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use mpi to run on cluster

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This commit is contained in:
Florian Stecker 2021-10-01 13:36:56 -05:00
parent b5bd9d398f
commit 528f329c59
2 changed files with 324 additions and 189 deletions
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18
Makefile
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@ -3,20 +3,24 @@ HEADERS=linalg.h mat.h coxeter.h
#SPECIAL_OPTIONS=-O0 -g -D_DEBUG #SPECIAL_OPTIONS=-O0 -g -D_DEBUG
#SPECIAL_OPTIONS=-O3 -pg -funroll-loops -fno-inline #SPECIAL_OPTIONS=-O3 -pg -funroll-loops -fno-inline
SPECIAL_OPTIONS=-O3 -flto -funroll-loops -Winline SPECIAL_OPTIONS=-O3 -flto -funroll-loops -Winline
#SPECIAL_OPTIONS=-O3 -flto -funroll-loops -Winline -mavx512f -mavx512cd -mavx512er -mavx512pf # KNL
#SPECIAL_OPTIONS= #SPECIAL_OPTIONS=
OPTIONS=-m64 -march=native -mtune=native -std=gnu99 -D_GNU_SOURCE $(SPECIAL_OPTIONS) OPTIONS=-I../mps/include -L../mps/lib -pthread -m64 -std=gnu99 -D_GNU_SOURCE $(SPECIAL_OPTIONS)
all: singular_values special_element all: singular_values special_element convert
singular_values: singular_values.o coxeter.o linalg.o mat.o convert: convert.hs
gcc $(OPTIONS) -o singular_values coxeter.o linalg.o singular_values.o mat.o -lm -lgsl -lcblas -lgmp -lmps -lpthread ghc --make -dynamic convert.hs
singular_values: singular_values.o coxeter.o mat.o
mpicc $(OPTIONS) -o singular_values coxeter.o singular_values.o mat.o -lm -lgmp -lmps
special_element: special_element.o coxeter.o linalg.o mat.o special_element: special_element.o coxeter.o linalg.o mat.o
gcc $(OPTIONS) -o special_element coxeter.o linalg.o special_element.o mat.o -lm -lgsl -lcblas -lgmp -lmps -lpthread gcc $(OPTIONS) -o special_element coxeter.o linalg.o special_element.o mat.o -lm -lgmp -lmps
singular_values.o: singular_values.c $(HEADERS) singular_values.o: singular_values.c $(HEADERS)
gcc $(OPTIONS) -c singular_values.c mpicc $(OPTIONS) -c singular_values.c
special_element.o: special_element.c $(HEADERS) special_element.o: special_element.c $(HEADERS)
gcc $(OPTIONS) -c special_element.c gcc $(OPTIONS) -c special_element.c
@ -31,4 +35,4 @@ mat.o: mat.c $(HEADERS)
gcc $(OPTIONS) -c mat.c gcc $(OPTIONS) -c mat.c
clean: clean:
rm -f singular_values special_element coxeter.o linalg.o singular_values.o mat.o special_element.o rm -f singular_values special_element coxeter.o linalg.o singular_values.o mat.o special_element.o convert.hi convert.o convert

495
singular_values.c
View File

@ -1,18 +1,65 @@
#include "coxeter.h" #include "coxeter.h"
#include "linalg.h" //#include "linalg.h"
#include "mat.h" #include "mat.h"
#include <gsl/gsl_poly.h> //#include <gsl/gsl_poly.h>
#include <mps/mps.h> #include <mps/mps.h>
#include <mpi.h>
#include <sys/stat.h>
#include <sys/mman.h>
#include <fcntl.h>
#include <errno.h>
#include <string.h>
#include <unistd.h>
#define MIN(x,y) ((x)<(y)?(x):(y))
#define SWAP(t,x,y) do { t _tmp = (x); (x) = (y); (y) = _tmp; } while (0); #define SWAP(t,x,y) do { t _tmp = (x); (x) = (y); (y) = _tmp; } while (0);
#define DEBUG(msg, ...) do { print_time(); fprintf(stderr, msg, ##__VA_ARGS__); } while (0); #define DEBUG(msg, ...) do { print_time(); fprintf(stderr, msg, ##__VA_ARGS__); } while (0);
//#define DEBUG(msg, ...) //#define DEBUG(msg, ...)
