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hyperrogue/devmods/solv-table.cpp
Zeno Rogue 85b4785447 devmods/solv-table updated
2022-07-12 14:46:31 +02:00

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// This generates the inverse geodesics tables.
// Usage:
// [executable] -geo sol -build -write solv-geodesics.dat
// -geo 3:2 -build -write shyp-geodesics.dat
// -geo 3:1/2 -build -write ssol-geodesics.dat
// -exit
// Loading generated tables and visualization:
// [executable] /hyper -fsol [filename] -geo sol -visualize filename-%03d.png
// You can also do -geo [...] -build to build and test the table
// without writing it.
// By default this generates 64x64x64 tables.
// Add e.g. '-dim 128 128 128' before -write to generate
// a more/less precise table.
// # ./hyper -rk-steps 100 -geo Sol -iz-list -sn-unittest -build -write solv-geodesics-a.dat -visualize devmods/san1/solva-%04d.png -improve -write solv-geodesics.dat -visualize devmods/san1/solvb-%04d.png
// # ./hyper -dim 32 32 32 -geo 3:1/2 -iz-list -sn-unittest -build -write ssol-geodesics-a.dat -visualize devmods/san1/ssola-%04d.png -improve -write ssol-geodesics.dat -visualize devmods/san1/ssolb-%04d.png
// # ./hyper -dim 32 32 32 -geo 3:2 -iz-list -sn-unittest -build -write shyp-geodesics.dat -visualize devmods/san1/shypa-%04d.png
#include "../hyper.h"
#include <thread>
#include <mutex>
namespace hr {
transmatrix parabolic1(ld u);
namespace sn {
template<class T> void parallelize(int threads, int Nmin, int Nmax, T action) {
std::vector<std::thread> v;
for(int k=0; k<threads; k++)
v.emplace_back([&,k] () {
for(int i=Nmin+k; i < Nmax; i += threads) action(k, i);
});
for(std::thread& t:v) t.join();
}
ld solerror(hyperpoint ok, hyperpoint chk) {
auto zok = point3( x_to_ix(ok[0]), x_to_ix(ok[1]), z_to_iz(ok[2]) );
auto zchk = point3( x_to_ix(chk[0]), x_to_ix(chk[1]), z_to_iz(chk[2]) );
return hypot_d(3, zok - zchk);
}
int max_iter = 999999;
hyperpoint fail(.1, .2, .3, .4);
hyperpoint iterative_solve(hyperpoint xp, hyperpoint candidate, ld minerr, bool debug = false) {
transmatrix T = Id; T[0][1] = 8; T[2][2] = 5;
auto f = [&] (hyperpoint x) { return nisot::numerical_exp(x); }; // T * x; };
auto ver = f(candidate);
ld err = solerror(xp, ver);
auto at = candidate;
ld eps = 1e-6;
hyperpoint c[3];
for(int a=0; a<3; a++) c[a] = point3(a==0, a==1, a==2);
int iter = 0;
while(err > minerr) {
iter++; if(iter > max_iter) return fail;
if(debug) println(hlog, "\n\nf(", at, "?) = ", ver, " (error ", err, ")");
array<hyperpoint, 3> pnear;
for(int a=0; a<3; a++) {
auto x = at + c[a] * eps;
if(debug) println(hlog, "f(", x, ") = ", f(x), " = y + ", f(x)-ver );
pnear[a] = (f(x) - ver) / eps; // (direct_exp(at + c[a] * eps, prec) - ver) / eps;
}
transmatrix U = Id;
for(int a=0; a<3; a++)
for(int b=0; b<3; b++)
U[a][b] = pnear[b][a];
hyperpoint diff = (xp - ver);
hyperpoint bonus = inverse(U) * diff;
if(hypot_d(3, bonus) > 0.1) bonus = bonus * 0.1 / hypot_d(3, bonus);
int fixes = 0;
if(debug)
println(hlog, "\nU = ", U, "\ndiff = ", diff, "\nbonus = ", bonus, "\n");
nextfix:
hyperpoint next = at + bonus;
hyperpoint nextver = f(next);
ld nexterr = solerror(xp, nextver);
if(debug) println(hlog, "f(", next, ") = ", nextver, ", error = ", nexterr);
if(nexterr < err) {
