triangle_reflection_complex/singular_values.c

#include "coxeter.h"
#include "linalg.h"
#include "mat.h"
#include "enumerate_triangle_group.h"

#include <time.h>

#define SWAP(t,x,y) do { t _tmp = (x); (x) = (y); (y) = _tmp; } while (0);

#define DEBUG(msg, ...) fprintf(stderr, "[%10.3f] " msg, runtime(), ##__VA_ARGS__);
//#define DEBUG(msg, ...)

struct result {
	int id;
	int count;
	mpq_t tr;
	mpq_t trinv;
	double x;
	double y;
};

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;
}

static int compare_result_by_id(const void *a_, const void *b_)
{
	int d = 0;

	struct result **a = (struct result **)a_;
	struct result **b = (struct result **)b_;

	return (*a)->id - (*b)->id;
}

static int compare_result_by_tr_trinv_id(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);
		if(d == 0) {
			d = (*b)->id - (*a)->id;
		}
	}

	return d;
}

static int compare_result_by_slope(const void *a_, const void *b_)
{
	int d = 0;

	struct result **a = (struct result **)a_;
	struct result **b = (struct result **)b_;

	double slopea = (*a)->x / (*a)->y;
	double slopeb = (*b)->x / (*b)->y;

	return slopea > slopeb ? -1 : slopea < slopeb ? 1 : 0;
}

struct timespec starttime;
static void start_timer()
{
	clock_gettime(CLOCK_MONOTONIC, &starttime);
}

static double runtime()
{
	struct timespec curtime;
	double diff;
	clock_gettime(CLOCK_MONOTONIC, &curtime);
	return (curtime.tv_sec - starttime.tv_sec) + (curtime.tv_nsec - starttime.tv_nsec) / 1e9;
}

int compute_invariants(group_t *group, mat *matrices, struct result **invariants, int *n, int unique)
{
	mpq_t tmp;
	mps_context *solver;
	mps_monomial_poly *poly;
	int index;
	int ntraces = *n, nuniq;
	int retval;
	double evs[3];
	int max_slope_id;
	double max_slope;
	char buf[100];

//	DEBUG("Compute traces\n");
	for(int i = 0; i < ntraces; i++) {
		int id = invariants[i]->id;
		int invid = group->elements[id].inverse->id;
		mat_trace(invariants[i]->tr, matrices[id]);
		mat_trace(invariants[i]->trinv, matrices[invid]);
	}

	if(!unique)
		nuniq = ntraces;
	else {
//		DEBUG("Get unique traces\n");
		qsort(invariants, ntraces, sizeof(struct result*), compare_result);

		nuniq = 0;
		for(int i = 0; i < ntraces; i++) {
			if(i == 0 || compare_result(&invariants[i], &invariants[nuniq-1]) != 0) {
				invariants[nuniq] = invariants[i];
				invariants[nuniq]->count = 1;
				nuniq++;
			} else {
				invariants[nuniq-1]->count++;
				int oldlength = group->elements[invariants[nuniq-1]->id].length;
				int newlength = group->elements[invariants[i]->id].length;
				if(newlength < oldlength)
					invariants[nuniq-1]->id = invariants[i]->id;
			}
		}
	}

	DEBUG("Solve characteristic polynomials\n");
	solver = mps_context_new();
	poly = mps_monomial_poly_new(solver, 3);
	mps_context_set_output_prec(solver, 20); // relative precision
	mps_context_set_output_goal(solver, MPS_OUTPUT_GOAL_APPROXIMATE);

	max_slope = 0;
	for(int i = 0; i < nuniq; i++) {
		retval = solve_characteristic_polynomial(solver, poly, invariants[i]->tr, invariants[i]->trinv, evs);
		retval = 0;evs[0] = 2;evs[1] = 1;evs[2] = 0.5; // fake solving the polynomial for memory leak test
		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]));

		invariants[i]->x = x;
		invariants[i]->y = y;

		if(y/x > max_slope + 1e-12 && (x > 0.1 || y > 0.1)) {
			max_slope_id = invariants[i]->id;
			max_slope = y/x;
		} else if(y/x > max_slope - 1e-12 && (x > 0.1 || y > 0.1)) {
//			DEBUG("%s didn't quite make it\n",
//			      print_word(&group->elements[invariants[i]->id], buf));
		}
	}
	mps_context_free(solver);

	qsort(invariants, nuniq, sizeof(struct result*), compare_result_by_id);

	*n = nuniq;
	return max_slope_id;
}

long check_memory_usage(mat *matrices, int n)
{
	mpq_t x;
	long total;

	for(int i = 0; i < n; i++)
	{
		LOOP(j,3) LOOP(k,3) {
			total += mpq_numref(M(matrices[i], j, k))->_mp_size;
			total += mpq_denref(M(matrices[i], j, k))->_mp_size;
		}
	}

	return total;
}

int main(int argc, char *argv[])
{
	mpq_t s, q, t, tmp;
	int p1, p2, p3;
	int sstart, send, sdenom, qstart, qend, qdenom;
	mat *matrices;
	group_t *group;
	int nmax, n;
	int max_slope_id;
	char buf[100];
	char buf2[100];
	struct result *invariants;
	struct result **distinct_invariants;

	start_timer();

	mpq_inits(s, q, t, tmp, NULL);
	if(argc < 11) {
		fprintf(stderr, "Usage: %s <N> <p1> <p2> <p3> <s start> <s end> <s denom> <q start> <q end> <q denom>\n", argv[0]);
		exit(1);
	}
	nmax = atoi(argv[1]);
	p1 = atoi(argv[2]);
	p2 = atoi(argv[3]);
	p3 = atoi(argv[4]);
	sstart = atoi(argv[5]);
	send = atoi(argv[6]);
	sdenom = atoi(argv[7]);
	qstart = atoi(argv[8]);
	qend = atoi(argv[9]);
	qdenom = atoi(argv[10]);

