-/* Copyright (c) 2007-2019. 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. */
-
-/*
- * Modeling the proportional fairness using the Lagrangian Optimization Approach. For a detailed description see:
- * "ssh://username@scm.gforge.inria.fr/svn/memo/people/pvelho/lagrange/ppf.ps".
- */
-#include "src/kernel/lmm/maxmin.hpp"
-#include "src/surf/surf_interface.hpp"
-#include "xbt/log.h"
-#include "xbt/sysdep.h"
-
-#include <algorithm>
-#include <cmath>
-#include <cstdlib>
-
-XBT_LOG_NEW_DEFAULT_SUBCATEGORY(surf_lagrange, surf, "Logging specific to SURF (lagrange)");
-XBT_LOG_NEW_SUBCATEGORY(surf_lagrange_dichotomy, surf_lagrange, "Logging specific to SURF (lagrange dichotomy)");
-
-static constexpr double VEGAS_SCALING = 1000.0;
-static constexpr double RENO_SCALING = 1.0;
-static constexpr double RENO2_SCALING = 1.0;
-
-namespace simgrid {
-namespace kernel {
-namespace lmm {
-
-System* make_new_lagrange_system(bool selective_update)
-{
- return new Lagrange(selective_update);
-}
-
-bool Lagrange::check_feasible(bool warn)
-{
- for (Constraint const& cnst : active_constraint_set) {
- double tmp = 0;
- for (Element const& elem : cnst.enabled_element_set_) {
- Variable* var = elem.variable;
- xbt_assert(var->sharing_weight_ > 0);
- tmp += var->value_;
- }
-
- if (double_positive(tmp - cnst.bound_, sg_maxmin_precision)) {
- if (warn)
- XBT_WARN("The link (%p) is over-used. Expected less than %f and got %f", &cnst, cnst.bound_, tmp);
- return false;
- }
- XBT_DEBUG("Checking feasability for constraint (%p): sat = %f, lambda = %f ", &cnst, tmp - cnst.bound_,
- cnst.lambda_);
- }
-
- for (Variable const& var : variable_set) {
- if (not var.sharing_weight_)
- break;
- if (var.bound_ < 0)
- continue;
- XBT_DEBUG("Checking feasability for variable (%p): sat = %f mu = %f", &var, var.value_ - var.bound_, var.mu_);
-
- if (double_positive(var.value_ - var.bound_, sg_maxmin_precision)) {
- if (warn)
- XBT_WARN("The variable (%p) is too large. Expected less than %f and got %f", &var, var.bound_, var.value_);
- return false;
- }
- }
- return true;
-}
-
-double Lagrange::new_value(const Variable& var)
-{
- double tmp = 0;
-
- for (Element const& elem : var.cnsts_) {
- tmp += elem.constraint->lambda_;
- }
- if (var.bound_ > 0)
- tmp += var.mu_;
- XBT_DEBUG("\t Working on var (%p). cost = %e; Weight = %e", &var, tmp, var.sharing_weight_);
- // uses the partial differential inverse function
- return func_fpi(var, tmp);
-}
-
-double Lagrange::new_mu(const Variable& var)
-{
- double mu_i = 0.0;
- double sigma_i = 0.0;
-
- for (Element const& elem : var.cnsts_) {
- sigma_i += elem.constraint->lambda_;
- }
- mu_i = func_fp(var, var.bound_) - sigma_i;
- if (mu_i < 0.0)
- return 0.0;
- return mu_i;
-}
-
-double Lagrange::dual_objective()
-{
- double obj = 0.0;
-
- for (Variable const& var : variable_set) {
- double sigma_i = 0.0;
-
- if (not var.sharing_weight_)
- break;
-
- for (Element const& elem : var.cnsts_)
- sigma_i += elem.constraint->lambda_;
-
- if (var.bound_ > 0)
- sigma_i += var.mu_;
-
- XBT_DEBUG("var %p : sigma_i = %1.20f", &var, sigma_i);
-
- obj += func_f(var, func_fpi(var, sigma_i)) - sigma_i * func_fpi(var, sigma_i);
-
- if (var.bound_ > 0)
- obj += var.mu_ * var.bound_;
- }
-
- for (Constraint const& cnst : active_constraint_set)
- obj += cnst.lambda_ * cnst.bound_;
-
- return obj;
-}
-
