-/* Copyright (c) 2007-2022. The SimGrid Team. All rights reserved. */
+/* Copyright (c) 2007-2023. The SimGrid Team. All rights reserved. */
/* This program is free software; you can redistribute it and/or modify it
* under the terms of the license (GNU LGPL) which comes with this package. */
#include "src/kernel/lmm/bmf.hpp"
-#include <eigen3/Eigen/LU>
+#include "src/simgrid/math_utils.h"
+
+#include <Eigen/LU>
#include <iostream>
#include <numeric>
#include <sstream>
XBT_LOG_NEW_DEFAULT_SUBCATEGORY(ker_bmf, kernel, "Kernel BMF solver");
-int sg_bmf_max_iterations = 1000; /* Change this with --cfg=bmf/max-iterations:VALUE */
-
-namespace simgrid {
-namespace kernel {
-namespace lmm {
+namespace simgrid::kernel::lmm {
AllocationGenerator::AllocationGenerator(Eigen::MatrixXd A) : A_(std::move(A)), alloc_(A_.cols(), 0)
{
return true;
}
- int n_resources = A_.rows();
+ auto n_resources = A_.rows();
size_t idx = 0;
while (idx < alloc_.size()) {
- alloc_[idx] = (++alloc_[idx]) % n_resources;
+ alloc_[idx] = (alloc_[idx] + 1) % n_resources;
if (alloc_[idx] == 0) {
idx++;
continue;
, C_shared_(std::move(shared))
, phi_(std::move(phi))
, gen_(A_)
+
{
xbt_assert(max_iteration_ > 0,
"Invalid number of iterations for BMF solver. Please check your \"bmf/max-iterations\" configuration.");
- xbt_assert(A_.cols() == maxA_.cols(), "Invalid number of cols in matrix A (%ld) or maxA (%ld)", A_.cols(),
+ xbt_assert(A_.cols() == maxA_.cols(), "Invalid number of cols in matrix A (%td) or maxA (%td)", A_.cols(),
maxA_.cols());
- xbt_assert(A_.cols() == static_cast<long>(phi_.size()), "Invalid size of phi vector (%ld)", phi_.size());
+ xbt_assert(A_.cols() == phi_.size(), "Invalid size of phi vector (%td)", phi_.size());
xbt_assert(static_cast<long>(C_shared_.size()) == C_.size(), "Invalid size param shared (%zu)", C_shared_.size());
}
std::string BmfSolver::debug_alloc(const allocation_map_t& alloc) const
{
std::stringstream debug;
- for (const auto& e : alloc) {
- debug << "{" + std::to_string(e.first) + ": [" + debug_vector(e.second) + "]}, ";
+ for (const auto& [resource, players] : alloc) {
+ debug << "{" + std::to_string(resource) + ": [" + debug_vector(players) + "]}, ";
}
return debug.str();
}
for (int p : bounded_players) {
capacity -= A_(resource, p) * phi_[p];
}
+ return std::max(0.0, capacity);
+}
+
+double BmfSolver::get_maxmin_share(int resource, const std::vector<int>& bounded_players) const
+{
+ auto n_players = (A_.row(resource).array() > 0).count() - bounded_players.size();
+ double capacity = get_resource_capacity(resource, bounded_players);
+ if (n_players > 0)
+ capacity /= n_players;
return capacity;
}
std::vector<int> BmfSolver::alloc_map_to_vector(const allocation_map_t& alloc) const
{
std::vector<int> alloc_by_player(A_.cols(), -1);
- for (auto it : alloc) {
- for (auto p : it.second) {
- alloc_by_player[p] = it.first;
+ for (const auto& [resource, players] : alloc) {
+ for (auto p : players) {
+ alloc_by_player[p] = resource;
}
}
return alloc_by_player;
}
+std::vector<int> BmfSolver::get_bounded_players(const allocation_map_t& alloc) const
+{
+ std::vector<int> bounded_players;
+ for (const auto& [resource, players] : alloc) {
+ if (resource == NO_RESOURCE) {
+ bounded_players.insert(bounded_players.end(), players.begin(), players.end());
+ }
