X-Git-Url: http://info.iut-bm.univ-fcomte.fr/pub/gitweb/simgrid.git/blobdiff_plain/d3d060aead49b9969ac0e9cb83d58b7959925460..f4d1afaaa1e4fee55a98707443c05bdbc9abb42c:/src/surf/lagrange.c

diff --git a/src/surf/lagrange.c b/src/surf/lagrange.c
index 7cf03324c6..62f2516b04 100644
--- a/src/surf/lagrange.c
+++ b/src/surf/lagrange.c
@@ -17,204 +17,339 @@
 #include <math.h>
 #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)");
 
-XBT_LOG_NEW_DEFAULT_SUBCATEGORY(surf_lagrange, surf, "Logging specific to SURF (lagrange)");
+#define SHOW_EXPR(expr) CDEBUG1(surf_lagrange,#expr " = %g",expr);
+
+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 dicotomi.
+ * Local prototypes to implement the lagrangian optimization with optimal step, also called dichotomy.
  */
-//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);
+//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  
-double partial_diff_mu      (double mu, void * param_var);
+static 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);
+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->weight)
+      break;
+    if (var->bound < 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;
+
+    if (!var->weight)
+      break;
+
+    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= 10000;
-  double epsilon_min_error = 1e-4;
-  double dicotomi_min_error = 1e-8;
-  double overall_error = 1;
+  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;
-
-  xbt_swag_t cnst_list  = NULL;
+  xbt_swag_t cnst_list = NULL;
   lmm_constraint_t cnst = NULL;
-  
-  xbt_swag_t var_list   = NULL;
-  lmm_variable_t var    = NULL;
+
+  xbt_swag_t var_list = NULL;
+  lmm_variable_t var = NULL;
 
   /*
    * Auxiliar variables.
    */
-  int iteration=0;
-  double tmp=0;
+  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("#### Minimum error tolerated (dicotomi) : %e", dicotomi_min_error);
+  DEBUG1("#### Minimum error tolerated            : %e",
+	 epsilon_min_error);
+  DEBUG1("#### Minimum error tolerated (dichotomy) : %e",
+	 dichotomy_min_error);
 
-  if ( !(sys->modified))
+  if (XBT_LOG_ISENABLED(surf_lagrange, xbt_log_priority_debug)) {
+    lmm_print(sys);
+  }
+
+  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(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;
+  i = 0;
+  xbt_swag_foreach(var, var_list) {
+    if (!var->weight)
+      var->value = 0.0;
+    else {
+      if (var->bound < 0.0) {
+	DEBUG1("#### NOTE var(%d) is a boundless variable", i);
+	var->mu = -1.0;
+	var->value = new_value(var);
+      } else {
+	var->mu = 1.0;
+	var->new_mu = 2.0;
+	var->value = new_value(var);
+      }
+      DEBUG3("#### var(%d) %p ->df :  %e", i, var, var->df);
+      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++;
     }
-    DEBUG2("#### var(%d)->mu :  %e", i, var->mu);
-    DEBUG2("#### var(%d)->weight: %e", i, var->weight);
-    i++;
   }
 
   /* 
-   * Initialize lambda.
+   * Compute dual objective.
    */
-  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);
-  }
-  
+  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);    
+    DEBUG1("************** ITERATION %d **************", iteration);
+    DEBUG0("-------------- Gradient Descent ----------");
 
     /*                       
-     * Compute the value of mu_i
+     * Improve the value of mu_i
      */
-    //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;
+      if (!var->weight)
+	break;
+      if (var->bound >= 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;
       }
     }
 
     /*
-     * Compute the value of lambda_i
+     * Improve 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);      
+      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;
-    }
 
-
-/*     /\*                        */
-/*      * Update values of mu and lambda */
-/*      *\/ */
-/*     //forall mu_i in mu_1, mu_2, ..., mu_n */
-/*     xbt_swag_foreach(var, var_list) { */
-/*       var->mu = var->new_mu ; */
-/*     } */
-  
-/*     //forall lambda_i in lambda_1, lambda_2, ..., lambda_n */
-/*     xbt_swag_foreach(cnst, cnst_list) { */
-/*       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;   
+    DEBUG0("-------------- Check convergence ----------");
+    overall_modification = 0;
     xbt_swag_foreach(var, var_list) {
-      if(var->weight <=0) 
+      if (var->weight <= 0)
 	var->value = 0.0;
       else {
-	tmp = 0;
-	for(i=0; i<var->cnsts_number; i++){
-	  tmp += (var->cnsts[i].constraint)->lambda;
-	  if(var->bound > 0) 
-	    tmp+=var->mu;
-	}
-
-	if(tmp == 0.0)
-	  WARN0("CAUTION: division by 0.0");
-
-	//computes de overall_error
-	if(overall_error < fabs(var->value - 1.0/tmp)){
-	  overall_error = fabs(var->value - 1.0/tmp);
-	}
-	var->value = 1.0 / tmp;
-      }
-      DEBUG4("======> value of var %s (%p)  = %e, overall_error = %e", (char *)var->id, var, var->value, overall_error);       
-    }
-  }
+	tmp = new_value(var);
 
