triangle_reflection_complex/singular_values.c
2021-10-01 13:36:56 -05:00

643 lines
16 KiB
C

#include "coxeter.h"
//#include "linalg.h"
#include "mat.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 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()
{
double diff;
struct timespec current;
clock_gettime(CLOCK_REALTIME, &current);
diff = (current.tv_sec - starttime.tv_sec) + (current.tv_nsec - starttime.tv_nsec)*1e-9;
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);
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_)
{
int d = 0;
struct result **a = (struct result **)a_;
struct result **b = (struct result **)b_;
d = mpq_cmp((*a)->tr,(*b)->tr);
if(d == 0)
d = mpq_cmp((*a)->trinv, (*b)->trinv);
return d;
}
int solve_characteristic_polynomial(mps_context *solv, mpq_t tr, mpq_t trinv, double *eigenvalues)
{
mpq_t coeff1, coeff2, zero;
cplx_t *roots;
double radii[3];
double *radii_p[3];
mps_monomial_poly *poly;
mps_boolean errors;
int result = 0;
mpq_inits(coeff1, coeff2, zero, NULL);
mpq_set(coeff1, trinv);
mpq_sub(coeff2, zero, tr);
poly = mps_monomial_poly_new(solv, 3);
mps_monomial_poly_set_coefficient_int(solv, poly, 0, -1, 0);
mps_monomial_poly_set_coefficient_q(solv, poly, 1, coeff1, zero);
mps_monomial_poly_set_coefficient_q(solv, poly, 2, coeff2, zero);
mps_monomial_poly_set_coefficient_int(solv, poly, 3, 1, 0);
mps_context_set_input_poly(solv, (mps_polynomial*)poly);
mps_mpsolve(solv);
roots = cplx_valloc(3);
for(int i = 0; i < 3; i++)
radii_p[i] = &(radii[i]);
mps_context_get_roots_d(solv, &roots, radii_p);
errors = mps_context_has_errors(solv);
if(errors) {
result = 1;
} else {
for(int i = 0; i < 3; i++) {
eigenvalues[i] = cplx_Re(roots[i]);
if(fabs(cplx_Im(roots[i])) > radii[i]) // non-real root
result = 2;
}
}
cplx_vfree(roots);
mpq_clears(coeff1, coeff2, zero, NULL);
return result;
}
void continued_fraction_approximation(mpq_t out, double in, int level)
{
mpq_t tmp;
if(in < 0) {
mpq_init(tmp);
mpq_set_ui(tmp, 0, 1);
continued_fraction_approximation(out, -in, level);
mpq_sub(out, tmp, out);
mpq_clear(tmp);
return;
}
if(level == 0) {
mpq_set_si(out, (signed long int)round(in), 1); // floor(in)
} else {
continued_fraction_approximation(out, 1/(in - floor(in)), level - 1);
mpq_init(tmp);
mpq_set_ui(tmp, 1, 1);
mpq_div(out, tmp, out); // out -> 1/out
mpq_set_si(tmp, (signed long int)in, 1); // floor(in)
mpq_add(out, out, tmp);
mpq_clear(tmp);
}
}
void quartic(mpq_t out, mpq_t in, int a, int b, int c, int d, int e)
{
mpq_t tmp;
mpq_init(tmp);
mpq_set_si(out, a, 1);
mpq_mul(out, out, in);
mpq_set_si(tmp, b, 1);
mpq_add(out, out, tmp);
mpq_mul(out, out, in);
mpq_set_si(tmp, c, 1);
mpq_add(out, out, tmp);
mpq_mul(out, out, in);
mpq_set_si(tmp, d, 1);
mpq_add(out, out, tmp);
mpq_mul(out, out, in);
mpq_set_si(tmp, e, 1);
mpq_add(out, out, tmp);
mpq_clear(tmp);
}
// this version is only for the (4,4,4) group
void initialize_triangle_generators(mat_workspace *ws, mat *gen, mpq_t m, mpq_t t)
{
mpq_t s,sinv,q,x,y;
mpq_t zero, one, two;
mpq_t tmp;
mpq_inits(s,sinv,q,x,y,zero,one,two,tmp,NULL);
mpq_set_ui(zero, 0, 1);
mpq_set_ui(one, 1, 1);
mpq_set_ui(two, 2, 1);
// s = (1-m^2)/2m
mpq_mul(s, m, m);
mpq_sub(s, one, s);
mpq_div(s, s, m);
mpq_div(s, s, two);
mpq_div(sinv, one, s);
// q = (1+m^2)/(1-m^2) = 2/(1-m^2) - 1
mpq_mul(q, m, m);
mpq_sub(q, one, q);
mpq_div(q, two, q);
mpq_sub(q, q, one);
// x = -tq, y = -q/t
mpq_mul(x, q, t);
mpq_sub(x, zero, x);
mpq_div(y, q, t);
mpq_sub(y, zero, y);
// q^2 = xy = 1 + 1/s^2
// [ -s s*y 0]
// [ -s*x s*x*y - 1/s 0]
// [ -s*y s*y^2 - x 1]
LOOP(i,3) {
mat_zero(gen[i]);
mpq_sub(tmp, zero, s);
mat_set(gen[i%3], i%3, i%3, tmp);
mpq_mul(tmp, s, y);
mat_set(gen[i%3], i%3, (i+1)%3, tmp);
mpq_mul(tmp, s, x);
mpq_sub(tmp, zero, tmp);
mat_set(gen[i%3], (i+1)%3, i%3, tmp);
mpq_mul(tmp, s, x);
mpq_mul(tmp, tmp, y);
mpq_sub(tmp, tmp, sinv);
mat_set(gen[i%3], (i+1)%3, (i+1)%3, tmp);
mpq_mul(tmp, s, y);
mpq_sub(tmp, zero, tmp);
mat_set(gen[i%3], (i+2)%3, i%3, tmp);
mpq_mul(tmp, s, y);
mpq_mul(tmp, tmp, y);
mpq_sub(tmp, tmp, x);
