X-Git-Url: http://info.iut-bm.univ-fcomte.fr/pub/gitweb/simgrid.git/blobdiff_plain/7ec790f5a5d5c9f82f7f984cbea4a5b886968902..da363bd916d329c438d990f47f939ed770959d95:/src/surf/lagrange.c

diff --git a/src/surf/lagrange.c b/src/surf/lagrange.c
index 01e22449c2..bdea17cde4 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:
@@ -20,310 +17,554 @@
 #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_SUBCATEGORY(surf_lagrange_dichotomy, surf_lagrange,
+			"Logging specific to SURF (lagrange dichotomy)");
+
+#define SHOW_EXPR(expr) CDEBUG1(surf_lagrange,#expr " = %g",expr);
 
-XBT_LOG_NEW_SUBCATEGORY(surf_writelambda, surf,
-				"Generates the lambda.in file. WARNING: the size of this file might be a few GBs.");
+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 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
+static 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  
+static double partial_diff_mu(double mu, void *param_var);
+//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)
+{
+  xbt_swag_t elem_list = NULL;
+  lmm_element_t elem = NULL;
+  lmm_constraint_t cnst = NULL;
+  lmm_variable_t var = NULL;
+
+  double tmp;
+
+  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 feasability for constraint (%p): sat = %f, lambda = %f ",
+	   cnst, tmp - cnst->bound, cnst->lambda);
+  }
+
+  xbt_swag_foreach(var, var_list) {
+    if (var->bound < 0 || var->weight <= 0)
+      continue;
+    DEBUG3("Checking feasability 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;
+}
+
+static double new_value(lmm_variable_t var)
+{
+  double tmp = 0;
+  int i;
+
+  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
+  return var->func_fpi(var, tmp);
+}
+
+static double new_mu(lmm_variable_t var)
+{
+  double mu_i = 0.0;
+  double sigma_i = 0.0;
+  int j;
+
+  for (j = 0; j < var->cnsts_number; j++) {
+    sigma_i += (var->cnsts[j].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)
+{
+  lmm_constraint_t cnst = NULL;
+  lmm_variable_t var = NULL;
+  
+  double obj = 0.0;
+
+  xbt_swag_foreach(var, var_list) {
+    double sigma_i=0.0;
+    int j;
+
+    for (j = 0; j < var->cnsts_number; j++)
+      sigma_i += (var->cnsts[j].constraint)->lambda;
+
+    if (var->bound > 0)
+      sigma_i += var->mu;
+
+    DEBUG2("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)
+    obj += cnst->lambda*cnst->bound;
+
+  return obj;
+}
 
 void lagrange_solve(lmm_system_t sys)
 {
   /*
    * Lagrange Variables.
    */
-  int max_iterations= 1000000;
-  double epsilon_min_error = 0.00001;
-  double overall_error = 1;
-  double sigma_step = LAMBDA_STEP;
-  //double capacity_error=0, bound_error=0;
-  int watch_out = 0;
+  int max_iterations = 100;
+  double epsilon_min_error = MAXMIN_PRECISION;
+  double dichotomy_min_error = 1e-14;
+  double overall_modification = 1;
 
   /*
    * 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 cnst_list = NULL;
-  //lmm_constraint_t cnst = 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;
-  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 iteration = 0;
+  double tmp = 0;
+  int i;
+  double obj,new_obj;
 
   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 (dichotomy) : %e",
+	 dichotomy_min_error);
 
-  if ( !(sys->modified))
+  if (!(sys->modified))
     return;
 
+
+  /* 
+   * Initialize lambda.
+   */
+  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);
+  }
+
   /* 
    * Initialize the var list variable with only the active variables. 
    * Associate an index in the swag variables. Initialize mu.
    */
   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;
-    } else{ 
-      var1->mu = 1.0;
-      var1->new_mu = 2.0;
+  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;
+      if(var->weight>0.0) 
+	var->value = new_value(var);
+      else 
+	var->value = 0;
+    } else {
+      var->mu = 1.0;
+      var->new_mu = 2.0;
+      var->value = new_value(var);
     }
-    DEBUG2("#### var1(%d)->mu:  %e", i, var1->mu);
-    DEBUG2("#### var1(%d)->weight: %e", i, var1->weight);
+    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++;
   }
 
   /* 
-   * Initialize lambda.
+   * Compute dual objective.
    */
-  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);
-  }
-
-  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");
-  }
+  obj = dual_objective(var_list,cnst_list);
 
