643 lines
16 KiB
C
643 lines
16 KiB
C
#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 <mpi.h>
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#include <sys/stat.h>
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#include <sys/mman.h>
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#include <fcntl.h>
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#include <errno.h>
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#include <string.h>
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#include <unistd.h>
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#define MIN(x,y) ((x)<(y)?(x):(y))
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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, ...) do { print_time(); fprintf(stderr, msg, ##__VA_ARGS__); } while (0);
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//#define DEBUG(msg, ...)
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#define TDIV 10
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#define TFROM 1
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#define TTO 9
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#define MDIV 10
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#define MFROM 1
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#define MTO 9
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#define JOBNR(t,m) (((t)-TFROM) + ((m)-MFROM)*(TTO-TFROM+1))
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#define NJOBS ((TTO-TFROM+1)*(MTO-MFROM+1))
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#define FLUSH_INTERVAL 100
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enum message_tag {
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JOB_ORDER,
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JOB_RESULT,
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JOB_SHUTDOWN,
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};
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struct job {
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int tparam, mparam;
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int done;
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double max_slope;
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double time;
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};
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struct result {
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mpq_t tr;
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mpq_t trinv;
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};
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struct global_data {
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int n;
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group_t *group;
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mat* matrices;
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struct result *invariants;
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struct result **distinct_invariants;
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mps_context *solver;
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};
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struct timespec starttime;
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char processor_name[MPI_MAX_PROCESSOR_NAME];
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int world_rank;
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int world_size;
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MPI_Datatype job_datatype;
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void print_time()
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{
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double diff;
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struct timespec current;
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clock_gettime(CLOCK_REALTIME, ¤t);
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diff = (current.tv_sec - starttime.tv_sec) + (current.tv_nsec - starttime.tv_nsec)*1e-9;
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fprintf(stderr, "[%04d %.3f] ", world_rank, diff);
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}
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static struct global_data allocate_global_data(int n)
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{
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struct global_data result;
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result.n = n;
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result.matrices = malloc(n*sizeof(mat));
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for(int i = 0; i < n; i++)
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mat_init(result.matrices[i], 3);
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result.invariants = malloc(n*sizeof(struct result));
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result.distinct_invariants = malloc(n*sizeof(struct result*));
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for(int i = 0; i < n; i++) {
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mpq_init(result.invariants[i].tr);
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mpq_init(result.invariants[i].trinv);
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result.distinct_invariants[i] = &result.invariants[i];
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}
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result.solver = mps_context_new();
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mps_context_set_output_prec(result.solver, 20); // relative precision
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mps_context_set_output_goal(result.solver, MPS_OUTPUT_GOAL_APPROXIMATE);
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return result;
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}
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void free_global_data(struct global_data dat)
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{
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for(int i = 0; i < dat.n; i++)
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mat_clear(dat.matrices[i]);
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free(dat.matrices);
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for(int i = 0; i < dat.n; i++) {
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mpq_clear(dat.invariants[i].tr);
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mpq_clear(dat.invariants[i].trinv);
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}
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free(dat.invariants);
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free(dat.distinct_invariants);
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mps_context_free(dat.solver);
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}
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static int compare_result(const void *a_, const void *b_)
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{
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int d = 0;
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struct result **a = (struct result **)a_;
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struct result **b = (struct result **)b_;
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d = mpq_cmp((*a)->tr,(*b)->tr);
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if(d == 0)
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d = mpq_cmp((*a)->trinv, (*b)->trinv);
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return d;
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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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// this version is only for the (4,4,4) group
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void initialize_triangle_generators(mat_workspace *ws, mat *gen, mpq_t m, mpq_t t)
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{
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mpq_t s,sinv,q,x,y;
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mpq_t zero, one, two;
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mpq_t tmp;
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mpq_inits(s,sinv,q,x,y,zero,one,two,tmp,NULL);
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mpq_set_ui(zero, 0, 1);
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mpq_set_ui(one, 1, 1);
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mpq_set_ui(two, 2, 1);
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// s = (1-m^2)/2m
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mpq_mul(s, m, m);
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mpq_sub(s, one, s);
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mpq_div(s, s, m);
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mpq_div(s, s, two);
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mpq_div(sinv, one, s);
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// q = (1+m^2)/(1-m^2) = 2/(1-m^2) - 1
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mpq_mul(q, m, m);
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mpq_sub(q, one, q);
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mpq_div(q, two, q);
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mpq_sub(q, q, one);
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// x = -tq, y = -q/t
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mpq_mul(x, q, t);
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mpq_sub(x, zero, x);
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mpq_div(y, q, t);
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mpq_sub(y, zero, y);
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// q^2 = xy = 1 + 1/s^2
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// [ -s s*y 0]
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// [ -s*x s*x*y - 1/s 0]
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// [ -s*y s*y^2 - x 1]
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LOOP(i,3) {
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mat_zero(gen[i]);
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mpq_sub(tmp, zero, s);
