/* $Id$ */
-
/* 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:
#endif
-XBT_LOG_NEW_DEFAULT_SUBCATEGORY(surf_lagrange, surf,
- "Logging specific to SURF (lagrange)");
+XBT_LOG_NEW_DEFAULT_SUBCATEGORY(surf_lagrange, surf, "Logging specific to SURF (lagrange)");
+
+/*
+ * Local prototypes to implement the lagrangian optimization with optimal step, also called dicotomi.
+ */
+//solves the proportional fairness using a lagrange optimizition with dicotomi step
+void lagrange_solve (lmm_system_t sys);
+//computes the value of the dicotomi using a initial values, init, with a specific variable or constraint
+double dicotomi(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);
-void lagrange_solve(lmm_system_t sys);
void lagrange_solve(lmm_system_t sys)
{
-
/*
* Lagrange Variables.
*/
- double epsilon_min_error = 1e-6;
+ int max_iterations= 10000;
+ double epsilon_min_error = 1e-4;
+ double dicotomi_min_error = 1e-8;
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;
-
- xbt_swag_t var_list = NULL;
- lmm_variable_t var1 = NULL;
- lmm_variable_t var2 = NULL;
+ xbt_swag_t elem_list = NULL;
+ lmm_element_t elem = NULL;
+ xbt_swag_t cnst_list = NULL;
+ lmm_constraint_t cnst = NULL;
+
+ xbt_swag_t var_list = 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 i;
+
+ 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 (dicotomi) : %e", dicotomi_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;
+ xbt_swag_foreach(var, var_list) {
+ if((var->bound > 0.0) || (var->weight <= 0.0)){
+ DEBUG1("#### NOTE var(%d) is a boundless variable", i);
+ var->mu = -1.0;
+ } else{
+ var->mu = 1.0;
+ var->new_mu = 2.0;
}
+ DEBUG2("#### var(%d)->mu : %e", i, var->mu);
+ DEBUG2("#### var(%d)->weight: %e", i, var->weight);
+ 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;
+ 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){
-
+
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);
+
+ /*
+ * 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; i<var1->cnsts_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) ){
+ var->new_mu = dicotomi(var->mu, partial_diff_mu, var, dicotomi_min_error);
+ if(var->new_mu < 0) var->new_mu = 0;
+ var->mu = var->new_mu;
}
-
- mu_partial = -1 / mu_partial + var1->initial_bound;
- var1->bound = var1->bound + sigma_step * mu_partial;
}
+ /*
+ * Compute the value of lambda_i
+ */
+ //forall lambda_i in lambda_1, lambda_2, ..., lambda_n
+ xbt_swag_foreach(cnst, cnst_list) {
+ cnst->new_lambda = dicotomi(cnst->lambda, partial_diff_lambda, cnst, dicotomi_min_error);
+ DEBUG2("====> cnst->lambda (%p) = %e", cnst, cnst->new_lambda);
+ cnst->lambda = cnst->new_lambda;
+ }
- /* d Dual
- * Compute the value of ------------- (\lambda^k, \mu^k) this portion
- * d \lambda_i^k
- * of code depends on function f(x).
+ /*
+ * 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) {
-
- lambda_partial = 0;
-
- elem_list = &(cnst1->active_element_set);
-
- xbt_swag_foreach(elem1, elem_list) {
- lambda_partial = 0;
-
- var2 = elem1->variable;
+ 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;
+ }
+
+ //uses the partial differential inverse function
+ tmp = var->func_fpi(var, tmp);
- //for each link with capacity cnsts[i] that uses flow of variable var1 do
- for(i=0; i<var2->cnsts_number; i++){
- elem2 = &(var2->cnsts[i]);
- tmp += (elem2->constraint)->bound + var2->bound;
+ //computes de overall_error
+ if(overall_error < fabs(var->value - tmp)){
+ overall_error = fabs(var->value - tmp);
}
- lambda_partial += -1 / tmp;
+ var->value = tmp;
}
-
- lambda_partial += cnst1->initial_bound;
- cnst1->bound = cnst1->bound + sigma_step * lambda_partial;
+ DEBUG4("======> value of var %s (%p) = %e, overall_error = %e", (char *)var->id, var, var->value, overall_error);
}
+ }
-
-
- /*
- * Verify for each capacity constraint (lambda) the error associated.