//#define OUTPUT_POINTS #define TDIV 10
#define OUTPUT_SUMMARY #define TFROM 1
#define TTO 9
#define MDIV 10
#define MFROM 1
#define MTO 9
#define JOBNR(t,m) (((t)-TFROM) + ((m)-MFROM)*(TTO-TFROM+1))
#define NJOBS ((TTO-TFROM+1)*(MTO-MFROM+1))
#define FLUSH_INTERVAL 100
enum message_tag {
JOB_ORDER,
JOB_RESULT,
JOB_SHUTDOWN,
};
struct job {
int tparam, mparam;
int done;
double max_slope;
double time;
};
struct result {
mpq_t tr;
mpq_t trinv;
};
struct global_data {
int n;
group_t *group;
mat* matrices;
struct result *invariants;
struct result **distinct_invariants;
mps_context *solver;
};
struct timespec starttime; struct timespec starttime;
char processor_name[MPI_MAX_PROCESSOR_NAME];
int world_rank;
int world_size;
MPI_Datatype job_datatype;
void print_time() void print_time()
{ {
@ -23,14 +70,43 @@ void print_time()
diff = (current.tv_sec - starttime.tv_sec) + (current.tv_nsec - starttime.tv_nsec)*1e-9; diff = (current.tv_sec - starttime.tv_sec) + (current.tv_nsec - starttime.tv_nsec)*1e-9;
fprintf(stderr, "[%.3f] ", diff); fprintf(stderr, "[%04d %.3f] ", world_rank, diff);
} }
static struct global_data allocate_global_data(int n)
{
struct global_data result;
result.n = n;
result.matrices = malloc(n*sizeof(mat));
for(int i = 0; i < n; i++)
mat_init(result.matrices[i], 3);
result.invariants = malloc(n*sizeof(struct result));
result.distinct_invariants = malloc(n*sizeof(struct result*));
for(int i = 0; i < n; i++) {
mpq_init(result.invariants[i].tr);
mpq_init(result.invariants[i].trinv);
result.distinct_invariants[i] = &result.invariants[i];
}
result.solver = mps_context_new();
mps_context_set_output_prec(result.solver, 20); // relative precision
mps_context_set_output_goal(result.solver, MPS_OUTPUT_GOAL_APPROXIMATE);
struct result { return result;
mpq_t tr; }
mpq_t trinv;
}; void free_global_data(struct global_data dat)
{
for(int i = 0; i < dat.n; i++)
mat_clear(dat.matrices[i]);
free(dat.matrices);
for(int i = 0; i < dat.n; i++) {
mpq_clear(dat.invariants[i].tr);
mpq_clear(dat.invariants[i].trinv);
}
free(dat.invariants);
free(dat.distinct_invariants);
mps_context_free(dat.solver);
}
static int compare_result(const void *a_, const void *b_) static int compare_result(const void *a_, const void *b_)
{ {
@ -272,23 +348,57 @@ void enumerate(group_t *group, mat *matrices, mpq_t m, mpq_t t)
mat_workspace_clear(ws); mat_workspace_clear(ws);
} }
void output_invariants(group_t *group, mat *matrices, mpq_t s, mpq_t q, mps_context *solver)
double compute_max_slope(struct global_data dat, mpq_t t, mpq_t m)
{ {
mpq_t tr, trinv; // mpq_set_ui(t, ttick, 100);
char buf[100]; // mpq_set_ui(m, mtick, 100); // 414/1000 ~ sqrt(2)-1 <-> s=1
double evs[3]; // s = (1-mpq_get_d(m)*mpq_get_d(m))/(2*mpq_get_d(m));
int n = 0;
int nmax = dat.n;
int nuniq;
double max_slope;
int retval; int retval;
double evs[3];
mpq_inits(tr, trinv, NULL); group_t *group = dat.group;
mat *matrices = dat.matrices;
struct result *invariants = dat.invariants;
struct result **distinct_invariants = dat.distinct_invariants;
mps_context *solver = dat.solver;
for(int i = 0; i < group->size; i++) { // DEBUG("Compute matrices\n");
enumerate(group, matrices, m, t);
