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restore old singular_values program in addition to mpi one

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This commit is contained in:
Florian Stecker 2021-10-23 12:09:40 -05:00
parent 75fd51423e
commit 6daac5888e
6 changed files with 1066 additions and 415 deletions
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1
.gitignore vendored
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@ -2,6 +2,7 @@
triangle_group/singular_values triangle_group/singular_values
.#* .#*
singular_values singular_values
singular_values_mpi
output/ output/
special_element special_element
max_slope_picture/generate max_slope_picture/generate

14
Makefile
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@ -8,7 +8,7 @@ SPECIAL_OPTIONS=-O3 -pg -funroll-loops -fno-inline
OPTIONS=-I../mps/include -L../mps/lib -pthread -m64 -std=gnu99 -D_GNU_SOURCE $(SPECIAL_OPTIONS) OPTIONS=-I../mps/include -L../mps/lib -pthread -m64 -std=gnu99 -D_GNU_SOURCE $(SPECIAL_OPTIONS)
all: singular_values special_element convert billiard_words all: singular_values special_element singular_values_mpi convert billiard_words
convert: convert.hs convert: convert.hs
ghc --make -dynamic convert.hs ghc --make -dynamic convert.hs
@ -17,13 +17,19 @@ billiard_words: billiard_words.hs
ghc --make -dynamic billiard_words.hs ghc --make -dynamic billiard_words.hs
singular_values: singular_values.o coxeter.o mat.o singular_values: singular_values.o coxeter.o mat.o
mpicc $(OPTIONS) -o singular_values coxeter.o singular_values.o mat.o -lm -lgmp -lmps gcc $(OPTIONS) -o singular_values coxeter.o singular_values.o mat.o -lm -lgmp -lmps
singular_values_mpi: singular_values_mpi.o coxeter.o mat.o
mpicc $(OPTIONS) -o singular_values_mpi coxeter.o singular_values_mpi.o mat.o -lm -lgmp -lmps
special_element: special_element.o coxeter.o linalg.o mat.o special_element: special_element.o coxeter.o linalg.o mat.o
gcc $(OPTIONS) -o special_element coxeter.o linalg.o special_element.o mat.o -lm -lgmp -lmps -lgsl -lcblas gcc $(OPTIONS) -o special_element coxeter.o linalg.o special_element.o mat.o -lm -lgmp -lmps -lgsl -lcblas
singular_values.o: singular_values.c $(HEADERS) singular_values.o: singular_values.c $(HEADERS)
mpicc $(OPTIONS) -c singular_values.c gcc $(OPTIONS) -c singular_values.c
singular_values_mpi.o: singular_values_mpi.c $(HEADERS)
mpicc $(OPTIONS) -c singular_values_mpi.c
special_element.o: special_element.c $(HEADERS) special_element.o: special_element.c $(HEADERS)
gcc $(OPTIONS) -c special_element.c gcc $(OPTIONS) -c special_element.c
@ -38,4 +44,4 @@ mat.o: mat.c $(HEADERS)
gcc $(OPTIONS) -c mat.c gcc $(OPTIONS) -c mat.c
clean: clean:
rm -f singular_values special_element coxeter.o linalg.o singular_values.o mat.o special_element.o convert.hi convert.o convert billiard_words.hi billiard_words.o billiard_words 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

57
cdf.plt Normal file
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@ -0,0 +1,57 @@
#if(!exists("logt")) logt = log(1.80)
if(!exists("n")) n = 263
if(!exists("logt")) logt = log(1)
if(!exists("logs")) logs = log(1)
#logt = 0.01*n
logt = log(1000000000)
file = sprintf("< ./singular_values 713698 %f %f", exp(logs), exp(logt))
#file = sprintf("< ./singular_values 1621 %f %f", exp(logs), exp(logt))
#outfile = sprintf("cdf/cdf_hires_%05d.png", n)
outfile = sprintf("cdf/cdf_hires_limit.png")
set log x
set zeroaxis
set samples 1000
set size square
set xrange [0.5:2]
set yrange [0:500000]
#set yrange [0:1000]
set trange [0:30]
set grid
set parametric
set terminal pngcairo enhanced size 1024, 1024
set output outfile
print sprintf("n = %d, t = %.2f", n, exp(logt))
# plot file using 2:3 w p pt 7 ps 0.5 lc 1 t title
#tr(a,b) = exp((2*a+b)/3) + exp((b-a)/3) + exp(-(a+2*b)/3)
#trinv(a,b) = exp(-(2*a+b)/3) + exp((a-b)/3) + exp((a+2*b)/3)
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 8:3 w steps lw 2 lc 1 t sprintf("t = %.2f", exp(logt))
#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 ""
#plot for[i=-10:10] t,log(tr(t,t*exp(log(2)*i/10.0)))-t w l lw 2 t ""
##plot for[i=20:20] t,log(tr(1/t,exp(2*log(2)*i/20.0-log(2)))) w l lw 2 t ""
#n=n+1
#if(n < 1000) reread
# pause mouse keypress
# if(MOUSE_KEY == 60) logt=logt-0.02
# if(MOUSE_KEY == 62) logt=logt+0.02
# if(MOUSE_KEY == 44) logs=logs-0.02
# if(MOUSE_KEY == 46) logs=logs+0.02
# if(MOUSE_KEY != 113) reread

735
singular_values.c
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@ -1,113 +1,26 @@
#include "coxeter.h" #include "coxeter.h"
//#include "linalg.h" #include "linalg.h"
#include "mat.h" #include "mat.h"
//#include <gsl/gsl_poly.h> #include <gsl/gsl_poly.h>
#include <mps/mps.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 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, ...) fprintf(stderr, msg, ##__VA_ARGS__)
//#define DEBUG(msg, ...) #define DEBUG(msg, ...)
