X-Git-Url: http://info.iut-bm.univ-fcomte.fr/pub/gitweb/simgrid.git/blobdiff_plain/8e70cf8c19e3bc258c6ee36d9a5a917008451337..25137bd6bc44e1260223b141b46cedd6e7ef1da0:/src/surf/lagrange.c

diff --git a/src/surf/lagrange.c b/src/surf/lagrange.c
index 48cd3277f8..9fc36c9e1e 100644
--- a/src/surf/lagrange.c
+++ b/src/surf/lagrange.c
@@ -1,6 +1,5 @@
-/* 	$Id$	 */
-
-/* Copyright (c) 2007 Arnaud Legrand, Pedro Velho. All rights reserved.     */
+/* Copyright (c) 2007, 2008, 2009, 2010. The SimGrid Team.
+ * 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. */
@@ -12,7 +11,6 @@
  */
 #include "xbt/log.h"
 #include "xbt/sysdep.h"
-#include "xbt/mallocator.h"
 #include "maxmin_private.h"
 
 #include <stdlib.h>
@@ -20,323 +18,641 @@
 #include <math.h>
 #endif
 
-
 XBT_LOG_NEW_DEFAULT_SUBCATEGORY(surf_lagrange, surf,
-				"Logging specific to SURF (lagrange)");
+                                "Logging specific to SURF (lagrange)");
+XBT_LOG_NEW_SUBCATEGORY(surf_lagrange_dichotomy, surf_lagrange,
+                        "Logging specific to SURF (lagrange dichotomy)");
+
+#define SHOW_EXPR(expr) XBT_CDEBUG(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;
 
-void lagrange_solve(lmm_system_t sys)
+  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)
+        XBT_WARN
+            ("The link (%p) is over-used. Expected less than %f and got %f",
+             cnst, cnst->bound, tmp);
+      return 0;
+    }
+    XBT_DEBUG
+        ("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;
+    XBT_DEBUG("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)
+        XBT_WARN
+            ("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;
+  XBT_DEBUG("\t Working on var (%p). cost = %e; Weight = %e", var, tmp,
+         var->weight);
+  //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;
+
+    XBT_DEBUG("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.
    */
-  double epsilon_min_error = 1e-6;
-  double overall_error = 1;
-  double sigma_step = 1e-3;
-  double capacity_error=0, bound_error=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 elem1 = NULL;
-  lmm_element_t elem = NULL;
-
   xbt_swag_t cnst_list = NULL;
-  lmm_constraint_t cnst1 = NULL;
-  lmm_constraint_t cnst2 = NULL;
   lmm_constraint_t cnst = NULL;
-  double sum;
+
   xbt_swag_t var_list = NULL;
-  lmm_variable_t var1 = NULL;
   lmm_variable_t var = NULL;
-  lmm_variable_t var2 = NULL;
-
 
   /*
    * Auxiliar variables.
    */
-  int iteration=0;
-  int max_iterations= 1000;
-  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));
-
-
+  int iteration = 0;
+  double tmp = 0;
+  int i;
+  double obj, new_obj;
+
+  XBT_DEBUG("Iterative method configuration snapshot =====>");
+  XBT_DEBUG("#### Maximum number of iterations       : %d", max_iterations);
+  XBT_DEBUG("#### Minimum error tolerated            : %e",
+         epsilon_min_error);
+  XBT_DEBUG("#### Minimum error tolerated (dichotomy) : %e",
+         dichotomy_min_error);
+
+  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;
+    XBT_DEBUG("#### cnst(%p)->lambda :  %e", cnst, cnst->lambda);
+  }
 
