combine singular_values and special_elements and test Charlie's prediction
This commit is contained in:
Florian Stecker
parent
ef1b48e86e
commit
7f0cb08787
15
Makefile
15
Makefile
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@ -1,4 +1,4 @@
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HEADERS=linalg.h mat.h coxeter.h
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HEADERS=linalg.h mat.h coxeter.h enumerate_triangle_group.h
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#SPECIAL_OPTIONS=-O0 -g -D_DEBUG
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SPECIAL_OPTIONS=-O3 -pg -funroll-loops -fno-inline
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@ -16,14 +16,14 @@ convert: convert.hs
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billiard_words: billiard_words.hs
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ghc --make -dynamic billiard_words.hs
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singular_values: singular_values.o coxeter.o mat.o
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gcc $(OPTIONS) -o singular_values coxeter.o singular_values.o mat.o -lm -lgmp -lmps
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singular_values: singular_values.o coxeter.o mat.o enumerate_triangle_group.o
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gcc $(OPTIONS) -o singular_values coxeter.o singular_values.o mat.o enumerate_triangle_group.o -lm -lgmp -lmps
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singular_values_mpi: singular_values_mpi.o coxeter.o mat.o
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mpicc $(OPTIONS) -o singular_values_mpi coxeter.o singular_values_mpi.o mat.o -lm -lgmp -lmps
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special_element: special_element.o coxeter.o linalg.o mat.o
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gcc $(OPTIONS) -o special_element coxeter.o linalg.o special_element.o mat.o -lm -lgmp -lmps -lgsl -lcblas
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special_element: special_element.o coxeter.o linalg.o mat.o enumerate_triangle_group.o
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gcc $(OPTIONS) -o special_element coxeter.o linalg.o special_element.o mat.o enumerate_triangle_group.o -lm -lgmp -lmps -lgsl -lcblas
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singular_values.o: singular_values.c $(HEADERS)
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gcc $(OPTIONS) -c singular_values.c
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@ -34,6 +34,9 @@ singular_values_mpi.o: singular_values_mpi.c $(HEADERS)
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special_element.o: special_element.c $(HEADERS)
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gcc $(OPTIONS) -c special_element.c
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enumerate_triangle_group.o: enumerate_triangle_group.c $(HEADERS)
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gcc $(OPTIONS) -c enumerate_triangle_group.c
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linalg.o: linalg.c $(HEADERS)
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gcc $(OPTIONS) -c linalg.c
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@ -44,4 +47,4 @@ mat.o: mat.c $(HEADERS)
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gcc $(OPTIONS) -c mat.c
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clean:
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rm -f singular_values special_element singular_values_mpi coxeter.o linalg.o singular_values.o singular_values_mpi.o mat.o special_element.o convert.hi convert.o convert billiard_words.hi billiard_words.o billiard_words
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rm -f singular_values special_element singular_values_mpi coxeter.o linalg.o singular_values.o singular_values_mpi.o mat.o special_element.o convert.hi convert.o convert billiard_words.hi billiard_words.o billiard_words enumerate_triangle_group.o
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@ -1,18 +1,22 @@
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import Data.List
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import Data.Ord
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import Text.Printf
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import System.Environment
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main = listWordsUpToLength 200
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main = do
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argv <- getArgs
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listWordsUpToLength $ read $ argv !! 0
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listWordsUpToLength :: Int -> IO ()
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listWordsUpToLength n = do
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putStrLn $ unlines [printf "%d/%d\t%d/%d\t%.7f\t%d\t%s" p q (x `div` gcd x y) (y `div` gcd x y) (sqrt 3 / (1 + 2*fromIntegral q / fromIntegral p) :: Double) (length w) w | ((p,q),w) <- wordlist (n`div`2) (n`div`2), length w <= n, let x = 2*q + p, let y = 2*p + q]
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putStrLn $ unlines [printf "%s %d/%d %f" w (x `div` gcd x y) (y `div` gcd x y) (fromIntegral x / fromIntegral y :: Double) | ((p,q),w) <- wordlist (n`div`2) (n`div`2), length w <= n, let x = 2*q + p, let y = 2*p + q]
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-- putStrLn $ unlines [printf "%d/%d\t%d/%d\t%.7f\t%d\t%s" p q (x `div` gcd x y) (y `div` gcd x y) (sqrt 3 / (1 + 2*fromIntegral q / fromIntegral p) :: Double) (length w) w | ((p,q),w) <- wordlist (n`div`2) (n`div`2), length w <= n, let x = 2*q + p, let y = 2*p + q]
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-- putStrLn $ unlines [printf "%d/%d\t%.5f\t%.5f\t%d\t%s" p q (fromIntegral p / fromIntegral q :: Double) (sqrt 3 / (1 + 2*fromIntegral q / fromIntegral p) :: Double) (length w) w | ((p,q),w) <- wordlist (n`div`2) (n`div`2), length w <= n]
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wordlist :: Int -> Int -> [((Int,Int),String)]