#define TDIV 10 #define OUTPUT_POINTS
#define TFROM 1 //#define OUTPUT_POINTS
#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 { struct result {
int id;
int count;
mpq_t tr; mpq_t tr;
mpq_t trinv; mpq_t trinv;
double x;
double y;
}; };
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_) static int compare_result(const void *a_, const void *b_)
{ {
int d = 0; int d = 0;
@ -116,12 +29,45 @@ static int compare_result(const void *a_, const void *b_)
struct result **b = (struct result **)b_; struct result **b = (struct result **)b_;
d = mpq_cmp((*a)->tr,(*b)->tr); d = mpq_cmp((*a)->tr,(*b)->tr);
if(d == 0) if(d == 0) {
d = mpq_cmp((*a)->trinv, (*b)->trinv); d = mpq_cmp((*a)->trinv, (*b)->trinv);
}
return d; return d;
} }
static int compare_result_with_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;
}
int solve_characteristic_polynomial(mps_context *solv, mpq_t tr, mpq_t trinv, double *eigenvalues) int solve_characteristic_polynomial(mps_context *solv, mpq_t tr, mpq_t trinv, double *eigenvalues)
{ {
mpq_t coeff1, coeff2, zero; mpq_t coeff1, coeff2, zero;
@ -215,75 +161,99 @@ void quartic(mpq_t out, mpq_t in, int a, int b, int c, int d, int e)
mpq_clear(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 s, mpq_t q)
void initialize_triangle_generators(mat_workspace *ws, mat *gen, mpq_t m, mpq_t t)
{ {
mpq_t s,sinv,q,x,y; mat r1,r2,r3;
mpq_t zero, one, two; mpq_t rho1, rho2, rho3;
mpq_t tmp; mpq_t b1,c1,a2,c2,a3,b3;
mpq_t sinv;
mpq_inits(s,sinv,q,x,y,zero,one,two,tmp,NULL); mpq_inits(sinv,rho1,rho2,rho3,b1,c1,a2,c2,a3,b3,NULL);
mpq_set_ui(zero, 0, 1); mat_init(r1, 3);
mpq_set_ui(one, 1, 1); mat_init(r2, 3);
mpq_set_ui(two, 2, 1); mat_init(r3, 3);
// s = (1-m^2)/2m mpq_set_ui(sinv, 1, 1);
mpq_mul(s, m, m); mpq_div(sinv, sinv, s);
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 quartic(rho1, s, 0, 0, 1, -1, 1);
mpq_mul(q, m, m); quartic(rho2, s, 0, 0, 1, -1, 1);
mpq_sub(q, one, q); quartic(rho3, s, 0, 0, 1, 0, 1);
mpq_div(q, two, q);
mpq_sub(q, q, one);
// x = -tq, y = -q/t mpq_mul(c1, rho2, q);
mpq_mul(x, q, t); mpq_mul(a2, rho3, q);
mpq_sub(x, zero, x); mpq_mul(b3, rho1, q);
mpq_div(y, q, t); mpq_set_ui(b1, 1, 1);
mpq_sub(y, zero, y); mpq_set_ui(c2, 1, 1);
mpq_set_ui(a3, 1, 1);
mpq_div(b1, b1, q);
mpq_div(c2, c2, q);
mpq_div(a3, a3, q);
// q^2 = xy = 1 + 1/s^2 // actually, we want minus everything
// [ -s s*y 0] mat_zero(r1);
// [ -s*x s*x*y - 1/s 0] mat_zero(r2);
// [ -s*y s*y^2 - x 1] mat_zero(r3);
LOOP(i,3) { mpq_set_si(*mat_ref(r1, 0, 0), -1, 1);
mat_zero(gen[i]); mpq_set_si(*mat_ref(r1, 1, 1), 1, 1);
mpq_sub(tmp, zero, s); mpq_set_si(*mat_ref(r1, 2, 2), 1, 1);
mat_set(gen[i%3], i%3, i%3, tmp); mpq_set_si(*mat_ref(r2, 0, 0), 1, 1);
mpq_mul(tmp, s, y); mpq_set_si(*mat_ref(r2, 1, 1), -1, 1);
mat_set(gen[i%3], i%3, (i+1)%3, tmp); mpq_set_si(*mat_ref(r2, 2, 2), 1, 1);
mpq_mul(tmp, s, x); mpq_set_si(*mat_ref(r3, 0, 0), 1, 1);
mpq_sub(tmp, zero, tmp); mpq_set_si(*mat_ref(r3, 1, 1), 1, 1);
mat_set(gen[i%3], (i+1)%3, i%3, tmp); mpq_set_si(*mat_ref(r3, 2, 2), -1, 1);
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_set(*mat_ref(r1, 1, 0), b1);
mpq_set(*mat_ref(r1, 2, 0), c1);
mpq_set(*mat_ref(r2, 0, 1), a2);
mpq_set(*mat_ref(r2, 2, 1), c2);
mpq_set(*mat_ref(r3, 0, 2), a3);
mpq_set(*mat_ref(r3, 1, 2), b3);
mat_zero(gen[0]);
mat_zero(gen[1]);
