1 /* Copyright (c) 2007-2014. The SimGrid Team.
2 * All rights reserved. */
4 /* This program is free software; you can redistribute it and/or modify it
5 * under the terms of the license (GNU LGPL) which comes with this package. */
8 * Modelling the proportional fairness using the Lagrange Optimization
9 * Approach. For a detailed description see:
10 * "ssh://username@scm.gforge.inria.fr/svn/memo/people/pvelho/lagrange/ppf.ps".
13 #include "xbt/sysdep.h"
14 #include "maxmin_private.hpp"
21 XBT_LOG_NEW_DEFAULT_SUBCATEGORY(surf_lagrange, surf,
22 "Logging specific to SURF (lagrange)");
23 XBT_LOG_NEW_SUBCATEGORY(surf_lagrange_dichotomy, surf_lagrange,
24 "Logging specific to SURF (lagrange dichotomy)");
26 #define SHOW_EXPR(expr) XBT_CDEBUG(surf_lagrange,#expr " = %g",expr);
28 double (*func_f_def) (lmm_variable_t, double);
29 double (*func_fp_def) (lmm_variable_t, double);
30 double (*func_fpi_def) (lmm_variable_t, double);
33 * Local prototypes to implement the lagrangian optimization with optimal step, also called dichotomy.
35 //solves the proportional fairness using a lagrange optimizition with dichotomy step
36 void lagrange_solve(lmm_system_t sys);
37 //computes the value of the dichotomy using a initial values, init, with a specific variable or constraint
38 static double dichotomy(double init, double diff(double, void *),
39 void *var_cnst, double min_error);
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 void *_cnst, *_elem, *_var;
47 xbt_swag_t elem_list = NULL;
48 lmm_element_t elem = NULL;
49 lmm_constraint_t cnst = NULL;
50 lmm_variable_t var = NULL;
54 xbt_swag_foreach(_cnst, cnst_list) {
55 cnst = (lmm_constraint_t)_cnst;
57 elem_list = &(cnst->enabled_element_set);
58 xbt_swag_foreach(_elem, elem_list) {
59 elem = (lmm_element_t)_elem;
61 xbt_assert(var->weight > 0);
65 if (double_positive(tmp - cnst->bound, sg_maxmin_precision)) {
68 ("The link (%p) is over-used. Expected less than %f and got %f",
69 cnst, cnst->bound, tmp);
73 ("Checking feasability for constraint (%p): sat = %f, lambda = %f ",
74 cnst, tmp - cnst->bound, cnst->lambda);
77 xbt_swag_foreach(_var, var_list) {
78 var = (lmm_variable_t)_var;
83 XBT_DEBUG("Checking feasability for variable (%p): sat = %f mu = %f", var,
84 var->value - var->bound, var->mu);
86 if (double_positive(var->value - var->bound, sg_maxmin_precision)) {
89 ("The variable (%p) is too large. Expected less than %f and got %f",
90 var, var->bound, var->value);
97 static double new_value(lmm_variable_t var)
102 for (i = 0; i < var->cnsts_number; i++) {
103 tmp += (var->cnsts[i].constraint)->lambda;
107 XBT_DEBUG("\t Working on var (%p). cost = %e; Weight = %e", var, tmp,
109 //uses the partial differential inverse function
110 return var->func_fpi(var, tmp);
113 static double new_mu(lmm_variable_t var)
116 double sigma_i = 0.0;
119 for (j = 0; j < var->cnsts_number; j++) {
120 sigma_i += (var->cnsts[j].constraint)->lambda;
122 mu_i = var->func_fp(var, var->bound) - sigma_i;
128 static double dual_objective(xbt_swag_t var_list, xbt_swag_t cnst_list)
131 lmm_constraint_t cnst = NULL;
132 lmm_variable_t var = NULL;
136 xbt_swag_foreach(_var, var_list) {
137 var = (lmm_variable_t)_var;
138 double sigma_i = 0.0;
144 for (j = 0; j < var->cnsts_number; j++)
145 sigma_i += (var->cnsts[j].constraint)->lambda;
150 XBT_DEBUG("var %p : sigma_i = %1.20f", var, sigma_i);
152 obj += var->func_f(var, var->func_fpi(var, sigma_i)) -
153 sigma_i * var->func_fpi(var, sigma_i);
156 obj += var->mu * var->bound;
159 xbt_swag_foreach(_cnst, cnst_list) {
160 cnst = (lmm_constraint_t)_cnst;
161 obj += cnst->lambda * cnst->bound;
167 void lagrange_solve(lmm_system_t sys)
170 * Lagrange Variables.
