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 * Modeling the proportional fairness using the Lagrangian Optimization Approach. For a detailed description see:
9 * "ssh://username@scm.gforge.inria.fr/svn/memo/people/pvelho/lagrange/ppf.ps".
12 #include "xbt/sysdep.h"
13 #include "maxmin_private.hpp"
20 XBT_LOG_NEW_DEFAULT_SUBCATEGORY(surf_lagrange, surf, "Logging specific to SURF (lagrange)");
21 XBT_LOG_NEW_SUBCATEGORY(surf_lagrange_dichotomy, surf_lagrange, "Logging specific to SURF (lagrange dichotomy)");
23 #define SHOW_EXPR(expr) XBT_CDEBUG(surf_lagrange,#expr " = %g",expr);
25 double (*func_f_def) (lmm_variable_t, double);
26 double (*func_fp_def) (lmm_variable_t, double);
27 double (*func_fpi_def) (lmm_variable_t, double);
30 * Local prototypes to implement the Lagrangian optimization with optimal step, also called dichotomy.
32 //solves the proportional fairness using a Lagrangian optimization with dichotomy step
33 void lagrange_solve(lmm_system_t sys);
34 //computes the value of the dichotomy using a initial values, init, with a specific variable or constraint
35 static double dichotomy(double init, double diff(double, void *), void *var_cnst, double min_error);
36 //computes the value of the differential of constraint param_cnst applied to lambda
37 static double partial_diff_lambda(double lambda, void *param_cnst);
39 static int __check_feasible(xbt_swag_t cnst_list, xbt_swag_t var_list, int warn)
41 void *_cnst, *_elem, *_var;
42 xbt_swag_t elem_list = nullptr;
43 lmm_element_t elem = nullptr;
44 lmm_constraint_t cnst = nullptr;
45 lmm_variable_t var = nullptr;
49 xbt_swag_foreach(_cnst, cnst_list) {
50 cnst = static_cast<lmm_constraint_t>(_cnst);
52 elem_list = &(cnst->enabled_element_set);
53 xbt_swag_foreach(_elem, elem_list) {
54 elem = static_cast<lmm_element_t>(_elem);
56 xbt_assert(var->weight > 0);
60 if (double_positive(tmp - cnst->bound, sg_maxmin_precision)) {
62 XBT_WARN ("The link (%p) is over-used. Expected less than %f and got %f", cnst, cnst->bound, tmp);
65 XBT_DEBUG ("Checking feasability for constraint (%p): sat = %f, lambda = %f ", cnst, tmp - cnst->bound,
69 xbt_swag_foreach(_var, var_list) {
70 var = static_cast<lmm_variable_t>(_var);
75 XBT_DEBUG("Checking feasability for variable (%p): sat = %f mu = %f", var, var->value - var->bound, var->mu);
77 if (double_positive(var->value - var->bound, sg_maxmin_precision)) {
79 XBT_WARN ("The variable (%p) is too large. Expected less than %f and got %f", var, var->bound, var->value);
86 static double new_value(lmm_variable_t var)
90 for (int i = 0; i < var->cnsts_number; i++) {
91 tmp += (var->cnsts[i].constraint)->lambda;
95 XBT_DEBUG("\t Working on var (%p). cost = %e; Weight = %e", var, tmp, var->weight);
96 //uses the partial differential inverse function
97 return var->func_fpi(var, tmp);
100 static double new_mu(lmm_variable_t var)
103 double sigma_i = 0.0;
105 for (int j = 0; j < var->cnsts_number; j++) {
106 sigma_i += (var->cnsts[j].constraint)->lambda;
108 mu_i = var->func_fp(var, var->bound) - sigma_i;
114 static double dual_objective(xbt_swag_t var_list, xbt_swag_t cnst_list)
118 lmm_constraint_t cnst = nullptr;
119 lmm_variable_t var = nullptr;
123 xbt_swag_foreach(_var, var_list) {
124 var = static_cast<lmm_variable_t>(_var);
125 double sigma_i = 0.0;
130 for (int j = 0; j < var->cnsts_number; j++)
131 sigma_i += (var->cnsts[j].constraint)->lambda;
136 XBT_DEBUG("var %p : sigma_i = %1.20f", var, sigma_i);
