use mpi to run on cluster
This commit is contained in:
Florian Stecker
parent
b5bd9d398f
commit
528f329c59
18
Makefile
18
Makefile
@ -3,20 +3,24 @@ HEADERS=linalg.h mat.h coxeter.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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SPECIAL_OPTIONS=-O3 -flto -funroll-loops -Winline
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#SPECIAL_OPTIONS=-O3 -flto -funroll-loops -Winline -mavx512f -mavx512cd -mavx512er -mavx512pf # KNL
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#SPECIAL_OPTIONS=
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OPTIONS=-m64 -march=native -mtune=native -std=gnu99 -D_GNU_SOURCE $(SPECIAL_OPTIONS)
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OPTIONS=-I../mps/include -L../mps/lib -pthread -m64 -std=gnu99 -D_GNU_SOURCE $(SPECIAL_OPTIONS)
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all: singular_values special_element
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all: singular_values special_element convert
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singular_values: singular_values.o coxeter.o linalg.o mat.o
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gcc $(OPTIONS) -o singular_values coxeter.o linalg.o singular_values.o mat.o -lm -lgsl -lcblas -lgmp -lmps -lpthread
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convert: convert.hs
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ghc --make -dynamic convert.hs
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singular_values: singular_values.o coxeter.o mat.o
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mpicc $(OPTIONS) -o singular_values coxeter.o singular_values.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 -lgsl -lcblas -lgmp -lmps -lpthread
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gcc $(OPTIONS) -o special_element coxeter.o linalg.o special_element.o mat.o -lm -lgmp -lmps
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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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mpicc $(OPTIONS) -c singular_values.c
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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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@ -31,4 +35,4 @@ 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 coxeter.o linalg.o singular_values.o mat.o special_element.o
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rm -f singular_values special_element coxeter.o linalg.o singular_values.o mat.o special_element.o convert.hi convert.o convert
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@ -1,18 +1,65 @@
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#include "coxeter.h"
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#include "linalg.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 <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 OUTPUT_POINTS
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#define OUTPUT_SUMMARY
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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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@ -23,14 +70,43 @@ void print_time()
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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, "[%.3f] ", diff);
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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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struct result {
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mpq_t tr;
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mpq_t trinv;
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};
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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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@ -272,167 +348,31 @@ void enumerate(group_t *group, mat *matrices, mpq_t m, mpq_t t)
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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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double compute_max_slope(struct global_data dat, mpq_t t, mpq_t m)
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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_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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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]));
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}
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mpq_clears(tr, trinv, NULL);
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}
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/*
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double max_slope(groupelement_t *group, mat *matrices, mpq_t s, mpq_t t, int *index)
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{
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double max = 0;
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double slope;
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mpq_t tr, trinv;
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char buf[100];
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mpq_inits(tr, trinv, NULL);
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for(int i = 0; i < MAX_ELEMENTS; i++) {
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if(group[i].length % 2 != 0 || !group[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[i].inverse->id]);
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slope = log(mpq_get_d(trinv))/log(mpq_get_d(tr));
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if(slope > max)
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{
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*index = i;
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max = slope;
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}
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}
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mpq_clears(tr, trinv, NULL);
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return max;
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}
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*/
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int main(int argc, char *argv[])
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{
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mpq_t m, t, tmp;
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double s;
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mat *matrices;
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group_t *group;
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int index;
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mps_context *solver;
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int acc = 100;
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int n, nuniq, nmax;
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int retval;
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double evs[3];
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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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char buf[100];
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char buf2[100];
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int retval;
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double evs[3];
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struct result *invariants;
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struct result **distinct_invariants;
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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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clock_gettime(CLOCK_REALTIME, &starttime);
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nmax = atoi(argv[1]);
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DEBUG("Allocate\n");
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mpq_inits(m, t, tmp, NULL);
