+++ /dev/null
-/* Copyright (c) 2007-2017. 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 "surf/maxmin.hpp"
-#include "xbt/log.h"
-#include "xbt/sysdep.h"
-
-#include <algorithm>
-#include <cstdlib>
-#ifndef MATH
-#include <cmath>
-#endif
-
-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)");
-
-#define SHOW_EXPR(expr) XBT_CDEBUG(surf_lagrange,#expr " = %g",expr);
-#define VEGAS_SCALING 1000.0
-#define RENO_SCALING 1.0
-#define RENO2_SCALING 1.0
-
-namespace simgrid {
-namespace surf {
-
-double (*func_f_def) (lmm_variable_t, double);
-double (*func_fp_def) (lmm_variable_t, double);
-double (*func_fpi_def) (lmm_variable_t, double);
-
-/*
- * Local prototypes to implement the Lagrangian optimization with optimal step, also called dichotomy.
- */
-//solves the proportional fairness using a Lagrangian optimization with dichotomy step
-void lagrange_solve(lmm_system_t sys);
-//computes the value of the dichotomy using a initial values, init, with a specific variable or constraint
-static double dichotomy(double init, double diff(double, void *), void *var_cnst, double min_error);
-//computes the value of the differential of constraint param_cnst applied to lambda
-static double partial_diff_lambda(double lambda, void *param_cnst);
-
-static int __check_feasible(xbt_swag_t cnst_list, xbt_swag_t var_list, int warn)
-{
- void* _cnst;
- void* _elem;
- void* _var;
- xbt_swag_t elem_list = nullptr;
- lmm_element_t elem = nullptr;
- lmm_constraint_t cnst = nullptr;
- lmm_variable_t var = nullptr;
-
- xbt_swag_foreach(_cnst, cnst_list) {
- cnst = static_cast<lmm_constraint_t>(_cnst);
- double tmp = 0;
- elem_list = &(cnst->enabled_element_set);
- xbt_swag_foreach(_elem, elem_list) {
- elem = static_cast<lmm_element_t>(_elem);
- 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 0;
- }
- XBT_DEBUG ("Checking feasability for constraint (%p): sat = %f, lambda = %f ", cnst, tmp - cnst->bound,
- cnst->lambda);
- }
-
- xbt_swag_foreach(_var, var_list) {
- var = static_cast<lmm_variable_t>(_var);
- 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 0;
- }
- }
- return 1;
-}
-
-static double new_value(lmm_variable_t var)
-{
- double tmp = 0;
-
- for (s_lmm_element_t 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 var->func_fpi(var, tmp);
-}
-
-static double new_mu(lmm_variable_t var)
-{
- double mu_i = 0.0;
- double sigma_i = 0.0;
-
- for (s_lmm_element_t const& elem : var->cnsts) {
- sigma_i += elem.constraint->lambda;
- }
- mu_i = var->func_fp(var, var->bound) - sigma_i;
- if (mu_i < 0.0)
- return 0.0;
- return mu_i;
-}
-
-static double dual_objective(xbt_swag_t var_list, xbt_swag_t cnst_list)
-{
- void *_cnst;
- void *_var;
- lmm_constraint_t cnst = nullptr;
- lmm_variable_t var = nullptr;
-
- double obj = 0.0;
-
- xbt_swag_foreach(_var, var_list) {
- var = static_cast<lmm_variable_t>(_var);
- double sigma_i = 0.0;
-
- if (not var->sharing_weight)
- break;
-
- for (s_lmm_element_t 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 += var->func_f(var, var->func_fpi(var, sigma_i)) - sigma_i * var->func_fpi(var, sigma_i);
-
- if (var->bound > 0)
- obj += var->mu * var->bound;
- }
-
- xbt_swag_foreach(_cnst, cnst_list) {
- cnst = static_cast<lmm_constraint_t>(_cnst);
- obj += cnst->lambda * cnst->bound;
- }
-
- return obj;
-}
-
-void lagrange_solve(lmm_system_t sys)
-{
- /* 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)) {
- sys->print();
- }
-
- if (not sys->modified)
- return;
-
- /* Initialize lambda. */
- xbt_swag_t cnst_list = &(sys->active_constraint_set);
- void* _cnst;
- xbt_swag_foreach(_cnst, cnst_list) {
- lmm_constraint_t cnst = (lmm_constraint_t)_cnst;
- cnst->lambda = 1.0;
- cnst->new_lambda = 2.0;
- XBT_DEBUG("#### cnst(%p)->lambda : %e", cnst, cnst->lambda);
- }
-
- /*
- * Initialize the var list variable with only the active variables.