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wordlist pmax qmax = nub $ sortBy (comparing sl) [((p `div` gcd p q, q `div` gcd p q), slopeWord "bca" p q) | p <- [0..200], q <- [0..200], p /= 0 || q /= 0]
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wordlist pmax qmax = nub $ sortBy (comparing sl) [((p `div` gcd p q, q `div` gcd p q), slopeWord "bca" p q) | p <- [0..pmax], q <- [0..qmax], p /= 0 || q /= 0]
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where
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sl ((p,q),_) = fromIntegral p / fromIntegral q
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@ -9,9 +9,9 @@
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group_t *coxeter_init_triangle(int p, int q, int r, int nmax)
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{
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int coxeter_matrix[9] = {
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1, p, r,
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p, 1, q,
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r, q, 1};
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1, r, q,
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r, 1, p,
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q, p, 1};
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return coxeter_init(3, coxeter_matrix, nmax);
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}
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@ -1,17 +1,12 @@
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#include "coxeter.h"
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#include "linalg.h"
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#include "mat.h"
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#include <gsl/gsl_poly.h>
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#include <mps/mps.h>
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#include "enumerate_triangle_group.h"
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#define SWAP(t,x,y) do { t _tmp = (x); (x) = (y); (y) = _tmp; } while (0);
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//#define DEBUG(msg, ...) fprintf(stderr, msg, ##__VA_ARGS__)
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#define DEBUG(msg, ...)
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#define OUTPUT_POINTS
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//#define OUTPUT_POINTS
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struct result {
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int id;
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int count;
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@ -67,326 +62,6 @@ static int compare_result_by_slope(const void *a_, const void *b_)
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return slopea > slopeb ? -1 : slopea < slopeb ? 1 : 0;
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}
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int solve_characteristic_polynomial(mps_context *solv, mpq_t tr, mpq_t trinv, double *eigenvalues)
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{
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mpq_t coeff1, coeff2, zero;
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cplx_t *roots;
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double radii[3];
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double *radii_p[3];
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mps_monomial_poly *poly;
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mps_boolean errors;
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int result = 0;
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mpq_inits(coeff1, coeff2, zero, NULL);
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mpq_set(coeff1, trinv);
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mpq_sub(coeff2, zero, tr);
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poly = mps_monomial_poly_new(solv, 3);
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mps_monomial_poly_set_coefficient_int(solv, poly, 0, -1, 0);
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mps_monomial_poly_set_coefficient_q(solv, poly, 1, coeff1, zero);
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mps_monomial_poly_set_coefficient_q(solv, poly, 2, coeff2, zero);
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mps_monomial_poly_set_coefficient_int(solv, poly, 3, 1, 0);
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mps_context_set_input_poly(solv, (mps_polynomial*)poly);
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mps_mpsolve(solv);
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roots = cplx_valloc(3);
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for(int i = 0; i < 3; i++)
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radii_p[i] = &(radii[i]);
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mps_context_get_roots_d(solv, &roots, radii_p);
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errors = mps_context_has_errors(solv);
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if(errors) {
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result = 1;
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} else {
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for(int i = 0; i < 3; i++) {
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eigenvalues[i] = cplx_Re(roots[i]);
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if(fabs(cplx_Im(roots[i])) > radii[i]) // non-real root
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result = 2;
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}
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}
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cplx_vfree(roots);
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mpq_clears(coeff1, coeff2, zero, NULL);
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return result;
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}
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void continued_fraction_approximation(mpq_t out, double in, int level)
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{
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mpq_t tmp;
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if(in < 0) {
