1 /* Copyright (c) 2007, 2008, 2009, 2010. 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.h"
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 variable param_var applied to mu
41 static double partial_diff_mu(double mu, void *param_var);
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,
48 xbt_swag_t elem_list = NULL;
49 lmm_element_t elem = NULL;
50 lmm_constraint_t cnst = NULL;
51 lmm_variable_t var = NULL;
55 xbt_swag_foreach(cnst, cnst_list) {
57 elem_list = &(cnst->element_set);
58 xbt_swag_foreach(elem, elem_list) {
65 if (double_positive(tmp - cnst->bound)) {
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) {
82 XBT_DEBUG("Checking feasability for variable (%p): sat = %f mu = %f", var,
83 var->value - var->bound, var->mu);
85 if (double_positive(var->value - var->bound)) {
88 ("The variable (%p) is too large. Expected less than %f and got %f",
89 var, var->bound, var->value);
96 static double new_value(lmm_variable_t var)
101 for (i = 0; i < var->cnsts_number; i++) {
102 tmp += (var->cnsts[i].constraint)->lambda;
106 XBT_DEBUG("\t Working on var (%p). cost = %e; Weight = %e", var, tmp,
108 //uses the partial differential inverse function
109 return var->func_fpi(var, tmp);
112 static double new_mu(lmm_variable_t var)
115 double sigma_i = 0.0;
118 for (j = 0; j < var->cnsts_number; j++) {
119 sigma_i += (var->cnsts[j].constraint)->lambda;
121 mu_i = var->func_fp(var, var->bound) - sigma_i;
127 static double dual_objective(xbt_swag_t var_list, xbt_swag_t cnst_list)
129 lmm_constraint_t cnst = NULL;
130 lmm_variable_t var = NULL;
134 xbt_swag_foreach(var, var_list) {
135 double sigma_i = 0.0;
141 for (j = 0; j < var->cnsts_number; j++)
142 sigma_i += (var->cnsts[j].constraint)->lambda;
147 XBT_DEBUG("var %p : sigma_i = %1.20f", var, sigma_i);
149 obj += var->func_f(var, var->func_fpi(var, sigma_i)) -
150 sigma_i * var->func_fpi(var, sigma_i);
153 obj += var->mu * var->bound;
156 xbt_swag_foreach(cnst, cnst_list)
157 obj += cnst->lambda * cnst->bound;
162 void lagrange_solve(lmm_system_t sys)
165 * Lagrange Variables.
167 int max_iterations = 100;
168 double epsilon_min_error = MAXMIN_PRECISION;
169 double dichotomy_min_error = 1e-14;
170 double overall_modification = 1;
173 * Variables to manipulate the data structure proposed to model the maxmin
174 * fairness. See docummentation for more details.
176 xbt_swag_t cnst_list = NULL;
177 lmm_constraint_t cnst = NULL;
179 xbt_swag_t var_list = NULL;
180 lmm_variable_t var = NULL;
183 * Auxiliar variables.
190 XBT_DEBUG("Iterative method configuration snapshot =====>");
191 XBT_DEBUG("#### Maximum number of iterations : %d", max_iterations);
192 XBT_DEBUG("#### Minimum error tolerated : %e",
194 XBT_DEBUG("#### Minimum error tolerated (dichotomy) : %e",
195 dichotomy_min_error);
197 if (XBT_LOG_ISENABLED(surf_lagrange, xbt_log_priority_debug)) {
201 if (!(sys->modified))
208 cnst_list = &(sys->active_constraint_set);
209 xbt_swag_foreach(cnst, cnst_list) {
211 cnst->new_lambda = 2.0;
212 XBT_DEBUG("#### cnst(%p)->lambda : %e", cnst, cnst->lambda);
216 * Initialize the var list variable with only the active variables.
217 * Associate an index in the swag variables. Initialize mu.
219 var_list = &(sys->variable_set);
221 xbt_swag_foreach(var, var_list) {
226 if (var->bound < 0.0) {
227 XBT_DEBUG("#### NOTE var(%d) is a boundless variable", i);
229 var->value = new_value(var);
233 var->value = new_value(var);
235 XBT_DEBUG("#### var(%p) ->weight : %e", var, var->weight);
236 XBT_DEBUG("#### var(%p) ->mu : %e", var, var->mu);
237 XBT_DEBUG("#### var(%p) ->weight: %e", var, var->weight);
238 XBT_DEBUG("#### var(%p) ->bound: %e", var, var->bound);
239 for (i = 0; i < var->cnsts_number; i++) {
240 if (var->cnsts[i].value == 0.0)
243 if (nb == var->cnsts_number)
249 * Compute dual objective.
