1 /* Copyright (c) 2007-2017. The SimGrid Team. 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. */
7 * Modeling the proportional fairness using the Lagrangian Optimization 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.hpp"
19 XBT_LOG_NEW_DEFAULT_SUBCATEGORY(surf_lagrange, surf, "Logging specific to SURF (lagrange)");
20 XBT_LOG_NEW_SUBCATEGORY(surf_lagrange_dichotomy, surf_lagrange, "Logging specific to SURF (lagrange dichotomy)");
22 #define SHOW_EXPR(expr) XBT_CDEBUG(surf_lagrange,#expr " = %g",expr);
24 double (*func_f_def) (lmm_variable_t, double);
25 double (*func_fp_def) (lmm_variable_t, double);
26 double (*func_fpi_def) (lmm_variable_t, double);
29 * Local prototypes to implement the Lagrangian optimization with optimal step, also called dichotomy.
31 //solves the proportional fairness using a Lagrangian optimization with dichotomy step
32 void lagrange_solve(lmm_system_t sys);
33 //computes the value of the dichotomy using a initial values, init, with a specific variable or constraint
34 static double dichotomy(double init, double diff(double, void *), void *var_cnst, double min_error);
35 //computes the value of the differential of constraint param_cnst applied to lambda
36 static double partial_diff_lambda(double lambda, void *param_cnst);
38 static int __check_feasible(xbt_swag_t cnst_list, xbt_swag_t var_list, int warn)
43 xbt_swag_t elem_list = nullptr;
44 lmm_element_t elem = nullptr;
45 lmm_constraint_t cnst = nullptr;
46 lmm_variable_t var = nullptr;
48 xbt_swag_foreach(_cnst, cnst_list) {
49 cnst = static_cast<lmm_constraint_t>(_cnst);
51 elem_list = &(cnst->enabled_element_set);
52 xbt_swag_foreach(_elem, elem_list) {
53 elem = static_cast<lmm_element_t>(_elem);
55 xbt_assert(var->sharing_weight > 0);
59 if (double_positive(tmp - cnst->bound, sg_maxmin_precision)) {
61 XBT_WARN ("The link (%p) is over-used. Expected less than %f and got %f", cnst, cnst->bound, tmp);
64 XBT_DEBUG ("Checking feasability for constraint (%p): sat = %f, lambda = %f ", cnst, tmp - cnst->bound,
68 xbt_swag_foreach(_var, var_list) {
69 var = static_cast<lmm_variable_t>(_var);
70 if (not var->sharing_weight)
74 XBT_DEBUG("Checking feasability for variable (%p): sat = %f mu = %f", var, var->value - var->bound, var->mu);
76 if (double_positive(var->value - var->bound, sg_maxmin_precision)) {
78 XBT_WARN ("The variable (%p) is too large. Expected less than %f and got %f", var, var->bound, var->value);
85 static double new_value(lmm_variable_t var)
89 for (int i = 0; i < var->cnsts_number; i++) {
90 tmp += (var->cnsts[i].constraint)->lambda;
94 XBT_DEBUG("\t Working on var (%p). cost = %e; Weight = %e", var, tmp, var->sharing_weight);
95 //uses the partial differential inverse function
96 return var->func_fpi(var, tmp);
99 static double new_mu(lmm_variable_t var)
102 double sigma_i = 0.0;
104 for (int j = 0; j < var->cnsts_number; j++) {
105 sigma_i += (var->cnsts[j].constraint)->lambda;
107 mu_i = var->func_fp(var, var->bound) - sigma_i;
113 static double dual_objective(xbt_swag_t var_list, xbt_swag_t cnst_list)
117 lmm_constraint_t cnst = nullptr;
118 lmm_variable_t var = nullptr;
122 xbt_swag_foreach(_var, var_list) {
123 var = static_cast<lmm_variable_t>(_var);
124 double sigma_i = 0.0;
126 if (not var->sharing_weight)
129 for (int j = 0; j < var->cnsts_number; j++)