// DEBUG("Compute traces\n");
n = 0;
for(int i = 0; i < nmax; i++) {
if(group->elements[i].length % 2 != 0 || !group->elements[i].inverse) if(group->elements[i].length % 2 != 0 || !group->elements[i].inverse)
continue; continue;
mat_trace(tr, matrices[i]); mat_trace(invariants[i].tr, matrices[i]);
mat_trace(trinv, matrices[group->elements[i].inverse->id]); mat_trace(invariants[i].trinv, matrices[group->elements[i].inverse->id]);
retval = solve_characteristic_polynomial(solver, tr, trinv, evs); distinct_invariants[n++] = &invariants[i];
}
// DEBUG("Get unique traces\n");
qsort(distinct_invariants, n, sizeof(struct result*), compare_result);
nuniq = 0;
for(int i = 0; i < n; i++) {
if(i == 0 || compare_result(&distinct_invariants[i], &distinct_invariants[nuniq-1]) != 0)
distinct_invariants[nuniq++] = distinct_invariants[i];
}
max_slope = 0;
int max_slope_index;
// DEBUG("Solve characteristic polynomials\n");
for(int i = 0; i < nuniq; i++) {
retval = solve_characteristic_polynomial(solver, distinct_invariants[i]->tr, distinct_invariants[i]->trinv, evs);
if(retval == 1) { if(retval == 1) {
fprintf(stderr, "Error! Could not solve polynomial.\n"); fprintf(stderr, "Error! Could not solve polynomial.\n");
continue; continue;
@ -303,209 +413,230 @@ void output_invariants(group_t *group, mat *matrices, mpq_t s, mpq_t q, mps_cont
if(fabs(evs[0]) < fabs(evs[1])) if(fabs(evs[0]) < fabs(evs[1]))
SWAP(double, evs[0], evs[1]); SWAP(double, evs[0], evs[1]);
gmp_printf("%d %d %s %Qd %Qd %f %f\n", i, group->elements[i].length, print_word(&group->elements[i], buf), tr, trinv, log(evs[0]), -log(evs[2])); double x = log(fabs(evs[0]));
double y = -log(fabs(evs[2]));
if(y/x > max_slope && (x > 0.1 || y > 0.1)) {
max_slope_index = distinct_invariants[i] - invariants;
max_slope = y/x;
}
// gmp_printf("%Qd %Qd %f %f %f\n", distinct_invariants[i]->tr, distinct_invariants[i]->trinv, x, y, y/x);
} }
mpq_clears(tr, trinv, NULL); return max_slope;
} }
/* void write_results_and_end(struct job *jobs, const char *outfile)
double max_slope(groupelement_t *group, mat *matrices, mpq_t s, mpq_t t, int *index)
{ {
double max = 0; DEBUG("writing output and shutting down\n");
double slope;
mpq_t tr, trinv; FILE *f = fopen(outfile, "w");
char buf[100]; for(int i = 0; i < NJOBS; i++)
fprintf(f, "%d/%d %d/%d %.10f %.10f %.10f %.3f\n",
jobs[i].tparam, TDIV, jobs[i].mparam, MDIV,
(double)jobs[i].tparam/TDIV, (double)jobs[i].mparam/MDIV, jobs[i].max_slope,
jobs[i].time);
fclose(f);
mpq_inits(tr, trinv, NULL); for(int i = 1; i < world_size; i++)
MPI_Send(NULL, 0, job_datatype, i, JOB_SHUTDOWN, MPI_COMM_WORLD);
for(int i = 0; i < MAX_ELEMENTS; i++) { }
if(group[i].length % 2 != 0 || !group[i].inverse)
continue;
mat_trace(tr, matrices[i]); void run_master_process(int nmax, const char *restart, const char *outfile)
mat_trace(trinv, matrices[group[i].inverse->id]); {
int total_jobs = NJOBS;
int completed = 0;
int queue_jobs = MIN(total_jobs, 2*world_size);
struct job current_job;
MPI_Status status;
FILE *f;
int continuing = 1;
int restartf;
struct job *alljobs;
struct job *current;
slope = log(mpq_get_d(trinv))/log(mpq_get_d(tr)); restartf = open(restart, O_RDWR);
