3 /* Copyright (c) 2007 Arnaud Legrand, Pedro Velho. All rights reserved. */
5 /* This program is free software; you can redistribute it and/or modify it
6 * under the terms of the license (GNU LGPL) which comes with this package. */
10 #include "xbt/sysdep.h"
11 #include "xbt/mallocator.h"
12 #include "maxmin_private.h"
20 * SDP specific variables.
22 #include <declarations.h>
25 static void create_cross_link(struct constraintmatrix *myconstraints, int k);
27 static void addentry(struct constraintmatrix *constraints,
28 struct blockmatrix *, int matno, int blkno, int indexi, int indexj, double ent, int blocksize);
31 XBT_LOG_NEW_DEFAULT_SUBCATEGORY(surf_sdp, surf,
32 "Logging specific to SURF (sdp)");
33 XBT_LOG_NEW_SUBCATEGORY(surf_sdp_out, surf,
34 "Logging specific to SURF (sdp)");
36 ########################################################################
37 ######################## Simple Proportionnal fairness #################
38 ########################################################################
39 ####### Original problem ##########
48 # We assume in the following that n=2^K
50 ####### Standard SDP form #########
52 # A SDP can be written in the following standard form:
54 # (P) min c1*x1+c2*x2+...+cm*xm
55 # st F1*x1+F2*x2+...+Fm*xm-F0=X
58 # Where F1, F2, ..., Fm are symetric matrixes of size n by n. The
59 # constraint X>0 means that X must be positive semidefinite positive.
61 ########## Equivalent SDP #########
65 # y(k,i) for k in [0,K] and i in [1,2^k]
70 # y(2,1) y(2,2) y(2,3) y(2,4)
71 # y(3,1) y(3,2) y(3,3) y(3,4) y(3,5) y(3,6) y(3,7) y(3,8)
72 # -------------------------------------------------------
73 # x_1 x_2 x_3 x_4 x_5 x_6 x_7 x_8
76 # Structure Constraints:
78 # forall k in [0,K-1], and i in [1,2^k]
79 # [ y(k, 2i-1) y(k-1, i) ]
80 # [ y(k-1, i ) y(k, 2i) ]
84 # Capacity Constraints:
86 # -(A.y(K,*))_l >= - b_l
88 # Positivity Constraints:
89 # forall k in [0,K], and i in [1,2^k]
95 //typedef struct lmm_system {
97 // s_xbt_swag_t variable_set; /* a list of lmm_variable_t */
98 // s_xbt_swag_t constraint_set; /* a list of lmm_constraint_t */
99 // s_xbt_swag_t active_constraint_set; /* a list of lmm_constraint_t */
100 // s_xbt_swag_t saturated_variable_set; /* a list of lmm_variable_t */
101 // s_xbt_swag_t saturated_constraint_set; /* a list of lmm_constraint_t_t */
102 // xbt_mallocator_t variable_mallocator;
105 #define get_y(a,b) (pow(2,a)+b-1)
107 void sdp_solve(lmm_system_t sys)
109 lmm_variable_t var = NULL;
112 * SDP mapping variables.
119 int nb_cnsts_capacity=0;
120 int nb_cnsts_struct=0;
121 int nb_cnsts_positivy=0;
124 int total_block_size=0;
126 // FILE *sdpout = fopen("SDPA-printf.tmp","w");
128 double *tempdiag = NULL;
135 * CSDP library specific variables.
137 struct blockmatrix C;
138 struct blockmatrix X,Z;
142 struct constraintmatrix *constraints;
145 * Classic maxmin variables.
147 lmm_constraint_t cnst = NULL;
148 lmm_element_t elem = NULL;
149 xbt_swag_t cnst_list = NULL;
150 xbt_swag_t var_list = NULL;
151 xbt_swag_t elem_list = NULL;
154 struct sparseblock *p;
160 if ( !(sys->modified))
164 * Initialize the var list variable with only the active variables.