130 sigma_i += (var->cnsts[j].constraint)->lambda;
135 XBT_DEBUG("var %p : sigma_i = %1.20f", var, sigma_i);
137 obj += var->func_f(var, var->func_fpi(var, sigma_i)) - sigma_i * var->func_fpi(var, sigma_i);
140 obj += var->mu * var->bound;
143 xbt_swag_foreach(_cnst, cnst_list) {
144 cnst = static_cast<lmm_constraint_t>(_cnst);
145 obj += cnst->lambda * cnst->bound;
151 void lagrange_solve(lmm_system_t sys)
153 /* Lagrange Variables. */
154 int max_iterations = 100;
155 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 */
156 double dichotomy_min_error = 1e-14;
157 double overall_modification = 1;
159 /* Variables to manipulate the data structure proposed to model the maxmin fairness. See documentation for details. */
160 xbt_swag_t cnst_list = nullptr;
162 lmm_constraint_t cnst = nullptr;
164 xbt_swag_t var_list = nullptr;
166 lmm_variable_t var = nullptr;
168 /* Auxiliary variables. */
175 XBT_DEBUG("Iterative method configuration snapshot =====>");
176 XBT_DEBUG("#### Maximum number of iterations : %d", max_iterations);
177 XBT_DEBUG("#### Minimum error tolerated : %e", epsilon_min_error);
178 XBT_DEBUG("#### Minimum error tolerated (dichotomy) : %e", dichotomy_min_error);
180 if (XBT_LOG_ISENABLED(surf_lagrange, xbt_log_priority_debug)) {
184 if (not sys->modified)
187 /* Initialize lambda. */
188 cnst_list = &(sys->active_constraint_set);
189 xbt_swag_foreach(_cnst, cnst_list) {
190 cnst = (lmm_constraint_t)_cnst;
192 cnst->new_lambda = 2.0;
193 XBT_DEBUG("#### cnst(%p)->lambda : %e", cnst, cnst->lambda);
197 * Initialize the var list variable with only the active variables.
198 * Associate an index in the swag variables. Initialize mu.
200 var_list = &(sys->variable_set);
202 xbt_swag_foreach(_var, var_list) {
203 var = static_cast<lmm_variable_t>(_var);
204 if (not var->sharing_weight)
208 if (var->bound < 0.0) {
209 XBT_DEBUG("#### NOTE var(%d) is a boundless variable", i);
211 var->value = new_value(var);
215 var->value = new_value(var);
217 XBT_DEBUG("#### var(%p) ->weight : %e", var, var->sharing_weight);
218 XBT_DEBUG("#### var(%p) ->mu : %e", var, var->mu);
219 XBT_DEBUG("#### var(%p) ->weight: %e", var, var->sharing_weight);
220 XBT_DEBUG("#### var(%p) ->bound: %e", var, var->bound);
221 for (i = 0; i < var->cnsts_number; i++) {
222 if (var->cnsts[i].consumption_weight == 0.0)
225 if (nb == var->cnsts_number)
230 /* Compute dual objective. */
231 obj = dual_objective(var_list, cnst_list);
233 /* While doesn't reach a minimum error or a number maximum of iterations. */
234 while (overall_modification > epsilon_min_error && iteration < max_iterations) {
236 XBT_DEBUG("************** ITERATION %d **************", iteration);
237 XBT_DEBUG("-------------- Gradient Descent ----------");
239 /* Improve the value of mu_i */
240 xbt_swag_foreach(_var, var_list) {
241 var = static_cast<lmm_variable_t>(_var);
242 if (not var->sharing_weight)
244 if (var->bound >= 0) {
245 XBT_DEBUG("Working on var (%p)", var);
246 var->new_mu = new_mu(var);
247 XBT_DEBUG("Updating mu : var->mu (%p) : %1.20f -> %1.20f", var, var->mu, var->new_mu);
248 var->mu = var->new_mu;
250 new_obj = dual_objective(var_list, cnst_list);
251 XBT_DEBUG("Improvement for Objective (%g -> %g) : %g", obj, new_obj, obj - new_obj);
252 xbt_assert(obj - new_obj >= -epsilon_min_error, "Our gradient sucks! (%1.20f)", obj - new_obj);