+ }
+ return bounded_players;
+}
+
Eigen::VectorXd BmfSolver::equilibrium(const allocation_map_t& alloc) const
{
- int n_players = A_.cols();
+ auto n_players = A_.cols();
Eigen::MatrixXd A_p = Eigen::MatrixXd::Zero(n_players, n_players); // square matrix with number of players
Eigen::VectorXd C_p = Eigen::VectorXd::Zero(n_players);
int row = 0;
- std::vector<int> bounded_players;
- for (const auto& e : alloc) {
+ auto bounded_players = get_bounded_players(alloc);
+ for (const auto& [resource, players] : alloc) {
// add one row for the resource with A[r,]
- int cur_resource = e.first;
- if (cur_resource == NO_RESOURCE) {
- bounded_players.insert(bounded_players.end(), e.second.begin(), e.second.end());
+ /* bounded players, nothing to do */
+ if (resource == NO_RESOURCE)
continue;
- }
- if (C_shared_[cur_resource]) {
- /* shared resource: fairly share it between players */
- A_p.row(row) = A_.row(cur_resource);
- C_p[row] = get_resource_capacity(cur_resource, bounded_players);
- row++;
- if (e.second.size() > 1) {
- // if 2 players have chosen the same resource
- // they must have a fair sharing of this resource, adjust A_p and C_p accordingly
- auto it = e.second.begin();
- int i = *it; // first player
- /* for each other player sharing this resource */
- for (++it; it != e.second.end(); ++it) {
- /* player i and k on this resource j: so maxA_ji*rho_i - maxA_jk*rho_k = 0 */
- int k = *it;
- C_p[row] = 0;
- A_p(row, i) = maxA_(cur_resource, i);
- A_p(row, k) = -maxA_(cur_resource, k);
- row++;
- }
+ /* not shared resource, each player can receive the full capacity of the resource */
+ if (not C_shared_[resource]) {
+ for (int i : players) {
+ C_p[row] = get_resource_capacity(resource, bounded_players);
+ A_p(row, i) = A_(resource, i);
+ row++;
}
- } else {
- /* not shared resource, each player can receive the full capacity of the resource */
- for (int i : e.second) {
- C_p[row] = get_resource_capacity(cur_resource, bounded_players);
- A_p(row, i) = A_(cur_resource, i);
+ continue;
+ }
+
+ /* shared resource: fairly share it between players */
+ A_p.row(row) = A_.row(resource);
+ C_p[row] = get_resource_capacity(resource, bounded_players);
+ row++;
+ if (players.size() > 1) {
+ // if 2 players have chosen the same resource
+ // they must have a fair sharing of this resource, adjust A_p and C_p accordingly
+ auto it = players.begin();
+ int i = *it; // first player
+ /* for each other player sharing this resource */
+ for (++it; it != players.end(); ++it) {
+ /* player i and k on this resource j: so maxA_ji*rho_i - maxA_jk*rho_k = 0 */
+ int k = *it;
+ C_p[row] = 0;
+ A_p(row, i) = maxA_(resource, i);
+ A_p(row, k) = -maxA_(resource, k);
row++;
}
}
XBT_DEBUG("A':\n%s", debug_eigen(A_p).c_str());
XBT_DEBUG("C':\n%s", debug_eigen(C_p).c_str());
+ /* PartialPivLU is much faster than FullPivLU but requires that the matrix is invertible
+ * FullPivLU however assures that it finds come solution even if the matrix is singular
+ * Ideally we would like to be optimist and try Partial and in case of error, go back
+ * to FullPivLU.
+ * However, this with isNaN doesn't work if compiler uses -Ofastmath. In our case,
+ * the icc compiler raises an error when compiling the code (comparison with NaN always evaluates to false in fast
+ * floating point modes).