if(slope > max) if(restartf == -1 && errno == ENOENT) {
{ restartf = open(restart, O_RDWR | O_CREAT, 0666);
*index = i; continuing = 0;
max = slope; }
if(restartf == -1) {
DEBUG("error opening restart file: %s\n", strerror(errno));
exit(1);
}
ftruncate(restartf, total_jobs*sizeof(struct job));
alljobs = (struct job*) mmap(0, total_jobs*sizeof(struct job), PROT_READ | PROT_WRITE, MAP_SHARED, restartf, 0);
if(alljobs == MAP_FAILED) {
DEBUG("error mapping restart file: %s\n", strerror(errno));
exit(1);
}
if(continuing) {
for(int i = 0; i < total_jobs; i++)
if(alljobs[i].done)
completed++;
} else {
for(int tparam = TFROM; tparam <= TTO; tparam++) {
for(int mparam = MFROM; mparam <= MTO; mparam++) {
alljobs[JOBNR(tparam,mparam)].tparam = tparam;
alljobs[JOBNR(tparam,mparam)].mparam = mparam;
alljobs[JOBNR(tparam,mparam)].done = 0;
}
} }
} }
mpq_clears(tr, trinv, NULL); fsync(restartf);
return max; if(continuing) {
DEBUG("continuing from restart file, %d/%d jobs completed, %d nodes\n", completed, total_jobs, world_size);
} else {
DEBUG("starting from scratch, %d jobs, %d nodes\n", total_jobs, world_size);
}
if(completed >= total_jobs)
{
write_results_and_end(alljobs, outfile);
goto cleanup;
}
// assign initial jobs
current = alljobs-1;
for(int i = 0; i < 2*world_size; i++) {
do {
current++;
} while(current < alljobs + total_jobs && current->done);
if(current >= alljobs + total_jobs) // all jobs are assigned
break;
MPI_Send(current, 1, job_datatype, 1 + i%(world_size-1), JOB_ORDER, MPI_COMM_WORLD);
}
while(1) {
MPI_Probe(MPI_ANY_SOURCE, MPI_ANY_TAG, MPI_COMM_WORLD, &status);
if(status.MPI_TAG == JOB_RESULT) {
MPI_Recv(&current_job, 1, job_datatype, MPI_ANY_SOURCE, JOB_RESULT, MPI_COMM_WORLD, &status);
completed++;
DEBUG("job (%d,%d) completed by instance %d in %f seconds, result = %.3f, %d/%d done\n",
current_job.tparam, current_job.mparam,
status.MPI_SOURCE, current_job.time, current_job.max_slope, completed, total_jobs);
int nr = JOBNR(current_job.tparam, current_job.mparam);
memcpy(&alljobs[nr], &current_job, sizeof(struct job));
alljobs[nr].done = 1;
if(completed % FLUSH_INTERVAL == 0)
fsync(restartf);
// find the next unassigned job
do {
current++;
} while(current < alljobs + total_jobs && current->done);
if(current < alljobs + total_jobs) {
MPI_Send(current, 1, job_datatype, status.MPI_SOURCE, JOB_ORDER, MPI_COMM_WORLD);
}
if(completed >= total_jobs) {
write_results_and_end(alljobs, outfile);
goto cleanup;
}
}
}
cleanup:
munmap(alljobs, total_jobs*sizeof(struct job));
close(restartf);
} }
*/
int main(int argc, char *argv[]) int main(int argc, char *argv[])
{ {
mpq_t m, t, tmp; int name_len;
double s;
mat *matrices;
group_t *group;
int index;
mps_context *solver;
int acc = 100;
int n, nuniq, nmax;
int retval;
double evs[3];
double max_slope;
char buf[100];
char buf2[100];
struct result *invariants; MPI_Status status;
struct result **distinct_invariants;
mpq_t m, t;
double s;
struct job current_job;
int nmax;
double max_slope;
struct global_data dat;
double jobtime;
clock_gettime(CLOCK_REALTIME, &starttime); clock_gettime(CLOCK_REALTIME, &starttime);
if(argc < 4) {
fprintf(stderr, "Usage: mpirun -n <nr> --hostfile <hostfile> %s <number of elements> <restartfile> <outfile>\n", argv[0]);
