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reorganize singular_values, do one precomputation and then only compute unique traces

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This commit is contained in:
Florian Stecker 2022-02-05 17:51:45 -06:00
parent 6c12f49db8
commit 2735281300
7 changed files with 273 additions and 157 deletions
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2
Makefile
View File

@ -1,7 +1,7 @@
HEADERS=linalg.h mat.h coxeter.h enumerate_triangle_group.h HEADERS=linalg.h mat.h coxeter.h enumerate_triangle_group.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 -g -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=-O3 -flto -funroll-loops -Winline -mavx512f -mavx512cd -mavx512er -mavx512pf # KNL
#SPECIAL_OPTIONS= #SPECIAL_OPTIONS=

10
billiard_words.hs
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@ -9,17 +9,21 @@ main = do
listWordsUpToLength :: Int -> IO () listWordsUpToLength :: Int -> IO ()
listWordsUpToLength n = do listWordsUpToLength n = do
putStrLn $ unlines [printf "%s %d/%d %f %s" putStr $ unlines [printf "%s %d/%d %f"
w w
(p `div` gcd p q) (p `div` gcd p q)
(q `div` gcd p q) (q `div` gcd p q)
(sqrt 3 / 2 * fromIntegral p / (fromIntegral q + fromIntegral p / 2) :: Double) (atan (sqrt 3 / (2*q_/p_ + 1))) |
(slopeWord "bca" (orthogonalSlope (p,q))) |
((p,q),w) <- wordlist (n `div` 2, n `div` 2), ((p,q),w) <- wordlist (n `div` 2, n `div` 2),
let p_ = fromIntegral p :: Double,
let q_ = fromIntegral q :: Double,
length w <= n, length w <= n,
let x = 2*q + p, let x = 2*q + p,
let y = 2*p + q] let y = 2*p + q]
-- (sqrt 3 / 2 * fromIntegral p / (fromIntegral q + fromIntegral p / 2) :: Double) |
-- (slopeWord "bca" (orthogonalSlope (p,q))) |
wordlist :: (Int,Int) -> [((Int,Int),String)] wordlist :: (Int,Int) -> [((Int,Int),String)]
wordlist (pmax,qmax) = nub $ wordlist (pmax,qmax) = nub $
sortBy (comparing sl) sortBy (comparing sl)

1
coxeter.h
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@ -7,6 +7,7 @@ typedef struct _groupelement {
int id; int id;
int letter; int letter;
struct _groupelement *parent; struct _groupelement *parent;
int need_to_compute; // optimization flag; if 0, will skip matrix computation
int length; int length;
struct _groupelement *inverse; struct _groupelement *inverse;

