* under the terms of the license (GNU LGPL) which comes with this package. */
-#include "xbt/sysdep.h"
#include "xbt/log.h"
+#include "xbt/sysdep.h"
#include "maxmin_private.h"
+
#include <stdlib.h>
+#ifndef MATH
+#include <math.h>
+#endif
+
+/*
+ * SDP specific variables.
+ */
+#define NOSHORTS
+#include <declarations.h>
+
+
+static void create_cross_link(struct constraintmatrix *myconstraints,
+ int k);
+
+static void addentry(struct constraintmatrix *constraints,
+ struct blockmatrix *, int matno, int blkno,
+ int indexi, int indexj, double ent, int blocksize);
+
+
XBT_LOG_NEW_DEFAULT_SUBCATEGORY(surf_sdp, surf,
"Logging specific to SURF (sdp)");
+XBT_LOG_NEW_SUBCATEGORY(surf_sdp_out, surf,
+ "Logging specific to SURF (sdp)");
+/*
+########################################################################
+######################## Simple Proportionnal fairness #################
+########################################################################
+####### Original problem ##########
+#
+# Max x_1*x_2*...*x_n
+# (A.x)_1 <= b_1
+# (A.x)_2 <= b_2
+# ...
+# (A.x)_m <= b_m
+# x_1 <= c_1
+# x_2 <= c_2
+# ...
+# x_m <= c_m
+# x>=0
+#
+# We assume in the following that n=2^K
+#
+####### Standard SDP form #########
+#
+# A SDP can be written in the following standard form:
+#
+# (P) min c1*x1+c2*x2+...+cm*xm
+# st F1*x1+F2*x2+...+Fm*xm-F0=X
+# X >= 0
+#
+# Where F1, F2, ..., Fm are symetric matrixes of size n by n. The
+# constraint X>0 means that X must be positive semidefinite positive.
+#
+########## Equivalent SDP #########
+#
+# Variables:
+#
+# y(k,i) for k in [0,K] and i in [1,2^k]
+#
+# Structure :
+# y(0,1)
+# y(1,1) y(1,2)
+# y(2,1) y(2,2) y(2,3) y(2,4)
+# y(3,1) y(3,2) y(3,3) y(3,4) y(3,5) y(3,6) y(3,7) y(3,8)
+# -------------------------------------------------------
+# x_1 x_2 x_3 x_4 x_5 x_6 x_7 x_8
+#
+#
+# Structure Constraints:
+#
+# forall k in [0,K-1], and i in [1,2^k]
+# [ y(k, 2i-1) y(k-1, i) ]
+# [ y(k-1, i ) y(k, 2i) ]
+#
+# 2^K-1
+#
+# Capacity Constraints:
+# forall l in [1,m]
+# -(A.y(K,*))_l >= - b_l
+#
+# Positivity Constraints:
+# forall k in [0,K], and i in [1,2^k]
+# y(k,i) >= 0
+#
+# Latency Constraints:
+# forall i in [1,2^k] and v in [0,m-1]
+# if(i <= m-1){
+# y(k-1, i) <= bound
+# }else{
+# y(k-1, i) <= 1
+# }
+# Minimize -y(0,1)
+*/
+
+//typedef struct lmm_system {
+// int modified;
+// s_xbt_swag_t variable_set; /* a list of lmm_variable_t */
+// s_xbt_swag_t constraint_set; /* a list of lmm_constraint_t */
+// s_xbt_swag_t active_constraint_set; /* a list of lmm_constraint_t */
+// s_xbt_swag_t saturated_variable_set; /* a list of lmm_variable_t */
+// s_xbt_swag_t saturated_constraint_set; /* a list of lmm_constraint_t_t */
+// xbt_mallocator_t variable_mallocator;
+//} s_lmm_system_t;
+
+#define get_y(a,b) (pow(2,a)+b-1)
void sdp_solve(lmm_system_t sys)
{
-/* lmm_variable_t var = NULL; */
-/* lmm_constraint_t cnst = NULL; */
-/* lmm_element_t elem = NULL; */
-/* xbt_swag_t cnst_list = NULL; */
-/* xbt_swag_t var_list = NULL; */
-/* xbt_swag_t elem_list = NULL; */
-/* double min_usage = -1; */
+
+ /*
+ * SDP mapping variables.