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matrices = malloc(nmax*sizeof(mat));
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for(int i = 0; i < nmax; i++)
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mat_init(matrices[i], 3);
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invariants = malloc(nmax*sizeof(struct result));
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distinct_invariants = malloc(nmax*sizeof(struct result));
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for(int i = 0; i < nmax; i++) {
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mpq_init(invariants[i].tr);
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mpq_init(invariants[i].trinv);
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distinct_invariants[i] = &invariants[i];
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}
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solver = mps_context_new();
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mps_context_set_output_prec(solver, 20); // relative precision
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mps_context_set_output_goal(solver, MPS_OUTPUT_GOAL_APPROXIMATE);
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/*
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DEBUG("Approximate parameters\n");
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// get approximate s and q values
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sapprox = atof(argv[2]);
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tapprox = atof(argv[3]);
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tqfactor = pow((sapprox*sapprox-sapprox+1)*(sapprox*sapprox-sapprox+1)*(sapprox*sapprox+1), 1/6.0);
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qapprox = tapprox/tqfactor;
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for(int i = 0; ; i++) {
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continued_fraction_approximation(tmp, sapprox, i);
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if(fabs(mpq_get_d(t)-sapprox) < 1e-10
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|| (mpz_cmpabs_ui(mpq_numref(tmp),acc) > 0 && mpz_cmpabs_ui(mpq_denref(tmp),acc) > 0))
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break;
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mpq_set(s, tmp);
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}
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mpq_canonicalize(s);
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for(int i = 0; ; i++) {
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continued_fraction_approximation(tmp, qapprox, i);
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if(fabs(mpq_get_d(t)-qapprox) < 1e-10
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|| (mpz_cmpabs_ui(mpq_numref(tmp),acc) > 0 && mpz_cmpabs_ui(mpq_denref(tmp),acc) > 0))
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break;
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mpq_set(q, tmp);
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}
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mpq_canonicalize(q);
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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);
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#ifdef OUTPUT_POINTS
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gmp_fprintf(stdout, "\"s = %Qd = %.3f, q = %Qd, t = %.3f\"\n", s, mpq_get_d(s), q, mpq_get_d(q)*tqfactor);
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#endif
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*/
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// group
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DEBUG("Generate group\n");
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group = coxeter_init_triangle(4, 4, 4, nmax);
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fprintf(stderr, "max word length = %d\n", group->elements[nmax-1].length);
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for(int ttick = 45; ttick <= 65; ttick++) {
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for(int mtick = 45; mtick < 65; mtick++) {
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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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DEBUG("Compute matrices\n");
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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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DEBUG("Compute traces\n");
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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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@ -441,11 +381,9 @@ int main(int argc, char *argv[])
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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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// gmp_printf("%Qd %Qd %d %s\n", invariants[i].tr, invariants[i].trinv, i, print_word(&group->elements[i], buf));
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}
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DEBUG("Get unique traces\n");
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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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@ -458,7 +396,7 @@ int main(int argc, char *argv[])
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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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// 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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@ -483,29 +421,222 @@ int main(int argc, char *argv[])
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max_slope = y/x;
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}
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#ifdef OUTPUT_POINTS
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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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#endif
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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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#ifdef OUTPUT_SUMMARY
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// fprintf(stdout, "%.5f %.5f %.5f %f %s\n", mpq_get_d(t), mpq_get_d(m), s, max_slope, print_word(&group->elements[max_slope_index], buf));
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fprintf(stdout, "%.5f %.5f %.5f %f %s\n", mpq_get_d(t), mpq_get_d(m), s, max_slope, print_word(&group->elements[max_slope_index], buf));
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#endif
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}
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}
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DEBUG("Clean up\n");
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for(int i = 0; i < nmax; i++) {
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mpq_clear(invariants[i].tr);
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mpq_clear(invariants[i].trinv);
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}
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free(invariants);
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free(distinct_invariants);
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for(int i = 0; i < nmax; i++)
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mat_clear(matrices[i]);
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free(matrices);
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coxeter_clear(group);
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mpq_clears(m, t, tmp, NULL);
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mps_context_free(solver);
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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;
|
||||
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(¤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();
|
||||
}
|
||||
|
||||
Loading…
Reference in New Issue
Block a user