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->element_set);
58 xbt_swag_foreach(_elem, elem_list) {
59 elem = (lmm_element_t)_elem;
66 if (double_positive(tmp - cnst->bound, sg_maxmin_precision)) {
69 ("The link (%p) is over-used. Expected less than %f and got %f",
70 cnst, cnst->bound, tmp);
74 ("Checking feasability for constraint (%p): sat = %f, lambda = %f ",
75 cnst, tmp - cnst->bound, cnst->lambda);
78 xbt_swag_foreach(_var, var_list) {
79 var = (lmm_variable_t)_var;
84 XBT_DEBUG("Checking feasability for variable (%p): sat = %f mu = %f", var,
85 var->value - var->bound, var->mu);
87 if (double_positive(var->value - var->bound, sg_maxmin_precision)) {
90 ("The variable (%p) is too large. Expected less than %f and got %f",
91 var, var->bound, var->value);
98 static double new_value(lmm_variable_t var)
103 for (i = 0; i < var->cnsts_number; i++) {
104 tmp += (var->cnsts[i].constraint)->lambda;
108 XBT_DEBUG("\t Working on var (%p). cost = %e; Weight = %e", var, tmp,
110 //uses the partial differential inverse function
111 return var->func_fpi(var, tmp);
114 static double new_mu(lmm_variable_t var)
117 double sigma_i = 0.0;
120 for (j = 0; j < var->cnsts_number; j++) {
121 sigma_i += (var->cnsts[j].constraint)->lambda;
123 mu_i = var->func_fp(var, var->bound) - sigma_i;
129 static double dual_objective(xbt_swag_t var_list, xbt_swag_t cnst_list)
132 lmm_constraint_t cnst = NULL;
133 lmm_variable_t var = NULL;
137 xbt_swag_foreach(_var, var_list) {
138 var = (lmm_variable_t)_var;
139 double sigma_i = 0.0;
145 for (j = 0; j < var->cnsts_number; j++)
146 sigma_i += (var->cnsts[j].constraint)->lambda;
151 XBT_DEBUG("var %p : sigma_i = %1.20f", var, sigma_i);
153 obj += var->func_f(var, var->func_fpi(var, sigma_i)) -
154 sigma_i * var->func_fpi(var, sigma_i);
157 obj += var->mu * var->bound;
160 xbt_swag_foreach(_cnst, cnst_list) {
161 cnst = (lmm_constraint_t)_cnst;
162 obj += cnst->lambda * cnst->bound;
168 void lagrange_solve(lmm_system_t sys)
171 * Lagrange Variables.
173 int max_iterations = 100;
174 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 */
175 double dichotomy_min_error = 1e-14;
176 double overall_modification = 1;
179 * Variables to manipulate the data structure proposed to model the maxmin
180 * fairness. See docummentation for more details.
182 xbt_swag_t cnst_list = NULL;
184 lmm_constraint_t cnst = NULL;
186 xbt_swag_t var_list = NULL;
188 lmm_variable_t var = NULL;
191 * Auxiliary variables.
198 XBT_DEBUG("Iterative method configuration snapshot =====>");
199 XBT_DEBUG("#### Maximum number of iterations : %d", max_iterations);
200 XBT_DEBUG("#### Minimum error tolerated : %e",
202 XBT_DEBUG("#### Minimum error tolerated (dichotomy) : %e",
203 dichotomy_min_error);
205 if (XBT_LOG_ISENABLED(surf_lagrange, xbt_log_priority_debug)) {
209 if (!(sys->modified))
216 cnst_list = &(sys->active_constraint_set);
217 xbt_swag_foreach(_cnst, cnst_list) {
218 cnst = (lmm_constraint_t)_cnst;
220 cnst->new_lambda = 2.0;
221 XBT_DEBUG("#### cnst(%p)->lambda : %e", cnst, cnst->lambda);
225 * Initialize the var list variable with only the active variables.
226 * Associate an index in the swag variables. Initialize mu.
228 var_list = &(sys->variable_set);
230 xbt_swag_foreach(_var, var_list) {
231 var = (lmm_variable_t)_var;
236 if (var->bound < 0.0) {
237 XBT_DEBUG("#### NOTE var(%d) is a boundless variable", i);
239 var->value = new_value(var);
243 var->value = new_value(var);
245 XBT_DEBUG("#### var(%p) ->weight : %e", var, var->weight);
246 XBT_DEBUG("#### var(%p) ->mu : %e", var, var->mu);
247 XBT_DEBUG("#### var(%p) ->weight: %e", var, var->weight);
248 XBT_DEBUG("#### var(%p) ->bound: %e", var, var->bound);
249 for (i = 0; i < var->cnsts_number; i++) {
250 if (var->cnsts[i].value == 0.0)
253 if (nb == var->cnsts_number)
259 * Compute dual objective.