172 int max_iterations = 100;
173 double epsilon_min_error = 0.00001; /* this is the precision on the objective function so it's none of the configurable values and this value is the legacy one */
174 double dichotomy_min_error = 1e-14;
175 double overall_modification = 1;
178 * Variables to manipulate the data structure proposed to model the maxmin
179 * fairness. See docummentation for more details.
181 xbt_swag_t cnst_list = NULL;
183 lmm_constraint_t cnst = NULL;
185 xbt_swag_t var_list = NULL;
187 lmm_variable_t var = NULL;
190 * Auxiliary variables.
197 XBT_DEBUG("Iterative method configuration snapshot =====>");
198 XBT_DEBUG("#### Maximum number of iterations : %d", max_iterations);
199 XBT_DEBUG("#### Minimum error tolerated : %e",
201 XBT_DEBUG("#### Minimum error tolerated (dichotomy) : %e",
202 dichotomy_min_error);
204 if (XBT_LOG_ISENABLED(surf_lagrange, xbt_log_priority_debug)) {
208 if (!(sys->modified))
215 cnst_list = &(sys->active_constraint_set);
216 xbt_swag_foreach(_cnst, cnst_list) {
217 cnst = (lmm_constraint_t)_cnst;
219 cnst->new_lambda = 2.0;
220 XBT_DEBUG("#### cnst(%p)->lambda : %e", cnst, cnst->lambda);
224 * Initialize the var list variable with only the active variables.
225 * Associate an index in the swag variables. Initialize mu.
227 var_list = &(sys->variable_set);
229 xbt_swag_foreach(_var, var_list) {
230 var = (lmm_variable_t)_var;
235 if (var->bound < 0.0) {
236 XBT_DEBUG("#### NOTE var(%d) is a boundless variable", i);
238 var->value = new_value(var);
242 var->value = new_value(var);
244 XBT_DEBUG("#### var(%p) ->weight : %e", var, var->weight);
245 XBT_DEBUG("#### var(%p) ->mu : %e", var, var->mu);
246 XBT_DEBUG("#### var(%p) ->weight: %e", var, var->weight);
247 XBT_DEBUG("#### var(%p) ->bound: %e", var, var->bound);
248 for (i = 0; i < var->cnsts_number; i++) {
249 if (var->cnsts[i].value == 0.0)
252 if (nb == var->cnsts_number)
258 * Compute dual objective.
260 obj = dual_objective(var_list, cnst_list);
263 * While doesn't reach a minimun error or a number maximum of iterations.
