sn:: solv-table generator: improve table (to compute shortest geodesics), bugfixer, visualizer
This commit is contained in:
Zeno Rogue
parent
e964ede86d
commit
80b6b536fc
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@ -2,11 +2,14 @@
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// Usage:
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// [executable] -geo sol -write solv-geodesics.dat
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// -geo 3:2 -write shyp-geodesics.dat
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// -geo 3:1/2 -write ssol-geodesics.dat
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// [executable] -geo sol -build -write solv-geodesics.dat
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// -geo 3:2 -build -write shyp-geodesics.dat
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// -geo 3:1/2 -build -write ssol-geodesics.dat
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// -exit
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// Loading generated tables and visualization:
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// [executable] /hyper -fsol [filename] -geo sol -visualize filename-%03d.png
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// You can also do -geo [...] -build to build and test the table
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// without writing it.
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@ -48,6 +51,10 @@ ld solerror(hyperpoint ok, hyperpoint chk) {
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return hypot_d(3, zok - zchk);
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}
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int max_iter = 999999;
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hyperpoint fail(.1, .2, .3, .4);
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hyperpoint iterative_solve(hyperpoint xp, hyperpoint candidate, int prec, ld minerr, bool debug = false) {
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transmatrix T = Id; T[0][1] = 8; T[2][2] = 5;
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@ -63,7 +70,12 @@ hyperpoint iterative_solve(hyperpoint xp, hyperpoint candidate, int prec, ld min
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hyperpoint c[3];
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for(int a=0; a<3; a++) c[a] = point3(a==0, a==1, a==2);
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int iter = 0;
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while(err > minerr) {
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iter++; if(iter > max_iter) return fail;
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if(debug) println(hlog, "\n\nf(", at, "?) = ", ver, " (error ", err, ")");
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array<hyperpoint, 3> pnear;
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for(int a=0; a<3; a++) {
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@ -120,7 +132,7 @@ hyperpoint iterative_solve(hyperpoint xp, hyperpoint candidate, int prec, ld min
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println(hlog, "cannot improve error ", err);
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exit(1);
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}
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break;
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return fail;
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}
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goto nextfix;
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}
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@ -216,6 +228,29 @@ ld ptd(ptlow p) {
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ptlow zflip(ptlow x) { return mlow(x[1], x[0], -x[2]); }
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void fix_boundaries(sn::tabled_inverses& tab, int last_x, int last_y, int last_z) {
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int PRECX = tab.PRECX;
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int PRECY = tab.PRECY;
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int PRECZ = tab.PRECZ;
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for(int x=0; x<last_x; x++)
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for(int y=0; y<last_y; y++) {
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for(int z=last_z; z<PRECZ; z++)
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tab.get_int(x,y,z) = tab.get_int(x,y,z-1) * 2 - tab.get_int(x,y,z-2);
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if(nih)
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tab.get_int(x,y,0) = tab.get_int(x,y,1) * 2 - tab.get_int(x,y,2);
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}
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for(int x=0; x<last_x; x++)
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for(int y=last_y; y<PRECY; y++)
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for(int z=0; z<PRECZ; z++)
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tab.get_int(x,y,z) = tab.get_int(x,y-1,z) * 2 - tab.get_int(x,y-2,z);
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for(int x=last_x; x<PRECX; x++)
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for(int y=0; y<PRECY; y++)
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for(int z=0; z<PRECZ; z++)
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tab.get_int(x,y,z) = tab.get_int(x-1,y,z) * 2 - tab.get_int(x-2,y,z);
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}
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void build_sols(int PRECX, int PRECY, int PRECZ) {
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std::mutex file_mutex;
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ld max_err = 0;
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@ -246,7 +281,7 @@ void build_sols(int PRECX, int PRECY, int PRECZ) {
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vector<hyperpoint> solved_candidates;
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for(auto c: candidates) {
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auto solt = iterative_solve(v, c, prec, 1e-6);
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auto solt = iterative_solve(v, c, prec, 1e-6, false);
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solved_candidates.push_back(solt);
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if(solerror(v, nisot::numerical_exp(solt, prec)) < 1e-9) break;
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}
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@ -257,7 +292,11 @@ void build_sols(int PRECX, int PRECY, int PRECZ) {
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auto xerr = solerror(v, nisot::numerical_exp(cand, prec));
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if(xerr > 1e-3) {
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if(cand == fail) {
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println(hlog, format("[%2d %2d %2d] FAIL", iz, iy, ix));
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}
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else if(xerr > 1e-3) {
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println(hlog, format("[%2d %2d %2d] ", iz, iy, ix));
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println(hlog, "f(?) = ", v);
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println(hlog, "f(", cand, ") = ", nisot::numerical_exp(cand, prec));
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@ -292,32 +331,256 @@ void build_sols(int PRECX, int PRECY, int PRECZ) {
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}
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if(it < last_x && it < last_y) solve_at(it, it);
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std::lock_guard<std::mutex> fm(file_mutex);
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println(hlog, format("%2d: %2d", iz, it));
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if(0) println(hlog, format("%2d: %2d", iz, it));
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}
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};
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parallelize(PRECZ, 0, PRECZ, act);
