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;
153 if ( !(sys->modified))
157 * Initialize the var list variable with only the active variables.
158 * Associate an index in the swag variables.
160 var_list = &(sys->variable_set);
162 xbt_swag_foreach(var, var_list) {
166 DEBUG1("Variable set : %d", xbt_swag_size(var_list));
167 xbt_swag_foreach(var, var_list) {
169 if(var->weight) var->index = i--;
172 cnst_list=&(sys->active_constraint_set);
173 DEBUG1("Active constraints : %d", xbt_swag_size(cnst_list));
176 * Those fields are the top level description of the platform furnished in the xml file.
178 links = xbt_swag_size(&(sys->active_constraint_set));
181 * This number is found based on the tree structure explained on top.
185 tmp_k = (double) log((double)flows)/log(2.0);
186 K = (int) ceil(tmp_k);
190 * The number of variables in the SDP program.
192 nb_var = get_y(K, pow(2,K));
193 DEBUG1("Number of variables in the SDP program : %d", nb_var);
194 CDEBUG1(surf_sdp_out,"%d", nb_var);
197 * Find the size of each group of constraints.
199 nb_cnsts_capacity = links + ((int)pow(2,K)) - flows;
200 nb_cnsts_struct = (int)pow(2,K) - 1;
201 nb_cnsts_positivy = (int)pow(2,K);
204 * The total number of constraints.
206 nb_cnsts = nb_cnsts_capacity + nb_cnsts_struct + nb_cnsts_positivy;
207 //fprintf(sdpout,"%d\n", nb_cnsts);
210 * Keep track of which blocks have off diagonal entries.
212 isdiag=(int *)calloc((nb_cnsts+1), sizeof(int));
213 for (i=1; i<=nb_cnsts; i++)
216 C.nblocks = nb_cnsts;
217 C.blocks = (struct blockrec *) calloc((C.nblocks+1),sizeof(struct blockrec));
218 constraints = (struct constraintmatrix *)calloc((nb_var+1),sizeof(struct constraintmatrix));
220 for(i = 1; i <= nb_var; i++){
221 constraints[i].blocks=NULL;
224 a = (double *)calloc(nb_var+1, sizeof(double));
233 * For each constraint block do.
235 for(i = 1; i <= nb_cnsts; i++){
238 * Structured blocks are size 2 and all others are size 1.
240 if(i <= nb_cnsts_struct){
241 total_block_size += block_size = 2;
242 //fprintf(sdpout,"2 ");
244 total_block_size += block_size = 1;
245 //fprintf(sdpout,"1 ");
249 * All blocks are matrices.
251 C.blocks[block_num].blockcategory = MATRIX;
252 C.blocks[block_num].blocksize = block_size;
253 C.blocks[block_num].data.mat = (double *)calloc(block_size * block_size, sizeof(double));
258 //fprintf(sdpout,"\n");
262 * Creates de objective function array.
264 a = (double *)calloc((nb_var+1), sizeof(double));
266 for(i = 1; i <= nb_var; i++){
268 //fprintf(sdpout,"-1 ");
271 //fprintf(sdpout,"0 ");
275 //fprintf(sdpout,"\n");
279 * Structure contraint blocks.
283 for(k = 1; k <= K; k++){
284 for(i = 1; i <= pow(2,k-1); i++){
285 matno=get_y(k,2*i-1);
286 //fprintf(sdpout,"%d %d 1 1 1\n", matno , block_num);
287 addentry(constraints, &C, matno, block_num, 1, 1, 1.0, C.blocks[block_num].blocksize);
290 //fprintf(sdpout,"%d %d 2 2 1\n", matno , block_num);
291 addentry(constraints, &C, matno, block_num, 2, 2, 1.0, C.blocks[block_num].blocksize);
294 //fprintf(sdpout,"%d %d 1 2 1\n", matno , block_num);
295 addentry(constraints, &C, matno, block_num, 1, 2, 1.0, C.blocks[block_num].blocksize);
298 //fprintf(sdpout,"%d %d 2 1 1\n", matno , block_num);
299 addentry(constraints, &C, matno, block_num, 2, 1, 1.0, C.blocks[block_num].blocksize);
301 isdiag[block_num] = 0;
308 * Capacity constraint block.