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mat_set(gen[i%3], i%3, i%3, tmp);
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mpq_mul(tmp, s, y);
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mat_set(gen[i%3], i%3, (i+1)%3, tmp);
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mpq_mul(tmp, s, x);
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mpq_sub(tmp, zero, tmp);
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mat_set(gen[i%3], (i+1)%3, i%3, tmp);
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mpq_mul(tmp, s, x);
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mpq_mul(tmp, tmp, y);
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mpq_sub(tmp, tmp, sinv);
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mat_set(gen[i%3], (i+1)%3, (i+1)%3, tmp);
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mpq_mul(tmp, s, y);
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mpq_sub(tmp, zero, tmp);
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mat_set(gen[i%3], (i+2)%3, i%3, tmp);
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mpq_mul(tmp, s, y);
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mpq_mul(tmp, tmp, y);
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mpq_sub(tmp, tmp, x);
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mat_set(gen[i%3], (i+2)%3, (i+1)%3, tmp);
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mat_set(gen[i%3], (i+2)%3, (i+2)%3, one);
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}
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LOOP(i,3) mat_pseudoinverse(ws, gen[i+3], gen[i]);
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// debug output
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/*
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gmp_printf("m = %Qd, s = %Qd, t = %Qd, q = %Qd, x = %Qd, y = %Qd\n", m, s, t, q, x, y);
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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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*/
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mpq_inits(s,sinv,q,x,y,zero,one,two,tmp,NULL);
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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 m, 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, m, 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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double compute_max_slope(struct global_data dat, mpq_t t, mpq_t m)
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{
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// mpq_set_ui(t, ttick, 100);
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// mpq_set_ui(m, mtick, 100); // 414/1000 ~ sqrt(2)-1 <-> s=1
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// s = (1-mpq_get_d(m)*mpq_get_d(m))/(2*mpq_get_d(m));
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int n = 0;
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int nmax = dat.n;
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int nuniq;
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double max_slope;
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int retval;
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double evs[3];
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group_t *group = dat.group;
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mat *matrices = dat.matrices;
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struct result *invariants = dat.invariants;
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struct result **distinct_invariants = dat.distinct_invariants;
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mps_context *solver = dat.solver;
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// DEBUG("Compute matrices\n");
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enumerate(group, matrices, m, t);
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// DEBUG("Compute traces\n");
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n = 0;
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for(int i = 0; i < nmax; 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(invariants[i].tr, matrices[i]);
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mat_trace(invariants[i].trinv, matrices[group->elements[i].inverse->id]);
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distinct_invariants[n++] = &invariants[i];
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}
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// DEBUG("Get unique traces\n");
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qsort(distinct_invariants, n, sizeof(struct result*), compare_result);
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nuniq = 0;
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for(int i = 0; i < n; i++) {
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if(i == 0 || compare_result(&distinct_invariants[i], &distinct_invariants[nuniq-1]) != 0)
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distinct_invariants[nuniq++] = distinct_invariants[i];
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}
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max_slope = 0;
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int max_slope_index;
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// DEBUG("Solve characteristic polynomials\n");
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for(int i = 0; i < nuniq; i++) {
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retval = solve_characteristic_polynomial(solver, distinct_invariants[i]->tr, distinct_invariants[i]->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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double x = log(fabs(evs[0]));
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double y = -log(fabs(evs[2]));
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if(y/x > max_slope && (x > 0.1 || y > 0.1)) {
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max_slope_index = distinct_invariants[i] - invariants;
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max_slope = y/x;
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}
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// gmp_printf("%Qd %Qd %f %f %f\n", distinct_invariants[i]->tr, distinct_invariants[i]->trinv, x, y, y/x);
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}
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return max_slope;
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}
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void write_results_and_end(struct job *jobs, const char *outfile)
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{
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DEBUG("writing output and shutting down\n");
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FILE *f = fopen(outfile, "w");
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for(int i = 0; i < NJOBS; i++)
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fprintf(f, "%d/%d %d/%d %.10f %.10f %.10f %.3f\n",
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jobs[i].tparam, TDIV, jobs[i].mparam, MDIV,
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(double)jobs[i].tparam/TDIV, (double)jobs[i].mparam/MDIV, jobs[i].max_slope,
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jobs[i].time);
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fclose(f);
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for(int i = 1; i < world_size; i++)
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MPI_Send(NULL, 0, job_datatype, i, JOB_SHUTDOWN, MPI_COMM_WORLD);
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}
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void run_master_process(int nmax, const char *restart, const char *outfile)
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{
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int total_jobs = NJOBS;
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int completed = 0;
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int queue_jobs = MIN(total_jobs, 2*world_size);
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struct job current_job;
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MPI_Status status;
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FILE *f;
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int continuing = 1;
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int restartf;
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struct job *alljobs;
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struct job *current;
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restartf = open(restart, O_RDWR);
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if(restartf == -1 && errno == ENOENT) {
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restartf = open(restart, O_RDWR | O_CREAT, 0666);
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continuing = 0;
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}
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if(restartf == -1) {
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DEBUG("error opening restart file: %s\n", strerror(errno));
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exit(1);
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}
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ftruncate(restartf, total_jobs*sizeof(struct job));
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alljobs = (struct job*) mmap(0, total_jobs*sizeof(struct job), PROT_READ | PROT_WRITE, MAP_SHARED, restartf, 0);
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if(alljobs == MAP_FAILED) {
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DEBUG("error mapping restart file: %s\n", strerror(errno));
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|
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(¤t_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], ¤t_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(¤t_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(¤t_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(¤t_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();
|
|
}
|