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".
10 #include "surf/maxmin.hpp"
12 #include "xbt/sysdep.h"
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);
24 #define VEGAS_SCALING 1000.0
25 #define RENO_SCALING 1.0
26 #define RENO2_SCALING 1.0
31 double (*func_f_def) (lmm_variable_t, double);
32 double (*func_fp_def) (lmm_variable_t, double);
33 double (*func_fpi_def) (lmm_variable_t, double);
36 * Local prototypes to implement the Lagrangian optimization with optimal step, also called dichotomy.
38 //solves the proportional fairness using a Lagrangian optimization with dichotomy step
39 void lagrange_solve(lmm_system_t sys);
40 //computes the value of the dichotomy using a initial values, init, with a specific variable or constraint
41 static double dichotomy(double init, double diff(double, void *), void *var_cnst, double min_error);
42 //computes the value of the differential of constraint param_cnst applied to lambda
43 static double partial_diff_lambda(double lambda, void *param_cnst);
45 static int __check_feasible(xbt_swag_t cnst_list, xbt_swag_t var_list, int warn)
50 xbt_swag_t elem_list = nullptr;
51 lmm_element_t elem = nullptr;
52 lmm_constraint_t cnst = nullptr;
53 lmm_variable_t var = nullptr;
55 xbt_swag_foreach(_cnst, cnst_list) {
56 cnst = static_cast<lmm_constraint_t>(_cnst);
58 elem_list = &(cnst->enabled_element_set);
59 xbt_swag_foreach(_elem, elem_list) {
60 elem = static_cast<lmm_element_t>(_elem);
62 xbt_assert(var->sharing_weight > 0);
66 if (double_positive(tmp - cnst->bound, sg_maxmin_precision)) {
68 XBT_WARN ("The link (%p) is over-used. Expected less than %f and got %f", cnst, cnst->bound, tmp);
71 XBT_DEBUG ("Checking feasability for constraint (%p): sat = %f, lambda = %f ", cnst, tmp - cnst->bound,
75 xbt_swag_foreach(_var, var_list) {
76 var = static_cast<lmm_variable_t>(_var);
77 if (not var->sharing_weight)
81 XBT_DEBUG("Checking feasability for variable (%p): sat = %f mu = %f", var, var->value - var->bound, var->mu);
83 if (double_positive(var->value - var->bound, sg_maxmin_precision)) {
85 XBT_WARN ("The variable (%p) is too large. Expected less than %f and got %f", var, var->bound, var->value);
92 static double new_value(lmm_variable_t var)
96 for (s_lmm_element_t const& elem : var->cnsts) {
97 tmp += elem.constraint->lambda;
101 XBT_DEBUG("\t Working on var (%p). cost = %e; Weight = %e", var, tmp, var->sharing_weight);
102 //uses the partial differential inverse function
103 return var->func_fpi(var, tmp);
106 static double new_mu(lmm_variable_t var)
109 double sigma_i = 0.0;
111 for (s_lmm_element_t const& elem : var->cnsts) {
112 sigma_i += elem.constraint->lambda;
114 mu_i = var->func_fp(var, var->bound) - sigma_i;
120 static double dual_objective(xbt_swag_t var_list, xbt_swag_t cnst_list)
124 lmm_constraint_t cnst = nullptr;
125 lmm_variable_t var = nullptr;
129 xbt_swag_foreach(_var, var_list) {
130 var = static_cast<lmm_variable_t>(_var);
131 double sigma_i = 0.0;
133 if (not var->sharing_weight)
136 for (s_lmm_element_t const& elem : var->cnsts)
137 sigma_i += elem.constraint->lambda;
142 XBT_DEBUG("var %p : sigma_i = %1.20f", var, sigma_i);
144 obj += var->func_f(var, var->func_fpi(var, sigma_i)) - sigma_i * var->func_fpi(var, sigma_i);
147 obj += var->mu * var->bound;
150 xbt_swag_foreach(_cnst, cnst_list) {
151 cnst = static_cast<lmm_constraint_t>(_cnst);
152 obj += cnst->lambda * cnst->bound;
158 void lagrange_solve(lmm_system_t sys)
160 /* Lagrange Variables. */
161 int max_iterations = 100;
162 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 */
163 double dichotomy_min_error = 1e-14;
164 double overall_modification = 1;
166 XBT_DEBUG("Iterative method configuration snapshot =====>");
167 XBT_DEBUG("#### Maximum number of iterations : %d", max_iterations);
168 XBT_DEBUG("#### Minimum error tolerated : %e", epsilon_min_error);
169 XBT_DEBUG("#### Minimum error tolerated (dichotomy) : %e", dichotomy_min_error);
171 if (XBT_LOG_ISENABLED(surf_lagrange, xbt_log_priority_debug)) {
175 if (not sys->modified)
178 /* Initialize lambda. */
179 xbt_swag_t cnst_list = &(sys->active_constraint_set);
181 xbt_swag_foreach(_cnst, cnst_list) {
182 lmm_constraint_t cnst = (lmm_constraint_t)_cnst;
184 cnst->new_lambda = 2.0;
185 XBT_DEBUG("#### cnst(%p)->lambda : %e", cnst, cnst->lambda);
189 * Initialize the var list variable with only the active variables.