-  if ( !(sys->modified))
-    return;
-  
   /* 
    * 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;
-    DEBUG2("## var1(%d)->mu:  %e", i, var1->mu);
-    DEBUG2("## var1(%d)->weight: %e", i, var1->weight);
-    i++;
+  i = 0;
+  xbt_swag_foreach(var, var_list) {
+    if (!var->weight)
+      var->value = 0.0;
+    else {
+      int nb = 0;
+      if (var->bound < 0.0) {
+        XBT_DEBUG("#### 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);
+      }
+      XBT_DEBUG("#### var(%p) ->weight :  %e", var, var->weight);
+      XBT_DEBUG("#### var(%p) ->mu :  %e", var, var->mu);
+      XBT_DEBUG("#### var(%p) ->weight: %e", var, var->weight);
+      XBT_DEBUG("#### var(%p) ->bound: %e", var, var->bound);
+      for (i = 0; i < var->cnsts_number; i++) {
+        if (var->cnsts[i].value == 0.0)
+          nb++;
+      }
+      if (nb == var->cnsts_number)
+        var->value = 1.0;
+    }
   }
 
   /* 
-   * Initialize lambda.
+   * Compute dual objective.
    */
-  cnst_list=&(sys->active_constraint_set); 
-  xbt_swag_foreach(cnst1, cnst_list) {
-    cnst1->lambda = 1.0;
-    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");
-  }
+  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){
-    iteration++;
-    /*                        d Dual
-     * Compute the value of ----------- (\lambda^k, \mu^k) this portion
-     *                       d \mu_i^k
-     * of code depends on function f(x).
-     */
-    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; 
-	/* Assert that var1->new_mu is positive */
-     }
-    }
+  while (overall_modification > epsilon_min_error
+         && iteration < max_iterations) {
+/*     int dual_updated=0; */
 
-    if(XBT_LOG_ISENABLED(surf_writelambda, xbt_log_priority_debug)) {
-      fprintf(gnuplot_file, "\n%d ", iteration);
-    }
+    iteration++;
+    XBT_DEBUG("************** ITERATION %d **************", iteration);
+    XBT_DEBUG("-------------- Gradient Descent ----------");
 
-    /*                         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 mu_i
      */
-
-    DEBUG1("######Lambda partial at iteration  %d", iteration);
-    cnst_list=&(sys->active_constraint_set);
-    j=0;
-    xbt_swag_foreach(cnst1, cnst_list) {
-      j++;
-
-      lambda_partial = 0;
-      
-      elem_list = &(cnst1->element_set);
-      xbt_swag_foreach(elem1, elem_list) {
-	lambda_partial = 0;
-   
-	var2 = elem1->variable;
-	
-	if(var2->weight<=0) continue;
-
-	tmp = 0;
-
-	//for each link with capacity cnsts[i] that uses flow of variable var1 do
-	if(var2->bound > 0)
-	  tmp += var2->mu;
-
-	for(i=0; i<var2->cnsts_number; i++)
-	  tmp += (var2->cnsts[i].constraint)->lambda;
-	
-	lambda_partial += -1 / tmp;
+    xbt_swag_foreach(var, var_list) {
+      if (!var->weight)
+        break;
+      if (var->bound >= 0) {
+        XBT_DEBUG("Working on var (%p)", var);
+        var->new_mu = new_mu(var);
+/* 	dual_updated += (fabs(var->new_mu-var->mu)>dichotomy_min_error); */
+/* 	XBT_DEBUG("dual_updated (%d) : %1.20f",dual_updated,fabs(var->new_mu-var->mu)); */
+        XBT_DEBUG("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);
+        XBT_DEBUG("Improvement for Objective (%g -> %g) : %g", obj, new_obj,
+               obj - new_obj);
+        xbt_assert(obj - new_obj >= -epsilon_min_error,
+                    "Our gradient sucks! (%1.20f)", obj - new_obj);
+        obj = new_obj;
       }
+    }
 
-      lambda_partial += cnst1->bound;
-
-      DEBUG2("###########Lambda partial %p : %e", cnst1, lambda_partial);
-
-      cnst1->new_lambda = cnst1->lambda - sigma_step * lambda_partial;
-      
-      if(XBT_LOG_ISENABLED(surf_writelambda, xbt_log_priority_debug)) {
-	fprintf(gnuplot_file, " %f", cnst1->lambda);
-      }
+    /*
+     * Improve the value of lambda_i
+     */
+    xbt_swag_foreach(cnst, cnst_list) {
+      XBT_DEBUG("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); */
+/*       XBT_DEBUG("dual_updated (%d) : %1.20f",dual_updated,fabs(cnst->new_lambda-cnst->lambda)); */
+      XBT_DEBUG("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);
+      XBT_DEBUG("Improvement for Objective (%g -> %g) : %g", obj, new_obj,
+             obj - new_obj);
+      xbt_assert(obj - new_obj >= -epsilon_min_error,
+                  "Our gradient sucks! (%1.20f)", obj - new_obj);
+      obj = new_obj;
     }
 
