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50
Sheet5/bench_funcs.h
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50
Sheet5/bench_funcs.h
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#pragma once
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#include <vector>
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#include <cstddef>
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//EXERCISE 4
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// scalar and vector operations
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double sum_basic(const std::vector<double>& x);
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double dot_basic(const std::vector<double>& x, const std::vector<double>& y);
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double dot_kahan(const std::vector<double>& x, const std::vector<double>& y);
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double norm_basic(const std::vector<double>& x);
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// matrix-vector, matrix-matrix, polynomial
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void matvec_rowmajor(const std::vector<double>& A, std::size_t M, std::size_t N,
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const std::vector<double>& x, std::vector<double>& b);
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void matmul_rowmajor(const std::vector<double>& A, std::size_t M, std::size_t L,
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const std::vector<double>& B, std::size_t N,
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std::vector<double>& C);
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void polyp_horner(const std::vector<double>& a, const std::vector<double>& x,
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std::vector<double>& y);
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// EXERCISE 5
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struct CSR {
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std::size_t n;
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std::vector<double> val;
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std::vector<std::size_t> col;
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std::vector<std::size_t> row_ptr;
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};
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void jacobi_csr(const CSR& K, const std::vector<double>& f, std::vector<double>& u,
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std::size_t max_iter, double omega, double tol);
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// build tridiagonal FEM matrix K and rhs f (parallel)
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void build_fem_system(std::size_t n, CSR& K, std::vector<double>& f);
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//Jacobi iteration (parallel)
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void jacobi_csr_parallel(const CSR& K, const std::vector<double>& f,
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std::vector<double>& u,
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std::size_t max_iter, double omega, double tol);
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// EXERCISE 6
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// parallel element assembly with atomics
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void build_fem_system_atomic(std::size_t n, CSR &K, std::vector<double> &f);
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// No-atomic grouped assembly (method (a))
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void build_fem_system_no_atomic(std::size_t n, CSR &K, std::vector<double> &f);
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