261 obj = dual_objective(var_list, cnst_list);
264 * While doesn't reach a minimun error or a number maximum of iterations.
266 while (overall_modification > epsilon_min_error
267 && iteration < max_iterations) {
268 /* int dual_updated=0; */
271 XBT_DEBUG("************** ITERATION %d **************", iteration);
272 XBT_DEBUG("-------------- Gradient Descent ----------");
275 * Improve the value of mu_i
277 xbt_swag_foreach(_var, var_list) {
278 var = (lmm_variable_t)_var;
281 if (var->bound >= 0) {
282 XBT_DEBUG("Working on var (%p)", var);
283 var->new_mu = new_mu(var);
284 /* dual_updated += (fabs(var->new_mu-var->mu)>dichotomy_min_error); */
285 /* XBT_DEBUG("dual_updated (%d) : %1.20f",dual_updated,fabs(var->new_mu-var->mu)); */
286 XBT_DEBUG("Updating mu : var->mu (%p) : %1.20f -> %1.20f", var,
287 var->mu, var->new_mu);
288 var->mu = var->new_mu;
290 new_obj = dual_objective(var_list, cnst_list);
291 XBT_DEBUG("Improvement for Objective (%g -> %g) : %g", obj, new_obj,
293 xbt_assert(obj - new_obj >= -epsilon_min_error,
294 "Our gradient sucks! (%1.20f)", obj - new_obj);
300 * Improve the value of lambda_i
302 xbt_swag_foreach(_cnst, cnst_list) {
303 cnst = (lmm_constraint_t)_cnst;
304 XBT_DEBUG("Working on cnst (%p)", cnst);
306 dichotomy(cnst->lambda, partial_diff_lambda, cnst,
307 dichotomy_min_error);
308 /* dual_updated += (fabs(cnst->new_lambda-cnst->lambda)>dichotomy_min_error); */
309 /* XBT_DEBUG("dual_updated (%d) : %1.20f",dual_updated,fabs(cnst->new_lambda-cnst->lambda)); */
310 XBT_DEBUG("Updating lambda : cnst->lambda (%p) : %1.20f -> %1.20f",
311 cnst, cnst->lambda, cnst->new_lambda);
312 cnst->lambda = cnst->new_lambda;
314 new_obj = dual_objective(var_list, cnst_list);
315 XBT_DEBUG("Improvement for Objective (%g -> %g) : %g", obj, new_obj,
317 xbt_assert(obj - new_obj >= -epsilon_min_error,
318 "Our gradient sucks! (%1.20f)", obj - new_obj);
323 * Now computes the values of each variable (\rho) based on
324 * the values of \lambda and \mu.
326 XBT_DEBUG("-------------- Check convergence ----------");
327 overall_modification = 0;
328 xbt_swag_foreach(_var, var_list) {
329 var = (lmm_variable_t)_var;
330 if (var->weight <= 0)
333 tmp = new_value(var);
335 overall_modification =
336 MAX(overall_modification, fabs(var->value - tmp));
339 XBT_DEBUG("New value of var (%p) = %e, overall_modification = %e",
340 var, var->value, overall_modification);
344 XBT_DEBUG("-------------- Check feasability ----------");
345 if (!__check_feasible(cnst_list, var_list, 0))
346 overall_modification = 1.0;
347 XBT_DEBUG("Iteration %d: overall_modification : %f", iteration,
348 overall_modification);
349 /* if(!dual_updated) { */
350 /* XBT_WARN("Could not improve the convergence at iteration %d. Drop it!",iteration); */
355 __check_feasible(cnst_list, var_list, 1);
357 if (overall_modification <= epsilon_min_error) {
358 XBT_DEBUG("The method converges in %d iterations.", iteration);
360 if (iteration >= max_iterations) {
362 ("Method reach %d iterations, which is the maximum number of iterations allowed.",
365 /* XBT_INFO("Method converged after %d iterations", iteration); */
367 if (XBT_LOG_ISENABLED(surf_lagrange, xbt_log_priority_debug)) {
373 * Returns a double value corresponding to the result of a dichotomy proccess with
374 * respect to a given variable/constraint (\mu in the case of a variable or \lambda in
375 * case of a constraint) and a initial value init.