251 obj = dual_objective(var_list, cnst_list);
254 * While doesn't reach a minimun error or a number maximum of iterations.
256 while (overall_modification > epsilon_min_error
257 && iteration < max_iterations) {
258 /* int dual_updated=0; */
261 XBT_DEBUG("************** ITERATION %d **************", iteration);
262 XBT_DEBUG("-------------- Gradient Descent ----------");
265 * Improve the value of mu_i
267 xbt_swag_foreach(var, var_list) {
270 if (var->bound >= 0) {
271 XBT_DEBUG("Working on var (%p)", var);
272 var->new_mu = new_mu(var);
273 /* dual_updated += (fabs(var->new_mu-var->mu)>dichotomy_min_error); */
274 /* XBT_DEBUG("dual_updated (%d) : %1.20f",dual_updated,fabs(var->new_mu-var->mu)); */
275 XBT_DEBUG("Updating mu : var->mu (%p) : %1.20f -> %1.20f", var,
276 var->mu, var->new_mu);
277 var->mu = var->new_mu;
279 new_obj = dual_objective(var_list, cnst_list);
280 XBT_DEBUG("Improvement for Objective (%g -> %g) : %g", obj, new_obj,
282 xbt_assert(obj - new_obj >= -epsilon_min_error,
283 "Our gradient sucks! (%1.20f)", obj - new_obj);
289 * Improve the value of lambda_i
291 xbt_swag_foreach(cnst, cnst_list) {
292 XBT_DEBUG("Working on cnst (%p)", cnst);
294 dichotomy(cnst->lambda, partial_diff_lambda, cnst,
295 dichotomy_min_error);
296 /* dual_updated += (fabs(cnst->new_lambda-cnst->lambda)>dichotomy_min_error); */
297 /* XBT_DEBUG("dual_updated (%d) : %1.20f",dual_updated,fabs(cnst->new_lambda-cnst->lambda)); */
298 XBT_DEBUG("Updating lambda : cnst->lambda (%p) : %1.20f -> %1.20f",
299 cnst, cnst->lambda, cnst->new_lambda);
300 cnst->lambda = cnst->new_lambda;
302 new_obj = dual_objective(var_list, cnst_list);
303 XBT_DEBUG("Improvement for Objective (%g -> %g) : %g", obj, new_obj,
305 xbt_assert(obj - new_obj >= -epsilon_min_error,
306 "Our gradient sucks! (%1.20f)", obj - new_obj);
311 * Now computes the values of each variable (\rho) based on
312 * the values of \lambda and \mu.
314 XBT_DEBUG("-------------- Check convergence ----------");
315 overall_modification = 0;
316 xbt_swag_foreach(var, var_list) {
317 if (var->weight <= 0)
320 tmp = new_value(var);
322 overall_modification =
323 MAX(overall_modification, fabs(var->value - tmp));
326 XBT_DEBUG("New value of var (%p) = %e, overall_modification = %e",
327 var, var->value, overall_modification);
331 XBT_DEBUG("-------------- Check feasability ----------");
332 if (!__check_feasible(cnst_list, var_list, 0))
333 overall_modification = 1.0;
334 XBT_DEBUG("Iteration %d: overall_modification : %f", iteration,
335 overall_modification);
336 /* if(!dual_updated) { */
337 /* XBT_WARN("Could not improve the convergence at iteration %d. Drop it!",iteration); */
342 __check_feasible(cnst_list, var_list, 1);
344 if (overall_modification <= epsilon_min_error) {
345 XBT_DEBUG("The method converges in %d iterations.", iteration);
347 if (iteration >= max_iterations) {
349 ("Method reach %d iterations, which is the maximum number of iterations allowed.",
352 /* XBT_INFO("Method converged after %d iterations", iteration); */
354 if (XBT_LOG_ISENABLED(surf_lagrange, xbt_log_priority_debug)) {
360 * Returns a double value corresponding to the result of a dichotomy proccess with
361 * respect to a given variable/constraint (\mu in the case of a variable or \lambda in
362 * case of a constraint) and a initial value init.
