2 /* Copyright (c) 2007 Arnaud Legrand, Pedro Velho. All rights reserved. */
3 /* This program is free software; you can redistribute it and/or modify it
4 * under the terms of the license (GNU LGPL) which comes with this package. */
6 * Modelling the proportional fairness using the Lagrange Optimization
7 * Approach. For a detailed description see:
8 * "ssh://username@scm.gforge.inria.fr/svn/memo/people/pvelho/lagrange/ppf.ps".
11 #include "xbt/sysdep.h"
12 #include "maxmin_private.h"
19 XBT_LOG_NEW_DEFAULT_SUBCATEGORY(surf_lagrange, surf,
20 "Logging specific to SURF (lagrange)");
21 XBT_LOG_NEW_SUBCATEGORY(surf_lagrange_dichotomy, surf_lagrange,
22 "Logging specific to SURF (lagrange dichotomy)");
24 #define SHOW_EXPR(expr) CDEBUG1(surf_lagrange,#expr " = %g",expr);
26 double (*func_f_def) (lmm_variable_t, double);
27 double (*func_fp_def) (lmm_variable_t, double);
28 double (*func_fpi_def) (lmm_variable_t, double);
31 * Local prototypes to implement the lagrangian optimization with optimal step, also called dichotomy.
33 //solves the proportional fairness using a lagrange optimizition with dichotomy step
34 void lagrange_solve(lmm_system_t sys);
35 //computes the value of the dichotomy using a initial values, init, with a specific variable or constraint
36 static double dichotomy(double init, double diff(double, void *),
37 void *var_cnst, double min_error);
38 //computes the value of the differential of variable param_var applied to mu
39 static double partial_diff_mu(double mu, void *param_var);
40 //computes the value of the differential of constraint param_cnst applied to lambda
41 static double partial_diff_lambda(double lambda, void *param_cnst);
43 static int __check_feasible(xbt_swag_t cnst_list, xbt_swag_t var_list,
46 xbt_swag_t elem_list = NULL;
47 lmm_element_t elem = NULL;
48 lmm_constraint_t cnst = NULL;
49 lmm_variable_t var = NULL;
53 xbt_swag_foreach(cnst, cnst_list) {
55 elem_list = &(cnst->element_set);
56 xbt_swag_foreach(elem, elem_list) {
63 if (double_positive(tmp - cnst->bound)) {
66 ("The link (%p) is over-used. Expected less than %f and got %f",
67 cnst, cnst->bound, tmp);
71 ("Checking feasability for constraint (%p): sat = %f, lambda = %f ",
72 cnst, tmp - cnst->bound, cnst->lambda);
75 xbt_swag_foreach(var, var_list) {
80 DEBUG3("Checking feasability for variable (%p): sat = %f mu = %f", var,
81 var->value - var->bound, var->mu);
83 if (double_positive(var->value - var->bound)) {
86 ("The variable (%p) is too large. Expected less than %f and got %f",
87 var, var->bound, var->value);
94 static double new_value(lmm_variable_t var)
99 for (i = 0; i < var->cnsts_number; i++) {
100 tmp += (var->cnsts[i].constraint)->lambda;
104 DEBUG3("\t Working on var (%p). cost = %e; Weight = %e", var, tmp,
106 //uses the partial differential inverse function
107 return var->func_fpi(var, tmp);
110 static double new_mu(lmm_variable_t var)
113 double sigma_i = 0.0;
116 for (j = 0; j < var->cnsts_number; j++) {
117 sigma_i += (var->cnsts[j].constraint)->lambda;
119 mu_i = var->func_fp(var, var->bound) - sigma_i;
125 static double dual_objective(xbt_swag_t var_list, xbt_swag_t cnst_list)
127 lmm_constraint_t cnst = NULL;
128 lmm_variable_t var = NULL;
132 xbt_swag_foreach(var, var_list) {
133 double sigma_i = 0.0;
139 for (j = 0; j < var->cnsts_number; j++)
140 sigma_i += (var->cnsts[j].constraint)->lambda;
145 DEBUG2("var %p : sigma_i = %1.20f", var, sigma_i);
147 obj += var->func_f(var, var->func_fpi(var, sigma_i)) -
148 sigma_i * var->func_fpi(var, sigma_i);
151 obj += var->mu * var->bound;
154 xbt_swag_foreach(cnst, cnst_list)
155 obj += cnst->lambda * cnst->bound;
160 void lagrange_solve(lmm_system_t sys)
163 * Lagrange Variables.