+ * Eigen::VectorXd rho = Eigen::PartialPivLU<Eigen::MatrixXd>(A_p).solve(C_p);
+ * if (rho.array().isNaN().any()) {
+ * XBT_DEBUG("rho with nan values, falling back to FullPivLU, rho:\n%s", debug_eigen(rho).c_str());
+ * rho = Eigen::FullPivLU<Eigen::MatrixXd>(A_p).solve(C_p);
+ * }
+ */
+
Eigen::VectorXd rho = Eigen::FullPivLU<Eigen::MatrixXd>(A_p).solve(C_p);
for (int p : bounded_players) {
rho[p] = phi_[p];
alloc.clear();
for (int player_idx = 0; player_idx < A_.cols(); player_idx++) {
int selected_resource = NO_RESOURCE;
- double bound = phi_[player_idx];
- double min_share = (bound <= 0 || initial) ? -1 : bound;
+
+ /* the player's maximal rate is the minimum among all resources */
+ double min_rate = -1;
for (int cnst_idx = 0; cnst_idx < A_.rows(); cnst_idx++) {
if (A_(cnst_idx, player_idx) <= 0.0)
continue;
- double share = fair_sharing[cnst_idx] / A_(cnst_idx, player_idx);
- if (min_share == -1 || double_positive(min_share - share, sg_maxmin_precision)) {
+ /* Note: the max_ may artificially increase the rate if priority < 0
+ * The equilibrium sets a rho which respects the C_ though */
+ if (double rate = fair_sharing[cnst_idx] / maxA_(cnst_idx, player_idx);
+ min_rate == -1 || double_positive(min_rate - rate, cfg_bmf_precision)) {
selected_resource = cnst_idx;
- min_share = share;
+ min_rate = rate;
+ }
+ /* Given that the priority may artificially increase the rate,
+ * we need to check that the bound given by user respects the resource capacity C_ */
+ if (double bound = initial ? -1 : phi_[player_idx]; bound > 0 &&
+ bound * A_(cnst_idx, player_idx) < C_[cnst_idx] &&
+ double_positive(min_rate - bound, cfg_bmf_precision)) {
+ selected_resource = NO_RESOURCE;
+ min_rate = bound;
}
}
alloc[selected_resource].insert(player_idx);
}
- bool is_stable = (alloc == last_alloc);
- if (is_stable)
+ if (alloc == last_alloc) // considered stable
return true;
- std::vector<int> alloc_by_player = alloc_map_to_vector(alloc);
-#if 0
- std::vector<int> last_alloc_by_player = alloc_map_to_vector(last_alloc);
- if (not initial) {
- std::for_each(allocations_age_.begin(), allocations_age_.end(), [](int& n) { n++; });
- std::vector<int> age_idx(allocations_age_.size());
- std::iota(age_idx.begin(), age_idx.end(), 0);
- std::stable_sort(age_idx.begin(), age_idx.end(),
- [this](auto a, auto b) { return this->allocations_age_[a] > this->allocations_age_[b]; });
- for (int p : age_idx) {
- if (alloc_by_player[p] != last_alloc_by_player[p]) {
- alloc = last_alloc;
- alloc[last_alloc_by_player[p]].erase(p);
- if (alloc[last_alloc_by_player[p]].empty())
- alloc.erase(last_alloc_by_player[p]);
- alloc[alloc_by_player[p]].insert(p);
- allocations_age_[p] = 0;
- }
- }
- alloc_by_player = alloc_map_to_vector(alloc);
- }
-#endif
- auto ret = allocations_.insert(alloc_by_player);
- /* oops, allocation already tried, let's pertube it a bit */
- if (not ret.second) {
+ if (auto alloc_by_player = alloc_map_to_vector(alloc); not allocations_.insert(alloc_by_player).second) {
+ /* oops, allocation already tried, let's pertube it a bit */
XBT_DEBUG("Allocation already tried: %s", debug_alloc(alloc).c_str());
return disturb_allocation(alloc, alloc_by_player);
}
void BmfSolver::set_fair_sharing(const allocation_map_t& alloc, const Eigen::VectorXd& rho,
Eigen::VectorXd& fair_sharing) const
{
+ std::vector<int> bounded_players = get_bounded_players(alloc);
+
for (int r = 0; r < fair_sharing.size(); r++) {
auto it = alloc.find(r);
- if (it != alloc.end()) { // resource selected by some player, fair share depends on rho
- int player = *(it->second.begin()); // equilibrium assures that every player receives the same, use one of them to
