static void chol_driver(blas_idx_t n_global)
{
auto grid = std::make_shared<blacs_grid_t>();
auto a = make_tridiagonal(grid, n_global);
// Compute Cholesky factorization of A in-place
char uplo ='U';
blas_idx_t ia = 1, ja = 1, info;
MPI_Barrier (MPI_COMM_WORLD);
double t0 = MPI_Wtime();
pdpotrf_ (uplo, n_global, a->local_data(), ia, ja, a->descriptor(), info);
assert(info == 0);
double t1 = MPI_Wtime() - t0;
double t_glob;
MPI_Reduce(&t1, &t_glob, 1, MPI_DOUBLE, MPI_MAX, 0, MPI_COMM_WORLD);
if (grid->iam() == 0)
{
double gflops = potrf_flops(n_global)/t_glob/grid->nprocs();
printf("\n"
"MATRIX CHOLESKY FACTORIZATION BENCHMARK SUMMARY\n"
"===============================================\n"
"N = %d\tNP = %d\tNP_ROW = %d\tNP_COL = %d\n"
"Time for PxPOTRF = %10.7f seconds\tGflops/Proc = %10.7f\n",
n_global, grid->nprocs(), grid->nprows(), grid->npcols(),
t_glob, gflops);fflush(stdout);
}
}
void Buddha::worker(uint64_t from, uint64_t to) {
uint64_t filled = 0;
std::vector<uint64_t> local_data(thread_vector_size_);
std::size_t progress_local = 0;
floating_type radius_sqr = radius_ * radius_;
floating_type subpixel_width = 2 * radius_ / x_size_;
floating_type subpixel_height = 2 * radius_ / y_size_;
for (uint64_t sub_x = 0; sub_x < subpixel_resolution_; ++sub_x) {
for (uint64_t sub_y = 0; sub_y < subpixel_resolution_; ++sub_y) {
for (uint64_t i = from; i < to; ++i) {
++progress_local;
if (filled + max_iterations_ >= thread_vector_size_)
flush_data(local_data, filled);
complex_type c = lin2complex(i);
c.real(c.real() + sub_x * subpixel_width);
c.imag(c.imag() + sub_y * subpixel_height);
complex_type z = c;
uint64_t pos = 0;
if (mandelbrot_hint(c))
continue;
while (z.real() * z.real() + z.imag() * z.imag() < radius_sqr
&& pos < max_iterations_) {
// TODO: Possible optimization when computing abs(z)^2.
uint64_t zpos = complex2lin(z);
if (zpos < data_.size()) {
local_data[filled + pos] = zpos;
}
z *= z;
z += c;
++pos;
}
if (pos >= min_iterations_ && pos < max_iterations_) {
filled += pos;
}
}
if (progress_local > 10000) {
progress_ += progress_local;
progress_local = 0;
}
}
}
flush_data(local_data, filled);
}
void umat(TUmatData &umat_data)
{
typedef LocalData<TUmatData> TLocalData;
/// localdata
TLocalData local_data(umat_data);
// PRINT(local_data.epsilon);
/// stiffness
local_data.H0(0, 0) = local_data.E0;
// PRINT(local_data.H0);
/// stress
local_data.sigma = local_data.H0 * local_data.epsilon;
// PRINT(local_data.sigma);
/// ener
local_data.ener = dot_vec_col(local_data.sigma, local_data.epsilon)/2;
// PRINT(local_data.ener);
} // void umat
void umat (TUmatData &umat_data)
{
typedef LocalData<TUmatData> TLocalData;
/// localdata
TLocalData local_data(umat_data);
// PRINT(local_data.epsilon);
/// stiffness
local_data.H0 = elasticity_isotrope_H<ndim> (
local_data.E0,
local_data.N0);
// PRINT(local_data.H0);
/// stress
local_data.sigma = local_data.H0 * local_data.epsilon;
// PRINT(local_data.sigma);
/// ener
local_data.ener = dot_vec_col(local_data.sigma, local_data.epsilon)/2;
// PRINT(local_data.ener);
} // void umat
/// 计算结果存储在矩阵a中
/// n_global: the order of the matrix
static void inv_driver(blas_idx_t n_global)
{
auto grid = std::make_shared<blacs_grid_t>();
//// self code
//n_global = 3;
//double *aaa = new double(n_global*n_global);
//for (int i = 0; i < 9; i++)
//{
// aaa[i] = i + 1;
//}
//aaa[8] = 10;
