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)");
34 ########################################################################
35 ######################## Simple Proportionnal fairness #################
36 ########################################################################
37 ####### Original problem ##########
46 # We assume in the following that n=2^K
48 ####### Standard SDP form #########
50 # A SDP can be written in the following standard form:
52 # (P) min c1*x1+c2*x2+...+cm*xm
53 # st F1*x1+F2*x2+...+Fm*xm-F0=X
56 # Where F1, F2, ..., Fm are symetric matrixes of size n by n. The
57 # constraint X>0 means that X must be positive semidefinite positive.
59 ########## Equivalent SDP #########
63 # y(k,i) for k in [0,K] and i in [1,2^k]
68 # y(2,1) y(2,2) y(2,3) y(2,4)
69 # y(3,1) y(3,2) y(3,3) y(3,4) y(3,5) y(3,6) y(3,7) y(3,8)
70 # -------------------------------------------------------
71 # x_1 x_2 x_3 x_4 x_5 x_6 x_7 x_8
74 # Structure Constraints:
76 # forall k in [0,K-1], and i in [1,2^k]
77 # [ y(k, 2i-1) y(k-1, i) ]
78 # [ y(k-1, i ) y(k, 2i) ]
82 # Capacity Constraints:
84 # -(A.y(K,*))_l >= - b_l
86 # Positivity Constraints:
87 # forall k in [0,K], and i in [1,2^k]
93 //typedef struct lmm_system {
95 // s_xbt_swag_t variable_set; /* a list of lmm_variable_t */
96 // s_xbt_swag_t constraint_set; /* a list of lmm_constraint_t */
97 // s_xbt_swag_t active_constraint_set; /* a list of lmm_constraint_t */
98 // s_xbt_swag_t saturated_variable_set; /* a list of lmm_variable_t */
99 // s_xbt_swag_t saturated_constraint_set; /* a list of lmm_constraint_t_t */
100 // xbt_mallocator_t variable_mallocator;
103 #define get_y(a,b) (pow(2,a)+b-1)
105 void sdp_solve(lmm_system_t sys)
107 lmm_variable_t var = NULL;
110 * SDP mapping variables.
117 int nb_cnsts_capacity=0;
118 int nb_cnsts_struct=0;
119 int nb_cnsts_positivy=0;
122 int total_block_size=0;
124 // FILE *sdpout = fopen("SDPA-printf.tmp","w");
126 double *tempdiag = NULL;
133 * CSDP library specific variables.
135 struct blockmatrix C;
136 struct blockmatrix X,Z;
140 struct constraintmatrix *constraints;
143 * Classic maxmin variables.
145 lmm_constraint_t cnst = NULL;
146 lmm_element_t elem = NULL;
147 xbt_swag_t cnst_list = NULL;
148 xbt_swag_t var_list = NULL;
149 xbt_swag_t elem_list = NULL;
151 if ( !(sys->modified))
155 * Initialize the var list variable with only the active variables.
156 * Associate an index in the swag variables.
158 var_list = &(sys->variable_set);
160 xbt_swag_foreach(var, var_list) {
164 DEBUG1("Variable set : %d", xbt_swag_size(var_list));
165 xbt_swag_foreach(var, var_list) {
167 if(var->weight) var->index = i--;
170 cnst_list=&(sys->active_constraint_set);
171 DEBUG1("Active constraints : %d", xbt_swag_size(cnst_list));
174 * Those fields are the top level description of the platform furnished in the xml file.
176 links = xbt_swag_size(&(sys->active_constraint_set));
179 * This number is found based on the tree structure explained on top.
183 tmp_k = (double) log((double)flows)/log(2.0);
184 K = (int) ceil(tmp_k);
188 * The number of variables in the SDP program.
190 nb_var = get_y(K, pow(2,K));
191 DEBUG1("Number of variables in the SDP program : %d", nb_var);
192 //fprintf(sdpout,"%d\n", nb_var);
195 * Find the size of each group of constraints.
197 nb_cnsts_capacity = links + ((int)pow(2,K)) - flows;
198 nb_cnsts_struct = (int)pow(2,K) - 1;
199 nb_cnsts_positivy = (int)pow(2,K);
202 * The total number of constraints.
204 nb_cnsts = nb_cnsts_capacity + nb_cnsts_struct + nb_cnsts_positivy;
205 //fprintf(sdpout,"%d\n", nb_cnsts);
208 * Keep track of which blocks have off diagonal entries.
210 isdiag=(int *)calloc((nb_cnsts+1), sizeof(int));
211 for (i=1; i<=nb_cnsts; i++)
214 C.nblocks = nb_cnsts;
215 C.blocks = (struct blockrec *) calloc((C.nblocks+1),sizeof(struct blockrec));
216 constraints = (struct constraintmatrix *)calloc((nb_var+1),sizeof(struct constraintmatrix));
218 for(i = 1; i <= nb_var; i++){
219 constraints[i].blocks=NULL;
222 a = (double *)calloc(nb_var+1, sizeof(double));
231 * For each constraint block do.