10
enumerate_triangle_group.c
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@ -1,13 +1,12 @@
#include "enumerate_triangle_group.h" #include "enumerate_triangle_group.h"
#include "linalg.h" #include "linalg.h"
int solve_characteristic_polynomial(mps_context *solv, mpq_t tr, mpq_t trinv, double *eigenvalues) int solve_characteristic_polynomial(mps_context *solv, mps_monomial_poly *poly, mpq_t tr, mpq_t trinv, double *eigenvalues)
{ {
mpq_t coeff1, coeff2, zero; mpq_t coeff1, coeff2, zero;
cplx_t *roots; cplx_t *roots;
double radii[3]; double radii[3];
double *radii_p[3]; double *radii_p[3];
mps_monomial_poly *poly;
mps_boolean errors; mps_boolean errors;
int result = 0; int result = 0;
@ -15,7 +14,6 @@ int solve_characteristic_polynomial(mps_context *solv, mpq_t tr, mpq_t trinv, do
mpq_set(coeff1, trinv); mpq_set(coeff1, trinv);
mpq_sub(coeff2, zero, tr); 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_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, 1, coeff1, zero);
mps_monomial_poly_set_coefficient_q(solv, poly, 2, coeff2, zero); mps_monomial_poly_set_coefficient_q(solv, poly, 2, coeff2, zero);
@ -215,7 +213,7 @@ char *print_word(groupelement_t *g, char *str)
return str; return str;
} }
void enumerate(group_t *group, mat *matrices, int p1, int p2, int p3, mpq_t s, mpq_t t) void enumerate(group_t *group, mat *matrices, int p1, int p2, int p3, mpq_t s, mpq_t q)
{ {
mat_workspace *ws; mat_workspace *ws;
mat tmp; mat tmp;
@ -228,7 +226,7 @@ void enumerate(group_t *group, mat *matrices, int p1, int p2, int p3, mpq_t s, m
mat_init(gen[i], 3); mat_init(gen[i], 3);
mat_init(tmp, 3); mat_init(tmp, 3);
initialize_triangle_generators(ws, gen, p1, p2, p3, s, t); initialize_triangle_generators(ws, gen, p1, p2, p3, s, q);
mat_identity(matrices[0]); mat_identity(matrices[0]);
for(int i = 1; i < group->size; i++) { for(int i = 1; i < group->size; i++) {
@ -236,6 +234,8 @@ void enumerate(group_t *group, mat *matrices, int p1, int p2, int p3, mpq_t s, m
continue; continue;
if(!group->elements[i].inverse) if(!group->elements[i].inverse)
continue; continue;
if(!group->elements[i].need_to_compute)
continue;
int parent = group->elements[i].parent->id; int parent = group->elements[i].parent->id;
int grandparent = group->elements[i].parent->parent->id; int grandparent = group->elements[i].parent->parent->id;

2
enumerate_triangle_group.h
View File

@ -6,7 +6,7 @@
#include <mps/mps.h> #include <mps/mps.h>
int solve_characteristic_polynomial(mps_context *solv, mpq_t tr, mpq_t trinv, double *eigenvalues); int solve_characteristic_polynomial(mps_context *solv, mps_monomial_poly *poly, mpq_t tr, mpq_t trinv, double *eigenvalues);
void continued_fraction_approximation(mpq_t out, double in, int level); void continued_fraction_approximation(mpq_t out, double in, int level);
void quartic(mpq_t out, mpq_t in, int a, int b, int c, int d, int e); void quartic(mpq_t out, mpq_t in, int a, int b, int c, int d, int e);
// p1,p2,p3 are only allowed to be 2,3,4,6 // p1,p2,p3 are only allowed to be 2,3,4,6