-    /* Updating lambda's and mu's */  
-    var_list = &(sys->variable_set); 
-    xbt_swag_foreach(var1, var_list)
-      if(!((var1->bound > 0.0) || (var1->weight <= 0.0)))
-	var1->mu = var1->new_mu;
-  
-
-    cnst_list=&(sys->active_constraint_set); 
-    xbt_swag_foreach(cnst1, cnst_list)
-      cnst1->lambda = cnst1->new_lambda;
-    
     /*
      * 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) {
-      if(var1->weight <=0) 
-	var1->value = 0.0;
+    XBT_DEBUG("-------------- Check convergence ----------");
+    overall_modification = 0;
+    xbt_swag_foreach(var, var_list) {
+      if (var->weight <= 0)
+        var->value = 0.0;
       else {
-	tmp = 0;
-	if(var1->bound >0) 
-	  tmp+=var1->mu;
-	for(i=0; i<var1->cnsts_number; i++)
-	  tmp += (var1->cnsts[i].constraint)->lambda;
+        tmp = new_value(var);
+
+        overall_modification =
+            MAX(overall_modification, fabs(var->value - tmp));
 
-	var1->value = 1 / tmp;
+        var->value = tmp;
+        XBT_DEBUG("New value of var (%p)  = %e, overall_modification = %e",
+               var, var->value, overall_modification);
       }
-	
-      
-      DEBUG2("var1->value (id=%s) : %e", (char *)var1->id, var1->value);
     }
 
-  /* Printing Objective */
-  var_list = &(sys->variable_set);
-  sprintf(print_buf,"MAX-MIN ( ");
-  trace_buf = xbt_realloc(trace_buf,strlen(trace_buf)+strlen(print_buf)+1);
-  strcat(trace_buf, print_buf);
-  xbt_swag_foreach(var, var_list) {
-    sprintf(print_buf,"'%p'(%f) ",var,var->weight);
-    trace_buf = xbt_realloc(trace_buf,strlen(trace_buf)+strlen(print_buf)+1);
-    strcat(trace_buf, print_buf);
+    XBT_DEBUG("-------------- Check feasability ----------");
+    if (!__check_feasible(cnst_list, var_list, 0))
+      overall_modification = 1.0;
+    XBT_DEBUG("Iteration %d: overall_modification : %f", iteration,
+           overall_modification);
+/*     if(!dual_updated) { */
+/*       XBT_WARN("Could not improve the convergence at iteration %d. Drop it!",iteration); */
+/*       break; */
+/*     } */
   }
-  sprintf(print_buf,")");
-  trace_buf = xbt_realloc(trace_buf,strlen(trace_buf)+strlen(print_buf)+1);
-  strcat(trace_buf, print_buf);
-  DEBUG1("%s",trace_buf);
-  trace_buf[0]='\000';
 