// println(hlog, "reduced error ", err, " to ", nexterr);
at = next;
ver = nextver;
err = nexterr;
continue;
}
else {
bonus /= 2;
fixes++;
if(fixes > 10) {
if(err > 999) {
for(ld s = 1; abs(s) > 1e-9; s *= 0.5)
for(int k=0; k<27; k++) {
int kk = k;
next = at;
for(int i=0; i<3; i++) { if(kk%3 == 1) next[i] += s; if(kk%3 == 2) next[i] -= s; kk /= 3; }
// next = at + c[k] * s;
nextver = f(next);
nexterr = solerror(xp, nextver);
// println(hlog, "f(", next, ") = ", nextver, ", error = ", nexterr);
if(nexterr < err) { at = next; ver = nextver; err = nexterr; goto nextiter; }
}
println(hlog, "cannot improve error ", err);
exit(1);
}
return fail;
}
goto nextfix;
}
nextiter: ;
}
// println(hlog, "#it = ", iter);
return at;
}
using ptlow = compressed_point;
ptlow operator +(ptlow a, ptlow b) { return make_array<float>(a[0]+b[0], a[1]+b[1], a[2]+b[2]); }
ptlow operator -(ptlow a, ptlow b) { return make_array<float>(a[0]-b[0], a[1]-b[1], a[2]-b[2]); }
ptlow operator *(ptlow a, ld x) { return make_array<float>(a[0]*x, a[1]*x, a[2]*x); }
void fint(FILE *f, int x) { fwrite(&x, sizeof(x), 1, f); }
void ffloat(FILE *f, float x) { fwrite(&x, sizeof(x), 1, f); }
void write_table(sn::tabled_inverses& tab, const char *fname) {
FILE *f = fopen(fname, "wb");
fint(f, tab.PRECX);
fint(f, tab.PRECY);
fint(f, tab.PRECZ);
fwrite(&tab.tab[0], sizeof(ptlow) * tab.PRECX * tab.PRECY * tab.PRECZ, 1, f);
fclose(f);
}
void alloc_table(sn::tabled_inverses& tab, int X, int Y, int Z) {
tab.PRECX = X;
tab.PRECY = Y;
tab.PRECZ = Z;
tab.tab.resize(X*Y*Z);
}
ld ptd(ptlow p) {
return p[0]*p[0] + p[1]*p[1] + p[2] * p[2];
}
void fix_boundaries(sn::tabled_inverses& tab, int last_x, int last_y, int last_z) {
int PRECX = tab.PRECX;
int PRECY = tab.PRECY;
int PRECZ = tab.PRECZ;
for(int x=0; x<last_x; x++)
for(int y=0; y<last_y; y++) {
for(int z=last_z; z<PRECZ; z++)
tab.get_int(x,y,z) = tab.get_int(x,y,z-1) * 2 - tab.get_int(x,y,z-2);
if(nih)
tab.get_int(x,y,0) = tab.get_int(x,y,1) * 2 - tab.get_int(x,y,2);
}
for(int x=0; x<last_x; x++)
for(int y=last_y; y<PRECY; y++)
for(int z=0; z<PRECZ; z++)
tab.get_int(x,y,z) = tab.get_int(x,y-1,z) * 2 - tab.get_int(x,y-2,z);
for(int x=last_x; x<PRECX; x++)
for(int y=0; y<PRECY; y++)
for(int z=0; z<PRECZ; z++)
tab.get_int(x,y,z) = tab.get_int(x-1,y,z) * 2 - tab.get_int(x-2,y,z);
}
void build_sols(int PRECX, int PRECY, int PRECZ) {
std::mutex file_mutex;
ld max_err = 0;
auto& tab = sn::get_tabled();
alloc_table(tab, PRECX, PRECY, PRECZ);
int last_x = PRECX-1, last_y = PRECY-1, last_z = PRECZ-1;
auto act = [&] (int tid, int iz) {
if((nih && iz == 0) || iz == PRECZ-1) return;
auto solve_at = [&] (int ix, int iy) {
// if(ix != 30 || iy <= 50 || iz) return;
ld x = ix_to_x(ix / (PRECX-1.));
ld y = ix_to_x(iy / (PRECY-1.));
ld z = iz_to_z(iz / (PRECZ-1.));
auto v = hyperpoint ({x,y,z,1});
vector<hyperpoint> candidates;
hyperpoint cand;
candidates.push_back(point3(0,0,0));
// sort(candidates.begin(), candidates.end(), [&] (hyperpoint a, hyperpoint b) { return solerror(v, direct_exp(a, prec)) > solerror(v, direct_exp(b, prec)); });
// cand_best = candidates.back();
vector<hyperpoint> solved_candidates;
for(auto c: candidates) {
auto solt = iterative_solve(v, c, 1e-6, false);
solved_candidates.push_back(solt);