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mpq_init(tmp);
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mpq_set_ui(tmp, 0, 1);
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continued_fraction_approximation(out, -in, level);
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mpq_sub(out, tmp, out);
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mpq_clear(tmp);
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return;
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}
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if(level == 0) {
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mpq_set_si(out, (signed long int)round(in), 1); // floor(in)
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} else {
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continued_fraction_approximation(out, 1/(in - floor(in)), level - 1);
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mpq_init(tmp);
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mpq_set_ui(tmp, 1, 1);
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mpq_div(out, tmp, out); // out -> 1/out
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mpq_set_si(tmp, (signed long int)in, 1); // floor(in)
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mpq_add(out, out, tmp);
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mpq_clear(tmp);
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}
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}
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void quartic(mpq_t out, mpq_t in, int a, int b, int c, int d, int e)
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{
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mpq_t tmp;
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mpq_init(tmp);
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mpq_set_si(out, a, 1);
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mpq_mul(out, out, in);
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mpq_set_si(tmp, b, 1);
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mpq_add(out, out, tmp);
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mpq_mul(out, out, in);
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mpq_set_si(tmp, c, 1);
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mpq_add(out, out, tmp);
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mpq_mul(out, out, in);
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mpq_set_si(tmp, d, 1);
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mpq_add(out, out, tmp);
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mpq_mul(out, out, in);
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mpq_set_si(tmp, e, 1);
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mpq_add(out, out, tmp);
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mpq_clear(tmp);
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}
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void initialize_triangle_generators(mat_workspace *ws, mat *gen, mpq_t s, mpq_t q)
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{
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mat r1,r2,r3;
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mpq_t rho1, rho2, rho3;
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mpq_t b1,c1,a2,c2,a3,b3;
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mpq_t sinv;
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mpq_inits(sinv,rho1,rho2,rho3,b1,c1,a2,c2,a3,b3,NULL);
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mat_init(r1, 3);
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mat_init(r2, 3);
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mat_init(r3, 3);
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mpq_set_ui(sinv, 1, 1);
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mpq_div(sinv, sinv, s);
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quartic(rho1, s, 0, 0, 1, -1, 1);
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quartic(rho2, s, 0, 0, 1, -1, 1);
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quartic(rho3, s, 0, 0, 1, 0, 1);
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mpq_mul(c1, rho2, q);
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mpq_mul(a2, rho3, q);
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mpq_mul(b3, rho1, q);
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mpq_set_ui(b1, 1, 1);
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mpq_set_ui(c2, 1, 1);
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mpq_set_ui(a3, 1, 1);
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mpq_div(b1, b1, q);
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mpq_div(c2, c2, q);
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mpq_div(a3, a3, q);
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// actually, we want minus everything
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mat_zero(r1);
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mat_zero(r2);
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mat_zero(r3);
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mpq_set_si(*mat_ref(r1, 0, 0), -1, 1);
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mpq_set_si(*mat_ref(r1, 1, 1), 1, 1);
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mpq_set_si(*mat_ref(r1, 2, 2), 1, 1);
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mpq_set_si(*mat_ref(r2, 0, 0), 1, 1);
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mpq_set_si(*mat_ref(r2, 1, 1), -1, 1);
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mpq_set_si(*mat_ref(r2, 2, 2), 1, 1);
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mpq_set_si(*mat_ref(r3, 0, 0), 1, 1);
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mpq_set_si(*mat_ref(r3, 1, 1), 1, 1);
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mpq_set_si(*mat_ref(r3, 2, 2), -1, 1);
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mpq_set(*mat_ref(r1, 1, 0), b1);
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mpq_set(*mat_ref(r1, 2, 0), c1);
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mpq_set(*mat_ref(r2, 0, 1), a2);
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mpq_set(*mat_ref(r2, 2, 1), c2);