-  /* Printing Constraints */
-  cnst_list = &(sys->active_constraint_set);
-  xbt_swag_foreach(cnst, cnst_list) {
-    sum=0.0;
-    elem_list = &(cnst->element_set);
-    sprintf(print_buf,"\t");
-    trace_buf = xbt_realloc(trace_buf,strlen(trace_buf)+strlen(print_buf)+1);
-    strcat(trace_buf, print_buf);
-    xbt_swag_foreach(elem, elem_list) {
-      sprintf(print_buf,"%f.'%p'(%f) + ",elem->value, 
-	      elem->variable,elem->variable->value);
-      trace_buf = xbt_realloc(trace_buf,strlen(trace_buf)+strlen(print_buf)+1);
-      strcat(trace_buf, print_buf);
-      sum += elem->value * elem->variable->value;
-    }
-    sprintf(print_buf,"0 <= %f ('%p')",cnst->bound,cnst);
-    trace_buf = xbt_realloc(trace_buf,strlen(trace_buf)+strlen(print_buf)+1);
-    strcat(trace_buf, print_buf);
-
-    if(!cnst->shared) {
-      sprintf(print_buf," [MAX-Constraint]");
-      trace_buf = xbt_realloc(trace_buf,strlen(trace_buf)+strlen(print_buf)+1);
-      strcat(trace_buf, print_buf);
-    }
-    DEBUG1("%s",trace_buf);
-    trace_buf[0]='\000';
-    if(!(sum<=cnst->bound))
-      DEBUG3("Incorrect value (%f is not smaller than %f): %g",
-		sum,cnst->bound,sum-cnst->bound);
+  __check_feasible(cnst_list, var_list, 1);
+
+  if (overall_modification <= epsilon_min_error) {
+    XBT_DEBUG("The method converges in %d iterations.", iteration);
   }
+  if (iteration >= max_iterations) {
+    XBT_DEBUG
+        ("Method reach %d iterations, which is the maximum number of iterations allowed.",
+         iteration);
+  }
+/*   XBT_INFO("Method converged after %d iterations", iteration); */
 
-  /* Printing Result */
-  xbt_swag_foreach(var, var_list) {
-    if(var->bound>0) {
-      DEBUG4("'%p'(%f) : %f (<=%f)",var,var->weight,var->value, var->bound);
-      if(var->value<=var->bound) 
-	DEBUG0("Incorrect value");
-    }
-    else 
-      DEBUG3("'%p'(%f) : %f",var,var->weight,var->value);
+  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;
 
-    /*
-     * Verify for each capacity constraint (lambda) the error associated. 
-     */
-    capacity_error = 0;
-    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->lambda - cnst2->lambda );
-      }
-    }
+  XBT_IN("");
 
-    /*
-     * 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->mu - var1->mu);
+  if (init == 0.0) {
+    min = max = 0.5;
+  }
+
+  min_diff = max_diff = middle_diff = 0.0;
+  overall_error = 1;
+
+  if ((diff_0 = diff(1e-16, var_cnst)) >= 0) {
+    XBT_CDEBUG(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) {
+    XBT_CDEBUG(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) {
+        XBT_CDEBUG(surf_lagrange_dichotomy, "Decreasing min");
+        min = min / 2.0;
+        min_diff = diff(min, var_cnst);
+      } else {
+        XBT_CDEBUG(surf_lagrange_dichotomy, "Decreasing max");
+        max = min;
+        max_diff = min_diff;
+      }
+    } else if (min_diff < 0 && max_diff < 0) {
+      if (min == max) {
+        XBT_CDEBUG(surf_lagrange_dichotomy, "Increasing max");
+        max = max * 2.0;
+        max_diff = diff(max, var_cnst);
+      } else {
+        XBT_CDEBUG(surf_lagrange_dichotomy, "Increasing min");
+        min = max;
+        min_diff = max_diff;
+      }
+    } else if (min_diff < 0 && max_diff > 0) {
+      middle = (max + min) / 2.0;
+      XBT_CDEBUG(surf_lagrange_dichotomy, "Trying (max+min)/2 : %1.20f",
+              middle);
+
+      if ((min == middle) || (max == middle)) {
+        XBT_CWARN(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) {
+        XBT_CDEBUG(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) {
+        XBT_CDEBUG(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) {
+      XBT_CWARN(surf_lagrange_dichotomy,
+             "The impossible happened, partial_diff(min) > 0 && partial_diff(max) < 0");
+      abort();
+    } else {
+      XBT_CWARN(surf_lagrange_dichotomy,
+             "diffmin (%1.20f) or diffmax (%1.20f) are something I don't know, taking no action.",
+             min_diff, max_diff);
+      abort();
     }
-
-    overall_error = capacity_error + bound_error;
   }
 
+  XBT_CDEBUG(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;
 
-  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);
-  }
+  XBT_IN("");
+  elem_list = &(cnst->element_set);
 
+  XBT_CDEBUG(surf_lagrange_dichotomy, "Computing diff of cnst (%p)", cnst);
 
