/* $Id$ */
-
/* 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:
#include <math.h>
#endif
-#define LAMBDA_STEP 0.01
-
-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)");
-XBT_LOG_NEW_SUBCATEGORY(surf_writelambda, surf,
- "Generates the lambda.in file. WARNING: the size of this file might be a few GBs.");
+/*
+ * 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.
*/
- int max_iterations= 1000000;
- double epsilon_min_error = 0.00001;
+ int max_iterations= 10000;
+ double epsilon_min_error = 1e-4;
+ double dicotomi_min_error = 1e-8;
double overall_error = 1;
- double sigma_step = LAMBDA_STEP;
- //double capacity_error=0, bound_error=0;
- int watch_out = 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 elem = NULL;
- lmm_element_t elem1 = NULL;
-
+ xbt_swag_t elem_list = NULL;
+ lmm_element_t elem = NULL;
- xbt_swag_t cnst_list = NULL;
- //lmm_constraint_t cnst = NULL;
- lmm_constraint_t cnst1 = NULL;
- //lmm_constraint_t cnst2 = NULL;
-
-
- xbt_swag_t var_list = NULL;
- //lmm_variable_t var = NULL;
- lmm_variable_t var1 = NULL;
- lmm_variable_t var2 = 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;
- double mu_partial=0;
- double lambda_partial=0;
double tmp=0;
- int i,j;
- FILE *gnuplot_file=NULL;
- //char print_buf[1024];
- //char *trace_buf=xbt_malloc0(sizeof(char));
- //double sum;
-
+ int i;
+
DEBUG0("Iterative method configuration snapshot =====>");
- DEBUG1("#### Maximum number of iterations : %d", max_iterations);
- DEBUG1("#### Minimum error tolerated : %e", epsilon_min_error);
- DEBUG1("#### Step : %e", sigma_step);
-
+ 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;
*/
var_list = &(sys->variable_set);
i=0;
- xbt_swag_foreach(var1, var_list) {
- if((var1->bound > 0.0) || (var1->weight <= 0.0)){
- DEBUG1("#### NOTE var1(%d) is a boundless variable", i);
- var1->mu = -1.0;
+ 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{
- var1->mu = 1.0;
- var1->new_mu = 2.0;
+ var->mu = 1.0;
+ var->new_mu = 2.0;
}
- DEBUG2("#### var1(%d)->mu: %e", i, var1->mu);
- DEBUG2("#### var1(%d)->weight: %e", i, var1->weight);
+ DEBUG2("#### var(%d)->mu : %e", i, var->mu);
+ DEBUG2("#### var(%d)->weight: %e", i, var->weight);
i++;
}
* Initialize lambda.
*/
cnst_list=&(sys->active_constraint_set);
- xbt_swag_foreach(cnst1, cnst_list) {
- cnst1->lambda = 1.0;
- cnst1->new_lambda = 2.0;
- DEBUG2("#### cnst1(%p)->lambda: %e", cnst1, cnst1->lambda);
+ xbt_swag_foreach(cnst, cnst_list){
+ cnst->lambda = 1.0;
+ cnst->new_lambda = 2.0;
+ DEBUG2("#### cnst(%p)->lambda : %e", cnst, cnst->lambda);
}
-
- if(XBT_LOG_ISENABLED(surf_writelambda, xbt_log_priority_debug)) {
- gnuplot_file = fopen("lambda.in", "w");
- fprintf(gnuplot_file, "# iteration lambda1 lambda2 lambda3 ... lambdaP\n");
- }
-
/*
* 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;
- if((var1->bound > 0) || (var1->weight <=0) ){
- //for each link with capacity cnsts[i] that uses flow of variable var1 do
- for(i=0; i<var1->cnsts_number; i++)
- mu_partial += (var1->cnsts[i].constraint)->lambda;
-
- mu_partial = -1.0 / mu_partial + var1->bound;
- var1->new_mu = var1->mu - sigma_step * mu_partial;
-
- if(var1->new_mu < 0){
- var1->new_mu = 0;
- }
+ //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;
}
}
-
- /* 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
*/
- j=0;
- if(XBT_LOG_ISENABLED(surf_writelambda, xbt_log_priority_debug)) {
- fprintf(gnuplot_file, "\n%d",iteration);
+ //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;
}
- xbt_swag_foreach(cnst1, cnst_list) {
- j++;
-
- lambda_partial = 0;
-
- elem_list = &(cnst1->element_set);
- watch_out=0;
- xbt_swag_foreach(elem1, elem_list) {
-
- var2 = elem1->variable;
-
- if(var2->weight<=0) continue;
+ /*
+ * Now computes the values of each variable (\rho) based on
+ * the values of \lambda and \mu.