265 while (overall_modification > epsilon_min_error
266 && iteration < max_iterations) {
267 /* int dual_updated=0; */
270 XBT_DEBUG("************** ITERATION %d **************", iteration);
271 XBT_DEBUG("-------------- Gradient Descent ----------");
274 * Improve the value of mu_i
276 xbt_swag_foreach(_var, var_list) {
277 var = (lmm_variable_t)_var;
280 if (var->bound >= 0) {
281 XBT_DEBUG("Working on var (%p)", var);
282 var->new_mu = new_mu(var);
283 /* dual_updated += (fabs(var->new_mu-var->mu)>dichotomy_min_error); */
284 /* XBT_DEBUG("dual_updated (%d) : %1.20f",dual_updated,fabs(var->new_mu-var->mu)); */
285 XBT_DEBUG("Updating mu : var->mu (%p) : %1.20f -> %1.20f", var,
286 var->mu, var->new_mu);
287 var->mu = var->new_mu;
289 new_obj = dual_objective(var_list, cnst_list);
290 XBT_DEBUG("Improvement for Objective (%g -> %g) : %g", obj, new_obj,
292 xbt_assert(obj - new_obj >= -epsilon_min_error,
293 "Our gradient sucks! (%1.20f)", obj - new_obj);
299 * Improve the value of lambda_i
301 xbt_swag_foreach(_cnst, cnst_list) {
302 cnst = (lmm_constraint_t)_cnst;
303 XBT_DEBUG("Working on cnst (%p)", cnst);
305 dichotomy(cnst->lambda, partial_diff_lambda, cnst,
306 dichotomy_min_error);
307 /* dual_updated += (fabs(cnst->new_lambda-cnst->lambda)>dichotomy_min_error); */
308 /* XBT_DEBUG("dual_updated (%d) : %1.20f",dual_updated,fabs(cnst->new_lambda-cnst->lambda)); */
309 XBT_DEBUG("Updating lambda : cnst->lambda (%p) : %1.20f -> %1.20f",
310 cnst, cnst->lambda, cnst->new_lambda);
311 cnst->lambda = cnst->new_lambda;
313 new_obj = dual_objective(var_list, cnst_list);
314 XBT_DEBUG("Improvement for Objective (%g -> %g) : %g", obj, new_obj,
316 xbt_assert(obj - new_obj >= -epsilon_min_error,
317 "Our gradient sucks! (%1.20f)", obj - new_obj);
322 * Now computes the values of each variable (\rho) based on
323 * the values of \lambda and \mu.
325 XBT_DEBUG("-------------- Check convergence ----------");
326 overall_modification = 0;
327 xbt_swag_foreach(_var, var_list) {
328 var = (lmm_variable_t)_var;
329 if (var->weight <= 0)
332 tmp = new_value(var);
334 overall_modification =
335 MAX(overall_modification, fabs(var->value - tmp));
338 XBT_DEBUG("New value of var (%p) = %e, overall_modification = %e",
339 var, var->value, overall_modification);
343 XBT_DEBUG("-------------- Check feasability ----------");
344 if (!__check_feasible(cnst_list, var_list, 0))
345 overall_modification = 1.0;
346 XBT_DEBUG("Iteration %d: overall_modification : %f", iteration,
347 overall_modification);
348 /* if(!dual_updated) { */
349 /* XBT_WARN("Could not improve the convergence at iteration %d. Drop it!",iteration); */
354 __check_feasible(cnst_list, var_list, 1);
356 if (overall_modification <= epsilon_min_error) {
357 XBT_DEBUG("The method converges in %d iterations.", iteration);
359 if (iteration >= max_iterations) {
361 ("Method reach %d iterations, which is the maximum number of iterations allowed.",
364 /* XBT_INFO("Method converged after %d iterations", iteration); */
366 if (XBT_LOG_ISENABLED(surf_lagrange, xbt_log_priority_debug)) {
372 * Returns a double value corresponding to the result of a dichotomy proccess with
373 * respect to a given variable/constraint (\mu in the case of a variable or \lambda in
374 * case of a constraint) and a initial value init.
376 * @param init initial value for \mu or \lambda
377 * @param diff a function that computes the differential of with respect a \mu or \lambda
378 * @param var_cnst a pointer to a variable or constraint
379 * @param min_erro a minimun error tolerated
381 * @return a double correponding to the result of the dichotomyal process
383 static double dichotomy(double init, double diff(double, void *),
384 void *var_cnst, double min_error)
387 double overall_error;
389 double min_diff, max_diff, middle_diff;
401 if ((diff_0 = diff(1e-16, var_cnst)) >= 0) {
402 XBT_CDEBUG(surf_lagrange_dichotomy, "returning 0.0 (diff = %e)", diff_0);
407 min_diff = diff(min, var_cnst);
408 max_diff = diff(max, var_cnst);
410 while (overall_error > min_error) {
411 XBT_CDEBUG(surf_lagrange_dichotomy,
412 "[min, max] = [%1.20f, %1.20f] || diffmin, diffmax = %1.20f, %1.20f",
413 min, max, min_diff, max_diff);
415 if (min_diff > 0 && max_diff > 0) {
417 XBT_CDEBUG(surf_lagrange_dichotomy, "Decreasing min");
419 min_diff = diff(min, var_cnst);
421 XBT_CDEBUG(surf_lagrange_dichotomy, "Decreasing max");
425 } else if (min_diff < 0 && max_diff < 0) {
427 XBT_CDEBUG(surf_lagrange_dichotomy, "Increasing max");
429 max_diff = diff(max, var_cnst);
431 XBT_CDEBUG(surf_lagrange_dichotomy, "Increasing min");
435 } else if (min_diff < 0 && max_diff > 0) {
436 middle = (max + min) / 2.0;
437 XBT_CDEBUG(surf_lagrange_dichotomy, "Trying (max+min)/2 : %1.20f",
440 if ((min == middle) || (max == middle)) {
441 XBT_CWARN(surf_lagrange_dichotomy,
442 "Cannot improve the convergence! min=max=middle=%1.20f, diff = %1.20f."