//auto a = block_cyclic_mat_t::createWithArray(grid, n_global, n_global, aaa);
// Create a NxN random matrix A
auto a = block_cyclic_mat_t::random(grid, n_global, n_global);
// Create a NxN matrix to hold A^{-1}
auto ai = block_cyclic_mat_t::constant(grid, n_global, n_global);
// Copy A to A^{-1} since it will be overwritten during factorization
std::copy_n(a->local_data(), a->local_size(), ai->local_data());
MPI_Barrier (MPI_COMM_WORLD);
double t0 = MPI_Wtime();
// Factorize A
blas_idx_t ia = 1, ja = 1;
std::vector<blas_idx_t> ipiv(a->local_rows() + a->row_block_size() + 100);
blas_idx_t info;
//含义应该是D-GE-TRF。
//第一个D表示我们的矩阵是double类型的
//GE表示我们的矩阵是General类型的
//TRF表示对矩阵进行三角分解也就是我们通常所说的LU分解。
pdgetrf_(n_global, n_global,
ai->local_data(), ia, ja, ai->descriptor(),
ipiv.data(),
info);
assert(info == 0);
double t_factor = MPI_Wtime() - t0;
// Compute A^{-1} based on the LU factorization
// Compute workspace for double and integer work arrays on each process
blas_idx_t lwork = 10;
blas_idx_t liwork = 10;
std::vector<double> work (lwork);
std::vector<blas_idx_t> iwork(liwork);
lwork = liwork = -1;
// 计算lwork与liwork的值
pdgetri_(n_global,
ai->local_data(), ia, ja, ai->descriptor(),
ipiv.data(),
work.data(), lwork, iwork.data(), liwork, info);
assert(info == 0);
lwork = static_cast<blas_idx_t>(work[0]);
liwork = static_cast<size_t>(iwork[0]);
work.resize(lwork);
iwork.resize(liwork);
// Now compute the inverse
t0 = MPI_Wtime();
pdgetri_(n_global,
ai->local_data(), ia, ja, ai->descriptor(),
ipiv.data(),
work.data(), lwork, iwork.data(), liwork, info);
assert(info == 0);
double t_solve = MPI_Wtime() - t0;
// Verify that the inverse is correct using A*A^{-1} = I
auto identity = block_cyclic_mat_t::diagonal(grid, n_global, n_global);
// Compute I = A * A^{-1} - I and verify that the ||I|| is small
char nein = 'N';
double alpha = 1.0, beta = -1.0;
pdgemm_(nein, nein, n_global, n_global, n_global, alpha,
a->local_data() , ia, ja, a->descriptor(),
ai->local_data(), ia, ja, ai->descriptor(),
beta,
identity->local_data(), ia, ja, identity->descriptor());
// Compute 1-norm of the result
char norm='1';
work.resize(identity->local_cols());
double err = pdlange_(norm, n_global, n_global,
identity->local_data(), ia, ja, identity->descriptor(), work.data());
double t_total = t_factor + t_solve;
double t_glob;
MPI_Reduce(&t_total, &t_glob, 1, MPI_DOUBLE, MPI_MAX, 0, MPI_COMM_WORLD);
if (grid->iam() == 0)
{
double gflops = getri_flops(n_global)/t_glob/grid->nprocs();
printf("\n"
"MATRIX INVERSE BENCHMARK SUMMARY\n"
"================================\n"
"N = %d\tNP = %d\tNP_ROW = %d\tNP_COL = %d\n"
"Time for PxGETRF + PxGETRI = %10.7f seconds\tGflops/Proc = %10.7f, Error = %f\n",
n_global, grid->nprocs(), grid->nprows(), grid->npcols(),
t_glob, gflops, err);fflush(stdout);
}
}
static void dgemm_driver(blas_idx_t m_global, blas_idx_t n_global, blas_idx_t k_global)
{
auto grid = std::make_shared<blacs_grid_t>();
auto a = block_cyclic_mat_t::random(grid, m_global, k_global);
// auto b = block_cyclic_mat_t::random(grid, k_global, n_global);
auto c = block_cyclic_mat_t::random(grid, m_global, n_global);
//for test TODO
double *dd = new double[m_global*k_global];
for (int i = 0; i < m_global*k_global; i++)
{
dd[i] = i;
}
auto b = block_cyclic_mat_t::createWithArray(grid, m_global, k_global, dd);
//从这里开始矩阵的运算
MPI_Barrier(MPI_COMM_WORLD);
double alpha = 1.0, beta = 0.0;
