X-Git-Url: http://info.iut-bm.univ-fcomte.fr/pub/gitweb/simgrid.git/blobdiff_plain/7b496924ab1db1e2168e21d85f1bb5c5db2ae264..493fc5668a6e4819bd820f86093ca3a7f0909d5a:/src/surf/lagrange.c diff --git a/src/surf/lagrange.c b/src/surf/lagrange.c index a768517eae..008c2108c5 100644 --- a/src/surf/lagrange.c +++ b/src/surf/lagrange.c @@ -1,10 +1,7 @@ /* $Id$ */ - /* Copyright (c) 2007 Arnaud Legrand, Pedro Velho. 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. */ - /* * Modelling the proportional fairness using the Lagrange Optimization * Approach. For a detailed description see: @@ -20,185 +17,483 @@ #include #endif +#define VEGAS_SCALING 1000.0 + XBT_LOG_NEW_DEFAULT_SUBCATEGORY(surf_lagrange, surf, "Logging specific to SURF (lagrange)"); +XBT_LOG_NEW_SUBCATEGORY(surf_lagrange_dichotomy, surf, + "Logging specific to SURF (lagrange dichotomy)"); +/* + * Local prototypes to implement the lagrangian optimization with optimal step, also called dichotomy. + */ +//solves the proportional fairness using a lagrange optimizition 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 +double dichotomy(double init, double diff(double, void *), void *var_cnst, + double min_error); +//computes the value of the differential of variable param_var applied to mu +double partial_diff_mu(double mu, void *param_var); +//computes the value of the differential of constraint param_cnst applied to lambda +double partial_diff_lambda(double lambda, void *param_cnst); +//auxiliar function to compute the partial_diff +double diff_aux(lmm_variable_t var, double x); + + +static int __check_kkt(xbt_swag_t cnst_list, xbt_swag_t var_list, int warn) +{ + xbt_swag_t elem_list = NULL; + lmm_element_t elem = NULL; + lmm_constraint_t cnst = NULL; + lmm_variable_t var = NULL; + + double tmp; + + //verify the KKT property for each link + xbt_swag_foreach(cnst, cnst_list) { + tmp = 0; + elem_list = &(cnst->element_set); + xbt_swag_foreach(elem, elem_list) { + var = elem->variable; + if (var->weight <= 0) + continue; + tmp += var->value; + } + + if (double_positive(tmp - cnst->bound)) { + if (warn) + WARN3 + ("The link (%p) is over-used. Expected less than %f and got %f", + cnst, cnst->bound, tmp); + return 0; + } + DEBUG3("Checking KKT for constraint (%p): sat = %f, lambda = %f ", + cnst, tmp - cnst->bound, cnst->lambda); + } + + //verify the KKT property of each flow + xbt_swag_foreach(var, var_list) { + if (var->bound < 0 || var->weight <= 0) + continue; + DEBUG3("Checking KKT for variable (%p): sat = %f mu = %f", var, + var->value - var->bound, var->mu); + + if (double_positive(var->value - var->bound)) { + if (warn) + WARN3 + ("The variable (%p) is too large. Expected less than %f and got %f", + var, var->bound, var->value); + return 0; + } + } + return 1; +} void lagrange_solve(lmm_system_t sys) { - /* * Lagrange Variables. */ - double epsilon_min_error = 1e-6; + int max_iterations = 100; + double epsilon_min_error = MAXMIN_PRECISION; + double dichotomy_min_error = 1e-20; double overall_error = 1; - double sigma_step = 0.5e-3; - double capacity_error=0, bound_error=0; - /* * Variables to manipulate the data structure proposed to model the maxmin * fairness. See docummentation for more details. */ - xbt_swag_t elem_list = NULL; - lmm_element_t elem1 = NULL; - lmm_element_t elem2 = NULL; - xbt_swag_t cnst_list = NULL; - lmm_constraint_t cnst1 = NULL; - lmm_constraint_t cnst2 = NULL; + lmm_constraint_t cnst = NULL; xbt_swag_t var_list = NULL; - lmm_variable_t var1 = NULL; - lmm_variable_t var2 = NULL; - + lmm_variable_t var = NULL; /* * Auxiliar variables. */ - int iteration=0; - int max_iterations=100000; - double mu_partial=0; - double lambda_partial=0; - double tmp=0; + int iteration = 0; + double tmp = 0; int i; - if ( !(sys->modified)) + DEBUG0("Iterative method configuration snapshot =====>"); + DEBUG1("#### Maximum number of iterations : %d", max_iterations); + DEBUG1("#### Minimum error tolerated : %e", + epsilon_min_error); + DEBUG1("#### Minimum error tolerated (dichotomy) : %e", + dichotomy_min_error); + + if (!