- */
- 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 );
- }
- }
- /*
- * 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);
- }
+ //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;
}
+
+ tmp = tmp - cnst->bound;
- overall_error = capacity_error + bound_error;
+ if(tmp > epsilon_min_error){
+ WARN4("The link %s(%p) doesn't match the KKT property, expected less than %e and got %e", (char *)cnst->id, cnst, epsilon_min_error, tmp);
+ }
+
}
+
+ //verify the KKT property of each flow
+ xbt_swag_foreach(var, var_list){
+ if(var->bound <= 0 || var->weight <= 0) continue;
+ tmp = 0;
+ tmp = (var->value - var->bound);
+
+ if(tmp != 0 || var->mu != 0){
+ WARN4("The flow %s(%p) doesn't match the KKT property, value expected (=0) got (lambda=%e) (sum_rho=%e)", (char *)var->id, var, var->mu, tmp);
+ }
- if(overall_error > epsilon_min_error){
+ }
+
+ if(overall_error <= epsilon_min_error){
DEBUG1("The method converge in %d iterations.", iteration);
+ }else{
+ WARN1("Method reach %d iterations, which is the maxmimun number of iterations allowed.", iteration);
}
+}
- /*
- * 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; i<var1->cnsts_number; i++){
- elem1 = &(var1->cnsts[i]);
- tmp += (elem1->constraint)->bound + var1->bound;
+/*
+ * Returns a double value corresponding to the result of a dicotomi 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 dicotomial process
+ */
+double dicotomi(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;
+
+ min = max = init;
+
+ if(init == 0){
+ min = max = 1;
+ }
+
+ min_diff = max_diff = middle_diff = 0.0;
+ overall_error = 1;
+
+ if(diff(0.0, var_cnst) > 0){
+ DEBUG1("====> returning 0.0 (diff = %e)", diff(0.0, var_cnst));
+ return 0.0;
+ }
+
+ DEBUG0("====> not detected positive diff in 0");
+
+ while(overall_error > min_error){
+
+ min_diff = diff(min, var_cnst);
+ max_diff = diff(max, var_cnst);
+
+ DEBUG2("DICOTOMI ===> min = %e , max = %e", min, max);
+ DEBUG2("DICOTOMI ===> diffmin = %e , diffmax = %e", min_diff, max_diff);
+
+ if( min_diff > 0 && max_diff > 0 ){
+ if(min == max){
+ min = min / 2.0;
+ }else{
+ max = min;
+ }
+ }else if( min_diff < 0 && max_diff < 0 ){
+ if(min == max){
+ max = max * 2.0;
+ }else{
+ min = max;
+ }
+ }else if( min_diff < 0 && max_diff > 0 ){
+ middle = (max + min)/2.0;
+ middle_diff = diff(middle, var_cnst);
+ overall_error = fabs(min - max);
+
+ if( middle_diff < 0 ){
+ min = middle;
+ }else if( middle_diff > 0 ){
+ max = middle;
+ }else{
+ WARN0("Found an optimal solution with 0 error!");
+ overall_error = 0;
+ return middle;
+ }
+
+ }else if(min_diff == 0){
+ return min;
+ }else if(max_diff == 0){
+ return max;
+ }else if(min_diff > 0 && max_diff < 0){
+ WARN0("The impossible happened, partial_diff(min) > 0 && partial_diff(max) < 0");
}
- var1->weight = 1 / tmp;
}
+ DEBUG1("====> returning %e", (min+max)/2.0);
+ 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;
+
+ //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 += var->mu;
+
+ //use auxiliar function passing (sigma_i + mu_i)
+ mu_partial = diff_aux(var, sigma_mu) ;
+ //add the RTT limit
+ mu_partial += var->bound;
+ 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_mu=0.0;
+
+ elem_list = &(cnst->element_set);
+
+ DEBUG2("Computting diff of cnst (%p) %s", cnst, (char *)cnst->id);
+
+ xbt_swag_foreach(elem, elem_list) {
+ var = elem->variable;
+ if(var->weight<=0) continue;
+
+ //initilize de sumation variable
+ sigma_mu = 0.0;
+
+ //compute sigma_i of variable var
+ for(i=0; i<var->cnsts_number; i++){
+ sigma_mu += (var->cnsts[i].constraint)->lambda;
+ }
+
+ //add mu_i if this flow has a RTT constraint associated
+ if(var->bound > 0) sigma_mu += var->mu;
+
+ //replace value of cnst->lambda by the value of parameter lambda
+ sigma_mu = (sigma_mu - cnst->lambda) + lambda;
+
+ //use the auxiliar function passing (\sigma_i + \mu_i)
+ lambda_partial += diff_aux(var, sigma_mu);
+ }
+
+ lambda_partial += cnst->bound;
+
+ return lambda_partial;
+}
+
+
+double diff_aux(lmm_variable_t var, double x){
+ double tmp_fp, tmp_fpi, tmp_fpip, result;
+
+ xbt_assert0(var->func_fp, "Initialize the protocol functions first create variables before.");
+
+ tmp_fp = var->func_fp(var, x);
+ tmp_fpi = var->func_fpi(var, x);
+ tmp_fpip = var->func_fpip(var, x);
+
+ result = tmp_fpip*(var->func_fp(var, tmp_fpi));
+
+ result = result - tmp_fpi;
+
+ result = result - (tmp_fpip * x);
+
+ return result;
+}
+
+
+
+
+
+
+
+