364 * @param init initial value for \mu or \lambda
365 * @param diff a function that computes the differential of with respect a \mu or \lambda
366 * @param var_cnst a pointer to a variable or constraint
367 * @param min_erro a minimun error tolerated
369 * @return a double correponding to the result of the dichotomyal process
371 static double dichotomy(double init, double diff(double, void *),
372 void *var_cnst, double min_error)
375 double overall_error;
377 double min_diff, max_diff, middle_diff;
387 min_diff = max_diff = middle_diff = 0.0;
390 if ((diff_0 = diff(1e-16, var_cnst)) >= 0) {
391 XBT_CDEBUG(surf_lagrange_dichotomy, "returning 0.0 (diff = %e)", diff_0);
396 min_diff = diff(min, var_cnst);
397 max_diff = diff(max, var_cnst);
399 while (overall_error > min_error) {
400 XBT_CDEBUG(surf_lagrange_dichotomy,
401 "[min, max] = [%1.20f, %1.20f] || diffmin, diffmax = %1.20f, %1.20f",
402 min, max, min_diff, max_diff);
404 if (min_diff > 0 && max_diff > 0) {
406 XBT_CDEBUG(surf_lagrange_dichotomy, "Decreasing min");
408 min_diff = diff(min, var_cnst);
410 XBT_CDEBUG(surf_lagrange_dichotomy, "Decreasing max");
414 } else if (min_diff < 0 && max_diff < 0) {
416 XBT_CDEBUG(surf_lagrange_dichotomy, "Increasing max");
418 max_diff = diff(max, var_cnst);
420 XBT_CDEBUG(surf_lagrange_dichotomy, "Increasing min");
424 } else if (min_diff < 0 && max_diff > 0) {
425 middle = (max + min) / 2.0;
426 XBT_CDEBUG(surf_lagrange_dichotomy, "Trying (max+min)/2 : %1.20f",
429 if ((min == middle) || (max == middle)) {
430 XBT_CWARN(surf_lagrange_dichotomy,
431 "Cannot improve the convergence! min=max=middle=%1.20f, diff = %1.20f."
432 " Reaching the 'double' limits. Maybe scaling your function would help ([%1.20f,%1.20f]).",
433 min, max - min, min_diff, max_diff);
436 middle_diff = diff(middle, var_cnst);
438 if (middle_diff < 0) {
439 XBT_CDEBUG(surf_lagrange_dichotomy, "Increasing min");
441 overall_error = max_diff - middle_diff;
442 min_diff = middle_diff;
443 /* SHOW_EXPR(overall_error); */
444 } else if (middle_diff > 0) {
445 XBT_CDEBUG(surf_lagrange_dichotomy, "Decreasing max");
447 overall_error = max_diff - middle_diff;
448 max_diff = middle_diff;
449 /* SHOW_EXPR(overall_error); */
452 /* SHOW_EXPR(overall_error); */
454 } else if (min_diff == 0) {
457 /* SHOW_EXPR(overall_error); */
458 } else if (max_diff == 0) {
461 /* SHOW_EXPR(overall_error); */
462 } else if (min_diff > 0 && max_diff < 0) {
463 XBT_CWARN(surf_lagrange_dichotomy,
464 "The impossible happened, partial_diff(min) > 0 && partial_diff(max) < 0");
467 XBT_CWARN(surf_lagrange_dichotomy,
468 "diffmin (%1.20f) or diffmax (%1.20f) are something I don't know, taking no action.",
474 XBT_CDEBUG(surf_lagrange_dichotomy, "returning %e", (min + max) / 2.0);
476 return ((min + max) / 2.0);
479 static double partial_diff_lambda(double lambda, void *param_cnst)
483 xbt_swag_t elem_list = NULL;
484 lmm_element_t elem = NULL;
485 lmm_variable_t var = NULL;
486 lmm_constraint_t cnst = (lmm_constraint_t) param_cnst;
488 double sigma_i = 0.0;
491 elem_list = &(cnst->element_set);
493 XBT_CDEBUG(surf_lagrange_dichotomy, "Computing diff of cnst (%p)", cnst);
495 xbt_swag_foreach(elem, elem_list) {
496 var = elem->variable;
497 if (var->weight <= 0)
500 XBT_CDEBUG(surf_lagrange_dichotomy, "Computing sigma_i for var (%p)",
502 // Initialize the summation variable
506 for (j = 0; j < var->cnsts_number; j++) {
507 sigma_i += (var->cnsts[j].constraint)->lambda;
510 //add mu_i if this flow has a RTT constraint associated
514 //replace value of cnst->lambda by the value of parameter lambda
515 sigma_i = (sigma_i - cnst->lambda) + lambda;
517 diff += -var->func_fpi(var, sigma_i);
523 XBT_CDEBUG(surf_lagrange_dichotomy,
524 "d D/d lambda for cnst (%p) at %1.20f = %1.20f", cnst, lambda,
530 /** \brief Attribute the value bound to var->bound.