-// solves the proportional fairness using a Lagrangian optimization with dichotomy step
-void Lagrange::lagrange_solve()
-{
- /* Lagrange Variables. */
- int max_iterations = 100;
- double epsilon_min_error = 0.00001; /* this is the precision on the objective function so it's none of the
- configurable values and this value is the legacy one */
- double dichotomy_min_error = 1e-14;
- double overall_modification = 1;
-
- XBT_DEBUG("Iterative method configuration snapshot =====>");
- XBT_DEBUG("#### Maximum number of iterations : %d", max_iterations);
- XBT_DEBUG("#### Minimum error tolerated : %e", epsilon_min_error);
- XBT_DEBUG("#### Minimum error tolerated (dichotomy) : %e", dichotomy_min_error);
-
- if (XBT_LOG_ISENABLED(surf_lagrange, xbt_log_priority_debug)) {
- print();
- }
-
- if (not modified_)
- return;
-
- /* Initialize lambda. */
- for (Constraint& cnst : active_constraint_set) {
- cnst.lambda_ = 1.0;
- cnst.new_lambda_ = 2.0;
- XBT_DEBUG("#### cnst(%p)->lambda : %e", &cnst, cnst.lambda_);
- }
-
- /*
- * Initialize the active variables. Initialize mu.
- */
- for (Variable& var : variable_set) {
- if (not var.sharing_weight_)
- var.value_ = 0.0;
- else {
- if (var.bound_ < 0.0) {
- XBT_DEBUG("#### NOTE var(%p) is a boundless variable", &var);
- var.mu_ = -1.0;
- } else {
- var.mu_ = 1.0;
- var.new_mu_ = 2.0;
- }
- var.value_ = new_value(var);
- XBT_DEBUG("#### var(%p) ->weight : %e", &var, var.sharing_weight_);
- XBT_DEBUG("#### var(%p) ->mu : %e", &var, var.mu_);
- XBT_DEBUG("#### var(%p) ->weight: %e", &var, var.sharing_weight_);
- XBT_DEBUG("#### var(%p) ->bound: %e", &var, var.bound_);
- auto weighted = std::find_if(begin(var.cnsts_), end(var.cnsts_),
- [](Element const& x) { return x.consumption_weight != 0.0; });
- if (weighted == end(var.cnsts_))
- var.value_ = 1.0;
- }
- }
-
- /* Compute dual objective. */
- double obj = dual_objective();
-
- /* While doesn't reach a minimum error or a number maximum of iterations. */
- int iteration = 0;
- while (overall_modification > epsilon_min_error && iteration < max_iterations) {
- iteration++;
- XBT_DEBUG("************** ITERATION %d **************", iteration);
- XBT_DEBUG("-------------- Gradient Descent ----------");
-
- /* Improve the value of mu_i */
- for (Variable& var : variable_set) {
- if (var.sharing_weight_ && var.bound_ >= 0) {
- XBT_DEBUG("Working on var (%p)", &var);
- var.new_mu_ = new_mu(var);
- XBT_DEBUG("Updating mu : var->mu (%p) : %1.20f -> %1.20f", &var, var.mu_, var.new_mu_);
- var.mu_ = var.new_mu_;
-
- double new_obj = dual_objective();
- XBT_DEBUG("Improvement for Objective (%g -> %g) : %g", obj, new_obj, obj - new_obj);
- xbt_assert(obj - new_obj >= -epsilon_min_error, "Our gradient sucks! (%1.20f)", obj - new_obj);
- obj = new_obj;
- }
- }
-
- /* Improve the value of lambda_i */
- for (Constraint& cnst : active_constraint_set) {
- XBT_DEBUG("Working on cnst (%p)", &cnst);
- cnst.new_lambda_ = dichotomy(cnst.lambda_, cnst, dichotomy_min_error);
- XBT_DEBUG("Updating lambda : cnst->lambda (%p) : %1.20f -> %1.20f", &cnst, cnst.lambda_, cnst.new_lambda_);
- cnst.lambda_ = cnst.new_lambda_;
-
- double new_obj = dual_objective();
- XBT_DEBUG("Improvement for Objective (%g -> %g) : %g", obj, new_obj, obj - new_obj);
- xbt_assert(obj - new_obj >= -epsilon_min_error, "Our gradient sucks! (%1.20f)", obj - new_obj);
- obj = new_obj;
- }
-
