use mpi to run on cluster
This commit is contained in:
Florian Stecker
parent
b5bd9d398f
commit
528f329c59
18
Makefile
18
Makefile
|
|
@ -3,20 +3,24 @@ HEADERS=linalg.h mat.h coxeter.h
|
|||
#SPECIAL_OPTIONS=-O0 -g -D_DEBUG
|
||||
#SPECIAL_OPTIONS=-O3 -pg -funroll-loops -fno-inline
|
||||
SPECIAL_OPTIONS=-O3 -flto -funroll-loops -Winline
|
||||
#SPECIAL_OPTIONS=-O3 -flto -funroll-loops -Winline -mavx512f -mavx512cd -mavx512er -mavx512pf # KNL
|
||||
#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
|
||||
gcc $(OPTIONS) -o singular_values coxeter.o linalg.o singular_values.o mat.o -lm -lgsl -lcblas -lgmp -lmps -lpthread
|
||||
convert: convert.hs
|
||||
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
|
||||
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)
|
||||
gcc $(OPTIONS) -c singular_values.c
|
||||
mpicc $(OPTIONS) -c singular_values.c
|
||||
|
||||
special_element.o: special_element.c $(HEADERS)
|
||||
gcc $(OPTIONS) -c special_element.c
|
||||
|
|
@ -31,4 +35,4 @@ mat.o: mat.c $(HEADERS)
|
|||
gcc $(OPTIONS) -c mat.c
|
||||
|
||||
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
|
||||
|
|
|
|||
|
|
@ -1,18 +1,65 @@
|
|||
#include "coxeter.h"
|
||||
#include "linalg.h"
|
||||
//#include "linalg.h"
|
||||
#include "mat.h"
|
||||
|
||||
#include <gsl/gsl_poly.h>
|
||||
//#include <gsl/gsl_poly.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 DEBUG(msg, ...) do { print_time(); fprintf(stderr, msg, ##__VA_ARGS__); } while (0);
|
||||
//#define DEBUG(msg, ...)
|
||||
|
||||
//#define OUTPUT_POINTS
|
||||
#define OUTPUT_SUMMARY
|
||||
#define TDIV 10
|
||||
#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;
|
||||
char processor_name[MPI_MAX_PROCESSOR_NAME];
|
||||
int world_rank;
|
||||
int world_size;
|
||||
MPI_Datatype job_datatype;
|
||||
|
||||
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;
|
||||
|
||||
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 {
|
||||
mpq_t tr;
|
||||
mpq_t trinv;
|
||||
};
|
||||
return result;
|
||||
}
|
||||
|
||||
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_)
|
||||
{
|
||||
|
|
@ -272,23 +348,57 @@ void enumerate(group_t *group, mat *matrices, mpq_t m, mpq_t t)
|
|||
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;
|
||||
char buf[100];
|
||||
double evs[3];
|
||||
// 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));
|
||||
|
||||
int n = 0;
|
||||
int nmax = dat.n;
|
||||
int nuniq;
|
||||
double max_slope;
|
||||
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)
|
||||
continue;
|
||||
|
||||
mat_trace(tr, matrices[i]);
|
||||
mat_trace(trinv, matrices[group->elements[i].inverse->id]);
|
||||
mat_trace(invariants[i].tr, matrices[i]);
|
||||
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) {
|
||||
fprintf(stderr, "Error! Could not solve polynomial.\n");
|
||||
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]))
|
||||
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;
|
||||
}
|
||||
|
||||
/*
|
||||
double max_slope(groupelement_t *group, mat *matrices, mpq_t s, mpq_t t, int *index)
|
||||
void write_results_and_end(struct job *jobs, const char *outfile)
|
||||
{
|
||||
double max = 0;
|
||||
double slope;
|
||||
DEBUG("writing output and shutting down\n");
|
||||
|
||||
mpq_t tr, trinv;
|
||||
char buf[100];
|
||||
FILE *f = fopen(outfile, "w");
|
||||
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]);
|
||||
mat_trace(trinv, matrices[group[i].inverse->id]);
|
||||
void run_master_process(int nmax, const char *restart, const char *outfile)
|
||||
{
|
||||
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));
|
||||
if(slope > max)
|
||||
{
|
||||
*index = i;
|
||||
max = slope;
|
||||
restartf = open(restart, O_RDWR);
|
||||
if(restartf == -1 && errno == ENOENT) {
|
||||
restartf = open(restart, O_RDWR | O_CREAT, 0666);
|
||||
continuing = 0;
|
||||
}
|
||||
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(¤t_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], ¤t_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[])
|
||||
{
|
||||
mpq_t m, t, tmp;
|
||||
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];
|
||||
int name_len;
|
||||
|
||||
struct result *invariants;
|
||||
struct result **distinct_invariants;
|
||||
