triangle_reflection_complex/singular_values.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();
}