+ */
+ int K = 0;
+ int nb_var = 0;
+ int nb_cnsts = 0;
+ int flows = 0;
+ int links = 0;
+ int nb_cnsts_capacity = 0;
+ int nb_cnsts_struct = 0;
+ int nb_cnsts_positivy = 0;
+ int nb_cnsts_latency = 0;
+ int block_num = 0;
+ int block_size;
+ int total_block_size = 0;
+ int *isdiag = NULL;
+ // FILE *sdpout = fopen("SDPA-printf.tmp","w");
+ int blocksz = 0;
+ double *tempdiag = NULL;
+ int matno = 0;
+ int i = 0;
+ int j = 0;
+ int k = 0;
+
+ /*
+ * CSDP library specific variables.
+ */
+ struct blockmatrix C;
+ struct blockmatrix X, Z;
+ double *y;
+ double pobj, dobj;
+ double *a;
+ struct constraintmatrix *constraints;
+
+ /*
+ * Classic maxmin variables.
+ */
+ lmm_constraint_t cnst = NULL;
+ lmm_element_t elem = NULL;
+ xbt_swag_t cnst_list = NULL;
+ xbt_swag_t var_list = NULL;
+ xbt_swag_t elem_list = NULL;
+ lmm_variable_t var = NULL;
+
+ double tmp_k;
+ struct sparseblock *p;
+ char *tmp = NULL;
+ FILE *stdout_sav;
+ int ret;
+
+
if (!(sys->modified))
return;
+ /*
+ * Initialize the var list variable with only the active variables.
+ * Associate an index in the swag variables.
+ */
+ var_list = &(sys->variable_set);
+ i = 0;
+ xbt_swag_foreach(var, var_list) {
+ if (var->weight != 0.0)
+ i++;
+ }
+
+
+
+ flows = i;
+ DEBUG1("Variable set : %d", xbt_swag_size(var_list));
+ DEBUG1("Flows : %d", flows);
+
+ if (flows == 0) {
+ return;
+ }
+
+
+ xbt_swag_foreach(var, var_list) {
+ var->value = 0.0;
+ if (var->weight) {
+ var->index = i--;
+ }
+ }
+
+ cnst_list = &(sys->active_constraint_set);
+ DEBUG1("Active constraints : %d", xbt_swag_size(cnst_list));
+ DEBUG1("Links : %d", links);
+
+ /*
+ * Those fields are the top level description of the platform furnished in the xml file.
+ */
+ links = xbt_swag_size(&(sys->active_constraint_set));
+
+ /*
+ * This number is found based on the tree structure explained on top.
+ */
+ tmp_k = (double) log((double) flows) / log(2.0);
+ K = (int) ceil(tmp_k);
+ //xbt_assert1(K!=0, "Invalide value of K (=%d) aborting.", K);
+
+
+ /*
+ * The number of variables in the SDP program.
+ */
+ nb_var = get_y(K, pow(2, K));
+ DEBUG1("Number of variables in the SDP program : %d", nb_var);
+
+
+ /*
+ * Find the size of each group of constraints.
+ */
+ nb_cnsts_capacity = links + ((int) pow(2, K)) - flows;
+ nb_cnsts_struct = (int) pow(2, K) - 1;
+ nb_cnsts_positivy = (int) pow(2, K);
+ nb_cnsts_latency = nb_var;
+
+
+ /*
+ * The total number of constraints.
+ */
+ nb_cnsts =
+ nb_cnsts_capacity + nb_cnsts_struct + nb_cnsts_positivy +
+ nb_cnsts_latency;
+ CDEBUG1(surf_sdp_out, "Number of constraints = %d", nb_cnsts);
+ DEBUG1("Number of constraints in the SDP program : %d", nb_cnsts);
+
+ /*
+ * Keep track of which blocks have off diagonal entries.
+ */
+ isdiag = (int *) calloc((nb_cnsts + 1), sizeof(int));
+ for (i = 1; i <= nb_cnsts; i++)
+ isdiag[i] = 1;
+
+ C.nblocks = nb_cnsts;
+ C.blocks =
+ (struct blockrec *) calloc((C.nblocks + 1), sizeof(struct blockrec));
+ constraints =
+ (struct constraintmatrix *) calloc((nb_var + 1),
+ sizeof(struct constraintmatrix));
+
+ for (i = 1; i <= nb_var; i++) {
+ constraints[i].blocks = NULL;
+ }
+
+ a = (double *) calloc(nb_var + 1, sizeof(double));
+
+ /*
+ * Block sizes.
+ */
+ block_num = 1;
+ block_size = 0;
+
+ /*
+ * For each constraint block do.