	DEBUG("Allocate\n");
	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);
	}

	// order of the triangle reflection generators: a, b, c
	// order of the rotation orders: bc, ac, ab
	DEBUG("Generate group\n");
	group = coxeter_init_triangle(p1, p2, p3, nmax);

	// first run; compute all matrices
	for(int i = 0; i < group->size; i++)
		group->elements[i].need_to_compute = 1;

	// use very generic values for the pilot run unless sstart=send and qstart=qend
	if(sstart == send && qstart == qend) {
		mpq_set_ui(s, sstart, sdenom);
		mpq_set_ui(q, qstart, qdenom);
		DEBUG("Single run for s = %d/%d, q = %d/%d\n", sstart, sdenom, qstart, qdenom);
	} else {
		mpq_set_ui(s, 4, 100);
		mpq_set_ui(q, 7, 100);
		DEBUG("Initial run for s = %d/%d, q = %d/%d\n", 4, 100, 7, 100);
	}

	DEBUG("Compute matrices\n");
	enumerate(group, matrices, p1, p2, p3, s, q);

	// prepare array of ids
	n = 0;
	for(int i = 0; i < group->size; i++)
	{
		if(group->elements[i].length % 2 != 0 || !group->elements[i].inverse)
			continue;
		invariants[i].id = i;
		distinct_invariants[n++] = &invariants[i];
	}

	DEBUG("Compute invariants\n");
	max_slope_id = compute_invariants(group, matrices, distinct_invariants, &n, 1);

	// prepare for next time; don't need to change ids in distinct_invariants!
	for(int i = 0; i < group->size; i++)
		group->elements[i].need_to_compute = 0;
	group->elements[0].need_to_compute = 1;
	int multiplication_count = 1;
	for(int i = 0; i < n; i++) {
		groupelement_t *cur = &group->elements[distinct_invariants[i]->id];
		while(cur->need_to_compute == 0) {
			cur->need_to_compute = 1;
			multiplication_count++;
			cur = cur->parent->parent;  // also need to compute its even-length ancestors
		}
		cur = group->elements[distinct_invariants[i]->id].inverse;
		while(cur->need_to_compute == 0) {
			cur->need_to_compute = 1;
			multiplication_count++;
			cur = cur->parent->parent;
		}

	}

	DEBUG("Would have needed %d matrix multiplications for %d unique traces up to reflection length %d\n", multiplication_count, n, group->elements[group->size-1].length);

	if(sstart != send || qstart != qend) {
		for(int sloop = sstart; sloop <= send; sloop++) {
			for(int qloop = qstart; qloop <= qend; qloop++) {
				DEBUG("Loop for s = %d/%d, q = %d/%d\n", sloop, sdenom, qloop, qdenom);
				mpq_set_ui(s, sloop, sdenom);
				mpq_set_ui(q, qloop, qdenom);
				DEBUG("Compute matrices\n");
				enumerate(group, matrices, p1, p2, p3, s, q);
				DEBUG("Compute invariants\n");
				max_slope_id = compute_invariants(group, matrices, distinct_invariants, &n, 0);
				// output
				gmp_printf("%Qd %Qd %s\n", s, q,
				           print_word(&group->elements[max_slope_id], buf));
				fflush(stdout);
			}
		}
	} else {
		// output
		for(int i = 0; i < n; i++) {
			double slope = distinct_invariants[i]->y/distinct_invariants[i]->x;

			// exclude tr = trinv = 2/1/0/-1/3
			mpq_set_si(tmp, 2, 1);
			if(mpq_cmp(distinct_invariants[i]->tr, tmp) == 0 &&
			   mpq_cmp(distinct_invariants[i]->trinv, tmp) == 0)
				continue;
			mpq_set_si(tmp, 1, 1);
			if(mpq_cmp(distinct_invariants[i]->tr, tmp) == 0 &&
			   mpq_cmp(distinct_invariants[i]->trinv, tmp) == 0)
				continue;
			mpq_set_si(tmp, 0, 1);
			if(mpq_cmp(distinct_invariants[i]->tr, tmp) == 0 &&
			   mpq_cmp(distinct_invariants[i]->trinv, tmp) == 0)
				continue;
			mpq_set_si(tmp, -1, 1);
			if(mpq_cmp(distinct_invariants[i]->tr, tmp) == 0 &&
			   mpq_cmp(distinct_invariants[i]->trinv, tmp) == 0)
				continue;
			mpq_set_si(tmp, 3, 1);
			if(mpq_cmp(distinct_invariants[i]->tr, tmp) == 0 &&
			   mpq_cmp(distinct_invariants[i]->trinv, tmp) == 0)
				continue;

			gmp_printf("%d %d %s %f\n",
			           distinct_invariants[i]->id, distinct_invariants[i]->count,
			           print_word(&group->elements[distinct_invariants[i]->id], buf),
			           slope
				);

			/*
			gmp_printf("%d %d %d %Qd %Qd %f %f %f %f %f %s\n",
			           distinct_invariants[i]->id, distinct_invariants[i]->count, cumulative,
			           distinct_invariants[i]->tr, distinct_invariants[i]->trinv,
			           log(fabs(mpq_get_d(distinct_invariants[i]->tr))), log(fabs(mpq_get_d(distinct_invariants[i]->trinv))),
			           distinct_invariants[i]->x, distinct_invariants[i]->y, slope,
			           print_word(&group->elements[distinct_invariants[i]->id], buf)
				);
			*/
		}

	}

	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(s, q, t, tmp, NULL);
}