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mpq_set(*mat_ref(r3, 0, 2), a3);
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mpq_set(*mat_ref(r3, 1, 2), b3);
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mat_zero(gen[0]);
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mat_zero(gen[1]);
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mat_zero(gen[2]);
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mpq_set_ui(*mat_ref(gen[0], 0, 0), 1, 1);
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mat_set(gen[0], 1, 1, sinv);
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mat_set(gen[0], 2, 2, s);
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mat_set(gen[1], 0, 0, s);
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mpq_set_ui(*mat_ref(gen[1], 1, 1), 1, 1);
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mat_set(gen[1], 2, 2, sinv);
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mat_set(gen[2], 0, 0, sinv);
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mat_set(gen[2], 1, 1, s);
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mpq_set_ui(*mat_ref(gen[2], 2, 2), 1, 1);
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mat_multiply(ws, gen[0], r2, gen[0]);
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mat_multiply(ws, gen[0], gen[0], r3);
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mat_multiply(ws, gen[1], r3, gen[1]);
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mat_multiply(ws, gen[1], gen[1], r1);
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mat_multiply(ws, gen[2], r1, gen[2]);
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mat_multiply(ws, gen[2], gen[2], r2);
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mat_pseudoinverse(ws, gen[3], gen[0]);
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mat_pseudoinverse(ws, gen[4], gen[1]);
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mat_pseudoinverse(ws, gen[5], gen[2]);
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/*
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mat_print(r1);
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mat_print(r2);
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mat_print(r3);
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mat_print(gen[0]);
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mat_print(gen[1]);
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mat_print(gen[2]);
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mat_print(gen[3]);
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mat_print(gen[4]);
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mat_print(gen[5]);
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*/
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mpq_clears(sinv,rho1,rho2,rho3,b1,c1,a2,c2,a3,b3,NULL);
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mat_clear(r1);
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mat_clear(r2);
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mat_clear(r3);
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}
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char *print_word(groupelement_t *g, char *str)
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{
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int i = g->length - 1;
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str[g->length] = 0;
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while(g->parent) {
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str[i--] = 'a' + g->letter;
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g = g->parent;
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}
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return str;
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}
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void enumerate(group_t *group, mat *matrices, mpq_t s, mpq_t t)
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{
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mat_workspace *ws;
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mat tmp;
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mat gen[6];
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char buf[100], buf2[100], buf3[100];
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// allocate stuff
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ws = mat_workspace_init(3);
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for(int i = 0; i < 6; i++)
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mat_init(gen[i], 3);
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mat_init(tmp, 3);
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initialize_triangle_generators(ws, gen, s, t);
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mat_identity(matrices[0]);
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for(int i = 1; i < group->size; i++) {
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if(group->elements[i].length % 2 != 0)
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continue;
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if(!group->elements[i].inverse)
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continue;
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int parent = group->elements[i].parent->id;
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int grandparent = group->elements[i].parent->parent->id;
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int letter;
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if(group->elements[parent].letter == 1 && group->elements[i].letter == 2)
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letter = 0; // p = bc
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else if(group->elements[parent].letter == 2 && group->elements[i].letter == 0)
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letter = 1; // q = ca
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else if(group->elements[parent].letter == 0 && group->elements[i].letter == 1)
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letter = 2; // r = ab
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if(group->elements[parent].letter == 2 && group->elements[i].letter == 1)