- * Associate an index in the swag variables. Initialize mu.
- */
- xbt_swag_t var_list = &(sys->variable_set);
- void* _var;
- xbt_swag_foreach(_var, var_list) {
- lmm_variable_t var = static_cast<lmm_variable_t>(_var);
- 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),
- [](s_lmm_element_t const& x) { return x.consumption_weight != 0.0; });
- if (weighted == end(var->cnsts))
- var->value = 1.0;
- }
- }
-
- /* Compute dual objective. */
- double obj = dual_objective(var_list, cnst_list);
-
- /* 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 */
- xbt_swag_foreach(_var, var_list) {
- lmm_variable_t var = static_cast<lmm_variable_t>(_var);
- 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(var_list, cnst_list);
- 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 */
- xbt_swag_foreach(_cnst, cnst_list) {
- lmm_constraint_t cnst = static_cast<lmm_constraint_t>(_cnst);
- XBT_DEBUG("Working on cnst (%p)", cnst);
- cnst->new_lambda = dichotomy(cnst->lambda, partial_diff_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(var_list, cnst_list);
- 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;
- xbt_swag_foreach(_var, var_list) {
- lmm_variable_t var = static_cast<lmm_variable_t>(_var);
- 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(cnst_list, var_list, 0))
- overall_modification = 1.0;
- XBT_DEBUG("Iteration %d: overall_modification : %f", iteration, overall_modification);
- }
-
- __check_feasible(cnst_list, var_list, 1);
-
- 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)) {
- sys->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
- */
-static double dichotomy(double init, double diff(double, void *), void *var_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 = diff(1e-16, var_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 = diff(min, var_cnst);
- double max_diff = diff(max, var_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 = diff(min, var_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 = diff(max, var_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 = diff(middle, var_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);
-}
-
-static double partial_diff_lambda(double lambda, void *param_cnst)
-{
- lmm_constraint_t cnst = static_cast<lmm_constraint_t>(param_cnst);
- double diff = 0.0;
-
- XBT_IN();
-
- XBT_CDEBUG(surf_lagrange_dichotomy, "Computing diff of cnst (%p)", cnst);
-
- xbt_swag_t elem_list = &(cnst->enabled_element_set);
- void* _elem;
- xbt_swag_foreach(_elem, elem_list) {
- lmm_element_t elem = static_cast<lmm_element_t>(_elem);
- lmm_variable_t 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 (s_lmm_element_t const& elem : var->cnsts) {
- sigma_i += elem.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 += -var->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 func_fpi inverse of the partial differential of f (f prime inverse, (f')^{-1})
- *
- * Set default functions to the ones passed as parameters. This is a polymorphism in C pure, enjoy the roots of
- * programming.
- *
- */
-void lmm_set_default_protocol_function(double (*func_f) (lmm_variable_t var, double x),
- double (*func_fp) (lmm_variable_t var, double x),
- double (*func_fpi) (lmm_variable_t var, double x))
-{
- func_f_def = func_f;
- func_fp_def = func_fp;
- func_fpi_def = func_fpi;
-}
-
-/**************** 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(lmm_variable_t 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(lmm_variable_t 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(lmm_variable_t 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(lmm_variable_t 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(lmm_variable_t var, double x)
-{
- return RENO_SCALING * 3.0 / (3.0 * var->sharing_weight * var->sharing_weight * x * x + 2.0);
-}
-
-double func_reno_fpi(lmm_variable_t 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(lmm_variable_t 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(lmm_variable_t var, double x)
-{
- return RENO2_SCALING * 3.0 / (var->sharing_weight * x * (2.0 * var->sharing_weight * x + 3.0));
-}
-
-double func_reno2_fpi(lmm_variable_t 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;
-}
-}
-}