310 xbt_swag_foreach(cnst, cnst_list) {
312 //fprintf(sdpout,"0 %d 1 1 %f\n", block_num, - (cnst->bound));
313 addentry(constraints, &C, 0, block_num, 1, 1, - (cnst->bound) , C.blocks[block_num].blocksize);
316 elem_list = &(cnst->element_set);
317 xbt_swag_foreach(elem, elem_list) {
318 if(elem->variable->weight <=0) break;
319 matno=get_y(K,elem->variable->index);
320 //fprintf(sdpout,"%d %d 1 1 %f\n", elem->variable->index, block_num, - (elem->value));
321 addentry(constraints, &C, matno, block_num, 1, 1, - (elem->value), C.blocks[block_num].blocksize);
329 * Positivy constraint blocks.
331 for(i = 1; i <= pow(2,K); i++){
333 //fprintf(sdpout,"%d %d 1 1 1\n", matno, block_num);
334 addentry(constraints, &C, matno, block_num, 1, 1, 1.0, C.blocks[block_num].blocksize);
340 * At this point, we'll stop to recognize whether any of the blocks
341 * are "hidden LP blocks" and correct the block type if needed.
343 for (i=1; i<=nb_cnsts; i++){
344 if ((C.blocks[i].blockcategory != DIAG) &&
345 (isdiag[i]==1) && (C.blocks[i].blocksize > 1)){
347 * We have a hidden diagonal block!
350 //printf("Block %d is actually diagonal.\n",i);
352 blocksz=C.blocks[i].blocksize;
353 tempdiag=(double *)calloc((blocksz+1), sizeof(double));
354 for (j=1; j<=blocksz; j++)
355 tempdiag[j]=C.blocks[i].data.mat[ijtok(j,j,blocksz)];
356 free(C.blocks[i].data.mat);
357 C.blocks[i].data.vec=tempdiag;
358 C.blocks[i].blockcategory=DIAG;
364 * Next, setup issparse and NULL out all nextbyblock pointers.
366 struct sparseblock *p=NULL;
367 for (i=1; i<=k; i++) {
368 p=constraints[i].blocks;
371 * First, set issparse.
373 if (((p->numentries) > 0.25*(p->blocksize)) && ((p->numentries) > 15)){
379 if (C.blocks[p->blocknum].blockcategory == DIAG)
383 * Setup the cross links.
393 * Create cross link reference.
395 create_cross_link(constraints, nb_var);
399 * Debuging print problem in SDPA format.
401 if(XBT_LOG_ISENABLED(surf_sdp, xbt_log_priority_debug)) {
402 DEBUG0("Printing SDPA...\n");
403 char *tmp=strdup("SURF-PROPORTIONNAL.sdpa");
404 write_prob(tmp,total_block_size,nb_var,C,a,constraints);
409 * Initialize parameters.
411 DEBUG0("Initializing solution...\n");
412 initsoln(total_block_size, nb_var, C, a, constraints, &X, &y, &Z);
419 DEBUG0("Calling the solver...\n");
420 FILE *stdout_sav=stdout;
421 stdout=fopen("/dev/null","w");
422 int ret = easy_sdp(total_block_size, nb_var, C, a, constraints, 0.0, &X, &y, &Z, &pobj, &dobj);
428 case 1: DEBUG0("SUCCESS The problem is primal infeasible\n");
431 case 2: DEBUG0("SUCCESS The problem is dual infeasible\n");
434 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.\n");
437 case 4: DEBUG0("Failure. Maximum number of iterations reached.");
440 case 5: DEBUG0("Failure. Stuck at edge of primal feasibility.");
445 if(XBT_LOG_ISENABLED(surf_sdp, xbt_log_priority_debug)) {
446 char *tmp=strdup("SURF-PROPORTIONNAL.sol");
447 write_sol(tmp,total_block_size, nb_var, X, y, Z);
452 * Write out the solution if necessary.