165 int max_iterations = 100;
166 double epsilon_min_error = MAXMIN_PRECISION;
167 double dichotomy_min_error = 1e-14;
168 double overall_modification = 1;
171 * Variables to manipulate the data structure proposed to model the maxmin
172 * fairness. See docummentation for more details.
174 xbt_swag_t cnst_list = NULL;
175 lmm_constraint_t cnst = NULL;
177 xbt_swag_t var_list = NULL;
178 lmm_variable_t var = NULL;
181 * Auxiliar variables.
188 DEBUG0("Iterative method configuration snapshot =====>");
189 DEBUG1("#### Maximum number of iterations : %d", max_iterations);
190 DEBUG1("#### Minimum error tolerated : %e", epsilon_min_error);
191 DEBUG1("#### Minimum error tolerated (dichotomy) : %e",
192 dichotomy_min_error);
194 if (XBT_LOG_ISENABLED(surf_lagrange, xbt_log_priority_debug)) {
198 if (!(sys->modified))
205 cnst_list = &(sys->active_constraint_set);
206 xbt_swag_foreach(cnst, cnst_list) {
208 cnst->new_lambda = 2.0;
209 DEBUG2("#### cnst(%p)->lambda : %e", cnst, cnst->lambda);
213 * Initialize the var list variable with only the active variables.
214 * Associate an index in the swag variables. Initialize mu.
216 var_list = &(sys->variable_set);
218 xbt_swag_foreach(var, var_list) {
223 if (var->bound < 0.0) {
224 DEBUG1("#### NOTE var(%d) is a boundless variable", i);
226 var->value = new_value(var);
230 var->value = new_value(var);
232 DEBUG2("#### var(%p) ->weight : %e", var, var->weight);
233 DEBUG2("#### var(%p) ->mu : %e", var, var->mu);
234 DEBUG2("#### var(%p) ->weight: %e", var, var->weight);
235 DEBUG2("#### var(%p) ->bound: %e", var, var->bound);
236 for (i = 0; i < var->cnsts_number; i++) {
237 if (var->cnsts[i].value == 0.0)
240 if (nb == var->cnsts_number)
246 * Compute dual objective.
248 obj = dual_objective(var_list, cnst_list);
251 * While doesn't reach a minimun error or a number maximum of iterations.