mat_zero(gen[2]);
mpq_set_ui(*mat_ref(gen[0], 0, 0), 1, 1);
mat_set(gen[0], 1, 1, sinv);
mat_set(gen[0], 2, 2, s);
mat_set(gen[1], 0, 0, s);
mpq_set_ui(*mat_ref(gen[1], 1, 1), 1, 1);
mat_set(gen[1], 2, 2, sinv);
mat_set(gen[2], 0, 0, sinv);
mat_set(gen[2], 1, 1, s);
mpq_set_ui(*mat_ref(gen[2], 2, 2), 1, 1);
mat_multiply(ws, gen[0], r2, gen[0]);
mat_multiply(ws, gen[0], gen[0], r3);
mat_multiply(ws, gen[1], r3, gen[1]);
mat_multiply(ws, gen[1], gen[1], r1);
mat_multiply(ws, gen[2], r1, gen[2]);
mat_multiply(ws, gen[2], gen[2], r2);
mat_pseudoinverse(ws, gen[3], gen[0]);
mat_pseudoinverse(ws, gen[4], gen[1]);
mat_pseudoinverse(ws, gen[5], gen[2]);
// 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(r1);
mat_print(r2);
mat_print(r3);
mat_print(gen[0]); mat_print(gen[0]);
mat_print(gen[1]); mat_print(gen[1]);
mat_print(gen[2]); mat_print(gen[2]);
mat_print(gen[3]);
mat_print(gen[4]);
mat_print(gen[5]);
*/ */
mpq_inits(s,sinv,q,x,y,zero,one,two,tmp,NULL); mpq_clears(sinv,rho1,rho2,rho3,b1,c1,a2,c2,a3,b3,NULL);
mat_clear(r1);
mat_clear(r2);
mat_clear(r3);
} }
char *print_word(groupelement_t *g, char *str) char *print_word(groupelement_t *g, char *str)
@ -299,7 +269,7 @@ char *print_word(groupelement_t *g, char *str)
return str; return str;
} }
void enumerate(group_t *group, mat *matrices, mpq_t m, mpq_t t) void enumerate(group_t *group, mat *matrices, mpq_t s, mpq_t t)
{ {
mat_workspace *ws; mat_workspace *ws;
mat tmp; mat tmp;
@ -312,7 +282,7 @@ void enumerate(group_t *group, mat *matrices, mpq_t m, mpq_t t)
mat_init(gen[i], 3); mat_init(gen[i], 3);
mat_init(tmp, 3); mat_init(tmp, 3);
initialize_triangle_generators(ws, gen, m, t); initialize_triangle_generators(ws, gen, s, t);
mat_identity(matrices[0]); mat_identity(matrices[0]);
for(int i = 1; i < group->size; i++) { for(int i = 1; i < group->size; i++) {
@ -348,55 +318,194 @@ void enumerate(group_t *group, mat *matrices, mpq_t m, mpq_t t)
mat_workspace_clear(ws); mat_workspace_clear(ws);
} }
void output_invariants(group_t *group, mat *matrices, mpq_t s, mpq_t q, mps_context *solver)
double compute_max_slope(struct global_data dat, mpq_t t, mpq_t m)
{ {
// mpq_set_ui(t, ttick, 100); mpq_t tr, trinv;
// mpq_set_ui(m, mtick, 100); // 414/1000 ~ sqrt(2)-1 <-> s=1 char buf[100];
// s = (1-mpq_get_d(m)*mpq_get_d(m))/(2*mpq_get_d(m)); double evs[3];
int retval;
int n = 0; mpq_inits(tr, trinv, NULL);
int nmax = dat.n;
int nuniq; for(int i = 0; i < group->size; i++) {
double max_slope; if(group->elements[i].length % 2 != 0 || !group->elements[i].inverse)
continue;
mat_trace(tr, matrices[i]);
mat_trace(trinv, matrices[group->elements[i].inverse->id]);
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->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;
double sapprox, tapprox, qapprox, tqfactor;
mat *matrices;
group_t *group;
int index;
mps_context *solver;
int acc = 100;
int n, nuniq, nmax;
int retval; int retval;
double evs[3]; double evs[3];
double max_slope;
char buf[100];
char buf2[100];
group_t *group = dat.group; struct result *invariants;
mat *matrices = dat.matrices; struct result **distinct_invariants;
struct result *invariants = dat.invariants;
struct result **distinct_invariants = dat.distinct_invariants;
mps_context *solver = dat.solver;
// DEBUG("Compute matrices\n"); if(argc < 4) {
