#include <math.h>
#endif
-
XBT_LOG_NEW_DEFAULT_SUBCATEGORY(surf_lagrange, surf,
"Logging specific to SURF (lagrange)");
-XBT_LOG_NEW_SUBCATEGORY(surf_lagrange_dichotomy, surf,
+XBT_LOG_NEW_SUBCATEGORY(surf_lagrange_dichotomy, surf_lagrange,
"Logging specific to SURF (lagrange dichotomy)");
+#define SHOW_EXPR(expr) CDEBUG1(surf_lagrange,#expr " = %g",expr);
+
+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
-double dichotomy(double init, double diff(double, void *), void *var_cnst,
- double min_error);
+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
-double partial_diff_mu(double mu, void *param_var);
+static 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);
-//auxiliar function to compute the partial_diff
-double diff_aux(lmm_variable_t var, double x);
-
+static double partial_diff_lambda(double lambda, void *param_cnst);
-static int __check_kkt(xbt_swag_t cnst_list, xbt_swag_t var_list, int warn)
+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;
double tmp;
- //verify the KKT property for each link
xbt_swag_foreach(cnst, cnst_list) {
tmp = 0;
elem_list = &(cnst->element_set);
cnst, cnst->bound, tmp);
return 0;
}
- DEBUG3("Checking KKT for constraint (%p): sat = %f, lambda = %f ",
+ DEBUG3("Checking feasability for constraint (%p): sat = %f, lambda = %f ",
cnst, tmp - cnst->bound, cnst->lambda);
-
-/* if(!((fabs(tmp - cnst->bound)<MAXMIN_PRECISION && cnst->lambda>=MAXMIN_PRECISION) || */
-/* (fabs(tmp - cnst->bound)>=MAXMIN_PRECISION && cnst->lambda<MAXMIN_PRECISION))) { */
-/* if(warn) WARN1("The KKT condition is not verified for cnst %p...", cnst); */
-/* return 0; */
-/* } */
}
- //verify the KKT property of each flow
xbt_swag_foreach(var, var_list) {
if (var->bound < 0 || var->weight <= 0)
continue;
- DEBUG3("Checking KKT for variable (%p): sat = %f mu = %f", var,
+ DEBUG3("Checking feasability for variable (%p): sat = %f mu = %f", var,
var->value - var->bound, var->mu);
if (double_positive(var->value - var->bound)) {
var, var->bound, var->value);
return 0;
}
-
-/* if(!((fabs(var->value - var->bound)<MAXMIN_PRECISION && var->mu>=MAXMIN_PRECISION) || */
-/* (fabs(var->value - var->bound)>=MAXMIN_PRECISION && var->mu<MAXMIN_PRECISION))) { */
-/* if(warn) WARN1("The KKT condition is not verified for var %p...",var); */
-/* 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;
+ DEBUG3("\t Working on var (%p). cost = %e; Df = %e", var, tmp,
+ var->df);
+ //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;
+
+ for (j = 0; j < var->cnsts_number; j++)
+ sigma_i += (var->cnsts[j].constraint)->lambda;
+
+ if (var->bound > 0)
+ sigma_i += var->mu;
+
+ DEBUG2("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.
*/
int max_iterations = 100;
- double epsilon_min_error = 1e-6;
- double dichotomy_min_error = 1e-20;
- double overall_error = 1;
+ 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
int iteration = 0;
double tmp = 0;
int i;
-
+ double obj,new_obj;
DEBUG0("Iterative method configuration snapshot =====>");
DEBUG1("#### Maximum number of iterations : %d", max_iterations);
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;
+ DEBUG2("#### cnst(%p)->lambda : %e", cnst, cnst->lambda);
+ }
+
/*
* Initialize the var list variable with only the active variables.
* Associate an index in the swag variables. Initialize mu.
if ((var->bound < 0.0) || (var->weight <= 0.0)) {
DEBUG1("#### NOTE var(%d) is a boundless (or inactive) variable", i);
var->mu = -1.0;
+ if(var->weight>0.0)
+ var->value = new_value(var);
+ else
+ var->value = 0;
} else {
var->mu = 1.0;
var->new_mu = 2.0;
+ var->value = new_value(var);
}
DEBUG3("#### var(%d) %p ->mu : %e", i, var, var->mu);
DEBUG3("#### var(%d) %p ->weight: %e", i, var, var->weight);
}
/*
- * Initialize lambda.
+ * Compute dual objective.