257 /* Improve the value of lambda_i */
258 xbt_swag_foreach(_cnst, cnst_list) {
259 cnst = static_cast<lmm_constraint_t>(_cnst);
260 XBT_DEBUG("Working on cnst (%p)", cnst);
261 cnst->new_lambda = dichotomy(cnst->lambda, partial_diff_lambda, cnst, dichotomy_min_error);
262 XBT_DEBUG("Updating lambda : cnst->lambda (%p) : %1.20f -> %1.20f", cnst, cnst->lambda, cnst->new_lambda);
263 cnst->lambda = cnst->new_lambda;
265 new_obj = dual_objective(var_list, cnst_list);
266 XBT_DEBUG("Improvement for Objective (%g -> %g) : %g", obj, new_obj, obj - new_obj);
267 xbt_assert(obj - new_obj >= -epsilon_min_error, "Our gradient sucks! (%1.20f)", obj - new_obj);
271 /* Now computes the values of each variable (\rho) based on the values of \lambda and \mu. */
272 XBT_DEBUG("-------------- Check convergence ----------");
273 overall_modification = 0;
274 xbt_swag_foreach(_var, var_list) {
275 var = static_cast<lmm_variable_t>(_var);
276 if (var->sharing_weight <= 0)
279 tmp = new_value(var);
281 overall_modification = MAX(overall_modification, fabs(var->value - tmp));
284 XBT_DEBUG("New value of var (%p) = %e, overall_modification = %e", var, var->value, overall_modification);
288 XBT_DEBUG("-------------- Check feasability ----------");
289 if (not __check_feasible(cnst_list, var_list, 0))
290 overall_modification = 1.0;
291 XBT_DEBUG("Iteration %d: overall_modification : %f", iteration, overall_modification);
294 __check_feasible(cnst_list, var_list, 1);
296 if (overall_modification <= epsilon_min_error) {
297 XBT_DEBUG("The method converges in %d iterations.", iteration);
299 if (iteration >= max_iterations) {
300 XBT_DEBUG ("Method reach %d iterations, which is the maximum number of iterations allowed.", iteration);
303 if (XBT_LOG_ISENABLED(surf_lagrange, xbt_log_priority_debug)) {
309 * Returns a double value corresponding to the result of a dichotomy process with respect to a given
310 * variable/constraint (\mu in the case of a variable or \lambda in case of a constraint) and a initial value init.
312 * @param init initial value for \mu or \lambda
313 * @param diff a function that computes the differential of with respect a \mu or \lambda
314 * @param var_cnst a pointer to a variable or constraint
315 * @param min_erro a minimum error tolerated
317 * @return a double corresponding to the result of the dichotomy process
319 static double dichotomy(double init, double diff(double, void *), void *var_cnst, double min_error)
323 double overall_error;
330 if (fabs(init) < 1e-20) {
337 diff_0 = diff(1e-16, var_cnst);
339 XBT_CDEBUG(surf_lagrange_dichotomy, "returning 0.0 (diff = %e)", diff_0);
344 double min_diff = diff(min, var_cnst);
345 double max_diff = diff(max, var_cnst);
347 while (overall_error > min_error) {
348 XBT_CDEBUG(surf_lagrange_dichotomy, "[min, max] = [%1.20f, %1.20f] || diffmin, diffmax = %1.20f, %1.20f",
349 min, max, min_diff, max_diff);
351 if (min_diff > 0 && max_diff > 0) {
353 XBT_CDEBUG(surf_lagrange_dichotomy, "Decreasing min");
355 min_diff = diff(min, var_cnst);
357 XBT_CDEBUG(surf_lagrange_dichotomy, "Decreasing max");
361 } else if (min_diff < 0 && max_diff < 0) {
363 XBT_CDEBUG(surf_lagrange_dichotomy, "Increasing max");
365 max_diff = diff(max, var_cnst);
367 XBT_CDEBUG(surf_lagrange_dichotomy, "Increasing min");
371 } else if (min_diff < 0 && max_diff > 0) {
372 middle = (max + min) / 2.0;