377 * @param init initial value for \mu or \lambda
378 * @param diff a function that computes the differential of with respect a \mu or \lambda
379 * @param var_cnst a pointer to a variable or constraint
380 * @param min_erro a minimun error tolerated
382 * @return a double correponding to the result of the dichotomyal process
384 static double dichotomy(double init, double diff(double, void *),
385 void *var_cnst, double min_error)
388 double overall_error;
390 double min_diff, max_diff, middle_diff;
402 if ((diff_0 = diff(1e-16, var_cnst)) >= 0) {
403 XBT_CDEBUG(surf_lagrange_dichotomy, "returning 0.0 (diff = %e)", diff_0);
408 min_diff = diff(min, var_cnst);
409 max_diff = diff(max, var_cnst);
411 while (overall_error > min_error) {
412 XBT_CDEBUG(surf_lagrange_dichotomy,
413 "[min, max] = [%1.20f, %1.20f] || diffmin, diffmax = %1.20f, %1.20f",
414 min, max, min_diff, max_diff);
416 if (min_diff > 0 && max_diff > 0) {
418 XBT_CDEBUG(surf_lagrange_dichotomy, "Decreasing min");
420 min_diff = diff(min, var_cnst);
422 XBT_CDEBUG(surf_lagrange_dichotomy, "Decreasing max");
426 } else if (min_diff < 0 && max_diff < 0) {
428 XBT_CDEBUG(surf_lagrange_dichotomy, "Increasing max");
430 max_diff = diff(max, var_cnst);
432 XBT_CDEBUG(surf_lagrange_dichotomy, "Increasing min");
436 } else if (min_diff < 0 && max_diff > 0) {
437 middle = (max + min) / 2.0;
438 XBT_CDEBUG(surf_lagrange_dichotomy, "Trying (max+min)/2 : %1.20f",
441 if ((min == middle) || (max == middle)) {
442 XBT_CWARN(surf_lagrange_dichotomy,
443 "Cannot improve the convergence! min=max=middle=%1.20f, diff = %1.20f."
444 " Reaching the 'double' limits. Maybe scaling your function would help ([%1.20f,%1.20f]).",
445 min, max - min, min_diff, max_diff);
448 middle_diff = diff(middle, var_cnst);
450 if (middle_diff < 0) {
451 XBT_CDEBUG(surf_lagrange_dichotomy, "Increasing min");
453 overall_error = max_diff - middle_diff;
454 min_diff = middle_diff;
455 /* SHOW_EXPR(overall_error); */
456 } else if (middle_diff > 0) {
457 XBT_CDEBUG(surf_lagrange_dichotomy, "Decreasing max");
459 overall_error = max_diff - middle_diff;
460 max_diff = middle_diff;
461 /* SHOW_EXPR(overall_error); */
464 /* SHOW_EXPR(overall_error); */
466 } else if (min_diff == 0) {
469 /* SHOW_EXPR(overall_error); */
470 } else if (max_diff == 0) {
473 /* SHOW_EXPR(overall_error); */
474 } else if (min_diff > 0 && max_diff < 0) {
475 XBT_CWARN(surf_lagrange_dichotomy,
476 "The impossible happened, partial_diff(min) > 0 && partial_diff(max) < 0");
479 XBT_CWARN(surf_lagrange_dichotomy,
480 "diffmin (%1.20f) or diffmax (%1.20f) are something I don't know, taking no action.",
486 XBT_CDEBUG(surf_lagrange_dichotomy, "returning %e", (min + max) / 2.0);
488 return ((min + max) / 2.0);
491 static double partial_diff_lambda(double lambda, void *param_cnst)
496 xbt_swag_t elem_list = NULL;
497 lmm_element_t elem = NULL;
498 lmm_variable_t var = NULL;
499 lmm_constraint_t cnst = (lmm_constraint_t) param_cnst;
501 double sigma_i = 0.0;
504 elem_list = &(cnst->element_set);
506 XBT_CDEBUG(surf_lagrange_dichotomy, "Computing diff of cnst (%p)", cnst);
508 xbt_swag_foreach(_elem, elem_list) {
509 elem = (lmm_element_t)_elem;
510 var = elem->variable;
511 if (var->weight <= 0)
514 XBT_CDEBUG(surf_lagrange_dichotomy, "Computing sigma_i for var (%p)",
516 // Initialize the summation variable
520 for (j = 0; j < var->cnsts_number; j++) {
521 sigma_i += (var->cnsts[j].constraint)->lambda;
524 //add mu_i if this flow has a RTT constraint associated
528 //replace value of cnst->lambda by the value of parameter lambda
529 sigma_i = (sigma_i - cnst->lambda) + lambda;
531 diff += -var->func_fpi(var, sigma_i);
537 XBT_CDEBUG(surf_lagrange_dichotomy,
538 "d D/d lambda for cnst (%p) at %1.20f = %1.20f", cnst, lambda,
544 /** \brief Attribute the value bound to var->bound.
