#endif
-XBT_LOG_NEW_DEFAULT_SUBCATEGORY(surf_lagrange, surf,
- "Logging specific to SURF (lagrange)");
+XBT_LOG_NEW_DEFAULT_SUBCATEGORY(surf_lagrange, surf, "Logging specific to SURF (lagrange)");
+
+
+/*
+ * Local prototypes to implement the lagrangian optimization with optimal step, also called dicotomi.
+ */
+//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);
+//computes the value of the differential of variable param_var applied to mu
+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);
+
+
void lagrange_solve(lmm_system_t sys)
{
-
/*
* Lagrange Variables.
*/
- double epsilon_min_error = 1e-6;
+ int max_iterations= 10;
+ double epsilon_min_error = 1e-10;
double overall_error = 1;
- double sigma_step = 0.5e-3;
- double capacity_error, bound_error;
- double sum_capacity = 0;
- double sum_bound = 0;
-
+
/*
* Variables to manipulate the data structure proposed to model the maxmin
* fairness. See docummentation for more details.
*/
- lmm_element_t elem = NULL;
- xbt_swag_t cnst_list = NULL;
- lmm_constraint_t cnst1 = NULL;
- lmm_constraint_t cnst2 = NULL;
- xbt_swag_t var_list = NULL;
- xbt_swag_t elem_list = NULL;
- lmm_variable_t var1 = NULL;
- lmm_variable_t var2 = NULL;
+ xbt_swag_t elem_list = NULL;
+ lmm_element_t elem = NULL;
+
+
+ xbt_swag_t cnst_list = NULL;
+ lmm_constraint_t cnst = NULL;
+
+ xbt_swag_t var_list = NULL;
+ lmm_variable_t var = NULL;
/*
* Auxiliar variables.
*/
int iteration=0;
- int max_iterations=100000;
- double mu_partial=0;
- double lambda_partial=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 and compute the sum
- * of all round trip time constraints. May change depending on the
- * function f(x).
+ * Associate an index in the swag variables. Initialize mu.
*/
- var_list = &(sys->active_variable_set);
+ var_list = &(sys->variable_set);
i=0;
- xbt_swag_foreach(var1, var_list) {
- if(var1->weight != 0.0){
- i++;
- sum_bound += var1->bound;
+ 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;
}
+ DEBUG2("#### var(%d)->mu : %e", i, var->mu);
+ DEBUG2("#### var(%d)->weight: %e", i, var->weight);
+ i++;
}
/*
- * Compute the sum of all capacities constraints. May change depending
- * on the function f(x).
+ * Initialize lambda.
*/
cnst_list=&(sys->active_constraint_set);
- xbt_swag_foreach(cnst1, cnst_list) {
- sum_capacity += cnst1->value;
+ xbt_swag_foreach(cnst, cnst_list) {
+ cnst->lambda = 1.0;
+ cnst->new_lambda = 2.0;
+ DEBUG2("#### cnst(%p)->lambda : %e", cnst, cnst->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).
+ /*
+ * Compute the value of mu_i
*/
- bound_error = 0;
- xbt_swag_foreach(var1, var_list) {
-
- mu_partial = 0;
-
- //for each link elem1 that uses flow of variable var1 do
- //mu_partial += elem1->weight + var1->bound;
-
- mu_partial = - (1 / mu_partial) + sum_bound;
-
- var1->bound = var1->bound + sigma_step * mu_partial;
+ var_list = &(sys->variable_set);
+ //forall mu_i in mu_1, mu_2, ..., mu_n
+ xbt_swag_foreach(var, var_list) {
+ if((var->bound >= 0) && (var->weight > 0) ){
+ var->mu = dicotomi(var->mu, partial_diff_mu, var, epsilon_min_error);
+ if(var->mu < 0) var->mu = 0;
+ }
}
-
-
+
/*
- * Verify for each capacity constraint (lambda) the error associated.
+ * Compute the value of lambda_i
*/
- xbt_swag_foreach(cnst1, cnst_list) {
- cnst2 = xbt_swag_getNext(cnst1,(var_list)->offset);
- if(cnst2 != NULL){
- capacity_error += fabs(cnst1->value - cnsts2->value);
- }
+ //forall lambda_i in lambda_1, lambda_2, ..., lambda_n
+ xbt_swag_foreach(cnst, cnst_list) {
+ cnst->lambda = dicotomi(cnst->lambda, partial_diff_lambda, cnst, epsilon_min_error);
+ if(cnst->lambda < 0) cnst->lambda = 0;
}
+
/*
- * Verify for each variable the error of round trip time constraint (mu).
+ * Now computes the values of each variable (\rho) based on
+ * the values of \lambda and \mu.
*/
- bound_error = 0;
- xbt_swag_foreach(var1, var_list) {
- var2 = xbt_swag_getNext(var1,(var_list)->offset);
- if(var2 != NULL){
- bound_error += fabs( var2->weight - var1->weight);
+ overall_error=0;
+ DEBUG1("Iteration %d ", iteration);
+ xbt_swag_foreach(var, var_list) {
+ 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;
+ }
+
+ //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;
+ }
+
+
+ DEBUG2("======> value of var (%p) = %e", var, var->value);
+ }
+ }
+
+
+ //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;
+ }
+
+ tmp = tmp - cnst->bound;
+
+
+ if(tmp != 0 || cnst->lambda != 0){
+ WARN4("The link %s(%p) doesn't match the KKT property, value expected (=0) got (lambda=%e) (sum_rho=%e)", (char *)cnst->id, cnst, cnst->lambda, tmp);
+ }
+
+ }
+
+
+ //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);
+ }
+
+ }
+
+
+ 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);
+ }
+
+
+
+}
+
+/*
+ * Returns a double value corresponding to the result of a dicotomi 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 dicotomial process
+ */
+double dicotomi(double init, double diff(double, void*), void *var_cnst, double min_error){
+ double min, max;
+ double overall_error;
+ double middle;
+
+ min = max = init;
+ overall_error = 1;
+
+ DEBUG0("STARTING DICOTOMI... Debuggin, format used [min, max], [D(min),D(max)]");
+
+ while(overall_error > min_error){
+ DEBUG4("====> [%e, %e] , [%e,%e]", min, max, diff(min, var_cnst), diff(max, var_cnst));
+
+ 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");
}
+ }
+
+ 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;
+}
- overall_error = capacity_error + bound_error;
+
+double partial_diff_lambda(double lambda, void *param_cnst){
+
+ double tmp=0.0;
+ int i;
+ 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;
+
+
+ elem_list = &(cnst->element_set);
+
+ xbt_swag_foreach(elem, elem_list) {
+ var = elem->variable;
+ if(var->weight<=0) continue;
+
+ tmp = 0;
+ for(i=0; i<var->cnsts_number; i++){
+ tmp += (var->cnsts[i].constraint)->lambda;
+ }
+
+ if(var->bound > 0)
+ tmp += var->mu;
+
+ tmp = tmp - cnst->lambda + lambda;
+
+ //avoid a disaster value of lambda
+ if(tmp==0) lambda_partial = 10e-8;
+
+ lambda_partial += (-1.0 /tmp);
}
+ lambda_partial += cnst->bound;
+
+ return lambda_partial;
}
+