*/
- 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);
- }
+ 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) {
- int dual_updated=0;
+ 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
+ * Improve 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)) {
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));
+ var->new_mu = new_mu(var);
+/* 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;
+
+ new_obj=dual_objective(var_list,cnst_list);
+ DEBUG3("Improvement for Objective (%g -> %g) : %g", obj, new_obj,
+ obj-new_obj);
+ xbt_assert1(obj-new_obj>=-epsilon_min_error,"Our gradient sucks! (%1.20f)",obj-new_obj);
+ obj = new_obj;
}
}
/*
- * Compute the value of lambda_i
+ * Improve the value of lambda_i
*/
- //forall lambda_i in lambda_1, lambda_2, ..., lambda_n
xbt_swag_foreach(cnst, cnst_list) {
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));
+/* 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;
+
+ new_obj=dual_objective(var_list,cnst_list);
+ DEBUG3("Improvement for Objective (%g -> %g) : %g", obj, new_obj,
+ obj-new_obj);
+ xbt_assert1(obj-new_obj>=-epsilon_min_error,"Our gradient sucks! (%1.20f)",obj-new_obj);
+ obj = new_obj;
}
/*
* the values of \lambda and \mu.
*/
DEBUG0("-------------- Check convergence ----------");
- overall_error = 0;
+ overall_modification = 0;
xbt_swag_foreach(var, var_list) {
if (var->weight <= 0)
var->value = 0.0;
else {
- //compute sigma_i + mu_i
- tmp = 0;
- for (i = 0; i < var->cnsts_number; i++) {
- tmp += (var->cnsts[i].constraint)->lambda;
- }
- if (var->bound > 0)
- tmp += var->mu;
- DEBUG3("\t Working on var (%p). cost = %e; Df = %e", var, tmp,
- var->df);
-
- //uses the partial differential inverse function
- tmp = var->func_fpi(var, tmp);
-
- //computes de overall_error using normalized value
- if (overall_error < (fabs(var->value - tmp))) {
- overall_error = (fabs(var->value - tmp));
- }
+ tmp = new_value(var);
+
+ overall_modification = MAX(overall_modification, fabs(var->value - tmp));
var->value = tmp;
- DEBUG3("New value of var (%p) = %e, overall_error = %e", var,
- var->value, overall_error);
+ DEBUG3("New value of var (%p) = %e, overall_modification = %e", var,
+ var->value, overall_modification);
}
}
- if (!__check_kkt(cnst_list, var_list, 0))
- overall_error = 1.0;
- DEBUG2("Iteration %d: Overall_error : %f", iteration, overall_error);
- if(!dual_updated) {
- WARN1("Could not improve the convergence at iteration %d. Drop it!",iteration);
- break;
- }
+ DEBUG0("-------------- Check feasability ----------");
+ 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; */
+/* } */
}
+ __check_feasible(cnst_list, var_list, 1);
- __check_kkt(cnst_list, var_list, 1);
-
- if (overall_error <= epsilon_min_error) {
+ if (overall_modification <= epsilon_min_error) {
DEBUG1("The method converges in %d iterations.", iteration);
}
if (iteration >= max_iterations) {
- WARN1
+ DEBUG1
("Method reach %d iterations, which is the maximum number of iterations allowed.",
iteration);
}
*
* @return a double correponding to the result of the dichotomyal process
*/
-double dichotomy(double init, double diff(double, void *), void *var_cnst,
- double min_error)
+static double dichotomy(double init, double diff(double, void *), void *var_cnst,
+ double min_error)
{
double min, max;
double overall_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, max] = [%1.20f, %1.20f] || diffmin, diffmax = %1.20f, %1.20f", min, max,
min_diff,max_diff);
if (min_diff > 0 && max_diff > 0) {
CDEBUG0(surf_lagrange_dichotomy, "Decreasing max");
max = min;
max_diff = min_diff;
-
}
} else if (min_diff < 0 && max_diff < 0) {
if (min == max) {
CDEBUG1(surf_lagrange_dichotomy, "Trying (max+min)/2 : %1.20f",middle);
if((min==middle) || (max==middle)) {
- WARN0("Cannot improve the convergence!");
+ CWARN4(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) {
CDEBUG0(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) {
CDEBUG0(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) {
CWARN0(surf_lagrange_dichotomy,
"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;
- 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;
-
- //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)
+static double partial_diff_lambda(double lambda, void *param_cnst)
{
- int i;
+ 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 lambda_partial = 0.0;
+ double diff = 0.0;