190 * Associate an index in the swag variables. Initialize mu.
192 xbt_swag_t var_list = &(sys->variable_set);
194 xbt_swag_foreach(_var, var_list) {
195 lmm_variable_t var = static_cast<lmm_variable_t>(_var);
196 if (not var->sharing_weight)
199 if (var->bound < 0.0) {
200 XBT_DEBUG("#### NOTE var(%p) is a boundless variable", var);
206 var->value = new_value(var);
207 XBT_DEBUG("#### var(%p) ->weight : %e", var, var->sharing_weight);
208 XBT_DEBUG("#### var(%p) ->mu : %e", var, var->mu);
209 XBT_DEBUG("#### var(%p) ->weight: %e", var, var->sharing_weight);
210 XBT_DEBUG("#### var(%p) ->bound: %e", var, var->bound);
211 auto weighted = std::find_if(begin(var->cnsts), end(var->cnsts),
212 [](s_lmm_element_t const& x) { return x.consumption_weight != 0.0; });
213 if (weighted == end(var->cnsts))
218 /* Compute dual objective. */
219 double obj = dual_objective(var_list, cnst_list);
221 /* While doesn't reach a minimum error or a number maximum of iterations. */
223 while (overall_modification > epsilon_min_error && iteration < max_iterations) {
225 XBT_DEBUG("************** ITERATION %d **************", iteration);
226 XBT_DEBUG("-------------- Gradient Descent ----------");
228 /* Improve the value of mu_i */
229 xbt_swag_foreach(_var, var_list) {
230 lmm_variable_t var = static_cast<lmm_variable_t>(_var);
231 if (var->sharing_weight && var->bound >= 0) {
232 XBT_DEBUG("Working on var (%p)", var);
233 var->new_mu = new_mu(var);
234 XBT_DEBUG("Updating mu : var->mu (%p) : %1.20f -> %1.20f", var, var->mu, var->new_mu);
235 var->mu = var->new_mu;
237 double new_obj = dual_objective(var_list, cnst_list);
238 XBT_DEBUG("Improvement for Objective (%g -> %g) : %g", obj, new_obj, obj - new_obj);
239 xbt_assert(obj - new_obj >= -epsilon_min_error, "Our gradient sucks! (%1.20f)", obj - new_obj);
244 /* Improve the value of lambda_i */
245 xbt_swag_foreach(_cnst, cnst_list) {
246 lmm_constraint_t cnst = static_cast<lmm_constraint_t>(_cnst);
247 XBT_DEBUG("Working on cnst (%p)", cnst);
248 cnst->new_lambda = dichotomy(cnst->lambda, partial_diff_lambda, cnst, dichotomy_min_error);
249 XBT_DEBUG("Updating lambda : cnst->lambda (%p) : %1.20f -> %1.20f", cnst, cnst->lambda, cnst->new_lambda);
250 cnst->lambda = cnst->new_lambda;
252 double new_obj = dual_objective(var_list, cnst_list);
253 XBT_DEBUG("Improvement for Objective (%g -> %g) : %g", obj, new_obj, obj - new_obj);
254 xbt_assert(obj - new_obj >= -epsilon_min_error, "Our gradient sucks! (%1.20f)", obj - new_obj);
258 /* Now computes the values of each variable (\rho) based on the values of \lambda and \mu. */
259 XBT_DEBUG("-------------- Check convergence ----------");
260 overall_modification = 0;
261 xbt_swag_foreach(_var, var_list) {
262 lmm_variable_t var = static_cast<lmm_variable_t>(_var);
263 if (var->sharing_weight <= 0)
266 double tmp = new_value(var);
268 overall_modification = std::max(overall_modification, fabs(var->value - tmp));
271 XBT_DEBUG("New value of var (%p) = %e, overall_modification = %e", var, var->value, overall_modification);
275 XBT_DEBUG("-------------- Check feasability ----------");
276 if (not __check_feasible(cnst_list, var_list, 0))
277 overall_modification = 1.0;
278 XBT_DEBUG("Iteration %d: overall_modification : %f", iteration, overall_modification);
281 __check_feasible(cnst_list, var_list, 1);
283 if (overall_modification <= epsilon_min_error) {
284 XBT_DEBUG("The method converges in %d iterations.", iteration);
286 if (iteration >= max_iterations) {
287 XBT_DEBUG ("Method reach %d iterations, which is the maximum number of iterations allowed.", iteration);
290 if (XBT_LOG_ISENABLED(surf_lagrange, xbt_log_priority_debug)) {
296 * Returns a double value corresponding to the result of a dichotomy process with respect to a given
297 * variable/constraint (\mu in the case of a variable or \lambda in case of a constraint) and a initial value init.
