+/* $Id$ */
+
+/* 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:
+ * "ssh://username@scm.gforge.inria.fr/svn/memo/people/pvelho/lagrange/ppf.ps".
+ */
+#include "xbt/log.h"
+#include "xbt/sysdep.h"
+#include "xbt/mallocator.h"
+#include "maxmin_private.h"
+
+#include <stdlib.h>
+#ifndef MATH
+#include <math.h>
+#endif
+
+
+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.");
+
+void lagrange_dicotomi_solve(lmm_system_t sys);
+
+double partial_diff_mu(double mu, lmm_variable_t var1);
+double partial_diff_lambda(double lambda, lmm_constraint_t cnst1);
+
+void lagrange_dicotomi_solve(lmm_system_t sys)
+{
+ /*
+ * Lagrange Variables.
+ */
+ int max_iterations= 1000000;
+ double epsilon_min_error = 0.00001;
+ double overall_error = 1;
+ double min, max, middle;
+
+
+ /*
+ * 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;
+
+
+ xbt_swag_t cnst_list = NULL;
+ lmm_constraint_t cnst1 = NULL;
+
+ xbt_swag_t var_list = NULL;
+ lmm_variable_t var1 = NULL;
+
+
+ /*
+ * Auxiliar variables.
+ */
+ int iteration=0;
+ double tmp=0;
+ int i;
+ FILE *gnuplot_file=NULL;
+
+
+ DEBUG0("Iterative method configuration snapshot =====>");
+ DEBUG1("#### Maximum number of iterations : %d", max_iterations);
+ DEBUG1("#### Minimum error tolerated : %e", epsilon_min_error);
+
+
+ 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;
+ var1->new_mu = 2.0;
+ }
+ DEBUG2("#### var1(%d)->mu : %e", i, var1->mu);
+ DEBUG2("#### var1(%d)->weight: %e", i, var1->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);
+ }
+
+
+
+ /*
+ * 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);
+ //forall mu_i in mu_1, mu_2, ..., mu_n
+ xbt_swag_foreach(var1, var_list) {
+ if((var1->bound >= 0) && (var1->weight > 0) ){
+ //for each link with capacity cnsts[i] that uses flow of variable var1 do
+ //begin dicotomi
+ min = max = 1.0;
+ overall_error = 1;
+ while(overall_error < epsilon_min_error){
+ if( partial_diff_mu(min, var1)>0 && partial_diff_mu(max, var1)>0 ){
+ if(min == max){
+ min = min / 2;
+ }else{
+ max = min;
+ }
+ }else if( partial_diff_mu(min, var1)<0 && partial_diff_mu(max, var1)<0 ){
+ if(min == max){
+ max = max * 2;
+ }else{
+ max = min;
+ }
+ }else if( partial_diff_mu(min,var1)<0 && partial_diff_mu(max,var1) > 0 ){
+ if(min == max){
+ middle = partial_diff_mu((fabs(min - max)/2), var1);
+ if( middle > 0 ){
+ max = (fabs(min - max)/2);
+ }else if( middle < 0 ){
+ min = (fabs(min - max)/2);
+ }else{
+ WARN0("Found an optimal solution with 0 error!");
+ overall_error = 0;
+ }
+ overall_error = fabs(min - max);
+ }
+ }else{
+ WARN0("The impossible happened, partial_diff(min) >0 && partial_diff(max) < 0");
+ }
+ }
+
+ var1->new_mu = max;
+
+ if(var1->new_mu < 0){
+ var1->new_mu = 0;
+ }
+ }
+ }
+
+
+ /* d Dual
+ * Compute the value of ------------- (\lambda^k, \mu^k) this portion
+ * d \lambda_i^k
+ * of code depends on function f(x).
+ */
+ xbt_swag_foreach(cnst1, cnst_list) {
+
+ //begin dicotomi
+ overall_error = 1;
+ min = max = 1.0;
+ while(overall_error < epsilon_min_error){
+ if( partial_diff_lambda(min, cnst1) > 0 && partial_diff_lambda(max, cnst1) > 0 ){
+ if(min == max){
+ min = min / 2;
+ }else{
+ max = min;
+ }
+ }else if( partial_diff_lambda(min, cnst1) < 0 && partial_diff_lambda(max, cnst1) < 0 ){
+ if(min == max){
+ max = max * 2;
+ }else{
+ max = min;
+ }
+ }else if( partial_diff_lambda(min,cnst1) < 0 && partial_diff_lambda(max,cnst1) > 0 ){
+ if(min == max){
+ middle = partial_diff_lambda((fabs(min - max)/2), cnst1);
+ if( middle > 0 ){
+ max = (fabs(min - max)/2);
+ }else if( middle < 0 ){
+ min = (fabs(min - max)/2);
+ }else{
+ WARN0("Found an optimal solution with 0 error!");
+ overall_error = 0;
+ }
+ overall_error = fabs(min - max);
+ }
+ }else{
+ WARN0("The impossible happened, partial_diff(min) >0 && partial_diff(max) < 0");
+ }
+ }
+
+ var1->new_mu = max;
+
+ cnst1->new_lambda = cnst1->lambda;
+
+ if(cnst1->new_lambda < 0){
+ cnst1->new_lambda = 0;
+ }
+ }
+
+
+ /*
+ * 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;
+ }
+
+ }
+
+
+ /* 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;
+ }
+
+
+ //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;
+ }
+
+ tmp = tmp - cnst1->bound;
+
+
+ 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);
+ }
+
+ }
+
+
+ xbt_swag_foreach(var1, var_list){
+ if(var1->bound <= 0 || var1->weight <= 0) continue;
+ tmp = 0;
+ tmp = (var1->value - var1->bound);
+
+
+ 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);
+ }
+
+ }
+
+
+ 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_writelambda, xbt_log_priority_debug)) {
+ fclose(gnuplot_file);
+ }
+
+
+}
+
+
+
+double partial_diff_mu(double mu, lmm_variable_t var1){
+ double mu_partial=0.0;
+ int i;
+
+ //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;
+
+ mu_partial = (-1.0/mu_partial) + var1->bound;
+
+ return mu_partial;
+}
+
+
+double partial_diff_lambda(double lambda, lmm_constraint_t cnst1){
+
+ double tmp=0.0;
+ int i;
+ double lambda_partial=0.0;
+ xbt_swag_t elem_list = NULL;
+ lmm_element_t elem1 = NULL;
+ lmm_variable_t var1 = NULL;
+
+
+ elem_list = &(cnst1->element_set);
+
+ xbt_swag_foreach(elem1, elem_list) {
+ var1 = elem1->variable;
+ if(var1->weight<=0) continue;
+
+ tmp = 0;
+ for(i=0; i<var1->cnsts_number; i++){
+ tmp += (var1->cnsts[i].constraint)->lambda;
+ }
+
+ if(var1->bound > 0)
+ tmp += var1->mu;
+
+ if(tmp==0) lambda_partial = 10e-8;
+ lambda_partial += (-1.0 / (tmp - 3*cnst1->lambda + 3*cnst1->lambda));
+ }
+
+ return lambda_partial;
+}
+