- /* Now computes the values of each variable (@rho) based on the values of @lambda and @mu. */
- XBT_DEBUG("-------------- Check convergence ----------");
- overall_modification = 0;
- for (Variable& var : variable_set) {
- if (var.sharing_weight_ <= 0)
- var.value_ = 0.0;
- else {
- double tmp = new_value(var);
-
- overall_modification = std::max(overall_modification, fabs(var.value_ - tmp));
-
- var.value_ = tmp;
- XBT_DEBUG("New value of var (%p) = %e, overall_modification = %e", &var, var.value_, overall_modification);
- }
- }
-
- XBT_DEBUG("-------------- Check feasability ----------");
- if (not check_feasible(false))
- overall_modification = 1.0;
- XBT_DEBUG("Iteration %d: overall_modification : %f", iteration, overall_modification);
- }
-
- check_feasible(true);
-
- if (overall_modification <= epsilon_min_error) {
- XBT_DEBUG("The method converges in %d iterations.", iteration);
- }
- if (iteration >= max_iterations) {
- XBT_DEBUG("Method reach %d iterations, which is the maximum number of iterations allowed.", iteration);
- }
-
- if (XBT_LOG_ISENABLED(surf_lagrange, xbt_log_priority_debug)) {
- print();
- }
-}
-
-/*
- * Returns a double value corresponding to the result of a dichotomy process with respect to a given
- * variable/constraint (@mu in the case of a variable or @lambda in case of a constraint) and a initial value init.
- *
- * @param init initial value for @mu or @lambda
- * @param diff a function that computes the differential of with respect a @mu or @lambda
- * @param var_cnst a pointer to a variable or constraint
- * @param min_erro a minimum error tolerated
- *
- * @return a double corresponding to the result of the dichotomy process
- */
-double Lagrange::dichotomy(double init, const Constraint& cnst, double min_error)
-{
- double min = init;
- double max = init;
- double overall_error;
- double middle;
- double middle_diff;
- double diff_0 = 0.0;
-
- XBT_IN();
-
- if (fabs(init) < 1e-20) {
- min = 0.5;
- max = 0.5;
- }
-
- overall_error = 1;
-
- diff_0 = partial_diff_lambda(1e-16, cnst);
- if (diff_0 >= 0) {
- XBT_CDEBUG(surf_lagrange_dichotomy, "returning 0.0 (diff = %e)", diff_0);
- XBT_OUT();
- return 0.0;
- }
-
- double min_diff = partial_diff_lambda(min, cnst);
- double max_diff = partial_diff_lambda(max, cnst);
-
- while (overall_error > min_error) {
- XBT_CDEBUG(surf_lagrange_dichotomy, "[min, max] = [%1.20f, %1.20f] || diffmin, diffmax = %1.20f, %1.20f", min, max,
- min_diff, max_diff);
-
- if (min_diff > 0 && max_diff > 0) {
- if (min == max) {
- XBT_CDEBUG(surf_lagrange_dichotomy, "Decreasing min");
- min = min / 2.0;
- min_diff = partial_diff_lambda(min, cnst);
- } else {
- XBT_CDEBUG(surf_lagrange_dichotomy, "Decreasing max");
- max = min;
- max_diff = min_diff;
- }
- } else if (min_diff < 0 && max_diff < 0) {
- if (min == max) {
- XBT_CDEBUG(surf_lagrange_dichotomy, "Increasing max");
- max = max * 2.0;
- max_diff = partial_diff_lambda(max, cnst);
- } else {
- XBT_CDEBUG(surf_lagrange_dichotomy, "Increasing min");
- min = max;
- min_diff = max_diff;
- }
- } else if (min_diff < 0 && max_diff > 0) {
- middle = (max + min) / 2.0;
- XBT_CDEBUG(surf_lagrange_dichotomy, "Trying (max+min)/2 : %1.20f", middle);
-
- if ((fabs(min - middle) < 1e-20) || (fabs(max - middle) < 1e-20)) {
- XBT_CWARN(surf_lagrange_dichotomy,
- "Cannot improve the convergence! min=max=middle=%1.20f, diff = %1.20f."