138 obj += var->func_f(var, var->func_fpi(var, sigma_i)) - sigma_i * var->func_fpi(var, sigma_i);
141 obj += var->mu * var->bound;
144 xbt_swag_foreach(_cnst, cnst_list) {
145 cnst = static_cast<lmm_constraint_t>(_cnst);
146 obj += cnst->lambda * cnst->bound;
152 void lagrange_solve(lmm_system_t sys)
154 /* Lagrange Variables. */
155 int max_iterations = 100;
156 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 */
157 double dichotomy_min_error = 1e-14;
158 double overall_modification = 1;
160 /* Variables to manipulate the data structure proposed to model the maxmin fairness. See documentation for details. */
161 xbt_swag_t cnst_list = nullptr;
163 lmm_constraint_t cnst = nullptr;
165 xbt_swag_t var_list = nullptr;
167 lmm_variable_t var = nullptr;
169 /* Auxiliary variables. */
176 XBT_DEBUG("Iterative method configuration snapshot =====>");
177 XBT_DEBUG("#### Maximum number of iterations : %d", max_iterations);
178 XBT_DEBUG("#### Minimum error tolerated : %e", epsilon_min_error);
179 XBT_DEBUG("#### Minimum error tolerated (dichotomy) : %e", dichotomy_min_error);
181 if (XBT_LOG_ISENABLED(surf_lagrange, xbt_log_priority_debug)) {
185 if (!(sys->modified))
188 /* Initialize lambda. */
189 cnst_list = &(sys->active_constraint_set);
190 xbt_swag_foreach(_cnst, cnst_list) {
191 cnst = (lmm_constraint_t)_cnst;
193 cnst->new_lambda = 2.0;
194 XBT_DEBUG("#### cnst(%p)->lambda : %e", cnst, cnst->lambda);
198 * Initialize the var list variable with only the active variables.
199 * Associate an index in the swag variables. Initialize mu.
201 var_list = &(sys->variable_set);
203 xbt_swag_foreach(_var, var_list) {
204 var = static_cast<lmm_variable_t>(_var);
209 if (var->bound < 0.0) {
210 XBT_DEBUG("#### NOTE var(%d) is a boundless variable", i);
212 var->value = new_value(var);
216 var->value = new_value(var);
218 XBT_DEBUG("#### var(%p) ->weight : %e", var, var->weight);
219 XBT_DEBUG("#### var(%p) ->mu : %e", var, var->mu);
220 XBT_DEBUG("#### var(%p) ->weight: %e", var, var->weight);
221 XBT_DEBUG("#### var(%p) ->bound: %e", var, var->bound);
222 for (i = 0; i < var->cnsts_number; i++) {
223 if (var->cnsts[i].value == 0.0)
226 if (nb == var->cnsts_number)
231 /* Compute dual objective. */
232 obj = dual_objective(var_list, cnst_list);
234 /* While doesn't reach a minimum error or a number maximum of iterations. */
235 while (overall_modification > epsilon_min_error && iteration < max_iterations) {
237 XBT_DEBUG("************** ITERATION %d **************", iteration);
238 XBT_DEBUG("-------------- Gradient Descent ----------");
240 /* Improve the value of mu_i */
241 xbt_swag_foreach(_var, var_list) {
242 var = static_cast<lmm_variable_t>(_var);
245 if (var->bound >= 0) {
246 XBT_DEBUG("Working on var (%p)", var);
247 var->new_mu = new_mu(var);
248 /* dual_updated += (fabs(var->new_mu-var->mu)>dichotomy_min_error); */
249 /* XBT_DEBUG("dual_updated (%d) : %1.20f",dual_updated,fabs(var->new_mu-var->mu)); */
250 XBT_DEBUG("Updating mu : var->mu (%p) : %1.20f -> %1.20f", var, var->mu, var->new_mu);
251 var->mu = var->new_mu;
253 new_obj = dual_objective(var_list, cnst_list);
254 XBT_DEBUG("Improvement for Objective (%g -> %g) : %g", obj, new_obj, obj - new_obj);
255 xbt_assert(obj - new_obj >= -epsilon_min_error, "Our gradient sucks! (%1.20f)", obj - new_obj);
260 /* Improve the value of lambda_i */
261 xbt_swag_foreach(_cnst, cnst_list) {
262 cnst = static_cast<lmm_constraint_t>(_cnst);
263 XBT_DEBUG("Working on cnst (%p)", cnst);