165 * Associate an index in the swag variables.
167 var_list = &(sys->variable_set);
169 xbt_swag_foreach(var, var_list) {
173 DEBUG1("Variable set : %d", xbt_swag_size(var_list));
174 xbt_swag_foreach(var, var_list) {
176 if(var->weight) var->index = i--;
179 cnst_list=&(sys->active_constraint_set);
180 DEBUG1("Active constraints : %d", xbt_swag_size(cnst_list));
183 * Those fields are the top level description of the platform furnished in the xml file.
185 links = xbt_swag_size(&(sys->active_constraint_set));
188 * This number is found based on the tree structure explained on top.
190 tmp_k = (double) log((double)flows)/log(2.0);
191 K = (int) ceil(tmp_k);
195 * The number of variables in the SDP program.
197 nb_var = get_y(K, pow(2,K));
198 DEBUG1("Number of variables in the SDP program : %d", nb_var);
202 * Find the size of each group of constraints.
204 nb_cnsts_capacity = links + ((int)pow(2,K)) - flows;
205 nb_cnsts_struct = (int)pow(2,K) - 1;
206 nb_cnsts_positivy = (int)pow(2,K);
209 * The total number of constraints.
211 nb_cnsts = nb_cnsts_capacity + nb_cnsts_struct + nb_cnsts_positivy;
212 CDEBUG1(surf_sdp_out,"Number of constraints = %d", nb_cnsts);
215 * Keep track of which blocks have off diagonal entries.
217 isdiag=(int *)calloc((nb_cnsts+1), sizeof(int));
218 for (i=1; i<=nb_cnsts; i++)
221 C.nblocks = nb_cnsts;
222 C.blocks = (struct blockrec *) calloc((C.nblocks+1),sizeof(struct blockrec));
223 constraints = (struct constraintmatrix *)calloc((nb_var+1),sizeof(struct constraintmatrix));
225 for(i = 1; i <= nb_var; i++){
226 constraints[i].blocks=NULL;
229 a = (double *)calloc(nb_var+1, sizeof(double));
238 * For each constraint block do.
240 for(i = 1; i <= nb_cnsts; i++){
243 * Structured blocks are size 2 and all others are size 1.
245 if(i <= nb_cnsts_struct){
246 total_block_size += block_size = 2;
249 total_block_size += block_size = 1;
250 CDEBUG0(surf_sdp_out,"1 ");
254 * All blocks are matrices.
256 C.blocks[block_num].blockcategory = MATRIX;
257 C.blocks[block_num].blocksize = block_size;
258 C.blocks[block_num].data.mat = (double *)calloc(block_size * block_size, sizeof(double));
263 CDEBUG0(surf_sdp_out," ");
267 * Creates de objective function array.
269 a = (double *)calloc((nb_var+1), sizeof(double));
271 for(i = 1; i <= nb_var; i++){
273 CDEBUG0(surf_sdp_out,"-1 ");
276 CDEBUG0(surf_sdp_out,"0 ");
280 CDEBUG0(surf_sdp_out,"\n");
284 * Structure contraint blocks.
288 for(k = 1; k <= K; k++){
289 for(i = 1; i <= pow(2,k-1); i++){
290 matno=get_y(k,2*i-1);
291 CDEBUG2(surf_sdp_out,"%d %d 1 1 1\n", matno , block_num);
292 addentry(constraints, &C, matno, block_num, 1, 1, 1.0, C.blocks[block_num].blocksize);
295 CDEBUG2(surf_sdp_out,"%d %d 2 2 1\n", matno , block_num);
296 addentry(constraints, &C, matno, block_num, 2, 2, 1.0, C.blocks[block_num].blocksize);
299 CDEBUG2(surf_sdp_out,"%d %d 1 2 1\n", matno , block_num);
300 addentry(constraints, &C, matno, block_num, 1, 2, 1.0, C.blocks[block_num].blocksize);
303 CDEBUG2(surf_sdp_out,"%d %d 2 1 1\n", matno , block_num);
304 addentry(constraints, &C, matno, block_num, 2, 1, 1.0, C.blocks[block_num].blocksize);
306 isdiag[block_num] = 0;
313 * Capacity constraint block.