454 xbt_swag_foreach(cnst, cnst_list) {
456 elem_list = &(cnst->element_set);
457 xbt_swag_foreach(elem, elem_list) {
458 if(elem->variable->weight <=0) break;
460 i = (int)get_y(K, elem->variable->index);
461 elem->variable->value = y[i];
470 free_prob(total_block_size, nb_var, C, a, constraints, X, y, Z);
476 if(XBT_LOG_ISENABLED(surf_sdp, xbt_log_priority_debug)) {
484 * Create the cross_link reference in order to have a byblock list.
486 void create_cross_link(struct constraintmatrix *myconstraints, int k){
490 struct sparseblock *p;
491 struct sparseblock *q;
493 struct sparseblock *prev;
499 for (i=1; i<=k; i++){
500 p=myconstraints[i].blocks;
502 if (p->nextbyblock == NULL){
506 * link in the remaining blocks.
508 for (j=i+1; j<=k; j++){
509 q=myconstraints[j].blocks;
512 if (q->blocknum == p->blocknum){
513 if (p->nextbyblock == NULL){
537 void addentry(struct constraintmatrix *constraints,
538 struct blockmatrix *C,
546 struct sparseblock *p;
547 struct sparseblock *p_sav;
549 p=constraints[matno].blocks;
554 * We haven't yet allocated any blocks.
556 p=(struct sparseblock *)calloc(1, sizeof(struct sparseblock));
558 //two entries because this library ignores indices starting in zerox
559 p->constraintnum=matno;
564 p->entries=calloc(p->numentries+1, sizeof(double));
565 p->iindices=calloc(p->numentries+1, sizeof(int));
566 p->jindices=calloc(p->numentries+1, sizeof(int));
568 p->entries[p->numentries]=ent;
569 p->iindices[p->numentries]=indexi;
570 p->jindices[p->numentries]=indexj;
572 p->blocksize=blocksize;
574 constraints[matno].blocks=p;
577 * We have some existing blocks. See whether this block is already
581 if (p->blocknum == blkno){
583 * Found the right block.
585 p->constraintnum=matno;
587 p->numentries=p->numentries+1;
589 p->entries = realloc(p->entries, (p->numentries+1) * sizeof(double) );
590 p->iindices = realloc(p->iindices, (p->numentries+1) * sizeof(int) );
591 p->jindices = realloc(p->jindices, (p->numentries+1) * sizeof(int) );
593 p->entries[p->numentries]=ent;
594 p->iindices[p->numentries]=indexi;
595 p->jindices[p->numentries]=indexj;
604 * If we get here, we have a non-empty structure but not the right block
605 * inside hence create a new structure.
608 p=(struct sparseblock *)calloc(1, sizeof(struct sparseblock));
610 //two entries because this library ignores indices starting in zerox
611 p->constraintnum=matno;
616 p->entries=calloc(p->numentries+1, sizeof(double));
617 p->iindices=calloc(p->numentries+1, sizeof(int));
618 p->jindices=calloc(p->numentries+1, sizeof(int));
620 p->entries[p->numentries]=ent;
621 p->iindices[p->numentries]=indexi;
622 p->jindices[p->numentries]=indexj;
624 p->blocksize=blocksize;
630 int blksz=C->blocks[blkno].blocksize;
631 if (C->blocks[blkno].blockcategory == DIAG){
632 C->blocks[blkno].data.vec[indexi]=ent;
634 C->blocks[blkno].data.mat[ijtok(indexi,indexj,blksz)]=ent;
635 C->blocks[blkno].data.mat[ijtok(indexj,indexi,blksz)]=ent;