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letter = 3; // p^{-1} = cb
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else if(group->elements[parent].letter == 0 && group->elements[i].letter == 2)
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letter = 4; // q^{-1} = ac
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else if(group->elements[parent].letter == 1 && group->elements[i].letter == 0)
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letter = 5; // r^{-1} = ba
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mat_multiply(ws, matrices[i], matrices[grandparent], gen[letter]);
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}
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// free stuff
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for(int i = 0; i < 6; i++)
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mat_clear(gen[i]);
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mat_clear(tmp);
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mat_workspace_clear(ws);
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}
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void output_invariants(group_t *group, mat *matrices, mpq_t s, mpq_t q, mps_context *solver)
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{
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mpq_t tr, trinv;
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char buf[100];
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double evs[3];
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int retval;
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mpq_inits(tr, trinv, NULL);
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for(int i = 0; i < group->size; i++) {
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if(group->elements[i].length % 2 != 0 || !group->elements[i].inverse)
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continue;
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mat_trace(tr, matrices[i]);
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mat_trace(trinv, matrices[group->elements[i].inverse->id]);
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retval = solve_characteristic_polynomial(solver, tr, trinv, evs);
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if(retval == 1) {
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fprintf(stderr, "Error! Could not solve polynomial.\n");
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continue;
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} else if(retval == 2) {
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continue;
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}
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if(fabs(evs[0]) < fabs(evs[1]))
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SWAP(double, evs[0], evs[1]);
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if(fabs(evs[1]) < fabs(evs[2]))
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SWAP(double, evs[1], evs[2]);
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if(fabs(evs[0]) < fabs(evs[1]))
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SWAP(double, evs[0], evs[1]);
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|
||||
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]));
|
||||
}
|
||||
|
||||
mpq_clears(tr, trinv, NULL);
|
||||
}
|
||||
|
||||
/*
|
||||
double max_slope(groupelement_t *group, mat *matrices, mpq_t s, mpq_t t, int *index)
|
||||
{
|
||||
double max = 0;
|
||||
double slope;
|
||||
|
||||
mpq_t tr, trinv;
|
||||
char buf[100];
|
||||
|
||||
mpq_inits(tr, trinv, NULL);
|
||||
|
||||
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]);
|
||||
|
||||
slope = log(mpq_get_d(trinv))/log(mpq_get_d(tr));
|
||||
if(slope > max)
|
||||
{
|
||||
*index = i;
|
||||
max = slope;
|
||||
}
|
||||
}
|
||||
|
||||
mpq_clears(tr, trinv, NULL);
|
||||
|
||||
return max;
|
||||
}
|
||||
*/
|
||||
|
||||
int main(int argc, char *argv[])
|
||||
{
|
||||
mpq_t s, q, t, tmp;
|
||||
|
|
@ -407,7 +82,7 @@ int main(int argc, char *argv[])
|
|||
struct result **distinct_invariants;
|
||||
|
||||
if(argc < 4) {
|
||||
fprintf(stderr, "Usage: %s <N> <s> <t>\n", argv[0]);
|
||||
fprintf(stderr, "Usage: %s <N> <s> <q>\n", argv[0]);
|
||||
exit(1);
|
||||
}
|
||||
|
||||
|
|
@ -435,9 +110,10 @@ int main(int argc, char *argv[])
|
|||
|
||||
// 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;
|
||||
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);
|
||||
|
|
@ -459,16 +135,14 @@ int main(int argc, char *argv[])
|
|||
|
||||
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
|
||||
// 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, s, q);
|
||||
enumerate(group, matrices, 4, 3, 3, s, q);
|
||||
|
||||
n = 0;
|
||||
DEBUG("Compute traces\n");
|
||||
|
|
@ -538,6 +212,8 @@ int main(int argc, char *argv[])
|
|||
|
||||
qsort(distinct_invariants, nuniq, sizeof(struct result*), compare_result_by_slope);
|
||||
|
||||
gmp_fprintf(stdout, "\"s = %Qd = %.3f, q = %Qd, t = %.3f\"\n", s, mpq_get_d(s), q, mpq_get_d(q)*tqfactor);
|
||||
|
||||
// printf("- 0 0 - - - - 0.5\n");
|
||||
int cumulative = 0;
|
||||
double slope;
|
||||
|
|
@ -572,19 +248,6 @@ int main(int argc, char *argv[])
|
|||
}
|
||||
// printf("- 0 %d - - - - 2.0\n", cumulative);
|
||||
|
||||
#ifdef OUTPUT_SUMMARY
|
||||
fprintf(stdout, "%.3f %.3f %f %s\n", mpq_get_d(s), mpq_get_d(q)*tqfactor, max_slope, print_word(&group->elements[max_slope_index], buf));
|
||||
#endif
|
||||
|
||||
// output_invariants(group, matrices, s, q, solver);
|
||||
|
||||
// for(int i = 0; i < 10; i++) {
|
||||
// mpq_set_ui(t,100+i,100);
|
||||
// mpq_canonicalize(t);
|
||||
|
||||
//printf("%f %f\n", mpq_get_d(t), max_slope(group, matrices, s, t, &index));
|
||||
// }
|
||||
|
||||
DEBUG("Clean up\n");
|
||||
for(int i = 0; i < nmax; i++) {
|
||||
mpq_clear(invariants[i].tr);
|
||||
|
|
|
|||
|
|
@ -1,10 +1,7 @@
|
|||
|
||||
#include "coxeter.h"
|
||||
#include "linalg.h"
|
||||
#include "mat.h"
|
||||
|
||||
#include <gsl/gsl_poly.h>
|
||||
#include <mps/mps.h>
|
||||
#include "enumerate_triangle_group.h"
|
||||
|
||||
#define SWAP(t,x,y) do { t _tmp = (x); (x) = (y); (y) = _tmp; } while (0);
|
||||
#define DEBUG(msg, ...)