MPI_Status status;
|
||||
|
||||
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);
|
||||
|
||||
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]);
|
||||
|
||||
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);
|
||||
matrices = malloc(nmax*sizeof(mat));
|
||||
for(int i = 0; i < nmax; i++)
|
||||
mat_init(matrices[i], 3);
|
||||
invariants = malloc(nmax*sizeof(struct result));
|
||||
distinct_invariants = malloc(nmax*sizeof(struct result));
|
||||
for(int i = 0; i < nmax; i++) {
|
||||
mpq_init(invariants[i].tr);
|
||||
mpq_init(invariants[i].trinv);
|
||||
distinct_invariants[i] = &invariants[i];
|
||||
// DEBUG("instance %d/%d started on %s\n", world_rank, world_size, processor_name);
|
||||
|
||||
int blocklengths[2] = {3, 2};
|
||||
MPI_Datatype types[2] = {MPI_INT, MPI_DOUBLE};
|
||||
MPI_Aint displacements[2] = {(size_t)&((struct job*)0)->tparam, (size_t)&((struct job*)0)->max_slope};
|
||||
MPI_Type_create_struct(2, blocklengths, displacements, types, &job_datatype);
|
||||
MPI_Type_commit(&job_datatype);
|
||||
|
||||
if(world_rank == 0) { // master processor
|
||||
run_master_process(nmax, argv[2], argv[3]);
|
||||
MPI_Finalize();
|
||||
return 0;
|
||||
}
|
||||
|
||||
solver = mps_context_new();
|
||||
mps_context_set_output_prec(solver, 20); // relative precision
|
||||
mps_context_set_output_goal(solver, MPS_OUTPUT_GOAL_APPROXIMATE);
|
||||
// DEBUG("Allocate & generate group\n");
|
||||
mpq_inits(m, t, NULL);
|
||||
dat = allocate_global_data(nmax);
|
||||
dat.group = coxeter_init_triangle(4, 4, 4, nmax);
|
||||
|
||||
/*
|
||||
DEBUG("Approximate parameters\n");
|
||||
// fprintf(stderr, "max word length = %d\n", dat.group->elements[nmax-1].length);
|
||||
|
||||
// get approximate s and q values
|
||||
sapprox = atof(argv[2]);
|
||||
tapprox = atof(argv[3]);
|
||||
tqfactor = pow((sapprox*sapprox-sapprox+1)*(sapprox*sapprox-sapprox+1)*(sapprox*sapprox+1), 1/6.0);
|
||||
qapprox = tapprox/tqfactor;
|
||||
|
||||
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))
|
||||
while(1) {
|
||||
MPI_Probe(0, MPI_ANY_TAG, MPI_COMM_WORLD, &status);
|
||||
// MPI_Recv(¤t_job, 1, job_datatype, 0, MPI_ANY_TAG, MPI_COMM_WORLD, &status);
|
||||
if(status.MPI_TAG == JOB_SHUTDOWN) {
|
||||
// DEBUG("instance %d shutting down\n", world_rank);
|
||||
break;
|
||||
mpq_set(s, tmp);
|
||||
}
|
||||
mpq_canonicalize(s);
|
||||
}
|
||||
else if(status.MPI_TAG == JOB_ORDER) {
|
||||
MPI_Recv(¤t_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++) {
|
||||
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);
|
||||
jobtime = -MPI_Wtime();
|
||||
|
||||
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);
|
||||
|
||||
#ifdef OUTPUT_POINTS
|
||||
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
|
||||
// do the actual work
|
||||
mpq_set_ui(t, current_job.tparam, TDIV);
|
||||
mpq_set_ui(m, current_job.mparam, MDIV);
|
||||
s = (1-mpq_get_d(m)*mpq_get_d(m))/(2*mpq_get_d(m));
|
||||
|
||||
DEBUG("Compute matrices\n");
|
||||
enumerate(group, matrices, m, t);
|
||||
max_slope = compute_max_slope(dat, t, m);
|
||||
|
||||
n = 0;
|
||||
DEBUG("Compute traces\n");
|
||||
for(int i = 0; i < nmax; i++) {
|
||||
if(group->elements[i].length % 2 != 0 || !group->elements[i].inverse)
|
||||
continue;
|
||||
jobtime += MPI_Wtime();
|
||||
|
||||
mat_trace(invariants[i].tr, matrices[i]);
|
||||
mat_trace(invariants[i].trinv, matrices[group->elements[i].inverse->id]);
|
||||
// fprintf(stdout, "%.5f %.5f %.5f %f\n",
|
||||
// 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));
|
||||
}
|
||||
|
||||
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
|
||||
MPI_Send(¤t_job, 1, job_datatype, 0, JOB_RESULT, MPI_COMM_WORLD);
|
||||
}
|
||||
}
|
||||
|
||||
DEBUG("Clean up\n");
|
||||
for(int i = 0; i < nmax; i++) {
|
||||
mpq_clear(invariants[i].tr);
|
||||
mpq_clear(invariants[i].trinv);
|
||||
}
|
||||
free(invariants);
|
||||
free(distinct_invariants);
|
||||
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);
|
||||
// DEBUG("Clean up\n");
|
||||
coxeter_clear(dat.group);
|
||||
free_global_data(dat);
|
||||
mpq_clears(m, t, NULL);
|
||||
|
||||
MPI_Type_free(&job_datatype);
|
||||
MPI_Finalize();
|
||||
}
|
||||
|
|
|
|||
Loading…
Reference in New Issue