233 for(i = 1; i <= nb_cnsts; i++){
236 * Structured blocks are size 2 and all others are size 1.
238 if(i <= nb_cnsts_struct){
239 total_block_size += block_size = 2;
240 //fprintf(sdpout,"2 ");
242 total_block_size += block_size = 1;
243 //fprintf(sdpout,"1 ");
247 * All blocks are matrices.
249 C.blocks[block_num].blockcategory = MATRIX;
250 C.blocks[block_num].blocksize = block_size;
251 C.blocks[block_num].data.mat = (double *)calloc(block_size * block_size, sizeof(double));
256 //fprintf(sdpout,"\n");
260 * Creates de objective function array.
262 a = (double *)calloc((nb_var+1), sizeof(double));
264 for(i = 1; i <= nb_var; i++){
266 //fprintf(sdpout,"-1 ");
269 //fprintf(sdpout,"0 ");
273 //fprintf(sdpout,"\n");
277 * Structure contraint blocks.
281 for(k = 1; k <= K; k++){
282 for(i = 1; i <= pow(2,k-1); i++){
283 matno=get_y(k,2*i-1);
284 //fprintf(sdpout,"%d %d 1 1 1\n", matno , block_num);
285 addentry(constraints, &C, matno, block_num, 1, 1, 1.0, C.blocks[block_num].blocksize);
288 //fprintf(sdpout,"%d %d 2 2 1\n", matno , block_num);
289 addentry(constraints, &C, matno, block_num, 2, 2, 1.0, C.blocks[block_num].blocksize);
292 //fprintf(sdpout,"%d %d 1 2 1\n", matno , block_num);
293 addentry(constraints, &C, matno, block_num, 1, 2, 1.0, C.blocks[block_num].blocksize);
296 //fprintf(sdpout,"%d %d 2 1 1\n", matno , block_num);
297 addentry(constraints, &C, matno, block_num, 2, 1, 1.0, C.blocks[block_num].blocksize);
299 isdiag[block_num] = 0;
306 * Capacity constraint block.
308 xbt_swag_foreach(cnst, cnst_list) {
310 //fprintf(sdpout,"0 %d 1 1 %f\n", block_num, - (cnst->bound));
311 addentry(constraints, &C, 0, block_num, 1, 1, - (cnst->bound) , C.blocks[block_num].blocksize);
314 elem_list = &(cnst->element_set);
315 xbt_swag_foreach(elem, elem_list) {
316 if(elem->variable->weight <=0) break;
317 matno=get_y(K,elem->variable->index);
318 //fprintf(sdpout,"%d %d 1 1 %f\n", elem->variable->index, block_num, - (elem->value));
319 addentry(constraints, &C, matno, block_num, 1, 1, - (elem->value), C.blocks[block_num].blocksize);
327 * Positivy constraint blocks.
329 for(i = 1; i <= pow(2,K); i++){
331 //fprintf(sdpout,"%d %d 1 1 1\n", matno, block_num);
332 addentry(constraints, &C, matno, block_num, 1, 1, 1.0, C.blocks[block_num].blocksize);
338 * At this point, we'll stop to recognize whether any of the blocks
339 * are "hidden LP blocks" and correct the block type if needed.
341 for (i=1; i<=nb_cnsts; i++){
342 if ((C.blocks[i].blockcategory != DIAG) &&
343 (isdiag[i]==1) && (C.blocks[i].blocksize > 1)){
345 * We have a hidden diagonal block!
348 printf("Block %d is actually diagonal.\n",i);
350 blocksz=C.blocks[i].blocksize;
351 tempdiag=(double *)calloc((blocksz+1), sizeof(double));
352 for (j=1; j<=blocksz; j++)
353 tempdiag[j]=C.blocks[i].data.mat[ijtok(j,j,blocksz)];
354 free(C.blocks[i].data.mat);
355 C.blocks[i].data.vec=tempdiag;
356 C.blocks[i].blockcategory=DIAG;
362 * Next, setup issparse and NULL out all nextbyblock pointers.
364 struct sparseblock *p=NULL;
365 for (i=1; i<=k; i++) {
366 p=constraints[i].blocks;
369 * First, set issparse.
371 if (((p->numentries) > 0.25*(p->blocksize)) && ((p->numentries) > 15)){
377 if (C.blocks[p->blocknum].blockcategory == DIAG)
381 * Setup the cross links.
391 * Create cross link reference.
393 create_cross_link(constraints, nb_var);
397 * Debuging print problem in SDPA format.