373 XBT_CDEBUG(surf_lagrange_dichotomy, "Trying (max+min)/2 : %1.20f", middle);
375 if ((fabs(min - middle) < 1e-20) || (fabs(max - middle) < 1e-20)){
376 XBT_CWARN(surf_lagrange_dichotomy, "Cannot improve the convergence! min=max=middle=%1.20f, diff = %1.20f."
377 " Reaching the 'double' limits. Maybe scaling your function would help ([%1.20f,%1.20f]).",
378 min, max - min, min_diff, max_diff);
381 middle_diff = diff(middle, var_cnst);
383 if (middle_diff < 0) {
384 XBT_CDEBUG(surf_lagrange_dichotomy, "Increasing min");
386 overall_error = max_diff - middle_diff;
387 min_diff = middle_diff;
388 } else if (middle_diff > 0) {
389 XBT_CDEBUG(surf_lagrange_dichotomy, "Decreasing max");
391 overall_error = max_diff - middle_diff;
392 max_diff = middle_diff;
396 } else if (fabs(min_diff) < 1e-20) {
399 } else if (fabs(max_diff) < 1e-20) {
402 } else if (min_diff > 0 && max_diff < 0) {
403 XBT_CWARN(surf_lagrange_dichotomy, "The impossible happened, partial_diff(min) > 0 && partial_diff(max) < 0");
406 XBT_CWARN(surf_lagrange_dichotomy,
407 "diffmin (%1.20f) or diffmax (%1.20f) are something I don't know, taking no action.",
413 XBT_CDEBUG(surf_lagrange_dichotomy, "returning %e", (min + max) / 2.0);
415 return ((min + max) / 2.0);
418 static double partial_diff_lambda(double lambda, void *param_cnst)
420 lmm_constraint_t cnst = static_cast<lmm_constraint_t>(param_cnst);
425 XBT_CDEBUG(surf_lagrange_dichotomy, "Computing diff of cnst (%p)", cnst);
427 xbt_swag_t elem_list = &(cnst->enabled_element_set);
429 xbt_swag_foreach(_elem, elem_list) {
430 lmm_element_t elem = static_cast<lmm_element_t>(_elem);
431 lmm_variable_t var = elem->variable;
432 xbt_assert(var->sharing_weight > 0);
433 XBT_CDEBUG(surf_lagrange_dichotomy, "Computing sigma_i for var (%p)", var);
434 // Initialize the summation variable
435 double sigma_i = 0.0;
438 for (int j = 0; j < var->cnsts_number; j++) {
439 sigma_i += (var->cnsts[j].constraint)->lambda;
442 //add mu_i if this flow has a RTT constraint associated
446 //replace value of cnst->lambda by the value of parameter lambda
447 sigma_i = (sigma_i - cnst->lambda) + lambda;
449 diff += -var->func_fpi(var, sigma_i);
454 XBT_CDEBUG(surf_lagrange_dichotomy, "d D/d lambda for cnst (%p) at %1.20f = %1.20f", cnst, lambda, diff);
459 /** \brief Attribute the value bound to var->bound.