|
||||
|
|
@ -14,180 +11,30 @@
|
|||
#define HEIGHT 300
|
||||
#define IDX(i,j) (((i)-1)*HEIGHT + ((j)-1))
|
||||
|
||||
int solve_characteristic_polynomial(mps_context *solv, mpq_t tr, mpq_t trinv, double *eigenvalues)
|
||||
double mpq_log(mpq_t m_op)
|
||||
{
|
||||
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;
|
||||
static double logB = log(ULONG_MAX);
|
||||
|
||||
mpq_inits(coeff1, coeff2, zero, NULL);
|
||||
mpq_set(coeff1, trinv);
|
||||
mpq_sub(coeff2, zero, tr);
|
||||
// Undefined logs (should probably return NAN in second case?)
|
||||
if (mpz_get_ui(mpq_numref(m_op)) == 0 || mpz_sgn(mpq_numref(m_op)) < 0)
|
||||
return -INFINITY;
|
||||
|
||||
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);
|
||||
// Log of numerator
|
||||
double lognum = log(mpq_numref(m_op)->_mp_d[abs(mpq_numref(m_op)->_mp_size) - 1]);
|
||||
lognum += (abs(mpq_numref(m_op)->_mp_size)-1) * logB;
|
||||
|
||||
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;
|
||||
}
|
||||
// Subtract log of denominator, if it exists
|
||||
if (abs(mpq_denref(m_op)->_mp_size) > 0)
|
||||
{
|
||||
lognum -= log(mpq_denref(m_op)->_mp_d[abs(mpq_denref(m_op)->_mp_size)-1]);
|
||||
lognum -= (abs(mpq_denref(m_op)->_mp_size)-1) * logB;
|
||||
}
|
||||
|
||||
cplx_vfree(roots);
|
||||
mpq_clears(coeff1, coeff2, zero, NULL);
|
||||
|
||||
return result;
|
||||
}
|
||||
|
||||
// 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]);
|
||||
|
||||
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);
|
||||
return lognum;
|
||||
}
|
||||
|
||||
int main(int argc, char *argv[])
|
||||
{
|
||||
mpq_t m, t, tmp;
|
||||
double s;
|
||||
mpq_t m, t, s, q, tmp, tmp2;
|
||||
mat_workspace *ws;
|
||||
mat gen[6];
|
||||
mps_context *solver;
|
||||
|
|
@ -203,7 +50,7 @@ int main(int argc, char *argv[])
|
|||
|
||||
DEBUG("Allocate\n");
|
||||
|
||||
mpq_inits(m, t, tmp, tr, trinv, NULL);
|
||||
mpq_inits(m, t, s, q, tmp, tmp2, tr, trinv, NULL);
|
||||
ws = mat_workspace_init(3);
|
||||
for(int i = 0; i < 6; i++)
|
||||
mat_init(gen[i], 3);
|
||||
|
|
@ -218,15 +65,18 @@ int main(int argc, char *argv[])
|
|||
mps_context_set_output_prec(solver, 20); // relative precision
|
||||
mps_context_set_output_goal(solver, MPS_OUTPUT_GOAL_APPROXIMATE);
|
||||
|
||||
for(int i = STARTX; i <= WIDTH; i++) {
|
||||
for(int j = 1; j <= HEIGHT; j++) {
|
||||
for(int w = 1; w < argc; w++) {
|
||||
mpq_set_ui(t, j, DENOMINATOR);