546 * \param func_fpi inverse of the partial differential of f (f prime inverse, (f')^{-1})
548 * Set default functions to the ones passed as parameters. This is a polimorfism in C pure, enjoy the roots of programming.
551 void lmm_set_default_protocol_function(double (*func_f)
558 (lmm_variable_t var, double x),
559 double (*func_fp) (lmm_variable_t
561 double (*func_fpi) (lmm_variable_t
565 func_fp_def = func_fp;
566 func_fpi_def = func_fpi;
570 /**************** Vegas and Reno functions *************************/
572 * NOTE for Reno: all functions consider the network
573 * coeficient (alpha) equal to 1.
577 * For Vegas: $f(x) = \alpha D_f\ln(x)$
578 * Therefore: $fp(x) = \frac{\alpha D_f}{x}$
579 * Therefore: $fpi(x) = \frac{\alpha D_f}{x}$
581 #define VEGAS_SCALING 1000.0
583 double func_vegas_f(lmm_variable_t var, double x)
585 xbt_assert(x > 0.0, "Don't call me with stupid values! (%1.20f)", x);
586 return VEGAS_SCALING * var->weight * log(x);
589 double func_vegas_fp(lmm_variable_t var, double x)
591 xbt_assert(x > 0.0, "Don't call me with stupid values! (%1.20f)", x);
592 return VEGAS_SCALING * var->weight / x;
595 double func_vegas_fpi(lmm_variable_t var, double x)
597 xbt_assert(x > 0.0, "Don't call me with stupid values! (%1.20f)", x);
598 return var->weight / (x / VEGAS_SCALING);
602 * For Reno: $f(x) = \frac{\sqrt{3/2}}{D_f} atan(\sqrt{3/2}D_f x)$
603 * Therefore: $fp(x) = \frac{3}{3 D_f^2 x^2+2}$
604 * Therefore: $fpi(x) = \sqrt{\frac{1}{{D_f}^2 x} - \frac{2}{3{D_f}^2}}$
606 #define RENO_SCALING 1.0
607 double func_reno_f(lmm_variable_t var, double x)
609 xbt_assert(var->weight > 0.0, "Don't call me with stupid values!");
611 return RENO_SCALING * sqrt(3.0 / 2.0) / var->weight *
612 atan(sqrt(3.0 / 2.0) * var->weight * x);
615 double func_reno_fp(lmm_variable_t var, double x)
617 return RENO_SCALING * 3.0 / (3.0 * var->weight * var->weight * x * x +
621 double func_reno_fpi(lmm_variable_t var, double x)
625 xbt_assert(var->weight > 0.0, "Don't call me with stupid values!");
626 xbt_assert(x > 0.0, "Don't call me with stupid values!");
629 1.0 / (var->weight * var->weight * (x / RENO_SCALING)) -
630 2.0 / (3.0 * var->weight * var->weight);
633 /* xbt_assert(res_fpi>0.0,"Don't call me with stupid values!"); */
634 return sqrt(res_fpi);
638 /* Implementing new Reno-2
639 * For Reno-2: $f(x) = U_f(x_f) = \frac{{2}{D_f}}*ln(2+x*D_f)$
640 * Therefore: $fp(x) = 2/(Weight*x + 2)
641 * Therefore: $fpi(x) = (2*Weight)/x - 4
643 #define RENO2_SCALING 1.0
644 double func_reno2_f(lmm_variable_t var, double x)
646 xbt_assert(var->weight > 0.0, "Don't call me with stupid values!");
647 return RENO2_SCALING * (1.0 / var->weight) * log((x * var->weight) /
648 (2.0 * x * var->weight +
652 double func_reno2_fp(lmm_variable_t var, double x)
654 return RENO2_SCALING * 3.0 / (var->weight * x *
655 (2.0 * var->weight * x + 3.0));
658 double func_reno2_fpi(lmm_variable_t var, double x)
663 xbt_assert(x > 0.0, "Don't call me with stupid values!");
664 tmp = x * var->weight * var->weight;
665 res_fpi = tmp * (9.0 * x + 24.0);
670 res_fpi = RENO2_SCALING * (-3.0 * tmp + sqrt(res_fpi)) / (4.0 * tmp);