399
singular_values.c
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@ -3,9 +3,12 @@
#include "mat.h" #include "mat.h"
#include "enumerate_triangle_group.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 SWAP(t,x,y) do { t _tmp = (x); (x) = (y); (y) = _tmp; } while (0);
//#define DEBUG(msg, ...) fprintf(stderr, msg, ##__VA_ARGS__)
#define DEBUG(msg, ...) #define DEBUG(msg, ...) fprintf(stderr, "[%10.3f] " msg, runtime(), ##__VA_ARGS__);
//#define DEBUG(msg, ...)
struct result { struct result {
int id; int id;
@ -31,7 +34,17 @@ static int compare_result(const void *a_, const void *b_)
return d; return d;
} }
static int compare_result_with_id(const void *a_, const void *b_) 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; int d = 0;
@ -62,128 +75,73 @@ static int compare_result_by_slope(const void *a_, const void *b_)
return slopea > slopeb ? -1 : slopea < slopeb ? 1 : 0; return slopea > slopeb ? -1 : slopea < slopeb ? 1 : 0;
} }
int main(int argc, char *argv[]) struct timespec starttime;
static void start_timer()
{ {
mpq_t s, q, t, tmp; clock_gettime(CLOCK_MONOTONIC, &starttime);
double sapprox, tapprox, qapprox, tqfactor; }
mat *matrices;
group_t *group; static double runtime()
int index; {
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_context *solver;
int acc = 100; mps_monomial_poly *poly;
int n, nuniq, nmax; int index;
int ntraces = *n, nuniq;
int retval; int retval;
double evs[3]; double evs[3];
int max_slope_id;
double max_slope; double max_slope;
char buf[100]; char buf[100];
char buf2[100];
struct result *invariants; // DEBUG("Compute traces\n");
struct result **distinct_invariants; for(int i = 0; i < ntraces; i++) {
int id = invariants[i]->id;
if(argc < 4) { int invid = group->elements[id].inverse->id;
fprintf(stderr, "Usage: %s <N> <s> <q>\n", argv[0]); mat_trace(invariants[i]->tr, matrices[id]);
exit(1); mat_trace(invariants[i]->trinv, matrices[invid]);
} }
nmax = atoi(argv[1]); if(!unique)
nuniq = ntraces;
else {
// DEBUG("Get unique traces\n");
qsort(invariants, ntraces, sizeof(struct result*), compare_result);
DEBUG("Allocate\n"); nuniq = 0;
for(int i = 0; i < ntraces; i++) {
mpq_inits(s, q, t, tmp, NULL); if(i == 0 || compare_result(&invariants[i], &invariants[nuniq-1]) != 0) {
matrices = malloc(nmax*sizeof(mat)); invariants[nuniq] = invariants[i];
for(int i = 0; i < nmax; i++) invariants[nuniq]->count = 1;
mat_init(matrices[i], 3); nuniq++;
invariants = malloc(nmax*sizeof(struct result)); } else {
distinct_invariants = malloc(nmax*sizeof(struct result)); invariants[nuniq-1]->count++;
for(int i = 0; i < nmax; i++) { int oldlength = group->elements[invariants[nuniq-1]->id].length;
mpq_init(invariants[i].tr); int newlength = group->elements[invariants[i]->id].length;
mpq_init(invariants[i].trinv); if(newlength < oldlength)
distinct_invariants[i] = &invariants[i]; invariants[nuniq-1]->id = invariants[i]->id;
}
}
} }
DEBUG("Solve characteristic polynomials\n");
solver = mps_context_new(); solver = mps_context_new();
poly = mps_monomial_poly_new(solver, 3);
mps_context_set_output_prec(solver, 20); // relative precision mps_context_set_output_prec(solver, 20); // relative precision
mps_context_set_output_goal(solver, MPS_OUTPUT_GOAL_APPROXIMATE); mps_context_set_output_goal(solver, MPS_OUTPUT_GOAL_APPROXIMATE);
DEBUG("Approximate parameters\n");
// get approximate s and q values
sapprox = atof(argv[2]);
qapprox = atof(argv[3]);
// 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))
break;
mpq_set(s, tmp);
}
mpq_canonicalize(s);
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);
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);
// group
// 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(4, 3, 3, nmax);
DEBUG("Compute matrices\n");
enumerate(group, matrices, 4, 3, 3, s, q);
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;
invariants[i].id = i;
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];
distinct_invariants[nuniq]->count = 1;
nuniq++;
} else {
distinct_invariants[nuniq-1]->count++;
int oldlength = group->elements[distinct_invariants[nuniq-1]->id].length;
int newlength = group->elements[distinct_invariants[i]->id].length;
if(newlength < oldlength)
distinct_invariants[nuniq-1]->id = distinct_invariants[i]->id;
}
// gmp_printf("%d %d %s\n", i, nuniq-1, print_word(&group->elements[i], buf));
}
max_slope = 0; max_slope = 0;
int max_slope_index;
DEBUG("Solve characteristic polynomials\n");
for(int i = 0; i < nuniq; i++) { for(int i = 0; i < nuniq; i++) {
retval = solve_characteristic_polynomial(solver, distinct_invariants[i]->tr, distinct_invariants[i]->trinv, evs); 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) { if(retval == 1) {
fprintf(stderr, "Error! Could not solve polynomial.\n"); fprintf(stderr, "Error! Could not solve polynomial.\n");
continue; continue;
@ -201,52 +159,204 @@ int main(int argc, char *argv[])
double x = log(fabs(evs[0])); double x = log(fabs(evs[0]));
double y = -log(fabs(evs[2])); double y = -log(fabs(evs[2]));
distinct_invariants[i]->x = x; invariants[i]->x = x;
distinct_invariants[i]->y = y; invariants[i]->y = y;
if(y/x > max_slope && (x > 0.1 || y > 0.1)) { if(y/x > max_slope + 1e-12 && (x > 0.1 || y > 0.1)) {
max_slope_index = distinct_invariants[i] - invariants; max_slope_id = invariants[i]->id;
max_slope = y/x; 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;
} }
} }
qsort(distinct_invariants, nuniq, sizeof(struct result*), compare_result_by_slope); return total;
}
gmp_fprintf(stdout, "\"s = %Qd = %.3f, q = %Qd, t = %.3f\"\n", s, mpq_get_d(s), q, mpq_get_d(q)*tqfactor); 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;
// printf("- 0 0 - - - - 0.5\n"); start_timer();
int cumulative = 0;
double slope; mpq_inits(s, q, t, tmp, NULL);
for(int i = 0; i < nuniq; i++) { if(argc < 11) {
slope = distinct_invariants[i]->y/distinct_invariants[i]->x; 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)
);
*/
}
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;
}
cumulative += distinct_invariants[i]->count;
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)
);
} }
// printf("- 0 %d - - - - 2.0\n", cumulative);
DEBUG("Clean up\n"); DEBUG("Clean up\n");
for(int i = 0; i < nmax; i++) { for(int i = 0; i < nmax; i++) {
@ -260,5 +370,4 @@ int main(int argc, char *argv[])
free(matrices); free(matrices);
coxeter_clear(group); coxeter_clear(group);
mpq_clears(s, q, t, tmp, NULL); mpq_clears(s, q, t, tmp, NULL);
mps_context_free(solver);
} }