enumerate(group, matrices, m, t); fprintf(stderr, "Usage: %s <N> <s> <t>\n", argv[0]);
exit(1);
}
nmax = atoi(argv[1]);
DEBUG("Allocate\n");
mpq_inits(s, q, t, tmp, NULL);
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);
distinct_invariants[i] = &invariants[i];
}
solver = mps_context_new();
mps_context_set_output_prec(solver, 20); // relative precision
mps_context_set_output_goal(solver, MPS_OUTPUT_GOAL_APPROXIMATE);
DEBUG("Approximate parameters\n");
// 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;
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);
#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
DEBUG("Generate group\n");
group = coxeter_init_triangle(4, 3, 3, nmax);
DEBUG("Compute matrices\n");
enumerate(group, matrices, s, q);
// DEBUG("Compute traces\n");
n = 0; n = 0;
DEBUG("Compute traces\n");
for(int i = 0; i < nmax; i++) { for(int i = 0; i < nmax; i++) {
if(group->elements[i].length % 2 != 0 || !group->elements[i].inverse) if(group->elements[i].length % 2 != 0 || !group->elements[i].inverse)
continue; continue;
invariants[i].id = i;
mat_trace(invariants[i].tr, matrices[i]); mat_trace(invariants[i].tr, matrices[i]);
mat_trace(invariants[i].trinv, matrices[group->elements[i].inverse->id]); mat_trace(invariants[i].trinv, matrices[group->elements[i].inverse->id]);
distinct_invariants[n++] = &invariants[i]; distinct_invariants[n++] = &invariants[i];
} }
// DEBUG("Get unique traces\n"); DEBUG("Get unique traces\n");
qsort(distinct_invariants, n, sizeof(struct result*), compare_result);
nuniq = 0; nuniq = 0;
for(int i = 0; i < n; i++) { for(int i = 0; i < n; i++) {
if(i == 0 || compare_result(&distinct_invariants[i], &distinct_invariants[nuniq-1]) != 0) if(i == 0 || compare_result(&distinct_invariants[i], &distinct_invariants[nuniq-1]) != 0) {
distinct_invariants[nuniq++] = distinct_invariants[i]; 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; int max_slope_index;
// DEBUG("Solve characteristic polynomials\n"); 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, distinct_invariants[i]->tr, distinct_invariants[i]->trinv, evs);
if(retval == 1) { if(retval == 1) {
@ -416,227 +525,75 @@ double compute_max_slope(struct global_data dat, mpq_t t, mpq_t m)
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;
distinct_invariants[i]->y = y;
if(y/x > max_slope && (x > 0.1 || y > 0.1)) { if(y/x > max_slope && (x > 0.1 || y > 0.1)) {
max_slope_index = distinct_invariants[i] - invariants; max_slope_index = distinct_invariants[i] - invariants;
max_slope = y/x; 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; qsort(distinct_invariants, nuniq, sizeof(struct result*), compare_result_by_slope);
// printf("- 0 0 - - - - 0.5\n");
int cumulative = 0;
double slope;
for(int i = 0; i < nuniq; i++) {
slope = distinct_invariants[i]->y/distinct_invariants[i]->x;
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;
} }
void write_results_and_end(struct job *jobs, const char *outfile) cumulative += distinct_invariants[i]->count;
{ gmp_printf("%d %d %d %f %f %f %f %f %s\n",
DEBUG("writing output and shutting down\n"); distinct_invariants[i]->id, distinct_invariants[i]->count, cumulative,
distinct_invariants[i]->tr, distinct_invariants[i]->trinv,
FILE *f = fopen(outfile, "w"); log(fabs(mpq_get_d(distinct_invariants[i]->tr))), log(fabs(mpq_get_d(distinct_invariants[i]->trinv))),