299 * @param init initial value for \mu or \lambda
300 * @param diff a function that computes the differential of with respect a \mu or \lambda
301 * @param var_cnst a pointer to a variable or constraint
302 * @param min_erro a minimum error tolerated
304 * @return a double corresponding to the result of the dichotomy process
306 static double dichotomy(double init, double diff(double, void *), void *var_cnst, double min_error)
310 double overall_error;
317 if (fabs(init) < 1e-20) {
324 diff_0 = diff(1e-16, var_cnst);
326 XBT_CDEBUG(surf_lagrange_dichotomy, "returning 0.0 (diff = %e)", diff_0);
331 double min_diff = diff(min, var_cnst);
332 double max_diff = diff(max, var_cnst);
334 while (overall_error > min_error) {
335 XBT_CDEBUG(surf_lagrange_dichotomy, "[min, max] = [%1.20f, %1.20f] || diffmin, diffmax = %1.20f, %1.20f",
336 min, max, min_diff, max_diff);
338 if (min_diff > 0 && max_diff > 0) {
340 XBT_CDEBUG(surf_lagrange_dichotomy, "Decreasing min");
342 min_diff = diff(min, var_cnst);
344 XBT_CDEBUG(surf_lagrange_dichotomy, "Decreasing max");
348 } else if (min_diff < 0 && max_diff < 0) {
350 XBT_CDEBUG(surf_lagrange_dichotomy, "Increasing max");
352 max_diff = diff(max, var_cnst);
354 XBT_CDEBUG(surf_lagrange_dichotomy, "Increasing min");
358 } else if (min_diff < 0 && max_diff > 0) {
359 middle = (max + min) / 2.0;
360 XBT_CDEBUG(surf_lagrange_dichotomy, "Trying (max+min)/2 : %1.20f", middle);
362 if ((fabs(min - middle) < 1e-20) || (fabs(max - middle) < 1e-20)){
363 XBT_CWARN(surf_lagrange_dichotomy, "Cannot improve the convergence! min=max=middle=%1.20f, diff = %1.20f."
364 " Reaching the 'double' limits. Maybe scaling your function would help ([%1.20f,%1.20f]).",
365 min, max - min, min_diff, max_diff);
368 middle_diff = diff(middle, var_cnst);
370 if (middle_diff < 0) {
371 XBT_CDEBUG(surf_lagrange_dichotomy, "Increasing min");
373 overall_error = max_diff - middle_diff;
374 min_diff = middle_diff;
375 } else if (middle_diff > 0) {
376 XBT_CDEBUG(surf_lagrange_dichotomy, "Decreasing max");
378 overall_error = max_diff - middle_diff;
379 max_diff = middle_diff;
383 } else if (fabs(min_diff) < 1e-20) {
386 } else if (fabs(max_diff) < 1e-20) {
389 } else if (min_diff > 0 && max_diff < 0) {
390 XBT_CWARN(surf_lagrange_dichotomy, "The impossible happened, partial_diff(min) > 0 && partial_diff(max) < 0");
393 XBT_CWARN(surf_lagrange_dichotomy,
394 "diffmin (%1.20f) or diffmax (%1.20f) are something I don't know, taking no action.",
400 XBT_CDEBUG(surf_lagrange_dichotomy, "returning %e", (min + max) / 2.0);
402 return ((min + max) / 2.0);
405 static double partial_diff_lambda(double lambda, void *param_cnst)
407 lmm_constraint_t cnst = static_cast<lmm_constraint_t>(param_cnst);
412 XBT_CDEBUG(surf_lagrange_dichotomy, "Computing diff of cnst (%p)", cnst);
414 xbt_swag_t elem_list = &(cnst->enabled_element_set);
416 xbt_swag_foreach(_elem, elem_list) {
417 lmm_element_t elem = static_cast<lmm_element_t>(_elem);
418 lmm_variable_t var = elem->variable;
419 xbt_assert(var->sharing_weight > 0);
420 XBT_CDEBUG(surf_lagrange_dichotomy, "Computing sigma_i for var (%p)", var);
421 // Initialize the summation variable
422 double sigma_i = 0.0;
425 for (s_lmm_element_t const& elem : var->cnsts) {
426 sigma_i += elem.constraint->lambda;
429 //add mu_i if this flow has a RTT constraint associated
433 //replace value of cnst->lambda by the value of parameter lambda
434 sigma_i = (sigma_i - cnst->lambda) + lambda;
436 diff += -var->func_fpi(var, sigma_i);
441 XBT_CDEBUG(surf_lagrange_dichotomy, "d D/d lambda for cnst (%p) at %1.20f = %1.20f", cnst, lambda, diff);
446 /** \brief Attribute the value bound to var->bound.