532 * \param func_fpi inverse of the partial differential of f (f prime inverse, (f')^{-1})
534 * Set default functions to the ones passed as parameters. This is a polimorfism in C pure, enjoy the roots of programming.
537 void lmm_set_default_protocol_function(double (*func_f)
544 (lmm_variable_t var, double x),
545 double (*func_fp) (lmm_variable_t
547 double (*func_fpi) (lmm_variable_t
551 func_fp_def = func_fp;
552 func_fpi_def = func_fpi;
556 /**************** Vegas and Reno functions *************************/
558 * NOTE for Reno: all functions consider the network
559 * coeficient (alpha) equal to 1.
563 * For Vegas: $f(x) = \alpha D_f\ln(x)$
564 * Therefore: $fp(x) = \frac{\alpha D_f}{x}$
565 * Therefore: $fpi(x) = \frac{\alpha D_f}{x}$
567 #define VEGAS_SCALING 1000.0
569 double func_vegas_f(lmm_variable_t var, double x)
571 xbt_assert(x > 0.0, "Don't call me with stupid values! (%1.20f)", x);
572 return VEGAS_SCALING * var->weight * log(x);
575 double func_vegas_fp(lmm_variable_t var, double x)
577 xbt_assert(x > 0.0, "Don't call me with stupid values! (%1.20f)", x);
578 return VEGAS_SCALING * var->weight / x;
581 double func_vegas_fpi(lmm_variable_t var, double x)
583 xbt_assert(x > 0.0, "Don't call me with stupid values! (%1.20f)", x);
584 return var->weight / (x / VEGAS_SCALING);
588 * For Reno: $f(x) = \frac{\sqrt{3/2}}{D_f} atan(\sqrt{3/2}D_f x)$
589 * Therefore: $fp(x) = \frac{3}{3 D_f^2 x^2+2}$
590 * Therefore: $fpi(x) = \sqrt{\frac{1}{{D_f}^2 x} - \frac{2}{3{D_f}^2}}$
592 #define RENO_SCALING 1.0
593 double func_reno_f(lmm_variable_t var, double x)
595 xbt_assert(var->weight > 0.0, "Don't call me with stupid values!");
597 return RENO_SCALING * sqrt(3.0 / 2.0) / var->weight *
598 atan(sqrt(3.0 / 2.0) * var->weight * x);
601 double func_reno_fp(lmm_variable_t var, double x)
603 return RENO_SCALING * 3.0 / (3.0 * var->weight * var->weight * x * x +
607 double func_reno_fpi(lmm_variable_t var, double x)
611 xbt_assert(var->weight > 0.0, "Don't call me with stupid values!");
612 xbt_assert(x > 0.0, "Don't call me with stupid values!");
615 1.0 / (var->weight * var->weight * (x / RENO_SCALING)) -
616 2.0 / (3.0 * var->weight * var->weight);
619 /* xbt_assert(res_fpi>0.0,"Don't call me with stupid values!"); */
620 return sqrt(res_fpi);
624 /* Implementing new Reno-2
625 * For Reno-2: $f(x) = U_f(x_f) = \frac{{2}{D_f}}*ln(2+x*D_f)$
626 * Therefore: $fp(x) = 2/(Weight*x + 2)
627 * Therefore: $fpi(x) = (2*Weight)/x - 4
629 #define RENO2_SCALING 1.0
630 double func_reno2_f(lmm_variable_t var, double x)
632 xbt_assert(var->weight > 0.0, "Don't call me with stupid values!");
633 return RENO2_SCALING * (1.0 / var->weight) * log((x * var->weight) /
634 (2.0 * x * var->weight +
638 double func_reno2_fp(lmm_variable_t var, double x)
640 return RENO2_SCALING * 3.0 / (var->weight * x *
641 (2.0 * var->weight * x + 3.0));
644 double func_reno2_fpi(lmm_variable_t var, double x)
649 xbt_assert(x > 0.0, "Don't call me with stupid values!");
650 tmp = x * var->weight * var->weight;
651 res_fpi = tmp * (9.0 * x + 24.0);
656 res_fpi = RENO2_SCALING * (-3.0 * tmp + sqrt(res_fpi)) / (4.0 * tmp);