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use multiprecision poly solver

This commit is contained in:
Florian Stecker 2020-07-29 20:23:15 -04:00
parent 4ee614cdd7
commit 2568b4ef71
3 changed files with 88 additions and 12 deletions
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6
Makefile
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@ -1,8 +1,8 @@
HEADERS=triangle.h linalg.h queue.h mat.h
#SPECIAL_OPTIONS=-O0 -g -D_DEBUG
#SPECIAL_OPTIONS=-O3 -pg -funroll-loops -fno-inline
SPECIAL_OPTIONS=-O3 -flto -funroll-loops -Winline
SPECIAL_OPTIONS=-O3 -pg -funroll-loops -fno-inline
#SPECIAL_OPTIONS=-O3 -flto -funroll-loops -Winline
#SPECIAL_OPTIONS=
OPTIONS=-m64 -march=native -mtune=native -std=gnu99 -D_GNU_SOURCE $(SPECIAL_OPTIONS)
@ -10,7 +10,7 @@ OPTIONS=-m64 -march=native -mtune=native -std=gnu99 -D_GNU_SOURCE $(SPECIAL_OPTI
all: singular_values
singular_values: singular_values.o triangle.o linalg.o mat.o
gcc $(OPTIONS) -o singular_values triangle.o linalg.o singular_values.o mat.o -lm -lgsl -lcblas -lgmp
gcc $(OPTIONS) -o singular_values triangle.o linalg.o singular_values.o mat.o -lm -lgsl -lcblas -lgmp -lmps -lpthread
singular_values.o: singular_values.c $(HEADERS)
gcc $(OPTIONS) -c singular_values.c

79
singular_values.c
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@ -3,12 +3,60 @@
#include "mat.h"
#include <gsl/gsl_poly.h>
#include <mps/mps.h>
//#define MAX_ELEMENTS 2800000
//#define MAX_ELEMENTS 720000
#define MAX_ELEMENTS 3000
#define MAX_ELEMENTS 1000
//#define DRAW_PICTURE 1
#define SWAP(t,x,y) do { t _tmp = (x); (x) = (y); (y) = _tmp; } while (0);
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;
@ -214,10 +262,12 @@ void enumerate(groupelement_t *group, mat *matrices, mpq_t s, mpq_t t)
mat_workspace_clear(ws);
}
void output_invariants(groupelement_t *group, mat *matrices, mpq_t s, mpq_t q)
void output_invariants(groupelement_t *group, mat *matrices, mpq_t s, mpq_t q, mps_context *solver)
{
mpq_t tr, trinv;
char buf[100];
double evs[3];
int retval;
mpq_inits(tr, trinv, NULL);
@ -228,7 +278,22 @@ void output_invariants(groupelement_t *group, mat *matrices, mpq_t s, mpq_t q)
mat_trace(tr, matrices[i]);
mat_trace(trinv, matrices[group[i].inverse->id]);
gmp_printf("%d %d %s %Qd %Qd %f %f\n", i, group[i].length, print_word(&group[i], buf), tr, trinv, log(mpq_get_d(tr)), log(mpq_get_d(trinv)));
retval = solve_characteristic_polynomial(solver, tr, 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]);
gmp_printf("%d %d %s %Qd %Qd %f %f\n", i, group[i].length, print_word(&group[i], buf), tr, trinv, log(evs[0]), -log(evs[2]));
}
mpq_clears(tr, trinv, NULL);
@ -271,6 +336,7 @@ int main(int argc, char *argv[])
mat *matrices;
groupelement_t *group;
int index;
mps_context *solver;
mpq_inits(s, q, t, tmp, NULL);
group = malloc(MAX_ELEMENTS*sizeof(groupelement_t));
@ -278,6 +344,10 @@ int main(int argc, char *argv[])
for(int i = 0; i < MAX_ELEMENTS; i++)
mat_init(matrices[i], 3);
solver = mps_context_new();
mps_context_set_output_prec(solver, 20); // relative precision
mps_context_set_output_goal(solver, MPS_OUTPUT_GOAL_APPROXIMATE);
int acc = 100;
sapprox = atof(argv[1]);
@ -315,7 +385,7 @@ int main(int argc, char *argv[])
enumerate(group, matrices, s, q);
//printf("%f %f\n", mpq_get_d(t), max_slope(group, matrices, s, t, &index));
output_invariants(group, matrices, s, q);
output_invariants(group, matrices, s, q, solver);
// }
for(int i = 0; i < MAX_ELEMENTS; i++)
@ -323,4 +393,5 @@ int main(int argc, char *argv[])
free(matrices);
free(group);
mpq_clears(s, q, t, tmp, NULL);
mps_context_free(solver);
}

15
singular_values.plt
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@ -6,9 +6,9 @@ file = sprintf("< ./singular_values %f %f", exp(logs), exp(logt))
set zeroaxis
set samples 1000
set size square
set xrange [0:20]
set yrange [0:20]
set trange [0:20]
set xrange [0:30]
set yrange [0:30]
set trange [0:30]
set grid
set parametric
@ -20,9 +20,14 @@ set parametric
tr(a,b) = exp(a) + exp(b-a) + exp(-b)
trinv(a,b) = exp(-a) + exp(a-b) + exp(b)
#plot file using 6:7 w p pt 7 ps 0.5 lc 1 t columnheader,
# log(tr(t,t*2)),log(trinv(t,2*t)) w l lw 2 t "", \
# log(tr(t,t/2)),log(trinv(t,t/2)) w l lw 2 t ""
plot file using 6:7 w p pt 7 ps 0.5 lc 1 t columnheader, \
log(tr(t,t*2)),log(trinv(t,2*t)) w l lw 2 t "", \
log(tr(t,t/2)),log(trinv(t,t/2)) w l lw 2 t ""
t,2*t w l lw 2 t "", \
t,t/2 w l lw 2 t ""
#plot for[i=-10:10] log(tr(t,t*exp(log(2)*i/10.0))),log(trinv(t,t*exp(log(2)*i/10.0))) w l lw 2 t ""