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for(int x=0; x<last_x; x++)
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for(int y=0; y<last_y; y++) {
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for(int z=last_z; z<PRECZ; z++)
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tab.get_int(x,y,z) = tab.get_int(x,y,z-1) * 2 - tab.get_int(x,y,z-2);
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if(nih)
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tab.get_int(x,y,0) = tab.get_int(x,y,1) * 2 - tab.get_int(x,y,2);
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}
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for(int x=0; x<last_x; x++)
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for(int y=last_y; y<PRECY; y++)
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for(int z=0; z<PRECZ; z++)
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tab.get_int(x,y,z) = tab.get_int(x,y-1,z) * 2 - tab.get_int(x,y-2,z);
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for(int x=last_x; x<PRECX; x++)
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for(int y=0; y<PRECY; y++)
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for(int z=0; z<PRECZ; z++)
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tab.get_int(x,y,z) = tab.get_int(x-1,y,z) * 2 - tab.get_int(x-2,y,z);
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fix_boundaries(tab, last_x, last_y, last_z);
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}
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int dimX, dimY, dimZ;
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std::mutex file_mutex_global;
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bool deb = false;
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hyperpoint find_optimal_geodesic(hyperpoint res) {
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auto p0 = point3(0, 0, 0);
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hyperpoint h = iterative_solve(res, p0, 100, 1e-9);
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if(h == fail) return fail;
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ld d = hypot_d(3, h);
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auto solve = [&] (hyperpoint m, pair<hyperpoint, hyperpoint> last) {
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hyperpoint t = // inverse_exp(m, iTable, false);
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iterative_solve(m, last.first, 100, 1e-9);
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hyperpoint u = // inverse_exp(inverse(nisot::translate(m)) * res, iTable, false);
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iterative_solve(inverse(nisot::translate(m)) * res, last.second, 100, 1e-6);
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return make_pair(t, u);
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};
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auto quality = [&] (pair<hyperpoint, hyperpoint> p) {
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return hypot_d(3, p.first) + hypot_d(3, p.second);
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};
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auto attempt = [&] (hyperpoint mid) {
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auto p = solve(mid, {p0, p0});
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ld qd = quality(p);
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if(true) {
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// println(hlog, "there is something better: ", qd, " vs ", d);
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bool found;
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bool failed = false;
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auto tryit = [&] (hyperpoint h) {
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auto p2 = solve(h, p);
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auto qd2 = quality(p2);
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if(p2.first == fail || p2.second == fail) failed = true;
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else if(qd2 < qd) {
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qd = qd2, p = p2, mid = h;
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found = true;
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return true;
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}
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return false;
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};
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ld delta = 1e-3;
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/*
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auto q_x = quality(solve(mid + point3(delta, 0, 0), p)) - qd;
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auto q_xx = quality(solve(mid + point3(delta+delta, 0, 0), p)) - qd - 2 * q_x;
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auto q_y = quality(solve(mid + point3(0, delta, 0), p)) - qd;
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auto q_yy = quality(solve(mid + point3(0, delta+delta, 0), p)) - qd - 2 * q_y;
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auto q_z = quality(solve(mid + point3(0, 0, delta), p)) - qd;
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auto q_zz = quality(solve(mid + point3(0, 0, delta+delta), p)) - qd - 2 * q_z;
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auto q_xy = quality(solve(mid + point3(delta, delta, 0), p)) - qd - q_x - q_y;
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auto q_xz = quality(solve(mid + point3(delta, 0, delta), p)) - qd - q_x - q_z;
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auto q_yz = quality(solve(mid + point3(0, delta, delta), p)) - qd - q_y - q_z;
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transmatrix T = build_matrix(
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hyperpoint(q_xx, q_xy, q_xz, 0),
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hyperpoint(q_xy, q_yy, q_yz, 0),
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hyperpoint(q_xz, q_yz, q_zz, 0),
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hyperpoint(0, 0, 0, 1)
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);
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hyperpoint q = hyperpoint(q_x, q_y, q_z, 0);
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*/
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int itera = 0;
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while(true) {
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itera++;
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if(itera % 1000 == 0) {
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std::lock_guard<std::mutex> fm(file_mutex_global);
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println(hlog, "itera = ", itera);
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if(itera >= 5000) return;
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}
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auto q_v = quality(solve(mid + point3(delta, -delta, 0), p)) - qd;
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auto q_vv = quality(solve(mid + point3(delta+delta, -delta-delta, 0), p)) - qd - 2 * q_v;
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auto q_z = quality(solve(mid + point3(0, 0, delta), p)) - qd;
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auto q_zz = quality(solve(mid + point3(0, 0, delta+delta), p)) - qd - 2 * q_z;
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auto q_vz = quality(solve(mid + point3(delta, -delta, delta), p)) - qd - q_v - q_z;
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ld d = q_vv * q_zz - q_vz * q_vz;
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if(d == 0 || isnan(d) || isinf(d)) {
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std::lock_guard<std::mutex> fm(file_mutex_global);
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println(hlog, "bad matrix in iteration #", itera);
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println(hlog, "p = ", p, " mid = ", mid);
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println(hlog, solve(mid, p));
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return;
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}