-  
   /*
    * While doesn't reach a minimun error or a number maximum of iterations.
    */
-  while(overall_error > epsilon_min_error && iteration < max_iterations){
+  while (overall_modification > epsilon_min_error && iteration < max_iterations) {
+/*     int dual_updated=0; */
+
     iteration++;
+    DEBUG1("************** ITERATION %d **************", iteration);
+    DEBUG0("-------------- Gradient Descent ----------");
 
-    /*                        d Dual
-     * Compute the value of ----------- (\lambda^k, \mu^k) this portion
-     *                       d \mu_i^k
-     * of code depends on function f(x).
+    /*                       
+     * Improve 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 + var1->mu;
-       
-        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;
-	}
+    xbt_swag_foreach(var, var_list) {
+      if ((var->bound >= 0) && (var->weight > 0)) {
+	DEBUG1("Working on var (%p)", var);
+	var->new_mu = new_mu(var);
+/* 	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;
+
+	new_obj=dual_objective(var_list,cnst_list);
+	DEBUG3("Improvement for Objective (%g -> %g) : %g", obj, new_obj,
+	      obj-new_obj);
+	xbt_assert1(obj-new_obj>=-epsilon_min_error,"Our gradient sucks! (%1.20f)",obj-new_obj);
+	obj = new_obj;
       }
     }
 
-
-    /*                         d Dual
-     * Compute the value of ------------- (\lambda^k, \mu^k) this portion
-     *                      d \lambda_i^k
-     * of code depends on function f(x).
+    /*
+     * Improve the value of lambda_i
      */
-    j=0;
-    if(XBT_LOG_ISENABLED(surf_writelambda, xbt_log_priority_debug)) {
-      fprintf(gnuplot_file, "\n%d",iteration);
-    }
-    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;
-
-	tmp = 0;
-
-	for(i=0; i<var2->cnsts_number; i++){
-	  tmp += (var2->cnsts[i].constraint)->lambda;
-	}
-	if(var2->bound > 0)
-	  tmp += var2->mu;
-
-	
-	if(tmp==0) break;
-
-	if (tmp==cnst1->lambda)
-	  watch_out=1;
-	lambda_partial += (-1.0 / 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;
-	}
-      }
-
-      if(XBT_LOG_ISENABLED(surf_writelambda, xbt_log_priority_debug)) {
-	fprintf(gnuplot_file, "  %e", cnst1->lambda);
-      }
-
+    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;
+
+      new_obj=dual_objective(var_list,cnst_list);
+      DEBUG3("Improvement for Objective (%g -> %g) : %g", obj, new_obj,
+	     obj-new_obj);
+      xbt_assert1(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.
      */
-    overall_error=0;
-    xbt_swag_foreach(var1, var_list) {
-      if(var1->weight <=0) 
-	var1->value = 0.0;
+    DEBUG0("-------------- Check convergence ----------");
+    overall_modification = 0;
+    xbt_swag_foreach(var, var_list) {
+      if (var->weight <= 0)
+	var->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;
+	tmp = new_value(var);
+
+	overall_modification = MAX(overall_modification, fabs(var->value - tmp));
+
+	var->value = tmp;
+	DEBUG3("New value of var (%p)  = %e, overall_modification = %e", var,
+	       var->value, overall_modification);
       }
-      
     }
 
+    DEBUG0("-------------- Check feasability ----------");
+    if (!__check_feasible(cnst_list, var_list, 0))
+      overall_modification = 1.0;
+    DEBUG2("Iteration %d: overall_modification : %f", iteration, overall_modification);
+/*     if(!dual_updated) { */
+/*       WARN1("Could not improve the convergence at iteration %d. Drop it!",iteration); */
+/*       break; */
+/*     } */
+  }
 
-    /* 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;
+  __check_feasible(cnst_list, var_list, 1);
+
+  if (overall_modification <= 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);
+  }
+}
 
+/*
+ * 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
+ */
+static 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;
 
-  //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 (init == 0.0) {
+    min = max = 0.5;
+  }
 
-    tmp = tmp - cnst1->bound;
- 
+  min_diff = max_diff = middle_diff = 0.0;
+  overall_error = 1;
 