|
||||
mpq_set_ui(m, i, DENOMINATOR); // 414/1000 ~ sqrt(2)-1 <-> s=1
|
||||
s = (1-mpq_get_d(m)*mpq_get_d(m))/(2*mpq_get_d(m));
|
||||
mpq_set_str(s, argv[1], 10);
|
||||
mpq_set_str(q, argv[2], 10);
|
||||
|
||||
// for(int i = STARTX; i <= WIDTH; i++) {
|
||||
// for(int j = 1; j <= HEIGHT; j++) {
|
||||
for(int w = 3; w < argc; w++) {
|
||||
// mpq_set_ui(t, j, DENOMINATOR);
|
||||
// mpq_set_ui(m, i, DENOMINATOR); // 414/1000 ~ sqrt(2)-1 <-> s=1
|
||||
// s = (1-mpq_get_d(m)*mpq_get_d(m))/(2*mpq_get_d(m));
|
||||
|
||||
DEBUG("Compute matrix\n");
|
||||
initialize_triangle_generators(ws, gen, m, t);
|
||||
initialize_triangle_generators(ws, gen, 6, 4, 3, s, q);
|
||||
|
||||
mat_identity(element);
|
||||
mat_identity(inverse);
|
||||
|
|
@ -272,25 +122,39 @@ int main(int argc, char *argv[])
|
|||
|
||||
x = log(fabs(evs[0]));
|
||||
y = -log(fabs(evs[2]));
|
||||
slope = y/x > 1 ? y/x : x/y;
|
||||
|
||||
if(slope > max_slope[IDX(i,j)]) {
|
||||
max_slope[IDX(i,j)] = slope;
|
||||
max_slope_index[IDX(i,j)] = w;
|
||||
if(x > DBL_MAX || y > DBL_MAX) {
|
||||
mpq_abs(tmp, tr);
|
||||
mpq_abs(tmp2, trinv);
|
||||
slope = mpq_log(tmp)/mpq_log(tmp2);
|
||||
} else {
|
||||
slope = y/x;
|
||||
}
|
||||
|
||||
if(slope < 1)
|
||||
slope = 1/slope;
|
||||
|
||||
|
||||
// if(slope > max_slope[IDX(i,j)]) {
|
||||
// max_slope[IDX(i,j)] = slope;
|
||||
// max_slope_index[IDX(i,j)] = w;
|
||||
// }
|
||||
|
||||
// gmp_printf("%Qd %Qd %f %f %f\n", tr, trinv, x, y, y/x);
|
||||
// gmp_printf("%.5f %.5f %.7f %.9f\n", mpq_get_d(t), mpq_get_d(m), s, slope);
|
||||
// gmp_printf("%s %.5f %.5f %Qd %Qd %.9f %.9f %.9f\n", argv[w], mpq_get_d(s), mpq_get_d(q),
|
||||
// tr, trinv,
|
||||
// x, y, slope);
|
||||
gmp_printf("%s %.9f\n", argv[w], slope);
|
||||
|
||||
}
|
||||
|
||||
printf("%.5f %.5f %d %.9f\n", (double)i/DENOMINATOR, (double)j/DENOMINATOR, max_slope_index[IDX(i,j)], max_slope[IDX(i,j)]);
|
||||
// printf("%.5f %.5f %d %.9f\n", (double)i/DENOMINATOR, (double)j/DENOMINATOR, max_slope_index[IDX(i,j)], max_slope[IDX(i,j)]);
|
||||
fflush(stdout);
|
||||
}
|
||||
}
|
||||
// }
|
||||
// }
|
||||
|
||||
DEBUG("Clean up\n");
|
||||
mpq_clears(m, t, tmp, tr, trinv, NULL);
|
||||
mpq_clears(m, t, s, q, tmp, tmp2, tr, trinv, NULL);
|
||||
mat_workspace_clear(ws);
|
||||
for(int i = 0; i < 6; i++)
|
||||
mat_clear(gen[i]);
|
||||
|
|
|
|||
Loading…
Reference in New Issue