253 while (overall_modification > epsilon_min_error
254 && iteration < max_iterations) {
255 /* int dual_updated=0; */
258 DEBUG1("************** ITERATION %d **************", iteration);
259 DEBUG0("-------------- Gradient Descent ----------");
262 * Improve the value of mu_i
264 xbt_swag_foreach(var, var_list) {
267 if (var->bound >= 0) {
268 DEBUG1("Working on var (%p)", var);
269 var->new_mu = new_mu(var);
270 /* dual_updated += (fabs(var->new_mu-var->mu)>dichotomy_min_error); */
271 /* DEBUG2("dual_updated (%d) : %1.20f",dual_updated,fabs(var->new_mu-var->mu)); */
272 DEBUG3("Updating mu : var->mu (%p) : %1.20f -> %1.20f", var,
273 var->mu, var->new_mu);
274 var->mu = var->new_mu;
276 new_obj = dual_objective(var_list, cnst_list);
277 DEBUG3("Improvement for Objective (%g -> %g) : %g", obj, new_obj,
279 xbt_assert1(obj - new_obj >= -epsilon_min_error,
280 "Our gradient sucks! (%1.20f)", obj - new_obj);
286 * Improve the value of lambda_i
288 xbt_swag_foreach(cnst, cnst_list) {
289 DEBUG1("Working on cnst (%p)", cnst);
291 dichotomy(cnst->lambda, partial_diff_lambda, cnst,
292 dichotomy_min_error);
293 /* dual_updated += (fabs(cnst->new_lambda-cnst->lambda)>dichotomy_min_error); */
294 /* DEBUG2("dual_updated (%d) : %1.20f",dual_updated,fabs(cnst->new_lambda-cnst->lambda)); */
295 DEBUG3("Updating lambda : cnst->lambda (%p) : %1.20f -> %1.20f",
296 cnst, cnst->lambda, cnst->new_lambda);
297 cnst->lambda = cnst->new_lambda;
299 new_obj = dual_objective(var_list, cnst_list);
300 DEBUG3("Improvement for Objective (%g -> %g) : %g", obj, new_obj,
302 xbt_assert1(obj - new_obj >= -epsilon_min_error,
303 "Our gradient sucks! (%1.20f)", obj - new_obj);
308 * Now computes the values of each variable (\rho) based on
309 * the values of \lambda and \mu.
311 DEBUG0("-------------- Check convergence ----------");
312 overall_modification = 0;
313 xbt_swag_foreach(var, var_list) {
314 if (var->weight <= 0)
317 tmp = new_value(var);
319 overall_modification =
320 MAX(overall_modification, fabs(var->value - tmp));
323 DEBUG3("New value of var (%p) = %e, overall_modification = %e",
324 var, var->value, overall_modification);
328 DEBUG0("-------------- Check feasability ----------");
329 if (!__check_feasible(cnst_list, var_list, 0))
330 overall_modification = 1.0;
331 DEBUG2("Iteration %d: overall_modification : %f", iteration,
332 overall_modification);
333 /* if(!dual_updated) { */
334 /* WARN1("Could not improve the convergence at iteration %d. Drop it!",iteration); */
339 __check_feasible(cnst_list, var_list, 1);
341 if (overall_modification <= epsilon_min_error) {
342 DEBUG1("The method converges in %d iterations.", iteration);
344 if (iteration >= max_iterations) {
346 ("Method reach %d iterations, which is the maximum number of iterations allowed.",
349 /* INFO1("Method converged after %d iterations", iteration); */
351 if (XBT_LOG_ISENABLED(surf_lagrange, xbt_log_priority_debug)) {
357 * Returns a double value corresponding to the result of a dichotomy proccess with
358 * respect to a given variable/constraint (\mu in the case of a variable or \lambda in
359 * case of a constraint) and a initial value init.
361 * @param init initial value for \mu or \lambda
362 * @param diff a function that computes the differential of with respect a \mu or \lambda
363 * @param var_cnst a pointer to a variable or constraint
364 * @param min_erro a minimun error tolerated
366 * @return a double correponding to the result of the dichotomyal process
368 static double dichotomy(double init, double diff(double, void *),
369 void *var_cnst, double min_error)
372 double overall_error;
374 double min_diff, max_diff, middle_diff;
384 min_diff = max_diff = middle_diff = 0.0;
387 if ((diff_0 = diff(1e-16, var_cnst)) >= 0) {
388 CDEBUG1(surf_lagrange_dichotomy, "returning 0.0 (diff = %e)", diff_0);
393 min_diff = diff(min, var_cnst);
394 max_diff = diff(max, var_cnst);
396 while (overall_error > min_error) {
397 CDEBUG4(surf_lagrange_dichotomy,
398 "[min, max] = [%1.20f, %1.20f] || diffmin, diffmax = %1.20f, %1.20f",
399 min, max, min_diff, max_diff);
401 if (min_diff > 0 && max_diff > 0) {
403 CDEBUG0(surf_lagrange_dichotomy, "Decreasing min");
405 min_diff = diff(min, var_cnst);
407 CDEBUG0(surf_lagrange_dichotomy, "Decreasing max");
411 } else if (min_diff < 0 && max_diff < 0) {
413 CDEBUG0(surf_lagrange_dichotomy, "Increasing max");
415 max_diff = diff(max, var_cnst);
417 CDEBUG0(surf_lagrange_dichotomy, "Increasing min");
421 } else if (min_diff < 0 && max_diff > 0) {
422 middle = (max + min) / 2.0;
423 CDEBUG1(surf_lagrange_dichotomy, "Trying (max+min)/2 : %1.20f", middle);
425 if ((min == middle) || (max == middle)) {
426 CWARN4(surf_lagrange_dichotomy,
427 "Cannot improve the convergence! min=max=middle=%1.20f, diff = %1.20f."