315 xbt_swag_foreach(cnst, cnst_list) {
317 CDEBUG2(surf_sdp_out,"0 %d 1 1 %f\n", block_num, - (cnst->bound));
318 addentry(constraints, &C, 0, block_num, 1, 1, - (cnst->bound) , C.blocks[block_num].blocksize);
320 elem_list = &(cnst->element_set);
321 xbt_swag_foreach(elem, elem_list){
322 if(elem->variable->weight <=0) break;
323 matno=get_y(K,elem->variable->index);
324 CDEBUG3(surf_sdp_out,"%d %d 1 1 %f\n", elem->variable->index, block_num, - (elem->value));
325 addentry(constraints, &C, matno, block_num, 1, 1, - (elem->value), C.blocks[block_num].blocksize);
333 * Positivy constraint blocks.
335 for(i = 1; i <= pow(2,K); i++){
337 CDEBUG2(surf_sdp_out,"%d %d 1 1 1\n", matno, block_num);
338 addentry(constraints, &C, matno, block_num, 1, 1, 1.0, C.blocks[block_num].blocksize);
344 * At this point, we'll stop to recognize whether any of the blocks
345 * are "hidden LP blocks" and correct the block type if needed.
347 for (i=1; i<=nb_cnsts; i++){
348 if ((C.blocks[i].blockcategory != DIAG) &&
349 (isdiag[i]==1) && (C.blocks[i].blocksize > 1)){
351 * We have a hidden diagonal block!
354 //printf("Block %d is actually diagonal.\n",i);
356 blocksz=C.blocks[i].blocksize;
357 tempdiag=(double *)calloc((blocksz+1), sizeof(double));
358 for (j=1; j<=blocksz; j++)
359 tempdiag[j]=C.blocks[i].data.mat[ijtok(j,j,blocksz)];
360 free(C.blocks[i].data.mat);
361 C.blocks[i].data.vec=tempdiag;
362 C.blocks[i].blockcategory=DIAG;
368 * Next, setup issparse and NULL out all nextbyblock pointers.
371 for (i=1; i<=k; i++) {
372 p=constraints[i].blocks;
375 * First, set issparse.
377 if (((p->numentries) > 0.25*(p->blocksize)) && ((p->numentries) > 15)){
383 if (C.blocks[p->blocknum].blockcategory == DIAG)
387 * Setup the cross links.
397 * Create cross link reference.
399 create_cross_link(constraints, nb_var);
403 * Debuging print problem in SDPA format.
405 if(XBT_LOG_ISENABLED(surf_sdp, xbt_log_priority_debug)) {
406 DEBUG0("Printing SDPA...");
407 tmp=strdup("SURF-PROPORTIONNAL.sdpa");
408 write_prob(tmp,total_block_size,nb_var,C,a,constraints);
413 * Initialize parameters.
415 DEBUG0("Initializing solution...");
416 initsoln(total_block_size, nb_var, C, a, constraints, &X, &y, &Z);
423 DEBUG0("Calling the solver...");
425 stdout=fopen("/dev/null","w");
426 ret = easy_sdp(total_block_size, nb_var, C, a, constraints, 0.0, &X, &y, &Z, &pobj, &dobj);
432 case 1: DEBUG0("SUCCESS The problem is primal infeasible");
435 case 2: DEBUG0("SUCCESS The problem is dual infeasible");
438 case 3: DEBUG0("Partial SUCCESS A solution has been found, but full accuracy was not achieved. One or more of primal infeasibility, dual infeasibility, or relative duality gap are larger than their tolerances, but by a factor of less than 1000.");
441 case 4: DEBUG0("Failure. Maximum number of iterations reached.");
444 case 5: DEBUG0("Failure. Stuck at edge of primal feasibility.");
449 if(XBT_LOG_ISENABLED(surf_sdp, xbt_log_priority_debug)) {
450 tmp=strdup("SURF-PROPORTIONNAL.sol");
451 write_sol(tmp,total_block_size, nb_var, X, y, Z);
456 * Write out the solution if necessary.
