#include <math.h>
#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)");
+XBT_LOG_NEW_SUBCATEGORY(surf_lagrange_dichotomy, surf,
+ "Logging specific to SURF (lagrange dichotomy)");
/*
- * 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
+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);
+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);
+double partial_diff_lambda(double lambda, void *param_cnst);
+//auxiliar function to compute the partial_diff
+double diff_aux(lmm_variable_t var, double x);
+
+
+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->bound < 0 || var->weight <= 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;
+}
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-18;
+ 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;
-
+
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 (!(sys->modified))
return;
/*
* 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);
+ i = 0;
+ xbt_swag_foreach(var, var_list) {
+ if ((var->bound < 0.0) || (var->weight <= 0.0)) {
+ DEBUG1("#### NOTE var(%d) is a boundless (or inactive) variable", i);
var->mu = -1.0;
- } else{
- 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);
+ 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++;
}
/*
* Initialize lambda.
*/
- cnst_list=&(sys->active_constraint_set);
- xbt_swag_foreach(cnst, cnst_list){
+ 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);
}
-
+
/*
* While doesn't reach a minimun error or a number maximum of iterations.
*/
- while(overall_error > epsilon_min_error && iteration < max_iterations){
-
- iteration++;
- DEBUG1("************** ITERATION %d **************", iteration);
+ while (overall_modification > epsilon_min_error && iteration < max_iterations) {
+ int dual_updated=0;
+ iteration++;
+ DEBUG1("************** ITERATION %d **************", iteration);
+ DEBUG0("-------------- Gradient Descent ----------");
/*
* Compute 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->bound >= 0) && (var->weight > 0)) {
+ DEBUG1("Working on var (%p)", var);
+ var->new_mu =
+ dichotomy(var->mu, partial_diff_mu, var, dichotomy_min_error);
+ 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;
}
}
*/
//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; */
-/* } */
-
/*
* 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 {
+ //compute sigma_i + mu_i
tmp = 0;
- for(i=0; i<var->cnsts_number; i++){
+ for (i = 0; i < var->cnsts_number; i++) {
tmp += (var->cnsts[i].constraint)->lambda;
- if(var->bound > 0)
- tmp+=var->mu;
}
+ if (var->bound > 0)
+ tmp += var->mu;
+ DEBUG3("\t Working on var (%p). cost = %e; Df = %e", var, tmp,
+ var->df);
- if(tmp == 0.0)
- WARN0("CAUTION: division by 0.0");
+ //uses the partial differential inverse function
+ tmp = var->func_fpi(var, tmp);
- //computes de overall_error
- if(overall_error < fabs(var->value - 1.0/tmp)){
- overall_error = fabs(var->value - 1.0/tmp);
+ if (overall_modification < (fabs(var->value - tmp)/tmp)) {
+ overall_modification = (fabs(var->value - tmp)/tmp);
}
- var->value = 1.0 / tmp;
- }
- DEBUG4("======> value of var %s (%p) = %e, overall_error = %e", (char *)var->id, var, var->value, overall_error);
- }
- }
-
- //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);
+ 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.
*
* @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){
+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");
+ min_diff = diff(min, var_cnst);
+ max_diff = diff(max, var_cnst);
- while(overall_error > min_error){
+ 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);
- min_diff = diff(min, var_cnst);
- max_diff = diff(max, var_cnst);
-
- 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)) {
+ CWARN2(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.",
+ min, max-min);
+ 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 ){
+ min_diff = middle_diff;
+ overall_error = max-middle_diff;
+ } else if (middle_diff > 0) {
+ CDEBUG0(surf_lagrange_dichotomy, "Decreasing max");
max = middle;
- }else{
- WARN0("Found an optimal solution with 0 error!");
+ max_diff = middle_diff;
+ overall_error = max-middle_diff;
+ } else {
overall_error = 0;
- return middle;
}
-
- }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;
+ } else if (max_diff == 0) {
+ min=max;
+ overall_error = 0;
+ } 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);
+ CDEBUG1(surf_lagrange_dichotomy, "returning %e", (min + max) / 2.0);
+ XBT_OUT;
+ 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;
+double partial_diff_mu(double mu, void *param_var)
+{
+ double mu_partial = 0.0;
+ double sigma_mu = 0.0;
+ lmm_variable_t var = (lmm_variable_t) param_var;
int i;
+ XBT_IN;
+ //compute sigma_i
+ for (i = 0; i < var->cnsts_number; i++)
+ sigma_mu += (var->cnsts[i].constraint)->lambda;
+
+ //compute sigma_i + mu_i
+ sigma_mu += mu;
- //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;
+ //use auxiliar function passing (sigma_i + mu_i)
+ mu_partial = diff_aux(var, sigma_mu);
+ //add the RTT limit
+ mu_partial += var->bound;
+
+ XBT_OUT;
return mu_partial;
}
/*
*
*/
-double partial_diff_lambda(double lambda, void *param_cnst){
+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;
-
+ lmm_constraint_t cnst = (lmm_constraint_t) param_cnst;
+ double lambda_partial = 0.0;
+ double sigma_i = 0.0;
+ XBT_IN;
elem_list = &(cnst->element_set);
+ CDEBUG1(surf_lagrange_dichotomy,"Computting 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);
+ //initilize de sumation 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 of variable var
+ for (i = 0; i < var->cnsts_number; i++) {
+ sigma_i += (var->cnsts[i].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));
+ //use the auxiliar function passing (\sigma_i + \mu_i)
+ lambda_partial += diff_aux(var, sigma_i);
}
- lambda_partial += cnst->bound;
- //DEBUG1("===> %e ", lambda_partial);
+ lambda_partial += cnst->bound;
+ XBT_OUT;
return lambda_partial;
}
-
-
+
+
+double diff_aux(lmm_variable_t var, double x)
+{
+ double tmp_fpi, result;
+
+ XBT_IN2("(var (%p), x (%1.20f))", var, x);
+ xbt_assert0(var->func_fpi,
+ "Initialize the protocol functions first create variables before.");
+
+ tmp_fpi = var->func_fpi(var, x);
+ result = - tmp_fpi;
+
+ XBT_OUT;
+ return result;
+}
+
+/** \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_fpi) (lmm_variable_t var, double x))
+{
+ 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: $fpi(x) = \frac{\alpha D_f}{x}$
+ */
+#define VEGAS_SCALING 1000.0
+double func_vegas_fpi(lmm_variable_t var, double x){
+ xbt_assert0(x>0.0,"Don't call me with stupid values!");
+ return VEGAS_SCALING*var->df/x;
+}
+
+/*
+ * For Reno: $f(x) = \frac{\sqrt{3/2}}{D_f} atan(\sqrt{3/2}D_f x)$
+ * Therefore: $fpi(x) = \sqrt{\frac{1}{{D_f}^2 x} - \frac{2}{3{D_f}^2}}$
+ */
+#define RENO_SCALING 1000.0
+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/(var->df*var->df*x) - 2/(3*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(RENO_SCALING*res_fpi);
+}
+