- " Reaching the 'double' limits. Maybe scaling your function would help ([%1.20f,%1.20f]).",
- min, max - min, min_diff, max_diff);
- break;
- }
- middle_diff = partial_diff_lambda(middle, cnst);
-
- if (middle_diff < 0) {
- XBT_CDEBUG(surf_lagrange_dichotomy, "Increasing min");
- min = middle;
- overall_error = max_diff - middle_diff;
- min_diff = middle_diff;
- } else if (middle_diff > 0) {
- XBT_CDEBUG(surf_lagrange_dichotomy, "Decreasing max");
- max = middle;
- overall_error = max_diff - middle_diff;
- max_diff = middle_diff;
- } else {
- overall_error = 0;
- }
- } else if (fabs(min_diff) < 1e-20) {
- max = min;
- overall_error = 0;
- } else if (fabs(max_diff) < 1e-20) {
- min = max;
- overall_error = 0;
- } else if (min_diff > 0 && max_diff < 0) {
- XBT_CWARN(surf_lagrange_dichotomy, "The impossible happened, partial_diff(min) > 0 && partial_diff(max) < 0");
- xbt_abort();
- } else {
- XBT_CWARN(surf_lagrange_dichotomy,
- "diffmin (%1.20f) or diffmax (%1.20f) are something I don't know, taking no action.", min_diff,
- max_diff);
- xbt_abort();
- }
- }
-
- XBT_CDEBUG(surf_lagrange_dichotomy, "returning %e", (min + max) / 2.0);
- XBT_OUT();
- return ((min + max) / 2.0);
-}
-
-double Lagrange::partial_diff_lambda(double lambda, const Constraint& cnst)
-{
- double diff = 0.0;
-
- XBT_IN();
-
- XBT_CDEBUG(surf_lagrange_dichotomy, "Computing diff of cnst (%p)", &cnst);
-
- for (Element const& elem : cnst.enabled_element_set_) {
- Variable& var = *elem.variable;
- xbt_assert(var.sharing_weight_ > 0);
- XBT_CDEBUG(surf_lagrange_dichotomy, "Computing sigma_i for var (%p)", &var);
- // Initialize the summation variable
- double sigma_i = 0.0;
-
- // Compute sigma_i
- for (Element const& elem2 : var.cnsts_)
- sigma_i += elem2.constraint->lambda_;
-
- // add mu_i if this flow has a RTT constraint associated
- if (var.bound_ > 0)
- sigma_i += var.mu_;
-
- // replace value of cnst.lambda by the value of parameter lambda
- sigma_i = (sigma_i - cnst.lambda_) + lambda;
-
- diff += -func_fpi(var, sigma_i);
- }
-
- diff += cnst.bound_;
-
- XBT_CDEBUG(surf_lagrange_dichotomy, "d D/d lambda for cnst (%p) at %1.20f = %1.20f", &cnst, lambda, diff);
- XBT_OUT();
- return diff;
-}
-
-/** @brief Attribute the value bound to var->bound.
- *
- * @param f function (f)
- * @param fp partial differential of f (f prime, (f'))
- * @param fpi inverse of the partial differential of f (f prime inverse, (f')^{-1})
- *
- * Set default functions to the ones passed as parameters.