458 xbt_swag_foreach(cnst, cnst_list) {
460 elem_list = &(cnst->element_set);
461 xbt_swag_foreach(elem, elem_list) {
462 if(elem->variable->weight <=0) break;
464 i = (int)get_y(K, elem->variable->index);
465 elem->variable->value = y[i];
474 free_prob(total_block_size, nb_var, C, a, constraints, X, y, Z);
487 if(XBT_LOG_ISENABLED(surf_sdp, xbt_log_priority_debug)) {
495 * Create the cross_link reference in order to have a byblock list.
497 void create_cross_link(struct constraintmatrix *myconstraints, int k){
501 struct sparseblock *p;
502 struct sparseblock *q;
504 struct sparseblock *prev;
510 for (i=1; i<=k; i++){
511 p=myconstraints[i].blocks;
513 if (p->nextbyblock == NULL){
517 * link in the remaining blocks.
519 for (j=i+1; j<=k; j++){
520 q=myconstraints[j].blocks;
523 if (q->blocknum == p->blocknum){
524 if (p->nextbyblock == NULL){
548 void addentry(struct constraintmatrix *constraints,
549 struct blockmatrix *C,
557 struct sparseblock *p;
558 struct sparseblock *p_sav;
560 p=constraints[matno].blocks;
565 * We haven't yet allocated any blocks.
567 p=(struct sparseblock *)calloc(1, sizeof(struct sparseblock));
569 //two entries because this library ignores indices starting in zerox
570 p->constraintnum=matno;
575 p->entries=calloc(p->numentries+1, sizeof(double));
576 p->iindices=calloc(p->numentries+1, sizeof(int));
577 p->jindices=calloc(p->numentries+1, sizeof(int));
579 p->entries[p->numentries]=ent;
580 p->iindices[p->numentries]=indexi;
581 p->jindices[p->numentries]=indexj;
583 p->blocksize=blocksize;
585 constraints[matno].blocks=p;
588 * We have some existing blocks. See whether this block is already
592 if (p->blocknum == blkno){
594 * Found the right block.
596 p->constraintnum=matno;
598 p->numentries=p->numentries+1;
600 p->entries = realloc(p->entries, (p->numentries+1) * sizeof(double) );
601 p->iindices = realloc(p->iindices, (p->numentries+1) * sizeof(int) );
602 p->jindices = realloc(p->jindices, (p->numentries+1) * sizeof(int) );
604 p->entries[p->numentries]=ent;
605 p->iindices[p->numentries]=indexi;
606 p->jindices[p->numentries]=indexj;
615 * If we get here, we have a non-empty structure but not the right block
616 * inside hence create a new structure.
619 p=(struct sparseblock *)calloc(1, sizeof(struct sparseblock));
621 //two entries because this library ignores indices starting in zerox
622 p->constraintnum=matno;
627 p->entries=calloc(p->numentries+1, sizeof(double));
628 p->iindices=calloc(p->numentries+1, sizeof(int));
629 p->jindices=calloc(p->numentries+1, sizeof(int));
631 p->entries[p->numentries]=ent;
632 p->iindices[p->numentries]=indexi;
633 p->jindices[p->numentries]=indexj;
635 p->blocksize=blocksize;
641 int blksz=C->blocks[blkno].blocksize;
642 if (C->blocks[blkno].blockcategory == DIAG){
643 C->blocks[blkno].data.vec[indexi]=ent;
645 C->blocks[blkno].data.mat[ijtok(indexi,indexj,blksz)]=ent;
646 C->blocks[blkno].data.mat[ijtok(indexj,indexi,blksz)]=ent;