return 0;
}
nmax = atoi(argv[1]); nmax = atoi(argv[1]);
DEBUG("Allocate\n"); MPI_Init(NULL, NULL);
MPI_Comm_size(MPI_COMM_WORLD, &world_size);
MPI_Comm_rank(MPI_COMM_WORLD, &world_rank);
MPI_Get_processor_name(processor_name, &name_len);
mpq_inits(m, t, tmp, NULL); // DEBUG("instance %d/%d started on %s\n", world_rank, world_size, processor_name);
matrices = malloc(nmax*sizeof(mat));
for(int i = 0; i < nmax; i++) int blocklengths[2] = {3, 2};
mat_init(matrices[i], 3); MPI_Datatype types[2] = {MPI_INT, MPI_DOUBLE};
invariants = malloc(nmax*sizeof(struct result)); MPI_Aint displacements[2] = {(size_t)&((struct job*)0)->tparam, (size_t)&((struct job*)0)->max_slope};
distinct_invariants = malloc(nmax*sizeof(struct result)); MPI_Type_create_struct(2, blocklengths, displacements, types, &job_datatype);
for(int i = 0; i < nmax; i++) { MPI_Type_commit(&job_datatype);
mpq_init(invariants[i].tr);
mpq_init(invariants[i].trinv); if(world_rank == 0) { // master processor
distinct_invariants[i] = &invariants[i]; run_master_process(nmax, argv[2], argv[3]);
MPI_Finalize();
return 0;
} }
solver = mps_context_new(); // DEBUG("Allocate & generate group\n");
mps_context_set_output_prec(solver, 20); // relative precision mpq_inits(m, t, NULL);
mps_context_set_output_goal(solver, MPS_OUTPUT_GOAL_APPROXIMATE); dat = allocate_global_data(nmax);
dat.group = coxeter_init_triangle(4, 4, 4, nmax);
/* // fprintf(stderr, "max word length = %d\n", dat.group->elements[nmax-1].length);
DEBUG("Approximate parameters\n");
// get approximate s and q values while(1) {
sapprox = atof(argv[2]); MPI_Probe(0, MPI_ANY_TAG, MPI_COMM_WORLD, &status);
tapprox = atof(argv[3]); // MPI_Recv(&current_job, 1, job_datatype, 0, MPI_ANY_TAG, MPI_COMM_WORLD, &status);
tqfactor = pow((sapprox*sapprox-sapprox+1)*(sapprox*sapprox-sapprox+1)*(sapprox*sapprox+1), 1/6.0); if(status.MPI_TAG == JOB_SHUTDOWN) {
qapprox = tapprox/tqfactor; // DEBUG("instance %d shutting down\n", world_rank);
for(int i = 0; ; i++) {
continued_fraction_approximation(tmp, sapprox, i);
if(fabs(mpq_get_d(t)-sapprox) < 1e-10
|| (mpz_cmpabs_ui(mpq_numref(tmp),acc) > 0 && mpz_cmpabs_ui(mpq_denref(tmp),acc) > 0))
break; break;
mpq_set(s, tmp); }
} else if(status.MPI_TAG == JOB_ORDER) {
mpq_canonicalize(s); MPI_Recv(&current_job, 1, job_datatype, 0, MPI_ANY_TAG, MPI_COMM_WORLD, &status);
DEBUG("instance %d starting order (%d,%d)\n", world_rank, current_job.tparam, current_job.mparam);
for(int i = 0; ; i++) { jobtime = -MPI_Wtime();
continued_fraction_approximation(tmp, qapprox, i);
if(fabs(mpq_get_d(t)-qapprox) < 1e-10
|| (mpz_cmpabs_ui(mpq_numref(tmp),acc) > 0 && mpz_cmpabs_ui(mpq_denref(tmp),acc) > 0))
break;
mpq_set(q, tmp);
}
mpq_canonicalize(q);
tqfactor = pow((mpq_get_d(s)*mpq_get_d(s)-mpq_get_d(s)+1)*(mpq_get_d(s)*mpq_get_d(s)-mpq_get_d(s)+1)*(mpq_get_d(s)*mpq_get_d(s)+1), 1/6.0); // do the actual work
mpq_set_ui(t, current_job.tparam, TDIV);
#ifdef OUTPUT_POINTS mpq_set_ui(m, current_job.mparam, MDIV);
gmp_fprintf(stdout, "\"s = %Qd = %.3f, q = %Qd, t = %.3f\"\n", s, mpq_get_d(s), q, mpq_get_d(q)*tqfactor);
#endif
*/
// group
DEBUG("Generate group\n");