264 cnst->new_lambda = dichotomy(cnst->lambda, partial_diff_lambda, cnst, dichotomy_min_error);
265 /* dual_updated += (fabs(cnst->new_lambda-cnst->lambda)>dichotomy_min_error); */
266 /* XBT_DEBUG("dual_updated (%d) : %1.20f",dual_updated,fabs(cnst->new_lambda-cnst->lambda)); */
267 XBT_DEBUG("Updating lambda : cnst->lambda (%p) : %1.20f -> %1.20f", cnst, cnst->lambda, cnst->new_lambda);
268 cnst->lambda = cnst->new_lambda;
270 new_obj = dual_objective(var_list, cnst_list);
271 XBT_DEBUG("Improvement for Objective (%g -> %g) : %g", obj, new_obj, obj - new_obj);
272 xbt_assert(obj - new_obj >= -epsilon_min_error, "Our gradient sucks! (%1.20f)", obj - new_obj);
276 /* Now computes the values of each variable (\rho) based on the values of \lambda and \mu. */
277 XBT_DEBUG("-------------- Check convergence ----------");
278 overall_modification = 0;
279 xbt_swag_foreach(_var, var_list) {
280 var = static_cast<lmm_variable_t>(_var);
281 if (var->weight <= 0)
284 tmp = new_value(var);
286 overall_modification = MAX(overall_modification, fabs(var->value - tmp));
289 XBT_DEBUG("New value of var (%p) = %e, overall_modification = %e", var, var->value, overall_modification);
293 XBT_DEBUG("-------------- Check feasability ----------");
294 if (!__check_feasible(cnst_list, var_list, 0))
295 overall_modification = 1.0;
296 XBT_DEBUG("Iteration %d: overall_modification : %f", iteration, overall_modification);
297 /* if(!dual_updated) { */
298 /* XBT_WARN("Could not improve the convergence at iteration %d. Drop it!",iteration); */
303 __check_feasible(cnst_list, var_list, 1);
305 if (overall_modification <= epsilon_min_error) {
306 XBT_DEBUG("The method converges in %d iterations.", iteration);
308 if (iteration >= max_iterations) {
309 XBT_DEBUG ("Method reach %d iterations, which is the maximum number of iterations allowed.", iteration);
312 if (XBT_LOG_ISENABLED(surf_lagrange, xbt_log_priority_debug)) {
318 * Returns a double value corresponding to the result of a dichotomy process with respect to a given
319 * variable/constraint (\mu in the case of a variable or \lambda in case of a constraint) and a initial value init.
321 * @param init initial value for \mu or \lambda
322 * @param diff a function that computes the differential of with respect a \mu or \lambda
323 * @param var_cnst a pointer to a variable or constraint
324 * @param min_erro a minimum error tolerated
326 * @return a double corresponding to the result of the dichotomy process
328 static double dichotomy(double init, double diff(double, void *), void *var_cnst, double min_error)
332 double overall_error;
339 if (fabs(init) < 1e-20) {
346 diff_0 = diff(1e-16, var_cnst);
348 XBT_CDEBUG(surf_lagrange_dichotomy, "returning 0.0 (diff = %e)", diff_0);
353 double min_diff = diff(min, var_cnst);
354 double max_diff = diff(max, var_cnst);
356 while (overall_error > min_error) {
357 XBT_CDEBUG(surf_lagrange_dichotomy, "[min, max] = [%1.20f, %1.20f] || diffmin, diffmax = %1.20f, %1.20f",
358 min, max, min_diff, max_diff);
360 if (min_diff > 0 && max_diff > 0) {
362 XBT_CDEBUG(surf_lagrange_dichotomy, "Decreasing min");
364 min_diff = diff(min, var_cnst);
366 XBT_CDEBUG(surf_lagrange_dichotomy, "Decreasing max");
370 } else if (min_diff < 0 && max_diff < 0) {
372 XBT_CDEBUG(surf_lagrange_dichotomy, "Increasing max");
374 max_diff = diff(max, var_cnst);
376 XBT_CDEBUG(surf_lagrange_dichotomy, "Increasing min");
380 } else if (min_diff < 0 && max_diff > 0) {
381 middle = (max + min) / 2.0;