+	overall_modification =
+	    MAX(overall_modification, fabs(var->value - 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;
+	var->value = tmp;
+	DEBUG3("New value of var (%p)  = %e, overall_modification = %e",
+	       var, var->value, overall_modification);
+      }
     }
-  
-    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);
-    }
-  
+    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; */
+/*     } */
   }
-  
-  //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);
-    }
+  __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(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);
+  if (XBT_LOG_ISENABLED(surf_lagrange, xbt_log_priority_debug)) {
+    lmm_print(sys);
   }
 }
 
 /*
- * Returns a double value corresponding to the result of a dicotomi proccess with
+ * 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. 
  *
@@ -223,149 +358,250 @@ void lagrange_solve(lmm_system_t sys)
  * @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
+ * @return a double correponding to the result of the dichotomyal process
  */
-double dicotomi(double init, double diff(double, void*), void *var_cnst, double min_error){
+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;
 
-  if(init == 0){
-    min = max = 1;
+  XBT_IN;
+
+  if (init == 0.0) {
+    min = max = 0.5;
   }
 
   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));
+  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;
   }
 
-  DEBUG0("====> not detected positive diff in 0");
-
-  while(overall_error > min_error){
+  min_diff = diff(min, var_cnst);
+  max_diff = diff(max, var_cnst);
 
-    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);
 
-    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){
+    if (min_diff > 0 && max_diff > 0) {
+      if (min == max) {
+	CDEBUG0(surf_lagrange_dichotomy, "Decreasing min");
 	min = min / 2.0;
-      }else{
+	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){
+    } else if (min_diff < 0 && max_diff < 0) {
+      if (min == max) {
+	CDEBUG0(surf_lagrange_dichotomy, "Increasing max");
 	max = max * 2.0;
-      }else{
+	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;
       }
-    }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 ){
+      if (middle_diff < 0) {
+	CDEBUG0(surf_lagrange_dichotomy, "Increasing min");
 	min = middle;
-      }else if( middle_diff > 0 ){
+	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;
-      }else{
-	WARN0("Found an optimal solution with 0 error!");
+	overall_error = max_diff - middle_diff;
+	max_diff = middle_diff;
+/* 	SHOW_EXPR(overall_error); */
+      } else {
 	overall_error = 0;
-	return middle;
+/* 	SHOW_EXPR(overall_error); */
       }
-
-    }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");
+    } 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();
     }
   }
 
-
-  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;
-  lmm_variable_t var = (lmm_variable_t)param_var;
-  int i;
-
-  //for each link with capacity cnsts[i] that uses flow of variable var do
-  for(i=0; i<var->cnsts_number; i++)
-    mu_partial += (var->cnsts[i].constraint)->lambda + mu;
-  
-  mu_partial = (-1.0/mu_partial) + var->bound;
-
-  return mu_partial;
+  CDEBUG1(surf_lagrange_dichotomy, "returning %e", (min + max) / 2.0);
+  XBT_OUT;
+  return ((min + max) / 2.0);
 }
 
-/*
- *
- */
-double partial_diff_lambda(double lambda, void *param_cnst){
+static double partial_diff_lambda(double lambda, void *param_cnst)
+{
 
-  double tmp=0.0;
-  int i;
+  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 lambda_partial=0.0;
-
+  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);
 
-  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;
-    
-    tmp = 0;
+    if (var->weight <= 0)
+      continue;
 
-    //DEBUG2("===> Variable (%p) %s", var, (char *)var->id);
+    CDEBUG1(surf_lagrange_dichotomy, "Computing sigma_i for var (%p)",
+	    var);
+    // Initialize the summation variable
+    sigma_i = 0.0;
 
-    for(i=0; i<var->cnsts_number; i++){
-      tmp += (var->cnsts[i].constraint)->lambda;
-      //DEBUG1("======> lambda %e + ", (var->cnsts[i].constraint)->lambda);
+    // Compute sigma_i 
+    for (j = 0; j < var->cnsts_number; j++) {
+      sigma_i += (var->cnsts[j].constraint)->lambda;
     }
-	
-    if(var->bound > 0)
-      tmp += var->mu;
-    
 
-    //DEBUG2("======> lambda - %e + %e ", cnst->lambda, lambda);
+    //add mu_i if this flow has a RTT constraint associated
+    if (var->bound > 0)
+      sigma_i += var->mu;
 
-    tmp = tmp - cnst->lambda + lambda;
-    
-    //avoid a disaster value of lambda
-    //if(tmp==0) tmp = 10e-8;
-    
-    lambda_partial += (-1.0/tmp);
+    //replace value of cnst->lambda by the value of parameter lambda
+    sigma_i = (sigma_i - cnst->lambda) + lambda;
 
-    //DEBUG1("======> %e ", (-1.0/tmp));
+    diff += -var->func_fpi(var, sigma_i);
   }
 
-  lambda_partial += cnst->bound;
 
-  //DEBUG1("===> %e ", lambda_partial);
+  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;
+}
+
+/** \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;
+}
+
 
-  return lambda_partial;
+/**************** 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);
+}
+
+/*
+ * 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!");
+
+  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);
 }
-  
-