- */
-void Lagrange::set_default_protocol_function(double (*f)(const Variable& var, double x),
- double (*fp)(const Variable& var, double x),
- double (*fpi)(const Variable& var, double x))
-{
- func_f = f;
- func_fp = fp;
- func_fpi = fpi;
-}
-
-double (*Lagrange::func_f)(const Variable&, double);
-double (*Lagrange::func_fp)(const Variable&, double);
-double (*Lagrange::func_fpi)(const Variable&, double);
-
-/**************** Vegas and Reno functions *************************/
-/* NOTE for Reno: all functions consider the network coefficient (alpha) equal to 1. */
-
-/*
- * For Vegas: $f(x) = @alpha D_f@ln(x)$
- * Therefore: $fp(x) = @frac{@alpha D_f}{x}$
- * Therefore: $fpi(x) = @frac{@alpha D_f}{x}$
- */
-double func_vegas_f(const Variable& var, double x)
-{
- xbt_assert(x > 0.0, "Don't call me with stupid values! (%1.20f)", x);
- return VEGAS_SCALING * var.sharing_weight_ * log(x);
-}
-
-double func_vegas_fp(const Variable& var, double x)
-{
- xbt_assert(x > 0.0, "Don't call me with stupid values! (%1.20f)", x);
- return VEGAS_SCALING * var.sharing_weight_ / x;
-}
-
-double func_vegas_fpi(const Variable& var, double x)
-{
- xbt_assert(x > 0.0, "Don't call me with stupid values! (%1.20f)", x);
- return var.sharing_weight_ / (x / VEGAS_SCALING);
-}
-
-/*
- * For Reno: $f(x) = @frac{@sqrt{3/2}}{D_f} atan(@sqrt{3/2}D_f x)$
- * Therefore: $fp(x) = @frac{3}{3 D_f^2 x^2+2}$
- * Therefore: $fpi(x) = @sqrt{@frac{1}{{D_f}^2 x} - @frac{2}{3{D_f}^2}}$
- */
-double func_reno_f(const Variable& var, double x)
-{
- xbt_assert(var.sharing_weight_ > 0.0, "Don't call me with stupid values!");
-
- return RENO_SCALING * sqrt(3.0 / 2.0) / var.sharing_weight_ * atan(sqrt(3.0 / 2.0) * var.sharing_weight_ * x);
-}
-
-double func_reno_fp(const Variable& var, double x)
-{
- return RENO_SCALING * 3.0 / (3.0 * var.sharing_weight_ * var.sharing_weight_ * x * x + 2.0);
-}
-
-double func_reno_fpi(const Variable& var, double x)
-{
- double res_fpi;
-
- xbt_assert(var.sharing_weight_ > 0.0, "Don't call me with stupid values!");
- xbt_assert(x > 0.0, "Don't call me with stupid values!");
-
- res_fpi = 1.0 / (var.sharing_weight_ * var.sharing_weight_ * (x / RENO_SCALING)) -
- 2.0 / (3.0 * var.sharing_weight_ * var.sharing_weight_);
- if (res_fpi <= 0.0)
- return 0.0;
- return sqrt(res_fpi);
-}
-
-/* Implementing new Reno-2
- * For Reno-2: $f(x) = U_f(x_f) = @frac{{2}{D_f}}*ln(2+x*D_f)$
- * Therefore: $fp(x) = 2/(Weight*x + 2)
- * Therefore: $fpi(x) = (2*Weight)/x - 4
- */
-double func_reno2_f(const Variable& var, double x)
-{
- xbt_assert(var.sharing_weight_ > 0.0, "Don't call me with stupid values!");
- return RENO2_SCALING * (1.0 / var.sharing_weight_) *
- log((x * var.sharing_weight_) / (2.0 * x * var.sharing_weight_ + 3.0));
-}
-
-double func_reno2_fp(const Variable& var, double x)
-{
- return RENO2_SCALING * 3.0 / (var.sharing_weight_ * x * (2.0 * var.sharing_weight_ * x + 3.0));
-}
-
-double func_reno2_fpi(const Variable& var, double x)
-{
- xbt_assert(x > 0.0, "Don't call me with stupid values!");
- double tmp = x * var.sharing_weight_ * var.sharing_weight_;
- double res_fpi = tmp * (9.0 * x + 24.0);
-
- if (res_fpi <= 0.0)
- return 0.0;
-
- res_fpi = RENO2_SCALING * (-3.0 * tmp + sqrt(res_fpi)) / (4.0 * tmp);
- return res_fpi;
-}
-}
-}
-}