if(solerror(v, nisot::numerical_exp(solt)) < 1e-9) break;
}
sort(solved_candidates.begin(), solved_candidates.end(), [&] (hyperpoint a, hyperpoint b) { return solerror(v, nisot::numerical_exp(a)) > solerror(v, nisot::numerical_exp(b)); });
cand = solved_candidates.back();
auto xerr = solerror(v, nisot::numerical_exp(cand));
if(cand == fail) {
println(hlog, format("[%2d %2d %2d] FAIL", iz, iy, ix));
}
else if(xerr > 1e-3) {
println(hlog, format("[%2d %2d %2d] ", iz, iy, ix));
println(hlog, "f(?) = ", v);
println(hlog, "f(", cand, ") = ", nisot::numerical_exp(cand));
println(hlog, "error = ", xerr);
println(hlog, "canned = ", compress(azeq_to_table(cand)));
max_err = xerr;
return;
}
auto& so = tab.get_int(ix, iy, iz);
so = compress(azeq_to_table(cand));
for(int z=0; z<3; z++) if(isnan(so[z]) || isinf(so[z])) {
println(hlog, cand, "canned to ", so);
exit(4);
}
};
for(int it=0; it<max(last_x, last_y); it++) {
for(int a=0; a<it; a++) {
if(it < last_x && a < last_y) solve_at(it, a);
if(a < last_x && it < last_y) solve_at(a, it);
}
if(it < last_x && it < last_y) solve_at(it, it);
std::lock_guard<std::mutex> fm(file_mutex);
if(0) println(hlog, format("%2d: %2d", iz, it));
}
};
parallelize(PRECZ, 0, PRECZ, act);
fix_boundaries(tab, last_x, last_y, last_z);
}
std::mutex file_mutex_global;
bool deb = false;
hyperpoint find_optimal_geodesic(hyperpoint res) {
auto p0 = point3(0, 0, 0);
hyperpoint h = iterative_solve(res, p0, 100, 1e-9);
if(h == fail) return fail;
ld d = hypot_d(3, h);
auto solve = [&] (hyperpoint m, pair<hyperpoint, hyperpoint> last) {
hyperpoint t = // inverse_exp(m, iTable, false);
iterative_solve(m, last.first, 100, 1e-9);
hyperpoint u = // inverse_exp(inverse(nisot::translate(m)) * res, iTable, false);
iterative_solve(inverse(nisot::translate(m)) * res, last.second, 100, 1e-6);
return make_pair(t, u);
};
auto quality = [&] (pair<hyperpoint, hyperpoint> p) {
return hypot_d(3, p.first) + hypot_d(3, p.second);
};
auto attempt = [&] (hyperpoint mid) {
auto p = solve(mid, {p0, p0});
ld qd = quality(p);
if(true) {
// println(hlog, "there is something better: ", qd, " vs ", d);
bool found;
bool failed = false;
auto tryit = [&] (hyperpoint h) {
auto p2 = solve(h, p);
auto qd2 = quality(p2);
if(p2.first == fail || p2.second == fail) failed = true;
else if(qd2 < qd) {
qd = qd2, p = p2, mid = h;
found = true;
return true;
}
return false;
};
ld delta = 1e-3;
/*
auto q_x = quality(solve(mid + point3(delta, 0, 0), p)) - qd;
auto q_xx = quality(solve(mid + point3(delta+delta, 0, 0), p)) - qd - 2 * q_x;
auto q_y = quality(solve(mid + point3(0, delta, 0), p)) - qd;
auto q_yy = quality(solve(mid + point3(0, delta+delta, 0), p)) - qd - 2 * q_y;
auto q_z = quality(solve(mid + point3(0, 0, delta), p)) - qd;
auto q_zz = quality(solve(mid + point3(0, 0, delta+delta), p)) - qd - 2 * q_z;
auto q_xy = quality(solve(mid + point3(delta, delta, 0), p)) - qd - q_x - q_y;
auto q_xz = quality(solve(mid + point3(delta, 0, delta), p)) - qd - q_x - q_z;
auto q_yz = quality(solve(mid + point3(0, delta, delta), p)) - qd - q_y - q_z;
transmatrix T = build_matrix(
hyperpoint(q_xx, q_xy, q_xz, 0),
hyperpoint(q_xy, q_yy, q_yz, 0),
hyperpoint(q_xz, q_yz, q_zz, 0),
hyperpoint(0, 0, 0, 1)
);
hyperpoint q = hyperpoint(q_x, q_y, q_z, 0);
*/
int itera = 0;
while(true) {