for(int i = 0; i < NJOBS; i++) distinct_invariants[i]->x, distinct_invariants[i]->y, slope,
fprintf(f, "%d/%d %d/%d %.10f %.10f %.10f %.3f\n", print_word(&group->elements[distinct_invariants[i]->id], buf)
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);
} }
// printf("- 0 %d - - - - 2.0\n", cumulative);
void run_master_process(int nmax, const char *restart, const char *outfile) #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));
int total_jobs = NJOBS; #endif
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); // output_invariants(group, matrices, s, q, solver);
if(restartf == -1 && errno == ENOENT) {
restartf = open(restart, O_RDWR | O_CREAT, 0666); // for(int i = 0; i < 10; i++) {
continuing = 0; // 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);
mpq_clear(invariants[i].trinv);
} }
if(restartf == -1) { free(invariants);
DEBUG("error opening restart file: %s\n", strerror(errno)); free(distinct_invariants);
exit(1); for(int i = 0; i < nmax; i++)
} mat_clear(matrices[i]);
ftruncate(restartf, total_jobs*sizeof(struct job)); free(matrices);
alljobs = (struct job*) mmap(0, total_jobs*sizeof(struct job), PROT_READ | PROT_WRITE, MAP_SHARED, restartf, 0); coxeter_clear(group);
if(alljobs == MAP_FAILED) { mpq_clears(s, q, t, tmp, NULL);
DEBUG("error mapping restart file: %s\n", strerror(errno)); mps_context_free(solver);
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();
} }

30
singular_values.plt
View File

@ -1,5 +1,5 @@
if(!exists("logt")) logt = log(1.78) if(!exists("logt")) logt = log(1)
if(!exists("logs")) logs = log(0.5) if(!exists("logs")) logs = log(1)
#file = sprintf("< ./singular_values 713698 %f %f", exp(logs), exp(logt)) #file = sprintf("< ./singular_values 713698 %f %f", exp(logs), exp(logt))
file = sprintf("< ./singular_values 1621 %f %f", exp(logs), exp(logt)) file = sprintf("< ./singular_values 1621 %f %f", exp(logs), exp(logt))
@ -7,28 +7,13 @@ file = sprintf("< ./singular_values 1621 %f %f", exp(logs), exp(logt))
set zeroaxis set zeroaxis
set samples 1000 set samples 1000
set size square set size square
set xrange [0:30] set xrange [0:3]
set yrange [0:30] set yrange [0:3]
set trange [0:30] set trange [0:5]
set grid set grid
set parametric set parametric
# plot file using 2:3 w p pt 7 ps 0.5 lc 1 t title plot file using ($8/$9):($6/$7) w p pt 7 ps 0.3 lc 1 t sprintf("t = %.2f", exp(logt)), t, t
#tr(a,b) = exp((2*a+b)/3) + exp((b-a)/3) + exp(-(a+2*b)/3)
#trinv(a,b) = exp(-(2*a+b)/3) + exp((a-b)/3) + exp((a+2*b)/3)
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 3:4 w p pt 7 ps 0.5 lc 1 t columnheader, \
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 "" #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 ""
@ -36,6 +21,9 @@ plot file using 3:4 w p pt 7 ps 0.5 lc 1 t columnheader, \
##plot for[i=20:20] t,log(tr(1/t,exp(2*log(2)*i/20.0-log(2)))) w l lw 2 t "" ##plot for[i=20:20] t,log(tr(1/t,exp(2*log(2)*i/20.0-log(2)))) w l lw 2 t ""
#n=n+1
#if(n < 1000) reread
pause mouse keypress pause mouse keypress
if(MOUSE_KEY == 60) logt=logt-0.02 if(MOUSE_KEY == 60) logt=logt-0.02
if(MOUSE_KEY == 62) logt=logt+0.02 if(MOUSE_KEY == 62) logt=logt+0.02

642
singular_values_mpi.c Normal file
View File

@ -0,0 +1,642 @@
#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();
}