443 " Reaching the 'double' limits. Maybe scaling your function would help ([%1.20f,%1.20f]).",
444 min, max - min, min_diff, max_diff);
447 middle_diff = diff(middle, var_cnst);
449 if (middle_diff < 0) {
450 XBT_CDEBUG(surf_lagrange_dichotomy, "Increasing min");
452 overall_error = max_diff - middle_diff;
453 min_diff = middle_diff;
454 /* SHOW_EXPR(overall_error); */
455 } else if (middle_diff > 0) {
456 XBT_CDEBUG(surf_lagrange_dichotomy, "Decreasing max");
458 overall_error = max_diff - middle_diff;
459 max_diff = middle_diff;
460 /* SHOW_EXPR(overall_error); */
463 /* SHOW_EXPR(overall_error); */
465 } else if (min_diff == 0) {
468 /* SHOW_EXPR(overall_error); */
469 } else if (max_diff == 0) {
472 /* SHOW_EXPR(overall_error); */
473 } else if (min_diff > 0 && max_diff < 0) {
474 XBT_CWARN(surf_lagrange_dichotomy,
475 "The impossible happened, partial_diff(min) > 0 && partial_diff(max) < 0");
478 XBT_CWARN(surf_lagrange_dichotomy,
479 "diffmin (%1.20f) or diffmax (%1.20f) are something I don't know, taking no action.",
485 XBT_CDEBUG(surf_lagrange_dichotomy, "returning %e", (min + max) / 2.0);
487 return ((min + max) / 2.0);
490 static double partial_diff_lambda(double lambda, void *param_cnst)
495 xbt_swag_t elem_list = NULL;
496 lmm_element_t elem = NULL;
497 lmm_variable_t var = NULL;
498 lmm_constraint_t cnst = (lmm_constraint_t) param_cnst;
500 double sigma_i = 0.0;
503 elem_list = &(cnst->enabled_element_set);
505 XBT_CDEBUG(surf_lagrange_dichotomy, "Computing diff of cnst (%p)", cnst);
507 xbt_swag_foreach(_elem, elem_list) {
508 elem = (lmm_element_t)_elem;
509 var = elem->variable;
510 xbt_assert(var->weight > 0);
511 XBT_CDEBUG(surf_lagrange_dichotomy, "Computing sigma_i for var (%p)",
513 // Initialize the summation variable
517 for (j = 0; j < var->cnsts_number; j++) {
518 sigma_i += (var->cnsts[j].constraint)->lambda;
521 //add mu_i if this flow has a RTT constraint associated
525 //replace value of cnst->lambda by the value of parameter lambda
526 sigma_i = (sigma_i - cnst->lambda) + lambda;
528 diff += -var->func_fpi(var, sigma_i);
534 XBT_CDEBUG(surf_lagrange_dichotomy,
535 "d D/d lambda for cnst (%p) at %1.20f = %1.20f", cnst, lambda,
541 /** \brief Attribute the value bound to var->bound.
543 * \param func_fpi inverse of the partial differential of f (f prime inverse, (f')^{-1})
545 * Set default functions to the ones passed as parameters. This is a polimorfism in C pure, enjoy the roots of programming.