+ */
+ for (i = 1; i <= nb_cnsts; i++) {
+
+ /*
+ * Structured blocks are size 2 and all others are size 1.
+ */
+ if (i <= nb_cnsts_struct) {
+ total_block_size += block_size = 2;
+ DEBUG0("2 ");
+ } else {
+ total_block_size += block_size = 1;
+ CDEBUG0(surf_sdp_out, "1 ");
+ }
+
+ /*
+ * All blocks are matrices.
+ */
+ C.blocks[block_num].blockcategory = MATRIX;
+ C.blocks[block_num].blocksize = block_size;
+ C.blocks[block_num].data.mat =
+ (double *) calloc(block_size * block_size, sizeof(double));
+
+ block_num++;
+ }
+
+ CDEBUG0(surf_sdp_out, " ");
+
+
+ /*
+ * Creates de objective function array.
+ */
+ a = (double *) calloc((nb_var + 1), sizeof(double));
+
+ for (i = 1; i <= nb_var; i++) {
+ if (get_y(0, 1) == i) {
+ //CDEBUG0(surf_sdp_out,"-1 ");
+ a[i] = -1;
+ } else {
+ //CDEBUG0(surf_sdp_out,"0 ");
+ a[i] = 0;
+ }
+ }
+
+
+ /*
+ * Structure contraint blocks.
+ */
+ block_num = 1;
+ matno = 1;
+ for (k = 1; k <= K; k++) {
+ for (i = 1; i <= pow(2, k - 1); i++) {
+ matno = get_y(k, 2 * i - 1);
+ CDEBUG2(surf_sdp_out, "%d %d 1 1 1", matno, block_num);
+ addentry(constraints, &C, matno, block_num, 1, 1, 1.0,
+ C.blocks[block_num].blocksize);
+
+ matno = get_y(k, 2 * i);
+ CDEBUG2(surf_sdp_out, "%d %d 2 2 1", matno, block_num);
+ addentry(constraints, &C, matno, block_num, 2, 2, 1.0,
+ C.blocks[block_num].blocksize);
+
+ matno = get_y(k - 1, i);
+ CDEBUG2(surf_sdp_out, "%d %d 1 2 1", matno, block_num);
+ addentry(constraints, &C, matno, block_num, 1, 2, 1.0,
+ C.blocks[block_num].blocksize);
+
+ matno = get_y(k - 1, i);
+ CDEBUG2(surf_sdp_out, "%d %d 2 1 1", matno, block_num);
+ addentry(constraints, &C, matno, block_num, 2, 1, 1.0,
+ C.blocks[block_num].blocksize);
+
+ isdiag[block_num] = 0;
+ block_num++;
+ }
+ }
+
+
+ /*
+ * Capacity constraint block.
+ */
+ xbt_swag_foreach(cnst, cnst_list) {
+
+ CDEBUG2(surf_sdp_out, "0 %d 1 1 %f", block_num, -(cnst->bound));
+ addentry(constraints, &C, 0, block_num, 1, 1, -(cnst->bound),
+ C.blocks[block_num].blocksize);
+
+ elem_list = &(cnst->element_set);
+ xbt_swag_foreach(elem, elem_list) {
+ if (elem->variable->weight <= 0)
+ break;
+ matno = get_y(K, elem->variable->index);
+ CDEBUG3(surf_sdp_out, "%d %d 1 1 %f", matno, block_num,
+ -(elem->value));
+ addentry(constraints, &C, matno, block_num, 1, 1, -(elem->value),
+ C.blocks[block_num].blocksize);
+
+ }
+ block_num++;
+ }
+
+
+ /*
+ * Positivy constraint blocks.
+ */
+ for (i = 1; i <= pow(2, K); i++) {
+ matno = get_y(K, i);
+ CDEBUG2(surf_sdp_out, "%d %d 1 1 1", matno, block_num);
+ addentry(constraints, &C, matno, block_num, 1, 1, 1.0,
+ C.blocks[block_num].blocksize);
+ block_num++;
+ }
+ /*
+ * Latency constraint blocks.
+ */
+ xbt_swag_foreach(var, var_list) {
+ var->value = 0.0;
+ if (var->weight && var->bound > 0) {
+ matno = get_y(K, var->index);
+ CDEBUG3(surf_sdp_out, "%d %d 1 1 %f", matno, block_num, var->bound);
+ addentry(constraints, &C, matno, block_num, 1, 1, var->bound,
+ C.blocks[block_num].blocksize);
+ }
+ }
+
+ /*
+ * At this point, we'll stop to recognize whether any of the blocks
+ * are "hidden LP blocks" and correct the block type if needed.