- // calculate the fair sharing for resource r
- fair_sharing[r] = A_(r, player) * rho[player];
+ if (it != alloc.end()) { // resource selected by some player, fair share depends on rho
+ double min_share = std::numeric_limits<double>::max();
+ for (int p : it->second) {
+ double share = A_(r, p) * rho[p];
+ min_share = std::min(min_share, share);
+ }
+ fair_sharing[r] = min_share;
} else { // nobody selects this resource, fair_sharing depends on resource saturation
// resource r is saturated (A[r,*] * rho > C), divide it among players
double consumption_r = A_.row(r) * rho;
- double_update(&consumption_r, C_[r], sg_maxmin_precision);
+ double_update(&consumption_r, C_[r], cfg_bmf_precision);
if (consumption_r > 0.0) {
- int n_players = std::count_if(A_.row(r).data(), A_.row(r).data() + A_.row(r).size(),
- [](double v) { return double_positive(v, sg_maxmin_precision); });
- fair_sharing[r] = C_[r] / n_players;
+ fair_sharing[r] = get_maxmin_share(r, bounded_players);
} else {
fair_sharing[r] = C_[r];
}
Eigen::VectorXd remaining = (A_ * rho) - C_;
remaining = remaining.array() * shared.array(); // ignore non shared resources
bmf = bmf && (not std::any_of(remaining.data(), remaining.data() + remaining.size(),
- [](double v) { return double_positive(v, sg_maxmin_precision); }));
+ [](double v) { return double_positive(v, sg_precision_workamount); }));
// 3) every player receives maximum share in at least 1 saturated resource
// due to subflows, compare with the maximum consumption and not the A matrix
// matrix_ji: boolean indicating player p has the maximum share at resource j
Eigen::MatrixXi player_max_share =
- ((usage.array().colwise() - max_share.array()).abs() <= sg_maxmin_precision).cast<int>();
+ ((usage.array().colwise() - max_share.array()).abs() <= sg_precision_workamount).cast<int>();
// but only saturated resources must be considered
- Eigen::VectorXi saturated = ((remaining.array().abs() <= sg_maxmin_precision)).cast<int>();
+ Eigen::VectorXi saturated = (remaining.array().abs() <= sg_precision_workamount).cast<int>();
XBT_DEBUG("Saturated_j resources:\n%s", debug_eigen(saturated).c_str());
player_max_share.array().colwise() *= saturated.array();
// just check if it has received at least it's bound
for (int p = 0; p < rho.size(); p++) {
- if (double_equals(rho[p], phi_[p], sg_maxmin_precision)) {
+ if (double_equals(rho[p], phi_[p], sg_precision_workamount)) {
player_max_share(0, p) = 1; // it doesn't really matter, just to say that it's a bmf
saturated[0] = 1;
}
XBT_DEBUG("Player_ji usage of saturated resources:\n%s", debug_eigen(player_max_share).c_str());
// for all columns(players) it has to be the max at least in 1
- bmf = bmf && (player_max_share.colwise().sum().all() >= 1);
+ bmf = bmf && (player_max_share.colwise().sum().array() >= 1).all();
return bmf;
}
XBT_DEBUG("A:\n%s", debug_eigen(A_).c_str());
XBT_DEBUG("maxA:\n%s", debug_eigen(maxA_).c_str());
XBT_DEBUG("C:\n%s", debug_eigen(C_).c_str());
+ XBT_DEBUG("phi:\n%s", debug_eigen(phi_).c_str());
/* no flows to share, just returns */
if (A_.cols() == 0)
auto fair_sharing = C_;
/* BMF allocation for each player (current and last one) stop when are equal */
- allocation_map_t last_alloc, cur_alloc;
+ allocation_map_t last_alloc;
+ allocation_map_t cur_alloc;
Eigen::VectorXd rho;
while (it < max_iteration_ && not get_alloc(fair_sharing, last_alloc, cur_alloc, it == 0)) {
fprintf(stderr, "Unable to find a BMF allocation for your system.\n"
"You may try to increase the maximum number of iterations performed by BMF solver "
"(\"--cfg=bmf/max-iterations\").\n"
- "Additionally, you could decrease numerical precision (\"--cfg=surf/precision\").\n");