428 " Reaching the 'double' limits. Maybe scaling your function would help ([%1.20f,%1.20f]).",
429 min, max - min, min_diff, max_diff);
432 middle_diff = diff(middle, var_cnst);
434 if (middle_diff < 0) {
435 CDEBUG0(surf_lagrange_dichotomy, "Increasing min");
437 overall_error = max_diff - middle_diff;
438 min_diff = middle_diff;
439 /* SHOW_EXPR(overall_error); */
440 } else if (middle_diff > 0) {
441 CDEBUG0(surf_lagrange_dichotomy, "Decreasing max");
443 overall_error = max_diff - middle_diff;
444 max_diff = middle_diff;
445 /* SHOW_EXPR(overall_error); */
448 /* SHOW_EXPR(overall_error); */
450 } else if (min_diff == 0) {
453 /* SHOW_EXPR(overall_error); */
454 } else if (max_diff == 0) {
457 /* SHOW_EXPR(overall_error); */
458 } else if (min_diff > 0 && max_diff < 0) {
459 CWARN0(surf_lagrange_dichotomy,
460 "The impossible happened, partial_diff(min) > 0 && partial_diff(max) < 0");
463 CWARN2(surf_lagrange_dichotomy,
464 "diffmin (%1.20f) or diffmax (%1.20f) are something I don't know, taking no action.",
470 CDEBUG1(surf_lagrange_dichotomy, "returning %e", (min + max) / 2.0);
472 return ((min + max) / 2.0);
475 static double partial_diff_lambda(double lambda, void *param_cnst)
479 xbt_swag_t elem_list = NULL;
480 lmm_element_t elem = NULL;
481 lmm_variable_t var = NULL;
482 lmm_constraint_t cnst = (lmm_constraint_t) param_cnst;
484 double sigma_i = 0.0;
487 elem_list = &(cnst->element_set);
489 CDEBUG1(surf_lagrange_dichotomy, "Computing diff of cnst (%p)", cnst);
491 xbt_swag_foreach(elem, elem_list) {
492 var = elem->variable;
493 if (var->weight <= 0)
496 CDEBUG1(surf_lagrange_dichotomy, "Computing sigma_i for var (%p)", var);
497 // Initialize the summation variable
501 for (j = 0; j < var->cnsts_number; j++) {
502 sigma_i += (var->cnsts[j].constraint)->lambda;
505 //add mu_i if this flow has a RTT constraint associated
509 //replace value of cnst->lambda by the value of parameter lambda
510 sigma_i = (sigma_i - cnst->lambda) + lambda;
512 diff += -var->func_fpi(var, sigma_i);
518 CDEBUG3(surf_lagrange_dichotomy,
519 "d D/d lambda for cnst (%p) at %1.20f = %1.20f", cnst, lambda,
525 /** \brief Attribute the value bound to var->bound.
527 * \param func_fpi inverse of the partial differential of f (f prime inverse, (f')^{-1})
529 * Set default functions to the ones passed as parameters. This is a polimorfism in C pure, enjoy the roots of programming.