6
special_element.c
View File

@ -33,6 +33,7 @@ int main(int argc, char *argv[])
mat_workspace *ws; mat_workspace *ws;
mat gen[6]; mat gen[6];
mps_context *solver; mps_context *solver;
mps_monomial_poly *poly;
mat element, inverse; mat element, inverse;
int letter1, letter2, letter; int letter1, letter2, letter;
mpq_t tr, trinv; mpq_t tr, trinv;
@ -68,6 +69,7 @@ int main(int argc, char *argv[])
mat_init(inverse, 3); mat_init(inverse, 3);
solver = mps_context_new(); solver = mps_context_new();
poly = mps_monomial_poly_new(solver, 3);
mps_context_set_output_prec(solver, 20); // relative precision mps_context_set_output_prec(solver, 20); // relative precision
mps_context_set_output_goal(solver, MPS_OUTPUT_GOAL_APPROXIMATE); mps_context_set_output_goal(solver, MPS_OUTPUT_GOAL_APPROXIMATE);
@ -112,7 +114,7 @@ int main(int argc, char *argv[])
mat_trace(tr, element); mat_trace(tr, element);
mat_trace(trinv, inverse); mat_trace(trinv, inverse);
retval = solve_characteristic_polynomial(solver, tr, trinv, evs); retval = solve_characteristic_polynomial(solver, poly, tr, trinv, evs);
if(retval == 1) { if(retval == 1) {
fprintf(stderr, "Error! Could not solve polynomial.\n"); fprintf(stderr, "Error! Could not solve polynomial.\n");
return 1; return 1;
@ -150,7 +152,7 @@ int main(int argc, char *argv[])
} }
if(mode != 2) if(mode != 2)
gmp_printf("%s %.9f\n", argv[w+3], slope); gmp_printf("%s %.9f %Qd %Qd\n", argv[w+3], slope, tr, trinv);
} }
if(mode != 0) if(mode != 0)