+ */
+ for (i = 1; i <= nb_cnsts; i++) {
+ if ((C.blocks[i].blockcategory != DIAG) &&
+ (isdiag[i] == 1) && (C.blocks[i].blocksize > 1)) {
+ /*
+ * We have a hidden diagonal block!
+ */
+
+ blocksz = C.blocks[i].blocksize;
+ tempdiag = (double *) calloc((blocksz + 1), sizeof(double));
+ for (j = 1; j <= blocksz; j++)
+ tempdiag[j] = C.blocks[i].data.mat[ijtok(j, j, blocksz)];
+ free(C.blocks[i].data.mat);
+ C.blocks[i].data.vec = tempdiag;
+ C.blocks[i].blockcategory = DIAG;
+ };
+ };
+
+
+ /*
+ * Next, setup issparse and NULL out all nextbyblock pointers.
+ */
+ p = NULL;
+ for (i = 1; i <= k; i++) {
+ p = constraints[i].blocks;
+ while (p != NULL) {
+ /*
+ * First, set issparse.
+ */
+ if (((p->numentries) > 0.25 * (p->blocksize))
+ && ((p->numentries) > 15)) {
+ p->issparse = 0;
+ } else {
+ p->issparse = 1;
+ };
+
+ if (C.blocks[p->blocknum].blockcategory == DIAG)
+ p->issparse = 1;
+
+ /*
+ * Setup the cross links.
+ */
+
+ p->nextbyblock = NULL;
+ p = p->next;
+ };
+ };
+
+
+ /*
+ * Create cross link reference.
+ */
+ create_cross_link(constraints, nb_var);
+
+
+ /*
+ * Debuging print problem in SDPA format.
+ */
+ if (XBT_LOG_ISENABLED(surf_sdp, xbt_log_priority_debug)) {
+ DEBUG0("Printing SDPA...");
+ tmp = strdup("SURF-PROPORTIONNAL.sdpa");
+ write_prob(tmp, total_block_size, nb_var, C, a, constraints);
+ }
+
+ /*
+ * Initialize parameters.
+ */
+ DEBUG0("Initializing solution...");
+ initsoln(total_block_size, nb_var, C, a, constraints, &X, &y, &Z);
+
+
+
+ /*
+ * Call the solver.
+ */
+ DEBUG0("Calling the solver...");
+ stdout_sav = stdout;
+ stdout = fopen("/dev/null", "w");
+ ret =
+ easy_sdp(total_block_size, nb_var, C, a, constraints, 0.0, &X, &y,
+ &Z, &pobj, &dobj);
+ fclose(stdout);
+ stdout = stdout_sav;
+
+ switch (ret) {
+ case 0:
+ case 1:
+ DEBUG0("SUCCESS The problem is primal infeasible");
+ break;
+
+ case 2:
+ DEBUG0("SUCCESS The problem is dual infeasible");
+ break;
+
+ 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.");
+ break;
+
+ case 4:
+ DEBUG0("Failure. Maximum number of iterations reached.");
+ break;
+
+ case 5:
+ DEBUG0("Failure. Stuck at edge of primal feasibility.");
+ break;
+
+ }
+
+ if (XBT_LOG_ISENABLED(surf_sdp, xbt_log_priority_debug)) {
+ tmp = strdup("SURF-PROPORTIONNAL.sol");
+ write_sol(tmp, total_block_size, nb_var, X, y, Z);
+ }
+
+ /*
+ * Write out the solution if necessary.
+ */
+ xbt_swag_foreach(cnst, cnst_list) {
+
+ elem_list = &(cnst->element_set);
+ xbt_swag_foreach(elem, elem_list) {
+ if (elem->variable->weight <= 0)
+ break;
+
+ i = (int) get_y(K, elem->variable->index);
+ elem->variable->value = y[i];
+
+ }
+ }
+
+
+ /*
+ * Free up memory.
+ */
+ free_prob(total_block_size, nb_var, C, a, constraints, X, y, Z);
+
+ free(isdiag);
+ free(tempdiag);
+ free(tmp);
+
+ sys->modified = 0;
+
+ if (XBT_LOG_ISENABLED(surf_sdp, xbt_log_priority_debug)) {
+ lmm_print(sys);
+ }
+
+}
+
+
+/*
+ * Create the cross_link reference in order to have a byblock list.