382 XBT_CDEBUG(surf_lagrange_dichotomy, "Trying (max+min)/2 : %1.20f", middle);
384 if ((fabs(min - middle) < 1e-20) || (fabs(max - middle) < 1e-20)){
385 XBT_CWARN(surf_lagrange_dichotomy, "Cannot improve the convergence! min=max=middle=%1.20f, diff = %1.20f."
386 " Reaching the 'double' limits. Maybe scaling your function would help ([%1.20f,%1.20f]).",
387 min, max - min, min_diff, max_diff);
390 middle_diff = diff(middle, var_cnst);
392 if (middle_diff < 0) {
393 XBT_CDEBUG(surf_lagrange_dichotomy, "Increasing min");
395 overall_error = max_diff - middle_diff;
396 min_diff = middle_diff;
397 /* SHOW_EXPR(overall_error); */
398 } else if (middle_diff > 0) {
399 XBT_CDEBUG(surf_lagrange_dichotomy, "Decreasing max");
401 overall_error = max_diff - middle_diff;
402 max_diff = middle_diff;
403 /* SHOW_EXPR(overall_error); */
406 /* SHOW_EXPR(overall_error); */
408 } else if (fabs(min_diff) < 1e-20) {
411 /* SHOW_EXPR(overall_error); */
412 } else if (fabs(max_diff) < 1e-20) {
415 /* SHOW_EXPR(overall_error); */
416 } else if (min_diff > 0 && max_diff < 0) {
417 XBT_CWARN(surf_lagrange_dichotomy, "The impossible happened, partial_diff(min) > 0 && partial_diff(max) < 0");
420 XBT_CWARN(surf_lagrange_dichotomy,
421 "diffmin (%1.20f) or diffmax (%1.20f) are something I don't know, taking no action.",
427 XBT_CDEBUG(surf_lagrange_dichotomy, "returning %e", (min + max) / 2.0);
429 return ((min + max) / 2.0);
432 static double partial_diff_lambda(double lambda, void *param_cnst)
436 xbt_swag_t elem_list = nullptr;
437 lmm_element_t elem = nullptr;
438 lmm_variable_t var = nullptr;
439 lmm_constraint_t cnst = static_cast<lmm_constraint_t>(param_cnst);
441 double sigma_i = 0.0;
444 elem_list = &(cnst->enabled_element_set);
446 XBT_CDEBUG(surf_lagrange_dichotomy, "Computing diff of cnst (%p)", cnst);
448 xbt_swag_foreach(_elem, elem_list) {
449 elem = static_cast<lmm_element_t>(_elem);
450 var = elem->variable;
451 xbt_assert(var->weight > 0);
452 XBT_CDEBUG(surf_lagrange_dichotomy, "Computing sigma_i for var (%p)", var);
453 // Initialize the summation variable
457 for (j = 0; j < var->cnsts_number; j++) {
458 sigma_i += (var->cnsts[j].constraint)->lambda;
461 //add mu_i if this flow has a RTT constraint associated
465 //replace value of cnst->lambda by the value of parameter lambda
466 sigma_i = (sigma_i - cnst->lambda) + lambda;
468 diff += -var->func_fpi(var, sigma_i);
473 XBT_CDEBUG(surf_lagrange_dichotomy, "d D/d lambda for cnst (%p) at %1.20f = %1.20f", cnst, lambda, diff);
478 /** \brief Attribute the value bound to var->bound.