+ "Additionally, you could adjust numerical precision (\"--cfg=bmf/precision\").\n");
fprintf(stderr, "Internal states (after %d iterations):\n", it);
fprintf(stderr, "A:\n%s\n", debug_eigen(A_).c_str());
fprintf(stderr, "maxA:\n%s\n", debug_eigen(maxA_).c_str());
fprintf(stderr, "C:\n%s\n", debug_eigen(C_).c_str());
+ fprintf(stderr, "C_shared:\n%s\n", debug_vector(C_shared_).c_str());
+ fprintf(stderr, "phi:\n%s\n", debug_eigen(phi_).c_str());
fprintf(stderr, "rho:\n%s\n", debug_eigen(rho).c_str());
xbt_abort();
}
/*****************************************************************************/
-void BmfSystem::get_flows_data(int number_cnsts, Eigen::MatrixXd& A, Eigen::MatrixXd& maxA, Eigen::VectorXd& phi)
+void BmfSystem::get_flows_data(Eigen::Index number_cnsts, Eigen::MatrixXd& A, Eigen::MatrixXd& maxA,
+ Eigen::VectorXd& phi)
{
A.resize(number_cnsts, variable_set.size());
A.setZero();
bool active = false;
bool linked = false; // variable is linked to some constraint (specially for selective_update)
for (const Element& elem : var.cnsts_) {
- boost::intrusive::list_member_hook<>& cnst_hook = selective_update_active
- ? elem.constraint->modified_constraint_set_hook_
- : elem.constraint->active_constraint_set_hook_;
- if (not cnst_hook.is_linked())
+ if (const auto& cnst_hook = selective_update_active ? elem.constraint->modified_constraint_set_hook_
+ : elem.constraint->active_constraint_set_hook_;
+ not cnst_hook.is_linked())
continue;
/* active and linked variable, lets check its consumption */
linked = true;
double consumption = elem.consumption_weight;
if (consumption > 0) {
- int cnst_idx = cnst2idx_[elem.constraint];
- A(cnst_idx, var_idx) = consumption;
- maxA(cnst_idx, var_idx) = elem.max_consumption_weight;
+ int cnst_idx = cnst2idx_[elem.constraint];
+ A(cnst_idx, var_idx) += consumption;
+ // a variable with double penalty must receive half share, so it max weight is greater
+ maxA(cnst_idx, var_idx) = std::max(maxA(cnst_idx, var_idx), elem.max_consumption_weight * var.sharing_penalty_);
active = true;
}
}
C(cnst_idx) = cnst.bound_;
if (cnst.get_sharing_policy() == Constraint::SharingPolicy::NONLINEAR && cnst.dyn_constraint_cb_) {
C(cnst_idx) = cnst.dyn_constraint_cb_(cnst.bound_, cnst.concurrency_current_);
- if (not warned_nonlinear_) {
- XBT_WARN("You are using dynamic constraint bound with parallel tasks and BMF model."
- " The BMF solver assumes that all flows (and subflows) are always active and executing."
- " This is quite pessimist, specially considering parallel tasks with small subflows."
- " Analyze your results with caution.");
- warned_nonlinear_ = true;
- }
}
cnst2idx_[&cnst] = cnst_idx;
// FATPIPE links aren't really shared
}
}
-void BmfSystem::solve()
+void BmfSystem::do_solve()
{
- if (modified_) {
- if (selective_update_active)
- bmf_solve(modified_constraint_set);
- else
- bmf_solve(active_constraint_set);
- }
+ if (selective_update_active)
+ bmf_solve(modified_constraint_set);
+ else
+ bmf_solve(active_constraint_set);
}
template <class CnstList> void BmfSystem::bmf_solve(const CnstList& cnst_list)
{
- /* initialize players' weight and constraint matrices */
idx2Var_.clear();
cnst2idx_.clear();
- Eigen::MatrixXd A, maxA;
- Eigen::VectorXd C, bounds;
+ Eigen::MatrixXd A;
+ Eigen::MatrixXd maxA;
+ Eigen::VectorXd C;
+ Eigen::VectorXd bounds;
std::vector<bool> shared;
get_constraint_data(cnst_list, C, shared);
get_flows_data(C.size(), A, maxA, bounds);
for (int i = 0; i < rho.size(); i++) {
idx2Var_[i]->value_ = rho[i];
}
-
- print();
}
-} // namespace lmm
-} // namespace kernel
-} // namespace simgrid
\ No newline at end of file
+} // namespace simgrid::kernel::lmm