532 void lmm_set_default_protocol_function(double (*func_f)
534 (lmm_variable_t var, double x),
535 double (*func_fp) (lmm_variable_t var,
537 double (*func_fpi) (lmm_variable_t var,
541 func_fp_def = func_fp;
542 func_fpi_def = func_fpi;
546 /**************** Vegas and Reno functions *************************/
548 * NOTE for Reno: all functions consider the network
549 * coeficient (alpha) equal to 1.
553 * For Vegas: $f(x) = \alpha D_f\ln(x)$
554 * Therefore: $fp(x) = \frac{\alpha D_f}{x}$
555 * Therefore: $fpi(x) = \frac{\alpha D_f}{x}$
557 #define VEGAS_SCALING 1000.0
559 double func_vegas_f(lmm_variable_t var, double x)
561 xbt_assert1(x > 0.0, "Don't call me with stupid values! (%1.20f)", x);
562 return VEGAS_SCALING * var->weight * log(x);
565 double func_vegas_fp(lmm_variable_t var, double x)
567 xbt_assert1(x > 0.0, "Don't call me with stupid values! (%1.20f)", x);
568 return VEGAS_SCALING * var->weight / x;
571 double func_vegas_fpi(lmm_variable_t var, double x)
573 xbt_assert1(x > 0.0, "Don't call me with stupid values! (%1.20f)", x);
574 return var->weight / (x / VEGAS_SCALING);
578 * For Reno: $f(x) = \frac{\sqrt{3/2}}{D_f} atan(\sqrt{3/2}D_f x)$
579 * Therefore: $fp(x) = \frac{3}{3 D_f^2 x^2+2}$
580 * Therefore: $fpi(x) = \sqrt{\frac{1}{{D_f}^2 x} - \frac{2}{3{D_f}^2}}$
582 #define RENO_SCALING 1.0
583 double func_reno_f(lmm_variable_t var, double x)
585 xbt_assert0(var->weight > 0.0, "Don't call me with stupid values!");
587 return RENO_SCALING * sqrt(3.0 / 2.0) / var->weight * atan(sqrt(3.0 / 2.0) *
591 double func_reno_fp(lmm_variable_t var, double x)
593 return RENO_SCALING * 3.0 / (3.0 * var->weight * var->weight * x * x + 2.0);
596 double func_reno_fpi(lmm_variable_t var, double x)
600 xbt_assert0(var->weight > 0.0, "Don't call me with stupid values!");
601 xbt_assert0(x > 0.0, "Don't call me with stupid values!");
604 1.0 / (var->weight * var->weight * (x / RENO_SCALING)) -
605 2.0 / (3.0 * var->weight * var->weight);
608 /* xbt_assert0(res_fpi>0.0,"Don't call me with stupid values!"); */
609 return sqrt(res_fpi);
613 /* Implementing new Reno-2
614 * For Reno-2: $f(x) = U_f(x_f) = \frac{{2}{D_f}}*ln(2+x*D_f)$
615 * Therefore: $fp(x) = 2/(Weight*x + 2)
616 * Therefore: $fpi(x) = (2*Weight)/x - 4
618 #define RENO2_SCALING 1.0
619 double func_reno2_f(lmm_variable_t var, double x)
621 xbt_assert0(var->weight > 0.0, "Don't call me with stupid values!");
622 return RENO2_SCALING * (1.0 / var->weight) * log((x * var->weight) /
623 (2.0 * x * var->weight +
627 double func_reno2_fp(lmm_variable_t var, double x)
629 return RENO2_SCALING * 3.0 / (var->weight * x *
630 (2.0 * var->weight * x + 3.0));
633 double func_reno2_fpi(lmm_variable_t var, double x)
638 xbt_assert0(x > 0.0, "Don't call me with stupid values!");
639 tmp = x * var->weight * var->weight;
640 res_fpi = tmp * (9.0 * x + 24.0);
645 res_fpi = RENO2_SCALING * (-3.0 * tmp + sqrt(res_fpi)) / (4.0 * tmp);