itera++;
if(itera % 1000 == 0) {
std::lock_guard<std::mutex> fm(file_mutex_global);
println(hlog, "itera = ", itera);
if(itera >= 5000) return;
}
auto q_v = quality(solve(mid + point3(delta, -delta, 0), p)) - qd;
auto q_vv = quality(solve(mid + point3(delta+delta, -delta-delta, 0), p)) - qd - 2 * q_v;
auto q_z = quality(solve(mid + point3(0, 0, delta), p)) - qd;
auto q_zz = quality(solve(mid + point3(0, 0, delta+delta), p)) - qd - 2 * q_z;
auto q_vz = quality(solve(mid + point3(delta, -delta, delta), p)) - qd - q_v - q_z;
ld d = q_vv * q_zz - q_vz * q_vz;
if(d == 0 || isnan(d) || isinf(d)) {
std::lock_guard<std::mutex> fm(file_mutex_global);
println(hlog, "bad matrix in iteration #", itera);
println(hlog, "p = ", p, " mid = ", mid);
println(hlog, solve(mid, p));
return;
}
transmatrix T = build_matrix(
hyperpoint(q_vv, 0, q_vz, 0),
hyperpoint(0, 1, 0, 0),
hyperpoint(q_vz, 0, q_zz, 0),
hyperpoint(0, 0, 0, 1)
);
hyperpoint q = hyperpoint(q_v, 0, q_z, 0);
hyperpoint res = inverse(T) * -q;
// println(hlog, "res = ", res);
// println(hlog, "check = ", q + T * res);
res[1] = -res[0];
res = res * delta;
res /= 10.;
if(tryit(mid + res)) continue;
if(tryit(mid + res/2)) continue;
if(tryit(mid + res/4)) continue;
break;
}
// q_x + q_xx * x + q_xy * y + q_xz * z == 0
// q + Txyz == 0
int it = 0;
ld qd0 = qd;
if(false) while(delta > 1e-6) {
it++;
// if(it % 1000 == 0) println(hlog, "iterations ", it);
if(it > 1000) return;
if(failed) return;
found = false;
while(tryit(mid + point3(delta, -delta, 0)));
while(tryit(mid + point3(-delta, +delta, 0)));
while(tryit(mid + point3(0, 0, delta)));
while(tryit(mid + point3(0, 0, -delta)));
// while(tryit(mid + point3(delta, delta, 0)));
// while(tryit(mid + point3(-delta, -delta, 0)));
if(found) println(hlog, "improved further from ", qd0, " to ", qd);
if(!found) delta /= 2;
}
max_iter = 1000;
auto h1 = iterative_solve(res, p.first * quality(p) / hypot_d(3, p.first), 100, 1e-6);
if(deb) println(hlog, "h1 returns ", h1, " of length ", hypot_d(3, h1), " and error ", hypot_d(3, nisot::numerical_exp(h1) - res));
if(h1 == fail) return;
auto d1 = hypot_d(3, h1);
if(d1 < d) h = h1, d = d1;
}
};
hyperpoint old = h;
attempt(point31(res[0], 0, res[2]/2));
attempt(point31(0, res[1], res[2]/2));
std::lock_guard<std::mutex> fm(file_mutex_global);
if(h != old && hypot_d(3, h) < hypot_d(3, old) - 1e-5)
println(hlog, "new = ", h, " vs old = ", old, " length ", hypot_d(3, h), " vs ", hypot_d(3, old));
else if(deb)
println(hlog, " not improved: ", old);
return h;
}
void fix_bugs(sn::tabled_inverses& tab) {
auto bug = compress(azeq_to_table(fail));
for(int iz=0; iz<tab.PRECZ; iz++)
for(int iy=0; iy<tab.PRECY; iy++)
for(int ix=0; ix<tab.PRECX; ix++) {
if(tab.get_int(ix, iy, iz) == bug)
for(int a=0; a<3; a++)
tab.get_int(ix, iy, iz)[a] = (tab.get_int(ix-1, iy, iz)[a]*2 - tab.get_int(ix-2, iy, iz)[a]);
}
}
void visualize_table(sn::tabled_inverses& tab, const string& s) {
renderbuffer rb(tab.PRECX, tab.PRECY, false);
rb.make_surface();
for(int iz=0; iz<tab.PRECZ; iz++) {
println(hlog, "iz=", iz);
for(int iy=0; iy<tab.PRECY; iy++)
for(int ix=0; ix<tab.PRECX; ix++) {
auto& p = qpixel(rb.srf, ix, iy);
if(ix == 52 && iy >= 30 && iy <= 40 && iz == 15)
println(hlog, "A ", tie(ix,iy,iz), " : ", tab.get_int(ix, iy, iz));