-  if(XBT_LOG_ISENABLED(surf_writelambda, xbt_log_priority_debug)) {
-    fclose(gnuplot_file);
-  }
+  xbt_swag_foreach(elem, elem_list) {
+    var = elem->variable;
+    if (var->weight <= 0)
+      continue;
 
+    XBT_CDEBUG(surf_lagrange_dichotomy, "Computing sigma_i for var (%p)",
+            var);
+    // Initialize the summation variable
+    sigma_i = 0.0;
 
-  /*
-   * 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;
+    // Compute sigma_i 
+    for (j = 0; j < var->cnsts_number; j++) {
+      sigma_i += (var->cnsts[j].constraint)->lambda;
     }
-    var1->weight = 1 / tmp;
 
-    DEBUG2("var1->weight (id=%s) : %e", (char *)var1->id, var1->weight);
+    //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;
+
+  XBT_CDEBUG(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;
+}
+
+
+/**************** 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_assert(x > 0.0, "Don't call me with stupid values! (%1.20f)", x);
+  return VEGAS_SCALING * var->weight * log(x);
+}
+
+double func_vegas_fp(lmm_variable_t var, double x)
+{
+  xbt_assert(x > 0.0, "Don't call me with stupid values! (%1.20f)", x);
+  return VEGAS_SCALING * var->weight / x;
+}
+
+double func_vegas_fpi(lmm_variable_t var, double x)
+{
+  xbt_assert(x > 0.0, "Don't call me with stupid values! (%1.20f)", x);
+  return var->weight / (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_assert(var->weight > 0.0, "Don't call me with stupid values!");
+
+  return RENO_SCALING * sqrt(3.0 / 2.0) / var->weight *
+      atan(sqrt(3.0 / 2.0) * var->weight * x);
+}
+
+double func_reno_fp(lmm_variable_t var, double x)
+{
+  return RENO_SCALING * 3.0 / (3.0 * var->weight * var->weight * x * x +
+                               2.0);
+}
+
+double func_reno_fpi(lmm_variable_t var, double x)
+{
+  double res_fpi;
+
+  xbt_assert(var->weight > 0.0, "Don't call me with stupid values!");
+  xbt_assert(x > 0.0, "Don't call me with stupid values!");
+
+  res_fpi =
+      1.0 / (var->weight * var->weight * (x / RENO_SCALING)) -
+      2.0 / (3.0 * var->weight * var->weight);
+  if (res_fpi <= 0.0)
+    return 0.0;
+/*   xbt_assert(res_fpi>0.0,"Don't call me with stupid values!"); */
+  return sqrt(res_fpi);
+}
+
+
+/* Implementing new Reno-2
+ * For Reno-2:  $f(x)   = U_f(x_f) = \frac{{2}{D_f}}*ln(2+x*D_f)$
+ * Therefore:   $fp(x)  = 2/(Weight*x + 2)
+ * Therefore:   $fpi(x) = (2*Weight)/x - 4
+ */
+#define RENO2_SCALING 1.0
+double func_reno2_f(lmm_variable_t var, double x)
+{
+  xbt_assert(var->weight > 0.0, "Don't call me with stupid values!");
+  return RENO2_SCALING * (1.0 / var->weight) * log((x * var->weight) /
+                                                   (2.0 * x * var->weight +
+                                                    3.0));
+}
+
+double func_reno2_fp(lmm_variable_t var, double x)
+{
+  return RENO2_SCALING * 3.0 / (var->weight * x *
+                                (2.0 * var->weight * x + 3.0));
+}
+
+double func_reno2_fpi(lmm_variable_t var, double x)
+{
+  double res_fpi;
+  double tmp;
+
+  xbt_assert(x > 0.0, "Don't call me with stupid values!");
+  tmp = x * var->weight * var->weight;
+  res_fpi = tmp * (9.0 * x + 24.0);
 
+  if (res_fpi <= 0.0)
+    return 0.0;
 
+  res_fpi = RENO2_SCALING * (-3.0 * tmp + sqrt(res_fpi)) / (4.0 * tmp);
+  return res_fpi;
 }