+ */
+void create_cross_link(struct constraintmatrix *myconstraints, int k)
+{
+
+ int i, j;
+ int blk;
+ struct sparseblock *p;
+ struct sparseblock *q;
+
+ struct sparseblock *prev;
+
+ /*
+ * Now, cross link.
+ */
+ prev = NULL;
+ for (i = 1; i <= k; i++) {
+ p = myconstraints[i].blocks;
+ while (p != NULL) {
+ if (p->nextbyblock == NULL) {
+ blk = p->blocknum;
+
+ /*
+ * link in the remaining blocks.
+ */
+ for (j = i + 1; j <= k; j++) {
+ q = myconstraints[j].blocks;
+
+ while (q != NULL) {
+ if (q->blocknum == p->blocknum) {
+ if (p->nextbyblock == NULL) {
+ p->nextbyblock = q;
+ q->nextbyblock = NULL;
+ prev = q;
+ } else {
+ prev->nextbyblock = q;
+ q->nextbyblock = NULL;
+ prev = q;
+ }
+ break;
+ }
+ q = q->next;
+ }
+ }
+ }
+ p = p->next;
+ }
+ }
+}
+
+
+
+
+void addentry(struct constraintmatrix *constraints,
+ struct blockmatrix *C,
+ int matno,
+ int blkno, int indexi, int indexj, double ent, int blocksize)
+{
+ struct sparseblock *p;
+ struct sparseblock *p_sav;
+
+ p = constraints[matno].blocks;
+
+ if (matno != 0.0) {
+ if (p == NULL) {
+ /*
+ * We haven't yet allocated any blocks.
+ */
+ p = (struct sparseblock *) calloc(1, sizeof(struct sparseblock));
+
+ //two entries because this library ignores indices starting in zerox
+ p->constraintnum = matno;
+ p->blocknum = blkno;
+ p->numentries = 1;
+ p->next = NULL;
+
+ p->entries = calloc(p->numentries + 1, sizeof(double));
+ p->iindices = calloc(p->numentries + 1, sizeof(int));
+ p->jindices = calloc(p->numentries + 1, sizeof(int));
+
+ p->entries[p->numentries] = ent;
+ p->iindices[p->numentries] = indexi;
+ p->jindices[p->numentries] = indexj;
+
+ p->blocksize = blocksize;
+
+ constraints[matno].blocks = p;
+ } else {
+ /*
+ * We have some existing blocks. See whether this block is already
+ * in the chain.
+ */
+ while (p != NULL) {
+ if (p->blocknum == blkno) {
+ /*
+ * Found the right block.
+ */
+ p->constraintnum = matno;
+ p->blocknum = blkno;
+ p->numentries = p->numentries + 1;
+
+ p->entries =
+ realloc(p->entries, (p->numentries + 1) * sizeof(double));
+ p->iindices =
+ realloc(p->iindices, (p->numentries + 1) * sizeof(int));
+ p->jindices =
+ realloc(p->jindices, (p->numentries + 1) * sizeof(int));
+
+ p->entries[p->numentries] = ent;
+ p->iindices[p->numentries] = indexi;
+ p->jindices[p->numentries] = indexj;
+
+ return;
+ }
+ p_sav = p;
+ p = p->next;
+ }
+
+ /*
+ * If we get here, we have a non-empty structure but not the right block
+ * inside hence create a new structure.
+ */
+
+ p = (struct sparseblock *) calloc(1, sizeof(struct sparseblock));
+
+ //two entries because this library ignores indices starting in zerox
+ p->constraintnum = matno;
+ p->blocknum = blkno;
+ p->numentries = 1;
+ p->next = NULL;
+
+ p->entries = calloc(p->numentries + 1, sizeof(double));
+ p->iindices = calloc(p->numentries + 1, sizeof(int));
+ p->jindices = calloc(p->numentries + 1, sizeof(int));
+
+ p->entries[p->numentries] = ent;
+ p->iindices[p->numentries] = indexi;
+ p->jindices[p->numentries] = indexj;
+
+ p->blocksize = blocksize;
+
+ p_sav->next = p;
+ }
+ } else {
+ if (ent != 0.0) {
+ int blksz = C->blocks[blkno].blocksize;
+ if (C->blocks[blkno].blockcategory == DIAG) {
+ C->blocks[blkno].data.vec[indexi] = ent;
+ } else {
+ C->blocks[blkno].data.mat[ijtok(indexi, indexj, blksz)] = ent;
+ C->blocks[blkno].data.mat[ijtok(indexj, indexi, blksz)] = ent;
+ };
+ };
+
+ }
}