double t0 = MPI_Wtime();
char NEIN = 'N'; //表示不进行转置
blas_idx_t ia = 1, ja = 1, ib = 1, jb = 1, ic = 1, jc = 1;
// sub(C) = alpha*op(sub(A))*op(sub(B)) + beta*sub(C)
pdgemm_ (NEIN, NEIN, m_global, n_global, k_global,
alpha,
a->local_data(), ia, ja, a->descriptor(),
b->local_data(), ib, jb, b->descriptor(),
beta,
c->local_data(), ic, jc, c->descriptor()
);
double t1 = MPI_Wtime() - t0;
double t_glob;
//获取所有进程所用时间中最长的时间
MPI_Reduce(&t1, &t_glob, 1, MPI_DOUBLE, MPI_MAX, 0, MPI_COMM_WORLD);
if (grid->iam() == 0) // 进程号为0的进程
{
double gflops = gemm_flops(m_global, n_global, k_global)/t_glob/grid->nprocs();
printf("\n"
"MATRIX MULTIPLY BENCHMARK SUMMARY\n"
"=================================\n"
"M = %d\tN = %d\tK = %d\tNP = %d\tNP_ROW = %d\tNP_COL = %d\n"
"Time for PxGEMM = %10.7f seconds\tGFlops/Proc = %10.7f\n",
m_global, n_global, k_global, grid->nprocs(), grid->nprows(), grid->npcols(),
t_glob, gflops); fflush(stdout);
for (int i = 0; i < 10; i++)
{
for (int j = 0; j < 10; j++)
{
printf("%f ", c->local_data()[i*k_global + j]);
}
printf("\n");
}
fflush(stdout);
}
}
double HDP_MEDOIDS (vector<Instance*>& data, vector< vector<double> >& means, Lookups* tables, vector<double> lambdas, dist_func df, int FIX_DIM) {
// STEP ZERO: validate input and initialization
int N = tables->nWords;
int D = tables->nDocs;
vector< pair<int, int> > doc_lookup = *(tables->doc_lookup);
double lambda_global = lambdas[0];
double lambda_local = lambdas[1];
vector< vector<double> > global_means (1, vector<double>(FIX_DIM, 0.0));
vector< vector<int> > k (D, vector<int>(1,0)); // global association
vector<int> z (N, 0); // local assignment
vector<int> global_asgn (N, 0); // global assignment
// STEP ONE: a. set initial *global* medoid as global mean
compute_assignment (global_asgn, k, z, tables);
compute_means (data, global_asgn, FIX_DIM, global_means);
double last_cost = compute_cost (data, global_means, k, z, lambdas, tables, df, FIX_DIM);
double new_cost = last_cost;
while (true) {
// 4. for each point x_ij,
for (int j = 0; j < D; j ++) {
for (int i = doc_lookup[j].first; i < doc_lookup[j].second; i++) {
int num_global_means = global_means.size();
vector<double> d_ij (num_global_means, 0.0);
for (int p = 0; p < num_global_means; p ++) {
Instance* temp_ins = vec2ins(global_means[p]);
double euc_dist = df(data[i], temp_ins, FIX_DIM);
d_ij[p] = euc_dist * euc_dist;
delete temp_ins;
}
set<int> temp;
for (int p = 0; p < num_global_means; p ++) temp.insert(p);
int num_local_means = k[j].size();
for (int q = 0; q < num_local_means; q ++) temp.erase(k[j][q]);
set<int>::iterator it;
for (it=temp.begin(); it!=temp.end();++it) d_ij[*it] += lambda_local;
int min_p = -1; double min_dij = INF;
for (int p = 0; p < num_global_means; p ++)
if (d_ij[p] < min_dij) {
min_p = p;
min_dij = d_ij[p];
}
if (min_dij > lambda_global + lambda_local) {
z[i] = num_local_means;
k[j].push_back(num_global_means);
vector<double> new_g(FIX_DIM, 0.0);
for (int f = 0; f < data[i]->fea.size(); f++)
new_g[data[i]->fea[f].first-1] = data[i]->fea[f].second;
global_means.push_back(new_g);
// cout << "global and local increment" << endl;
} else {
bool c_exist = false;
for (int c = 0; c < num_local_means; c ++)
if (k[j][c] == min_p) {
z[i] = c;
c_exist = true;
break;
}
if (!c_exist) {
z[i] = num_local_means;
k[j].push_back(min_p);
// cout << "local increment" << endl;
}
}
}
}
/*
cout << "half..........." << endl;