// println(hlog, ix, ", ", iy);
p = 0xFFFFFFFF;
for(int i=0; i<3; i++)
part(p, i) = 0x80 + 0x70 * tab.get_int(ix, iy, iz)[i];
}
SDL_SavePNG(rb.srf, format(s.c_str(), iz).c_str());
}
}
void improve(sn::tabled_inverses& tab) {
int PRECX = tab.PRECX;
int PRECY = tab.PRECY;
int PRECZ = tab.PRECZ;
int last_x = PRECX-1, last_y = PRECY-1, last_z = PRECZ-1;
max_iter = 1000;
auto act = [&] (int tid, int iz) {
if((nih && iz == 0) || iz == PRECZ-1) return;
for(int iy=0; iy<last_y; iy++)
for(int ix=0; ix<last_x; ix++) {
if(ix < 32 || iy < 32) continue;
if(deb) { if(ix < 50 || ix > 54 || iy != 46 || iz != 6) continue; }
if(deb) println(hlog, tie(ix, iy, iz), ":");
ld x = ix_to_x(ix / (PRECX-1.));
ld y = ix_to_x(iy / (PRECY-1.));
ld z = iz_to_z(iz / (PRECZ-1.));
hyperpoint p = point31(x, y, z);
// hyperpoint h1 = inverse_exp(p, iTable, false);
hyperpoint h2 = find_optimal_geodesic(p);
std::lock_guard<std::mutex> fm(file_mutex_global);
if(ix == last_x-1) println(hlog, "solved ", tie(ix, iy, iz));
if(h2 != fail) {
auto& so = tab.get_int(ix, iy, iz);
so = compress(azeq_to_table(h2));
}
}
};
max_iter = 1000000;
parallelize(PRECZ, 0, PRECZ, act);
if(deb) exit(7);
fix_boundaries(tab, last_x, last_y, last_z);
}
int dimX=64, dimY=64, dimZ=64;
EX hyperpoint recompress(hyperpoint h) { return decompress(compress(h)); }
int readArgs() {
using namespace arg;
if(0) ;
else if(argis("-dim")) {
PHASEFROM(2);
shift(); dimX = argi();
shift(); dimY = argi();
shift(); dimZ = argi();
}
else if(argis("-build")) {
PHASEFROM(2);
build_sols(dimX, dimY, dimZ);
}
else if(argis("-load-old")) {
sn::get_tabled().load();
}
else if(argis("-improve")) {
sn::get_tabled().load();
improve(sn::get_tabled());
}
else if(argis("-write")) {
shift();
write_table(sn::get_tabled(), argcs());
}
else if(argis("-fix-bugs")) {
sn::get_tabled().load();
fix_bugs(sn::get_tabled());
}
else if(argis("-iz-list")) {
sn::get_tabled().load();
for(int iz=0; iz<dimZ-1; iz++)
println(hlog, "iz=", iz, " z=", iz_to_z(iz / (dimZ-1.)));
}
else if(argis("-visualize")) {
shift();
sn::get_tabled().load();
visualize_table(sn::get_tabled(), argcs());
}
else if(argis("-sn-unittest")) {
println(hlog, "nih = ", (bool)nih);
ld maxerr;
auto test_result = [&maxerr] (ld a, ld b) { maxerr = max(maxerr, (a-b)); };
auto test_result_p = [&maxerr] (hyperpoint a, hyperpoint b) { maxerr = max(maxerr, hypot_d(3, a-b)); };
auto test = [&maxerr] (string s, reaction_t tester) {
maxerr = 0;
tester();
println(hlog, "unittest: ", s, " error = ", maxerr);
};
test("x_to_ix", [&] { for(ld a=0; a<=20; a+=.1) test_result(a, sn::ix_to_x(sn::x_to_ix(a))); });
test("z_to_iz", [&] { for(ld a=nih?-20:0; a<=20; a+=.1) test_result(a, sn::iz_to_z(sn::z_to_iz(a))); });
test("azeq_to_table", [&] { for(ld a=-5; a<=5; a++) for(ld b=-5; b<=5; b++) for(ld c=-5; c<=5; c++) { hyperpoint h = point3(a,b,c); test_result_p(h, sn::table_to_azeq(sn::azeq_to_table(h))); }});
test("azeq_to_table recompressed", [&] {
for(ld a=-5; a<=5; a++) for(ld b=-5; b<=5; b++) for(ld c=-5; c<=5; c++) {
hyperpoint h = point3(a,b,c); test_result_p(h, sn::table_to_azeq(recompress(sn::azeq_to_table(h))));
}
});
}
else return 1;
return 0;
}
auto hook = addHook(hooks_args, 100, readArgs);
}
}
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