548 void lmm_set_default_protocol_function(double (*func_f)
555 (lmm_variable_t var, double x),
556 double (*func_fp) (lmm_variable_t
558 double (*func_fpi) (lmm_variable_t
562 func_fp_def = func_fp;
563 func_fpi_def = func_fpi;
567 /**************** Vegas and Reno functions *************************/
569 * NOTE for Reno: all functions consider the network
570 * coeficient (alpha) equal to 1.
574 * For Vegas: $f(x) = \alpha D_f\ln(x)$
575 * Therefore: $fp(x) = \frac{\alpha D_f}{x}$
576 * Therefore: $fpi(x) = \frac{\alpha D_f}{x}$
578 #define VEGAS_SCALING 1000.0
580 double func_vegas_f(lmm_variable_t var, double x)
582 xbt_assert(x > 0.0, "Don't call me with stupid values! (%1.20f)", x);
583 return VEGAS_SCALING * var->weight * log(x);
586 double func_vegas_fp(lmm_variable_t var, double x)
588 xbt_assert(x > 0.0, "Don't call me with stupid values! (%1.20f)", x);
589 return VEGAS_SCALING * var->weight / x;
592 double func_vegas_fpi(lmm_variable_t var, double x)
594 xbt_assert(x > 0.0, "Don't call me with stupid values! (%1.20f)", x);
595 return var->weight / (x / VEGAS_SCALING);
599 * For Reno: $f(x) = \frac{\sqrt{3/2}}{D_f} atan(\sqrt{3/2}D_f x)$
600 * Therefore: $fp(x) = \frac{3}{3 D_f^2 x^2+2}$
601 * Therefore: $fpi(x) = \sqrt{\frac{1}{{D_f}^2 x} - \frac{2}{3{D_f}^2}}$
603 #define RENO_SCALING 1.0
604 double func_reno_f(lmm_variable_t var, double x)
606 xbt_assert(var->weight > 0.0, "Don't call me with stupid values!");
608 return RENO_SCALING * sqrt(3.0 / 2.0) / var->weight *
609 atan(sqrt(3.0 / 2.0) * var->weight * x);
612 double func_reno_fp(lmm_variable_t var, double x)
614 return RENO_SCALING * 3.0 / (3.0 * var->weight * var->weight * x * x +
618 double func_reno_fpi(lmm_variable_t var, double x)
622 xbt_assert(var->weight > 0.0, "Don't call me with stupid values!");
623 xbt_assert(x > 0.0, "Don't call me with stupid values!");
626 1.0 / (var->weight * var->weight * (x / RENO_SCALING)) -
627 2.0 / (3.0 * var->weight * var->weight);
630 /* xbt_assert(res_fpi>0.0,"Don't call me with stupid values!"); */
631 return sqrt(res_fpi);
635 /* Implementing new Reno-2
636 * For Reno-2: $f(x) = U_f(x_f) = \frac{{2}{D_f}}*ln(2+x*D_f)$
637 * Therefore: $fp(x) = 2/(Weight*x + 2)
638 * Therefore: $fpi(x) = (2*Weight)/x - 4
640 #define RENO2_SCALING 1.0
641 double func_reno2_f(lmm_variable_t var, double x)
643 xbt_assert(var->weight > 0.0, "Don't call me with stupid values!");
644 return RENO2_SCALING * (1.0 / var->weight) * log((x * var->weight) /
645 (2.0 * x * var->weight +
649 double func_reno2_fp(lmm_variable_t var, double x)
651 return RENO2_SCALING * 3.0 / (var->weight * x *
652 (2.0 * var->weight * x + 3.0));
655 double func_reno2_fpi(lmm_variable_t var, double x)
660 xbt_assert(x > 0.0, "Don't call me with stupid values!");
661 tmp = x * var->weight * var->weight;
662 res_fpi = tmp * (9.0 * x + 24.0);
667 res_fpi = RENO2_SCALING * (-3.0 * tmp + sqrt(res_fpi)) / (4.0 * tmp);