cout << "#global created: " << global_means.size()
<< ", #global used: " << get_num_global_means(k);
*/
new_cost = compute_cost (data, global_means, k, z, lambdas, tables, df, FIX_DIM);
// 5. for all local clusters,
for (int j = 0; j < D; j ++) {
int begin_i = doc_lookup[j].first;
int end_i = doc_lookup[j].second;
int doc_len = doc_lookup[j].second - doc_lookup[j].first;
int num_local_means = k[j].size();
// all local clusters are distinct to each other
/*
set<int> temp;
for (int y = 0; y < num_local_means; y++)
temp.insert(k[j][y]);
cout << temp.size() << " ==? " << num_local_means << endl;
assert (temp.size() == num_local_means);
*/
// compute means of local clusters
vector< vector<double> > local_means (num_local_means, vector<double>(FIX_DIM, 0.0));
vector<int> local_asgn (z.begin()+begin_i, z.begin()+end_i);
vector<Instance*> local_data (data.begin()+begin_i,data.begin()+end_i);
compute_means (local_data, local_asgn, FIX_DIM, local_means);
assert (num_local_means == local_means.size());
// pre-compute instances for global means
int num_global_means = global_means.size();
vector<Instance*> temp_global_means (num_global_means, NULL);
for (int p = 0; p < num_global_means; p ++)
temp_global_means[p] = vec2ins (global_means[p]);
// pre-compute instances for local means
vector<Instance*> temp_local_means (num_local_means, NULL);
for (int c = 0; c < num_local_means; c ++)
temp_local_means[c] = vec2ins (local_means[c]);
for (int c = 0; c < num_local_means; c++) {
// compute distance of local clusters to each global cluster
num_global_means = global_means.size();
vector<double> d_jcp (num_global_means, 0.0);
double sum_d_ijc = 0.0;
for (int i = doc_lookup[j].first; i < doc_lookup[j].second; i ++) {
if (z[i] != c) continue;
double local_dist = df (data[i], temp_local_means[c], FIX_DIM);
sum_d_ijc += local_dist * local_dist;
for (int p = 0; p < num_global_means; p ++) {
double dist = df (data[i], temp_global_means[p], FIX_DIM);
d_jcp[p] += dist * dist;
}
}
int min_p = -1; double min_d_jcp = INF;
for (int p = 0; p < num_global_means; p ++)
if (d_jcp[p] < min_d_jcp) {
min_p = p;
min_d_jcp = d_jcp[p];
}
assert (min_p >= 0);
// cout << min_d_jcp << " " << lambda_global << " " << sum_d_ijc << endl;
if (min_d_jcp > lambda_global + sum_d_ijc) {
global_means.push_back(local_means[c]); // push mu_jc
temp_global_means.push_back(vec2ins (local_means[c]));
k[j][c] = num_global_means;
// cout << "global increment" << endl;
} else {
k[j][c] = min_p;
}
}
for (int c = 0; c < num_local_means; c ++)
delete temp_local_means[c];
num_global_means = global_means.size();
for (int p = 0; p < num_global_means; p ++)
delete temp_global_means[p];
}
// 6. for each global clusters,
compute_assignment (global_asgn, k, z, tables);
/*
cout << "compute global means.." << endl;
cout << "#global created: " << global_means.size()
<< ", #global used: " << get_num_global_means(k);
*/
compute_means (data, global_asgn, FIX_DIM, global_means);
// 7. convergence?
new_cost = compute_cost (data, global_means, k, z, lambdas, tables, df, FIX_DIM);
if ( new_cost < objmin ) objmin = new_cost;
objmin_trace << omp_get_wtime()-start_time << " " << objmin << endl;
if (new_cost == last_cost)
break;
if (new_cost < last_cost) {
last_cost = new_cost;
} else {
cerr << "failure" << endl;
return INF;
assert(false);
}
}
means = global_means;
return last_cost;
}// entry main function