(sys->modified)) return; - + /* * Initialize the var list variable with only the active variables. - * Associate an index in the swag variables. Saves the initial value - * of bound associated with. + * Associate an index in the swag variables. Initialize mu. */ var_list = &(sys->variable_set); - i=0; - xbt_swag_foreach(var1, var_list) { - if(var1->weight != 0.0){ - i++; - var1->initial_bound = var1->bound; + i = 0; + xbt_swag_foreach(var, var_list) { + if ((var->bound < 0.0) || (var->weight <= 0.0)) { + DEBUG1("#### NOTE var(%d) is a boundless (or inactive) variable", i); + var->mu = -1.0; + } else { + var->mu = 1.0; + var->new_mu = 2.0; } + DEBUG3("#### var(%d) %p ->mu : %e", i, var, var->mu); + DEBUG3("#### var(%d) %p ->weight: %e", i, var, var->weight); + DEBUG3("#### var(%d) %p ->bound: %e", i, var, var->bound); + i++; } /* - * Saves the initial bound of each constraint. + * Initialize lambda. */ - cnst_list=&(sys->active_constraint_set); - xbt_swag_foreach(cnst1, cnst_list) { - cnst1->initial_bound = cnst1->bound; + cnst_list = &(sys->active_constraint_set); + xbt_swag_foreach(cnst, cnst_list) { + cnst->lambda = 1.0; + cnst->new_lambda = 2.0; + DEBUG2("#### cnst(%p)->lambda : %e", cnst, cnst->lambda); } - /* * While doesn't reach a minimun error or a number maximum of iterations. */ - while(overall_error > epsilon_min_error && iteration < max_iterations){ + while (overall_error > epsilon_min_error && iteration < max_iterations) { + int dual_updated=0; iteration++; - - - /* d Dual - * Compute the value of ----------- (\lambda^k, \mu^k) this portion - * d \mu_i^k - * of code depends on function f(x). + DEBUG1("************** ITERATION %d **************", iteration); + DEBUG0("-------------- Gradient Descent ----------"); + /* + * Compute the value of mu_i */ - var_list = &(sys->variable_set); - xbt_swag_foreach(var1, var_list) { - - mu_partial = 0; - - //for each link with capacity cnsts[i] that uses flow of variable var1 do - for(i=0; icnsts_number; i++){ - elem1 = &(var1->cnsts[i]); - mu_partial += (elem1->constraint)->bound + var1->initial_bound; + //forall mu_i in mu_1, mu_2, ..., mu_n + xbt_swag_foreach(var, var_list) { + if ((var->bound >= 0) && (var->weight > 0)) { + DEBUG1("Working on var (%p)", var); + var->new_mu = + dichotomy(var->mu, partial_diff_mu, var, dichotomy_min_error); + dual_updated += (fabs(var->new_mu-var->mu)>dichotomy_min_error); + DEBUG2("dual_updated (%d) : %1.20f",dual_updated,fabs(var->new_mu-var->mu)); + DEBUG3("Updating mu : var->mu (%p) : %1.20f -> %1.20f", var, var->mu, var->new_mu); + var->mu = var->new_mu; } - - mu_partial = -1 / mu_partial + var1->initial_bound; - var1->bound = var1->bound + sigma_step * mu_partial; } - - /* d Dual - * Compute the value of ------------- (\lambda^k, \mu^k) this portion - * d \lambda_i^k - * of code depends on function f(x). + /* + * Compute the value of lambda_i */ - cnst_list=&(sys->active_constraint_set); - xbt_swag_foreach(cnst1, cnst_list) { - - lambda_partial = 0; - - elem_list = &(cnst1->active_element_set); - - xbt_swag_foreach(elem1, elem_list) { - lambda_partial = 0; - - var2 = elem1->variable; - - //for each link with capacity cnsts[i] that uses flow of variable var1 do - for(i=0; icnsts_number; i++){ - elem2 = &(var2->cnsts[i]); - tmp += (elem2->constraint)->bound + var2->bound; - } - - lambda_partial += -1 / tmp; - } - - lambda_partial += cnst1->initial_bound; - cnst1->bound = cnst1->bound + sigma_step * lambda_partial; + //forall lambda_i in lambda_1, lambda_2, ..., lambda_n + xbt_swag_foreach(cnst, cnst_list) { + DEBUG1("Working on cnst (%p)", cnst); + cnst->new_lambda = + dichotomy(cnst->lambda, partial_diff_lambda, cnst, + dichotomy_min_error); + dual_updated += (fabs(cnst->new_lambda-cnst->lambda)>dichotomy_min_error); + DEBUG2("dual_updated (%d) : %1.20f",dual_updated,fabs(cnst->new_lambda-cnst->lambda)); + DEBUG3("Updating lambda : cnst->lambda (%p) : %1.20f -> %1.20f", cnst, cnst->lambda, cnst->new_lambda); + cnst->lambda = cnst->new_lambda; } - - /* - * Verify for each capacity constraint (lambda) the error associated. + * Now computes the values of each variable (\rho) based on + * the values of \lambda and \mu. */ - cnst_list=&(sys->active_constraint_set); - xbt_swag_foreach(cnst1, cnst_list) { - cnst2 = xbt_swag_getNext(cnst1,(var_list)->offset); - if(cnst2 != NULL){ - capacity_error += fabs( cnst1->bound - cnst2->bound ); + DEBUG0("-------------- Check convergence ----------"); + overall_error = 0; + xbt_swag_foreach(var, var_list) { + if (var->weight <= 0) + var->value = 0.0; + else { + //compute sigma_i + mu_i + tmp = 0; + for (i = 0; i < var->cnsts_number; i++) { + tmp += (var->cnsts[i].constraint)->lambda; + } + if (var->bound > 0) + tmp += var->mu; + DEBUG3("\t Working on var (%p). cost = %e; Df = %e", var, tmp, + var->df); + + //uses the partial differential inverse function + tmp = var->func_fpi(var, tmp); + + //computes de overall_error using normalized value + if (overall_error < (fabs(var->value - tmp)/tmp)) { + overall_error = (fabs(var->value - tmp)/tmp); + } + + if (overall_error < (fabs(var->value - tmp))) { + overall_error = (fabs(var->value - tmp)); + } + + var->value = tmp; + DEBUG3("New value of var (%p) = %e, overall_error = %e", var, + var->value, overall_error); } } - /* - * Verify for each variable the error of round trip time constraint (mu). - */ - bound_error = 0; - var_list = &(sys->variable_set); - xbt_swag_foreach(var1, var_list) { - var2 = xbt_swag_getNext(var1,(var_list)->offset); - if(var2 != NULL){ - bound_error += fabs( var2->bound - var1->bound); - } + if (!__check_kkt(cnst_list, var_list, 0)) + overall_error = 1.0; + DEBUG2("Iteration %d: Overall_error : %f", iteration, overall_error); + if(!dual_updated) { + DEBUG1("Could not improve the convergence at iteration %d. Drop it!",iteration); + break; } + } + - overall_error = capacity_error + bound_error; + __check_kkt(cnst_list, var_list, 1); + + if (overall_error <= epsilon_min_error) { + DEBUG1("The method converges in %d iterations.", iteration); + } + if (iteration >= max_iterations) { + DEBUG1 + ("Method reach %d iterations, which is the maximum number of iterations allowed.", + iteration); } +/* INFO1("Method converged after %d iterations", iteration); */ + if (XBT_LOG_ISENABLED(surf_lagrange, xbt_log_priority_debug)) { + lmm_print(sys); + } +} - if(overall_error > epsilon_min_error){ - DEBUG1("The method converge in %d iterations.", iteration); +/* + * Returns a double value corresponding to the result of a dichotomy proccess 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 minimun error tolerated + * + * @return a double correponding to the result of the dichotomyal process + */ +double dichotomy(double init, double diff(double, void *), void *var_cnst, + double min_error) +{ + double min, max; + double overall_error; + double middle; + double min_diff, max_diff, middle_diff; + double diff_0 = 0.0; + min = max = init; + + XBT_IN; + + if (init == 0.0) { + min = max = 0.5; } - /* - * Now computes the values of each variable (\rho) based on - * the values of \lambda and \mu. - */ - var_list = &(sys->variable_set); - xbt_swag_foreach(var1, var_list) { - tmp = 0; - for(i=0; icnsts_number; i++){ - elem1 = &(var1->cnsts[i]); - tmp += (elem1->constraint)->bound + var1->bound; + min_diff = max_diff = middle_diff = 0.0; + overall_error = 1; + + if ((diff_0 = diff(1e-16, var_cnst)) >= 0) { + CDEBUG1(surf_lagrange_dichotomy, "returning 0.0 (diff = %e)", + diff_0); + XBT_OUT; + return 0.0; + } + + min_diff = diff(min, var_cnst); + max_diff = diff(max, var_cnst); + + while (overall_error > min_error) { + CDEBUG4(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) { + CDEBUG0(surf_lagrange_dichotomy, "Decreasing min"); + min = min / 2.0; + min_diff = diff(min, var_cnst); + } else { + CDEBUG0(surf_lagrange_dichotomy, "Decreasing max"); + max = min; + max_diff = min_diff; + + } + } else if (min_diff < 0 && max_diff < 0) { + if (min == max) { + CDEBUG0(surf_lagrange_dichotomy, "Increasing max"); + max = max * 2.0; + max_diff = diff(max, var_cnst); + } else { + CDEBUG0(surf_lagrange_dichotomy, "Increasing min"); + min = max; + min_diff = max_diff; + } + } else if (min_diff < 0 && max_diff > 0) { + middle = (max + min) / 2.0; + CDEBUG1(surf_lagrange_dichotomy, "Trying (max+min)/2 : %1.20f",middle); + + if((min==middle) || (max==middle)) { + DEBUG0("Cannot improve the convergence!"); + break; + } + middle_diff = diff(middle, var_cnst); + + if (middle_diff < 0) { + CDEBUG0(surf_lagrange_dichotomy, "Increasing min"); + min = middle; + min_diff = middle_diff; + } else if (middle_diff > 0) { + CDEBUG0(surf_lagrange_dichotomy, "Decreasing max"); + max = middle; + max_diff = middle_diff; + } else { + overall_error = 0; + } + } else if (min_diff == 0) { + max=min; + overall_error = 0; + } else if (max_diff == 0) { + min=max; + overall_error = 0; + } else if (min_diff > 0 && max_diff < 0) { + CWARN0(surf_lagrange_dichotomy, + "The impossible happened, partial_diff(min) > 0 && partial_diff(max) < 0"); + abort(); + } else { + CWARN2(surf_lagrange_dichotomy, + "diffmin (%1.20f) or diffmax (%1.20f) are something I don't know, taking no action.", + min_diff, max_diff); + abort(); + } + } + + CDEBUG1(surf_lagrange_dichotomy, "returning %e", (min + max) / 2.0); + XBT_OUT; + return ((min + max) / 2.0); +} + +/* + * + */ +double partial_diff_mu(double mu, void *param_var) +{ + double mu_partial = 0.0; + double sigma_mu = 0.0; + lmm_variable_t var = (lmm_variable_t) param_var; + int i; + XBT_IN; + //compute sigma_i + for (i = 0; i < var->cnsts_number; i++) + sigma_mu += (var->cnsts[i].constraint)->lambda; + + //compute sigma_i + mu_i + sigma_mu += mu; + + //use auxiliar function passing (sigma_i + mu_i) + mu_partial = diff_aux(var, sigma_mu); + + //add the RTT limit + mu_partial += var->bound; + + XBT_OUT; + return mu_partial; +} + +/* + * + */ +double partial_diff_lambda(double lambda, void *param_cnst) +{ + + int i; + xbt_swag_t elem_list = NULL; + lmm_element_t elem = NULL; + lmm_variable_t var = NULL; + lmm_constraint_t cnst = (lmm_constraint_t) param_cnst; + double lambda_partial = 0.0; + double sigma_i = 0.0; + + XBT_IN; + elem_list = &(cnst->element_set); + + CDEBUG1(surf_lagrange_dichotomy,"Computting diff of cnst (%p)", cnst); + + xbt_swag_foreach(elem, elem_list) { + var = elem->variable; + if (var->weight <= 0) + continue; + + //initilize de sumation variable + sigma_i = 0.0; + + //compute sigma_i of variable var + for (i = 0; i < var->cnsts_number; i++) { + sigma_i += (var->cnsts[i].constraint)->lambda; } - var1->weight = 1 / tmp; + + //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; + + //use the auxiliar function passing (\sigma_i + \mu_i) + lambda_partial += diff_aux(var, sigma_i); } - + lambda_partial += cnst->bound; + XBT_OUT; + return lambda_partial; } + + +double diff_aux(lmm_variable_t var, double x) +{ + double tmp_fpi, result; + + XBT_IN2("(var (%p), x (%1.20f))", var, x); + xbt_assert0(var->func_fpi, + "Initialize the protocol functions first create variables before."); + + tmp_fpi = var->func_fpi(var, x); + result = - tmp_fpi; + + XBT_OUT; + return result; +} + + +/**************** Vegas and Reno functions *************************/ +/* + * NOTE for Reno: all functions consider the network + * coeficient (alpha) equal to 1. + */ + +/* + * For Vegas fpi: $\frac{\alpha D_f}{x}$ + */ +double func_vegas_fpi(lmm_variable_t var, double x){ + xbt_assert0(x>0.0,"Don't call me with stupid values!"); + return VEGAS_SCALING*var->df/x; +} + +/* + * For Reno fpi: $\sqrt{\frac{1}{{D_f}^2 x} - \frac{2}{3{D_f}^2}}$ + */ +double func_reno_fpi(lmm_variable_t var, double x){ + double res_fpi; + + xbt_assert0(var->df>0.0,"Don't call me with stupid values!"); + xbt_assert0(x>0.0,"Don't call me with stupid values!"); + + res_fpi = 1/(var->df*var->df*x) - 2/(3*var->df*var->df); + if(res_fpi<=0.0) return 0.0; + xbt_assert0(res_fpi>0.0,"Don't call me with stupid values!"); + return sqrt(res_fpi); +} +