448 * \param func_fpi inverse of the partial differential of f (f prime inverse, (f')^{-1})
450 * Set default functions to the ones passed as parameters. This is a polymorphism in C pure, enjoy the roots of
454 void lmm_set_default_protocol_function(double (*func_f) (lmm_variable_t var, double x),
455 double (*func_fp) (lmm_variable_t var, double x),
456 double (*func_fpi) (lmm_variable_t var, double x))
459 func_fp_def = func_fp;
460 func_fpi_def = func_fpi;
463 /**************** Vegas and Reno functions *************************/
464 /* NOTE for Reno: all functions consider the network coefficient (alpha) equal to 1. */
467 * For Vegas: $f(x) = \alpha D_f\ln(x)$
468 * Therefore: $fp(x) = \frac{\alpha D_f}{x}$
469 * Therefore: $fpi(x) = \frac{\alpha D_f}{x}$
471 double func_vegas_f(lmm_variable_t var, double x)
473 xbt_assert(x > 0.0, "Don't call me with stupid values! (%1.20f)", x);
474 return VEGAS_SCALING * var->sharing_weight * log(x);
477 double func_vegas_fp(lmm_variable_t var, double x)
479 xbt_assert(x > 0.0, "Don't call me with stupid values! (%1.20f)", x);
480 return VEGAS_SCALING * var->sharing_weight / x;
483 double func_vegas_fpi(lmm_variable_t var, double x)
485 xbt_assert(x > 0.0, "Don't call me with stupid values! (%1.20f)", x);
486 return var->sharing_weight / (x / VEGAS_SCALING);
490 * For Reno: $f(x) = \frac{\sqrt{3/2}}{D_f} atan(\sqrt{3/2}D_f x)$
491 * Therefore: $fp(x) = \frac{3}{3 D_f^2 x^2+2}$
492 * Therefore: $fpi(x) = \sqrt{\frac{1}{{D_f}^2 x} - \frac{2}{3{D_f}^2}}$
494 double func_reno_f(lmm_variable_t var, double x)
496 xbt_assert(var->sharing_weight > 0.0, "Don't call me with stupid values!");
498 return RENO_SCALING * sqrt(3.0 / 2.0) / var->sharing_weight * atan(sqrt(3.0 / 2.0) * var->sharing_weight * x);
501 double func_reno_fp(lmm_variable_t var, double x)
503 return RENO_SCALING * 3.0 / (3.0 * var->sharing_weight * var->sharing_weight * x * x + 2.0);
506 double func_reno_fpi(lmm_variable_t var, double x)
510 xbt_assert(var->sharing_weight > 0.0, "Don't call me with stupid values!");
511 xbt_assert(x > 0.0, "Don't call me with stupid values!");
513 res_fpi = 1.0 / (var->sharing_weight * var->sharing_weight * (x / RENO_SCALING)) -
514 2.0 / (3.0 * var->sharing_weight * var->sharing_weight);
517 return sqrt(res_fpi);
520 /* Implementing new Reno-2
521 * For Reno-2: $f(x) = U_f(x_f) = \frac{{2}{D_f}}*ln(2+x*D_f)$
522 * Therefore: $fp(x) = 2/(Weight*x + 2)
523 * Therefore: $fpi(x) = (2*Weight)/x - 4
525 double func_reno2_f(lmm_variable_t var, double x)
527 xbt_assert(var->sharing_weight > 0.0, "Don't call me with stupid values!");
528 return RENO2_SCALING * (1.0 / var->sharing_weight) *
529 log((x * var->sharing_weight) / (2.0 * x * var->sharing_weight + 3.0));
532 double func_reno2_fp(lmm_variable_t var, double x)
534 return RENO2_SCALING * 3.0 / (var->sharing_weight * x * (2.0 * var->sharing_weight * x + 3.0));
537 double func_reno2_fpi(lmm_variable_t var, double x)
539 xbt_assert(x > 0.0, "Don't call me with stupid values!");
540 double tmp = x * var->sharing_weight * var->sharing_weight;
541 double res_fpi = tmp * (9.0 * x + 24.0);
546 res_fpi = RENO2_SCALING * (-3.0 * tmp + sqrt(res_fpi)) / (4.0 * tmp);