-    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);
+  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)) {
+	CWARN4(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) {
+	CDEBUG0(surf_lagrange_dichotomy, "Increasing min");
+	min = middle;
+	overall_error = max_diff-middle_diff;
+	min_diff = middle_diff;
+/* 	SHOW_EXPR(overall_error); */
+      } else if (middle_diff > 0) {
+	CDEBUG0(surf_lagrange_dichotomy, "Decreasing max");
+	max = middle;
+	overall_error = max_diff-middle_diff;
+	max_diff = middle_diff;
+/* 	SHOW_EXPR(overall_error); */
+      } else {
+	overall_error = 0;
+/* 	SHOW_EXPR(overall_error); */
+      }
+    } else if (min_diff == 0) {
+      max=min;
+      overall_error = 0;
+/*       SHOW_EXPR(overall_error); */
+    } else if (max_diff == 0) {
+      min=max;
+      overall_error = 0;
+/*       SHOW_EXPR(overall_error); */
+    } 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();
     }
-    
   }
 
-    
-  xbt_swag_foreach(var1, var_list){
-    if(var1->bound <= 0 || var1->weight <= 0) continue;
-    tmp = 0;
-    tmp = (var1->value - var1->bound);
+  CDEBUG1(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)
+{
+
+  int j;
+  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 diff = 0.0;
+  double sigma_i = 0.0;
+
+  XBT_IN;
+  elem_list = &(cnst->element_set);
+
+  CDEBUG1(surf_lagrange_dichotomy,"Computing diff of cnst (%p)", cnst);
+
+  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);
+    CDEBUG1(surf_lagrange_dichotomy,"Computing sigma_i for var (%p)", var);
+    // Initialize the summation variable
+    sigma_i = 0.0;
+
+    // Compute sigma_i 
+    for (j = 0; j < var->cnsts_number; j++) {
+      sigma_i += (var->cnsts[j].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;
 
+  CDEBUG3(surf_lagrange_dichotomy,"d D/d lambda for cnst (%p) at %1.20f = %1.20f",
+	  cnst, lambda, diff);
+  XBT_OUT;
+  return diff;
+}
 
-  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);
-  }
+/** \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 polimorfism 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;
+}
 
 
-  if(XBT_LOG_ISENABLED(surf_writelambda, xbt_log_priority_debug)) {
-    fclose(gnuplot_file);
-  }
+/**************** Vegas and Reno functions *************************/
+/*
+ * NOTE for Reno: all functions consider the network
+ * coeficient (alpha) equal to 1.
+ */
 
+/*
+ * For Vegas: $f(x) = \alpha D_f\ln(x)$
+ * Therefore: $fp(x) = \frac{\alpha D_f}{x}$
+ * Therefore: $fpi(x) = \frac{\alpha D_f}{x}$
+ */
+#define VEGAS_SCALING 1000.0
 
+double func_vegas_f(lmm_variable_t var, double x){
+  xbt_assert1(x>0.0,"Don't call me with stupid values! (%1.20f)",x);
+  return VEGAS_SCALING*var->df*log(x);
+}
 
+double func_vegas_fp(lmm_variable_t var, double x){
+  xbt_assert1(x>0.0,"Don't call me with stupid values! (%1.20f)",x);
+  return VEGAS_SCALING*var->df/x;
+}
 
+double func_vegas_fpi(lmm_variable_t var, double x){
+  xbt_assert1(x>0.0,"Don't call me with stupid values! (%1.20f)",x);
+  return var->df/(x/VEGAS_SCALING);
+}
 
-/*   /\* */
-/*    * 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; */
+/*
+ * 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: $fpi(x)  = \sqrt{\frac{1}{{D_f}^2 x} - \frac{2}{3{D_f}^2}}$
+ */
+#define RENO_SCALING 1.0
+double func_reno_f(lmm_variable_t var, double x){
+  xbt_assert0(var->df>0.0,"Don't call me with stupid values!");
 
-/*     DEBUG2("var1->weight (id=%s) : %e", (char *)var1->id, var1->weight); */
-/*   } */
+  return RENO_SCALING*sqrt(3.0/2.0)/var->df*atan(sqrt(3.0/2.0)*var->df*x);
+}
 
+double func_reno_fp(lmm_variable_t var, double x){
+  return RENO_SCALING*3.0/(3.0*var->df*var->df*x*x +2.0);
+}
 
+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 = 1.0/(var->df*var->df*(x/RENO_SCALING)) - 2.0/(3.0*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);
 }
+
+