+ */
+ 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<var2->cnsts_number; i++){
- tmp += (var2->cnsts[i].constraint)->lambda;
+ for(i=0; i<var->cnsts_number; i++){
+ tmp += (var->cnsts[i].constraint)->lambda;
+ if(var->bound > 0)
+ tmp+=var->mu;
}
- if(var2->bound > 0)
- tmp += var2->mu;
-
-
- if(tmp==0) break;
- if (tmp==cnst1->lambda)
- watch_out=1;
- lambda_partial += (-1.0 / tmp);
- }
+ //uses the partial differential inverse function
+ tmp = var->func_fpi(var, tmp);
- if(tmp == 0)
- cnst1->new_lambda = LAMBDA_STEP;
- else {
- lambda_partial += cnst1->bound;
- if(watch_out && (lambda_partial>0)) {
- /* INFO6("Watch Out (%d) %p! lambda_partial: %e; lambda : %e ; (%e %e) \n",iteration, cnst1, */
- /* lambda_partial, cnst1->lambda, cnst1->lambda / 2, */
- /* cnst1->lambda - sigma_step * lambda_partial); */
-
- if(cnst1->lambda < 0) WARN2("Value of cnst1->lambda(%p) = %e < 0", cnst1, cnst1->lambda);
- if((cnst1->lambda - sigma_step * lambda_partial) < 0) WARN1("Value of lambda_new = %e < 0", (cnst1->lambda - sigma_step * lambda_partial));
-
- if(cnst1->lambda - sigma_step * lambda_partial < cnst1->lambda / 2)
- cnst1->new_lambda = cnst1->lambda / 2;
- else
- cnst1->new_lambda = cnst1->lambda - sigma_step * lambda_partial;
- } else
- cnst1->new_lambda = cnst1->lambda - sigma_step * lambda_partial;
- if(cnst1->new_lambda < 0){
- cnst1->new_lambda = 0;
+ //computes de overall_error using normalized value
+ if(overall_error < (fabs(var->value - tmp)/tmp) ){
+ overall_error = (fabs(var->value - tmp)/tmp);
}
+
+ var->value = tmp;
}
+ DEBUG4("======> value of var %s (%p) = %e, overall_error = %e", (char *)var->id, var, var->value, overall_error);
+ }
+ }
- if(XBT_LOG_ISENABLED(surf_writelambda, xbt_log_priority_debug)) {
- fprintf(gnuplot_file, " %e", cnst1->lambda);
- }
+ //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;
+ 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);
- /*
- * Now computes the values of each variable (\rho) based on
- * the values of \lambda and \mu.
- */
- overall_error=0;
- xbt_swag_foreach(var1, var_list) {
- if(var1->weight <=0)
- var1->value = 0.0;
- else {
- tmp = 0;
- for(i=0; i<var1->cnsts_number; i++){
- tmp += (var1->cnsts[i].constraint)->lambda;
- if(var1->bound > 0)
- tmp+=var1->mu;
- }
-
- //computes de overall_error
- if(overall_error < fabs(var1->value - 1.0/tmp)){
- overall_error = fabs(var1->value - 1.0/tmp);
- }
-
- var1->value = 1.0 / tmp;
- }
-
+
+ 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);
}
+ }
- /* Updating lambda's and mu's */
- xbt_swag_foreach(var1, var_list)
- if(!((var1->bound > 0.0) || (var1->weight <= 0.0)))
- var1->mu = var1->new_mu;
-
-
- xbt_swag_foreach(cnst1, cnst_list)
- cnst1->lambda = cnst1->new_lambda;
+ 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);
}
+}
+/*
+ * 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;
- //verify the KKT property
- xbt_swag_foreach(cnst1, cnst_list){
- tmp = 0;
- elem_list = &(cnst1->element_set);
- xbt_swag_foreach(elem1, elem_list) {
- var1 = elem1->variable;
- if(var1->weight<=0) continue;
- tmp += var1->value;
- }
+ if(diff(0.0, var_cnst) > 0){
+ DEBUG1("====> returning 0.0 (diff = %e)", diff(0.0, var_cnst));
+ return 0.0;
+ }
- tmp = tmp - cnst1->bound;
-
+ 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;
+ }
- if(tmp != 0 || cnst1->lambda != 0){
- WARN4("The link %s(%p) doesn't match the KKT property, value expected (=0) got (lambda=%e) (sum_rho=%e)", (char *)cnst1->id, cnst1, cnst1->lambda, tmp);
+ }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");
}
-
}
-
- xbt_swag_foreach(var1, var_list){
- if(var1->bound <= 0 || var1->weight <= 0) continue;
- tmp = 0;
- tmp = (var1->value - var1->bound);
+ 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;
- if(tmp != 0 || var1->mu != 0){
- WARN4("The flow %s(%p) doesn't match the KKT property, value expected (=0) got (lambda=%e) (sum_rho=%e)", (char *)var1->id, var1, var1->mu, tmp);
+ //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;
+}
- 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);
- }
+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.");
- if(XBT_LOG_ISENABLED(surf_writelambda, xbt_log_priority_debug)) {
- fclose(gnuplot_file);
- }
+ 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;
+}
+
-/* /\* */
-/* * 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)->lambda + var1->mu; */
-/* } */
-/* var1->weight = 1 / tmp; */
-/* DEBUG2("var1->weight (id=%s) : %e", (char *)var1->id, var1->weight); */
-/* } */
-}