399 printf("Printing SDPA...\n");
400 if(XBT_LOG_ISENABLED(surf_sdp, xbt_log_priority_debug)) {
401 char *tmp=strdup("SURF-PROPORTIONNAL.sdpa");
402 write_prob(tmp,total_block_size,nb_var,C,a,constraints);
407 * Initialize parameters.
409 printf("Initializing solution...\n");
410 initsoln(total_block_size, nb_var, C, a, constraints, &X, &y, &Z);
417 printf("Calling the solver...\n");
418 int ret = easy_sdp(total_block_size, nb_var, C, a, constraints, 0.0, &X, &y, &Z, &pobj, &dobj);
422 case 1: printf("SUCCESS The problem is primal infeasible\n");
425 case 2: printf("SUCCESS The problem is dual infeasible\n");
428 case 3: printf("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");
431 case 4: printf("Failure. Maximum number of iterations reached.");
434 case 5: printf("Failure. Stuck at edge of primal feasibility.");
439 if(XBT_LOG_ISENABLED(surf_sdp, xbt_log_priority_debug)) {
440 char *tmp=strdup("SURF-PROPORTIONNAL.sol");
441 write_sol(tmp,total_block_size, nb_var, X, y, Z);
446 * Write out the solution if necessary.
448 xbt_swag_foreach(cnst, cnst_list) {
450 elem_list = &(cnst->element_set);
451 xbt_swag_foreach(elem, elem_list) {
452 if(elem->variable->weight <=0) break;
454 i = (int)get_y(K, elem->variable->index);
455 elem->variable->value = y[i];
464 free_prob(total_block_size, nb_var, C, a, constraints, X, y, Z);
470 if(XBT_LOG_ISENABLED(surf_sdp, xbt_log_priority_debug)) {
478 * Create the cross_link reference in order to have a byblock list.
480 void create_cross_link(struct constraintmatrix *myconstraints, int k){
484 struct sparseblock *p;
485 struct sparseblock *q;
487 struct sparseblock *prev;
493 for (i=1; i<=k; i++){
494 p=myconstraints[i].blocks;
496 if (p->nextbyblock == NULL){
500 * link in the remaining blocks.
502 for (j=i+1; j<=k; j++){
503 q=myconstraints[j].blocks;
506 if (q->blocknum == p->blocknum){
507 if (p->nextbyblock == NULL){
531 void addentry(struct constraintmatrix *constraints,
532 struct blockmatrix *C,
540 struct sparseblock *p;
541 struct sparseblock *p_sav;
543 p=constraints[matno].blocks;
548 * We haven't yet allocated any blocks.
550 p=(struct sparseblock *)calloc(1, sizeof(struct sparseblock));
552 //two entries because this library ignores indices starting in zerox
553 p->constraintnum=matno;
558 p->entries=calloc(p->numentries+1, sizeof(double));
559 p->iindices=calloc(p->numentries+1, sizeof(int));
560 p->jindices=calloc(p->numentries+1, sizeof(int));
562 p->entries[p->numentries]=ent;
563 p->iindices[p->numentries]=indexi;
564 p->jindices[p->numentries]=indexj;
566 p->blocksize=blocksize;
568 constraints[matno].blocks=p;
571 * We have some existing blocks. See whether this block is already
575 if (p->blocknum == blkno){
577 * Found the right block.
579 p->constraintnum=matno;
581 p->numentries=p->numentries+1;
583 p->entries = realloc(p->entries, (p->numentries+1) * sizeof(double) );
584 p->iindices = realloc(p->iindices, (p->numentries+1) * sizeof(int) );
585 p->jindices = realloc(p->jindices, (p->numentries+1) * sizeof(int) );
587 p->entries[p->numentries]=ent;
588 p->iindices[p->numentries]=indexi;
589 p->jindices[p->numentries]=indexj;
598 * If we get here, we have a non-empty structure but not the right block
599 * inside hence create a new structure.
602 p=(struct sparseblock *)calloc(1, sizeof(struct sparseblock));
604 //two entries because this library ignores indices starting in zerox
605 p->constraintnum=matno;
610 p->entries=calloc(p->numentries+1, sizeof(double));
611 p->iindices=calloc(p->numentries+1, sizeof(int));
612 p->jindices=calloc(p->numentries+1, sizeof(int));
614 p->entries[p->numentries]=ent;
615 p->iindices[p->numentries]=indexi;
616 p->jindices[p->numentries]=indexj;
618 p->blocksize=blocksize;
624 int blksz=C->blocks[blkno].blocksize;
625 if (C->blocks[blkno].blockcategory == DIAG){
626 C->blocks[blkno].data.vec[indexi]=ent;
628 C->blocks[blkno].data.mat[ijtok(indexi,indexj,blksz)]=ent;
629 C->blocks[blkno].data.mat[ijtok(indexj,indexi,blksz)]=ent;