double sigma_i = 0.0;
XBT_IN;
elem_list = &(cnst->element_set);
- CDEBUG1(surf_lagrange_dichotomy,"Computting diff of cnst (%p)", cnst);
+ CDEBUG1(surf_lagrange_dichotomy,"Computing diff of cnst (%p)", cnst);
xbt_swag_foreach(elem, elem_list) {
var = elem->variable;
if (var->weight <= 0)
continue;
- //initilize de sumation variable
+ CDEBUG1(surf_lagrange_dichotomy,"Computing sigma_i for var (%p)", var);
+ // Initialize the summation variable
sigma_i = 0.0;
- //compute sigma_i of variable var
- for (i = 0; i < var->cnsts_number; i++) {
- sigma_i += (var->cnsts[i].constraint)->lambda;
+ // Compute sigma_i
+ for (j = 0; j < var->cnsts_number; j++) {
+ sigma_i += (var->cnsts[j].constraint)->lambda;
}
//add mu_i if this flow has a RTT constraint associated
//replace value of cnst->lambda by the value of parameter lambda
sigma_i = (sigma_i - cnst->lambda) + lambda;
- //use the auxiliar function passing (\sigma_i + \mu_i)
- lambda_partial += diff_aux(var, sigma_i);
+ diff += -var->func_fpi(var, sigma_i);
}
- lambda_partial += cnst->bound;
-
-
-/* CDEBUG1(surf_lagrange_dichotomy, "returning = %1.20f", lambda_partial); */
+ diff += cnst->bound;
+ CDEBUG3(surf_lagrange_dichotomy,"d D/d lambda for cnst (%p) at %1.20f = %1.20f",
+ cnst, lambda, diff);
XBT_OUT;
- return lambda_partial;
+ return diff;
}
-
-double diff_aux(lmm_variable_t var, double x)
+/** \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))
{
- double tmp_fpi, result;
-
- XBT_IN2("(var (%p), x (%1.20f))", var, x);
- xbt_assert0(var->func_fp,
- "Initialize the protocol functions first create variables before.");
-
- tmp_fpi = var->func_fpi(var, x);
- result = - tmp_fpi;
-
-/* CDEBUG1(surf_lagrange_dichotomy, "returning %1.20f", result); */
- XBT_OUT;
- return result;
+ func_f_def = func_f;
+ func_fp_def = func_fp;
+ func_fpi_def = func_fpi;
}
*/
/*
- * For Vegas f: $\alpha_f d_f \log\left(x_f\right)$
+ * 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){
- return VEGAS_SCALING*var->df * log(x);
+ xbt_assert0(x>0.0,"Don't call me with stupid values!");
+ return VEGAS_SCALING*var->df*log(x);
}
-/*
- * For Vegas fp: $\frac{\alpha D_f}{x}$
- */
double func_vegas_fp(lmm_variable_t var, double x){
- //avoid a disaster value - c'est du bricolage mais ca marche
-/* if(x == 0) x = 10e-8; */
+ xbt_assert0(x>0.0,"Don't call me with stupid values!");
return VEGAS_SCALING*var->df/x;
}
-/*
- * For Vegas fpi: $\frac{\alpha D_f}{x}$
- */
double func_vegas_fpi(lmm_variable_t var, double x){
- //avoid a disaster value - c'est du bricolage mais ca marche
-/* if(x == 0) x = 10e-8; */
- return VEGAS_SCALING*var->df/x;
-}
-
-/*
- * For Vegas fpip: $-\frac{\alpha D_f}{x^2}$
- */
-double func_vegas_fpip(lmm_variable_t var, double x){
- //avoid a disaster value - c'est du bricolage mais ca marche
-/* if(x == 0) x = 10e-8; */
- return -( VEGAS_SCALING*var->df/(x*x) ) ;
+ xbt_assert0(x>0.0,"Don't call me with stupid values!");
+ return var->df/(x/VEGAS_SCALING);
}
-
/*
- * For Reno f: $\frac{\sqrt{\frac{3}{2}}}{D_f} \arctan\left(\sqrt{\frac{3}{2}}x_f D_f\right)$
+ * 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_assert0(var->df>0.0,"Don't call me with stupid values!");
- // \sqrt{3/2} = 0.8164965808
- return (0.8164965808 / var->df) * atan( (0.8164965808 / var->df)*x );
+
+ return RENO_SCALING*sqrt(3.0/2.0)/var->df*atan(sqrt(3.0/2.0)*var->df*x);
}
-/*
- * For Reno fp: $\frac{3}{3 {D_f}^2 x^2 + 2}$
- */
double func_reno_fp(lmm_variable_t var, double x){
- return 3 / (3*var->df*var->df*x*x + 2);
+ return RENO_SCALING*3.0/(3.0*var->df*var->df*x*x +2.0);
}
-/*
- * For Reno fpi: $\sqrt{\frac{1}{{D_f}^2 x} - \frac{2}{3{D_f}^2}}$
- */
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);
+ res_fpi = 1.0/(var->df*var->df*(x/RENO_SCALING)) - 2.0/(3.0*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!");
+/* xbt_assert0(res_fpi>0.0,"Don't call me with stupid values!"); */
return sqrt(res_fpi);
}
-/*
- * For Reno fpip: $-\frac{1}{2 {D_f}^2 x^2\sqrt{\frac{1}{{D_f}^2 x} - \frac{2}{3{D_f}^2}}}$
- */
-double func_reno_fpip(lmm_variable_t var, double x){
- double res_fpip;
- double critical_test;
- 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_fpip = 1/(var->df*var->df*x) - 2/(3*var->df*var->df);
- xbt_assert0(res_fpip>0.0,"Don't call me with stupid values!");
- critical_test = (2*var->df*var->df*x*x*sqrt(res_fpip));
-
- return -(1.0/critical_test);
-}