group = coxeter_init_triangle(4, 4, 4, nmax);
fprintf(stderr, "max word length = %d\n", group->elements[nmax-1].length);
for(int ttick = 45; ttick <= 65; ttick++) {
for(int mtick = 45; mtick < 65; mtick++) {
mpq_set_ui(t, ttick, 100);
mpq_set_ui(m, mtick, 100); // 414/1000 ~ sqrt(2)-1 <-> s=1
s = (1-mpq_get_d(m)*mpq_get_d(m))/(2*mpq_get_d(m)); s = (1-mpq_get_d(m)*mpq_get_d(m))/(2*mpq_get_d(m));
DEBUG("Compute matrices\n"); max_slope = compute_max_slope(dat, t, m);
enumerate(group, matrices, m, t);
n = 0; jobtime += MPI_Wtime();
DEBUG("Compute traces\n");
for(int i = 0; i < nmax; i++) {
if(group->elements[i].length % 2 != 0 || !group->elements[i].inverse)
continue;
mat_trace(invariants[i].tr, matrices[i]); // fprintf(stdout, "%.5f %.5f %.5f %f\n",
mat_trace(invariants[i].trinv, matrices[group->elements[i].inverse->id]); // mpq_get_d(t), mpq_get_d(m), s, max_slope);
current_job.max_slope = max_slope;
current_job.time = jobtime;
distinct_invariants[n++] = &invariants[i]; DEBUG("instance %d finished order (%d,%d) in %f seconds\n", world_rank, current_job.tparam, current_job.mparam, jobtime);
// gmp_printf("%Qd %Qd %d %s\n", invariants[i].tr, invariants[i].trinv, i, print_word(&group->elements[i], buf)); MPI_Send(&current_job, 1, job_datatype, 0, JOB_RESULT, MPI_COMM_WORLD);
}
DEBUG("Get unique traces\n");
qsort(distinct_invariants, n, sizeof(struct result*), compare_result);
nuniq = 0;
for(int i = 0; i < n; i++) {
if(i == 0 || compare_result(&distinct_invariants[i], &distinct_invariants[nuniq-1]) != 0)
distinct_invariants[nuniq++] = distinct_invariants[i];
}
max_slope = 0;
int max_slope_index;
DEBUG("Solve characteristic polynomials\n");
for(int i = 0; i < nuniq; i++) {
retval = solve_characteristic_polynomial(solver, distinct_invariants[i]->tr, distinct_invariants[i]->trinv, evs);
if(retval == 1) {
fprintf(stderr, "Error! Could not solve polynomial.\n");
continue;
} else if(retval == 2) {
continue;
}
if(fabs(evs[0]) < fabs(evs[1]))
SWAP(double, evs[0], evs[1]);
if(fabs(evs[1]) < fabs(evs[2]))
SWAP(double, evs[1], evs[2]);
if(fabs(evs[0]) < fabs(evs[1]))
SWAP(double, evs[0], evs[1]);
double x = log(fabs(evs[0]));
double y = -log(fabs(evs[2]));
if(y/x > max_slope && (x > 0.1 || y > 0.1)) {
max_slope_index = distinct_invariants[i] - invariants;
max_slope = y/x;
}
#ifdef OUTPUT_POINTS
gmp_printf("%Qd %Qd %f %f %f\n", distinct_invariants[i]->tr, distinct_invariants[i]->trinv, x, y, y/x);
#endif
}
#ifdef OUTPUT_SUMMARY
// fprintf(stdout, "%.5f %.5f %.5f %f %s\n", mpq_get_d(t), mpq_get_d(m), s, max_slope, print_word(&group->elements[max_slope_index], buf));
fprintf(stdout, "%.5f %.5f %.5f %f %s\n", mpq_get_d(t), mpq_get_d(m), s, max_slope, print_word(&group->elements[max_slope_index], buf));
#endif
} }
} }
DEBUG("Clean up\n"); // DEBUG("Clean up\n");
for(int i = 0; i < nmax; i++) { coxeter_clear(dat.group);
mpq_clear(invariants[i].tr); free_global_data(dat);
mpq_clear(invariants[i].trinv); mpq_clears(m, t, NULL);
}
free(invariants); MPI_Type_free(&job_datatype);
free(distinct_invariants); MPI_Finalize();
for(int i = 0; i < nmax; i++)
mat_clear(matrices[i]);
free(matrices);
coxeter_clear(group);
mpq_clears(m, t, tmp, NULL);
mps_context_free(solver);
} }