480 * \param func_fpi inverse of the partial differential of f (f prime inverse, (f')^{-1})
482 * Set default functions to the ones passed as parameters. This is a polymorphism in C pure, enjoy the roots of
486 void lmm_set_default_protocol_function(double (*func_f) (lmm_variable_t var, double x),
487 double (*func_fp) (lmm_variable_t var, double x),
488 double (*func_fpi) (lmm_variable_t var, double x))
491 func_fp_def = func_fp;
492 func_fpi_def = func_fpi;
495 /**************** Vegas and Reno functions *************************/
496 /* NOTE for Reno: all functions consider the network coefficient (alpha) equal to 1. */
499 * For Vegas: $f(x) = \alpha D_f\ln(x)$
500 * Therefore: $fp(x) = \frac{\alpha D_f}{x}$
501 * Therefore: $fpi(x) = \frac{\alpha D_f}{x}$
503 #define VEGAS_SCALING 1000.0
505 double func_vegas_f(lmm_variable_t var, double x)
507 xbt_assert(x > 0.0, "Don't call me with stupid values! (%1.20f)", x);
508 return VEGAS_SCALING * var->weight * log(x);
511 double func_vegas_fp(lmm_variable_t var, double x)
513 xbt_assert(x > 0.0, "Don't call me with stupid values! (%1.20f)", x);
514 return VEGAS_SCALING * var->weight / x;
517 double func_vegas_fpi(lmm_variable_t var, double x)
519 xbt_assert(x > 0.0, "Don't call me with stupid values! (%1.20f)", x);
520 return var->weight / (x / VEGAS_SCALING);
524 * For Reno: $f(x) = \frac{\sqrt{3/2}}{D_f} atan(\sqrt{3/2}D_f x)$
525 * Therefore: $fp(x) = \frac{3}{3 D_f^2 x^2+2}$
526 * Therefore: $fpi(x) = \sqrt{\frac{1}{{D_f}^2 x} - \frac{2}{3{D_f}^2}}$
528 #define RENO_SCALING 1.0
529 double func_reno_f(lmm_variable_t var, double x)
531 xbt_assert(var->weight > 0.0, "Don't call me with stupid values!");
533 return RENO_SCALING * sqrt(3.0 / 2.0) / var->weight * atan(sqrt(3.0 / 2.0) * var->weight * x);
536 double func_reno_fp(lmm_variable_t var, double x)
538 return RENO_SCALING * 3.0 / (3.0 * var->weight * var->weight * x * x + 2.0);
541 double func_reno_fpi(lmm_variable_t var, double x)
545 xbt_assert(var->weight > 0.0, "Don't call me with stupid values!");
546 xbt_assert(x > 0.0, "Don't call me with stupid values!");
548 res_fpi = 1.0 / (var->weight * var->weight * (x / RENO_SCALING)) - 2.0 / (3.0 * var->weight * var->weight);
551 /* xbt_assert(res_fpi>0.0,"Don't call me with stupid values!"); */
552 return sqrt(res_fpi);
555 /* Implementing new Reno-2
556 * For Reno-2: $f(x) = U_f(x_f) = \frac{{2}{D_f}}*ln(2+x*D_f)$
557 * Therefore: $fp(x) = 2/(Weight*x + 2)
558 * Therefore: $fpi(x) = (2*Weight)/x - 4
560 #define RENO2_SCALING 1.0
561 double func_reno2_f(lmm_variable_t var, double x)
563 xbt_assert(var->weight > 0.0, "Don't call me with stupid values!");
564 return RENO2_SCALING * (1.0 / var->weight) * log((x * var->weight) / (2.0 * x * var->weight + 3.0));
567 double func_reno2_fp(lmm_variable_t var, double x)
569 return RENO2_SCALING * 3.0 / (var->weight * x * (2.0 * var->weight * x + 3.0));
572 double func_reno2_fpi(lmm_variable_t var, double x)
574 xbt_assert(x > 0.0, "Don't call me with stupid values!");
575 double tmp = x * var->weight * var->weight;
576 double res_fpi = tmp * (9.0 * x + 24.0);
581 res_fpi = RENO2_SCALING * (-3.0 * tmp + sqrt(res_fpi)) / (4.0 * tmp);