461 * \param func_fpi inverse of the partial differential of f (f prime inverse, (f')^{-1})
463 * Set default functions to the ones passed as parameters. This is a polymorphism in C pure, enjoy the roots of
467 void lmm_set_default_protocol_function(double (*func_f) (lmm_variable_t var, double x),
468 double (*func_fp) (lmm_variable_t var, double x),
469 double (*func_fpi) (lmm_variable_t var, double x))
472 func_fp_def = func_fp;
473 func_fpi_def = func_fpi;
476 /**************** Vegas and Reno functions *************************/
477 /* NOTE for Reno: all functions consider the network coefficient (alpha) equal to 1. */
480 * For Vegas: $f(x) = \alpha D_f\ln(x)$
481 * Therefore: $fp(x) = \frac{\alpha D_f}{x}$
482 * Therefore: $fpi(x) = \frac{\alpha D_f}{x}$
484 #define VEGAS_SCALING 1000.0
486 double func_vegas_f(lmm_variable_t var, double x)
488 xbt_assert(x > 0.0, "Don't call me with stupid values! (%1.20f)", x);
489 return VEGAS_SCALING * var->sharing_weight * log(x);
492 double func_vegas_fp(lmm_variable_t var, double x)
494 xbt_assert(x > 0.0, "Don't call me with stupid values! (%1.20f)", x);
495 return VEGAS_SCALING * var->sharing_weight / x;
498 double func_vegas_fpi(lmm_variable_t var, double x)
500 xbt_assert(x > 0.0, "Don't call me with stupid values! (%1.20f)", x);
501 return var->sharing_weight / (x / VEGAS_SCALING);
505 * For Reno: $f(x) = \frac{\sqrt{3/2}}{D_f} atan(\sqrt{3/2}D_f x)$
506 * Therefore: $fp(x) = \frac{3}{3 D_f^2 x^2+2}$
507 * Therefore: $fpi(x) = \sqrt{\frac{1}{{D_f}^2 x} - \frac{2}{3{D_f}^2}}$
509 #define RENO_SCALING 1.0
510 double func_reno_f(lmm_variable_t var, double x)
512 xbt_assert(var->sharing_weight > 0.0, "Don't call me with stupid values!");
514 return RENO_SCALING * sqrt(3.0 / 2.0) / var->sharing_weight * atan(sqrt(3.0 / 2.0) * var->sharing_weight * x);
517 double func_reno_fp(lmm_variable_t var, double x)
519 return RENO_SCALING * 3.0 / (3.0 * var->sharing_weight * var->sharing_weight * x * x + 2.0);
522 double func_reno_fpi(lmm_variable_t var, double x)
526 xbt_assert(var->sharing_weight > 0.0, "Don't call me with stupid values!");
527 xbt_assert(x > 0.0, "Don't call me with stupid values!");
529 res_fpi = 1.0 / (var->sharing_weight * var->sharing_weight * (x / RENO_SCALING)) -
530 2.0 / (3.0 * var->sharing_weight * var->sharing_weight);
533 return sqrt(res_fpi);
536 /* Implementing new Reno-2
537 * For Reno-2: $f(x) = U_f(x_f) = \frac{{2}{D_f}}*ln(2+x*D_f)$
538 * Therefore: $fp(x) = 2/(Weight*x + 2)
539 * Therefore: $fpi(x) = (2*Weight)/x - 4
541 #define RENO2_SCALING 1.0
542 double func_reno2_f(lmm_variable_t var, double x)
544 xbt_assert(var->sharing_weight > 0.0, "Don't call me with stupid values!");
545 return RENO2_SCALING * (1.0 / var->sharing_weight) *
546 log((x * var->sharing_weight) / (2.0 * x * var->sharing_weight + 3.0));
549 double func_reno2_fp(lmm_variable_t var, double x)
551 return RENO2_SCALING * 3.0 / (var->sharing_weight * x * (2.0 * var->sharing_weight * x + 3.0));
554 double func_reno2_fpi(lmm_variable_t var, double x)
556 xbt_assert(x > 0.0, "Don't call me with stupid values!");
557 double tmp = x * var->sharing_weight * var->sharing_weight;
558 double res_fpi = tmp * (9.0 * x + 24.0);
563 res_fpi = RENO2_SCALING * (-3.0 * tmp + sqrt(res_fpi)) / (4.0 * tmp);