-/* $Id$ */
-
-/* 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_lagrangedico, surf,
- "Logging specific to SURF (lagrange)");
-
-
-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= 10;
- double epsilon_min_error = 1e-10;
- 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;
-_variable_t var1 = NULL;
-
-
- /*
- * Auxiliar variables.
- */
- int iteration=0;
- double tmp=0;
- int i;
-
-
- 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 = var1->mu;
- 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->mu = max;
-
- if(var1->mu < 0){
- var1->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) {
-
-
- DEBUG2("cnst1 (id=%s) (%p)", (char *)cnst1->id, cnst1);
-
- //begin dicotomi
- i=0;
- overall_error = 1;
- min = max = cnst1->lambda;
- while(overall_error > epsilon_min_error){
- i++;
-
-
- // DEBUG4("====> Dicotomi debug. [%e, %e], D(min,max) = [%e, %e]", min, max, partial_diff_lambda(min, cnst1), partial_diff_lambda(max, cnst1));
-
- if( partial_diff_lambda(min, cnst1) > 0 && partial_diff_lambda(max, cnst1) > 0 ){
- if(min == max){
- min = min / 2.0;
- }else{
- max = min;
- }
- }else if( partial_diff_lambda(min, cnst1) < 0 && partial_diff_lambda(max, cnst1) < 0 ){
- if(min == max){
- max = max * 2.0;
- }else{
- min = max;
- }
- }else if( partial_diff_lambda(min,cnst1) < 0 && partial_diff_lambda(max,cnst1) > 0 ){
- middle = (max + min)/2.0;
-
-
- //DEBUG2("Ideal state reached middle = %e, D(fabs(min-max)/2.0) = %e", middle, partial_diff_lambda(middle, cnst1));
- if( partial_diff_lambda(middle, cnst1) < 0 ){
- min = middle;
- }else if( partial_diff_lambda(middle, cnst1) > 0 ){
- max = middle;
- }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");
- }
- }
-
-
- DEBUG1("Number of iteration in the dicotomi %d", i);
-
- cnst1->lambda = min;
-
- if(cnst1->lambda < 0){
- cnst1->lambda = 0;
- }
- }
-
-
- /*
- * Now computes the values of each variable (\rho) based on
- * the values of \lambda and \mu.
- */
- overall_error=0;
- DEBUG1("Iteration %d ", iteration);
- 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;
- }
-
-
- DEBUG2("======> value of var1 (%p) = %e", var1, var1->value);
- }
- }
-
-
-
-
-
- //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);
- }
-
-
-
-}
-
-
-double dicotomi(double init, void *diff(double, void*), void *var_cnst){
- double min, max;
- double overall_error;
-
- min = max = init;
- overall_error = 1;
-
- while(overall_error > epsilon_min_error){
- if( diff(min, var_cnst) > 0 && diff(max, var_cnst) > 0 ){
- if(min == max){
- min = min / 2.0;
- }else{
- max = min;
- }
- }else if( diff(min, var_cnst) < 0 && diff(max, var_cnst) < 0 ){
- if(min == max){
- max = max * 2.0;
- }else{
- min = max;
- }
- }else if( diff(min, var_cnst) < 0 && diff(max, var_cnst) > 0 ){
- middle = (max + min)/2.0;
-
- if( diff(middle, var_cnst) < 0 ){
- min = middle;
- }else if( diff(middle, var_cnst) > 0 ){
- max = middle;
- }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");
- }
- }
-}
-
-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;
-
- tmp = tmp - cnst1->lambda + lambda;
-
- //un peux du bricolage pour evite la catastrophe
- if(tmp==0) lambda_partial = 10e-8;
-
- lambda_partial += (-1.0 /tmp);
- }
-
-
- lambda_partial += cnst1->bound;
-
- //DEBUG3("Partial diff lambda result cnst1 %s (%p) : %e", (char *)cnst1->id, cnst1, lambda_partial);
- return lambda_partial;
-}
-