mat_set(gen[i%3], (i+2)%3, (i+1)%3, tmp);
mat_set(gen[i%3], (i+2)%3, (i+2)%3, one);
}
LOOP(i,3) mat_pseudoinverse(ws, gen[i+3], gen[i]);
// debug output
/*
gmp_printf("m = %Qd, s = %Qd, t = %Qd, q = %Qd, x = %Qd, y = %Qd\n", m, s, t, q, x, y);
mat_print(gen[0]);
mat_print(gen[1]);
mat_print(gen[2]);
*/
mpq_inits(s,sinv,q,x,y,zero,one,two,tmp,NULL);
}
char *print_word(groupelement_t *g, char *str)
{
int i = g->length - 1;
str[g->length] = 0;
while(g->parent) {
str[i--] = 'a' + g->letter;
g = g->parent;
}
return str;
}
void enumerate(group_t *group, mat *matrices, mpq_t m, mpq_t t)
{
mat_workspace *ws;
mat tmp;
mat gen[6];
char buf[100], buf2[100], buf3[100];
// allocate stuff
ws = mat_workspace_init(3);
for(int i = 0; i < 6; i++)
mat_init(gen[i], 3);
mat_init(tmp, 3);
initialize_triangle_generators(ws, gen, m, t);
mat_identity(matrices[0]);
for(int i = 1; i < group->size; i++) {
if(group->elements[i].length % 2 != 0)
continue;
if(!group->elements[i].inverse)
continue;
int parent = group->elements[i].parent->id;
int grandparent = group->elements[i].parent->parent->id;
int letter;
if(group->elements[parent].letter == 1 && group->elements[i].letter == 2)
letter = 0; // p = bc
else if(group->elements[parent].letter == 2 && group->elements[i].letter == 0)
letter = 1; // q = ca
else if(group->elements[parent].letter == 0 && group->elements[i].letter == 1)
letter = 2; // r = ab
if(group->elements[parent].letter == 2 && group->elements[i].letter == 1)
letter = 3; // p^{-1} = cb
else if(group->elements[parent].letter == 0 && group->elements[i].letter == 2)
letter = 4; // q^{-1} = ac
else if(group->elements[parent].letter == 1 && group->elements[i].letter == 0)
letter = 5; // r^{-1} = ba
mat_multiply(ws, matrices[i], matrices[grandparent], gen[letter]);
}
// free stuff
for(int i = 0; i < 6; i++)
mat_clear(gen[i]);
mat_clear(tmp);
mat_workspace_clear(ws);
}
double compute_max_slope(struct global_data dat, mpq_t t, mpq_t m)
{
// 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];
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;
// 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(invariants[i].tr, matrices[i]);
mat_trace(invariants[i].trinv, matrices[group->elements[i].inverse->id]);
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;
} 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;
}
// gmp_printf("%Qd %Qd %f %f %f\n", distinct_invariants[i]->tr, distinct_invariants[i]->trinv, x, y, y/x);
}
return max_slope;
}
void write_results_and_end(struct job *jobs, const char *outfile)
{
DEBUG("writing output and shutting down\n");
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);
for(int i = 1; i < world_size; i++)
MPI_Send(NULL, 0, job_datatype, i, JOB_SHUTDOWN, MPI_COMM_WORLD);
}
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;
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;
}
}
}
fsync(restartf);
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 name_len;
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]);
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);
// 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;
}
// DEBUG("Allocate & generate group\n");
mpq_inits(m, t, NULL);
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);
while(1) {
MPI_Probe(0, MPI_ANY_TAG, MPI_COMM_WORLD, &status);
// MPI_Recv(&current_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;
}
else if(status.MPI_TAG == JOB_ORDER) {
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);
jobtime = -MPI_Wtime();
// 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));
max_slope = compute_max_slope(dat, t, m);
jobtime += MPI_Wtime();
// 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;
DEBUG("instance %d finished order (%d,%d) in %f seconds\n", world_rank, current_job.tparam, current_job.mparam, jobtime);
MPI_Send(&current_job, 1, job_datatype, 0, JOB_RESULT, MPI_COMM_WORLD);
}
}
// DEBUG("Clean up\n");
coxeter_clear(dat.group);
free_global_data(dat);
mpq_clears(m, t, NULL);
MPI_Type_free(&job_datatype);
MPI_Finalize();
}