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transmatrix T = build_matrix(
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hyperpoint(q_vv, 0, q_vz, 0),
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hyperpoint(0, 1, 0, 0),
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hyperpoint(q_vz, 0, q_zz, 0),
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hyperpoint(0, 0, 0, 1)
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);
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hyperpoint q = hyperpoint(q_v, 0, q_z, 0);
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hyperpoint res = inverse(T) * -q;
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// println(hlog, "res = ", res);
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// println(hlog, "check = ", q + T * res);
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res[1] = -res[0];
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res = res * delta;
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res /= 10.;
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if(tryit(mid + res)) continue;
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if(tryit(mid + res/2)) continue;
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if(tryit(mid + res/4)) continue;
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break;
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}
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// q_x + q_xx * x + q_xy * y + q_xz * z == 0
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// q + Txyz == 0
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int it = 0;
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ld qd0 = qd;
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if(false) while(delta > 1e-6) {
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it++;
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// if(it % 1000 == 0) println(hlog, "iterations ", it);
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if(it > 1000) return;
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if(failed) return;
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found = false;
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while(tryit(mid + point3(delta, -delta, 0)));
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while(tryit(mid + point3(-delta, +delta, 0)));
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while(tryit(mid + point3(0, 0, delta)));
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while(tryit(mid + point3(0, 0, -delta)));
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// while(tryit(mid + point3(delta, delta, 0)));
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// while(tryit(mid + point3(-delta, -delta, 0)));
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if(found) println(hlog, "improved further from ", qd0, " to ", qd);
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if(!found) delta /= 2;
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}
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max_iter = 1000;
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auto h1 = iterative_solve(res, p.first * quality(p) / hypot_d(3, p.first), 100, 1e-6);
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if(deb) println(hlog, "h1 returns ", h1, " of length ", hypot_d(3, h1), " and error ", hypot_d(3, numerical_exp(h1, 100) - res));
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if(h1 == fail) return;
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auto d1 = hypot_d(3, h1);
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if(d1 < d) h = h1, d = d1;
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}
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};
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hyperpoint old = h;
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attempt(point31(res[0], 0, res[2]/2));
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attempt(point31(0, res[1], res[2]/2));
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std::lock_guard<std::mutex> fm(file_mutex_global);
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if(h != old && hypot_d(3, h) < hypot_d(3, old) - 1e-5)
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println(hlog, "new = ", h, " vs old = ", old, " length ", hypot_d(3, h), " vs ", hypot_d(3, old));
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else if(deb)
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println(hlog, " not improved: ", old);
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return h;
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}
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void fix_bugs(sn::tabled_inverses& tab) {
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auto bug = can(fail);
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for(int iz=0; iz<tab.PRECZ; iz++)
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for(int iy=0; iy<tab.PRECY; iy++)
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for(int ix=0; ix<tab.PRECX; ix++) {
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if(tab.get_int(ix, iy, iz) == bug)
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for(int a=0; a<3; a++)
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tab.get_int(ix, iy, iz)[a] = (tab.get_int(ix-1, iy, iz)[a]*2 - tab.get_int(ix-2, iy, iz)[a]);
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}
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}
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void visualize_table(sn::tabled_inverses& tab, const string& s) {
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renderbuffer rb(tab.PRECX, tab.PRECY, false);
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rb.make_surface();
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for(int iz=0; iz<tab.PRECZ; iz++) {
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println(hlog, "iz=", iz);
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for(int iy=0; iy<tab.PRECY; iy++)
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for(int ix=0; ix<tab.PRECX; ix++) {
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auto& p = qpixel(rb.srf, ix, iy);
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if(ix == 52 && iy >= 30 && iy <= 40 && iz == 15)
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println(hlog, "A ", tie(ix,iy,iz), " : ", tab.get_int(ix, iy, iz));
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// println(hlog, ix, ", ", iy);
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p = 0xFFFFFFFF;
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for(int i=0; i<3; i++)
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part(p, i) = 0x80 + 0x70 * tab.get_int(ix, iy, iz)[i];
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}
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SDL_SavePNG(rb.srf, format(s.c_str(), iz).c_str());
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}
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}
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void improve(sn::tabled_inverses& tab) {
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int PRECX = tab.PRECX;
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int PRECY = tab.PRECY;
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int PRECZ = tab.PRECZ;
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int last_x = PRECX-1, last_y = PRECY-1, last_z = PRECZ-1;
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max_iter = 1000;
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auto act = [&] (int tid, int iz) {
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if((nih && iz == 0) || iz == PRECZ-1) return;
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for(int iy=0; iy<last_y; iy++)
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for(int ix=0; ix<last_x; ix++) {
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if(ix < 32 || iy < 32) continue;
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if(deb) { if(ix < 50 || ix > 54 || iy != 46 || iz != 6) continue; }
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if(deb) println(hlog, tie(ix, iy, iz), ":");
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ld x = ix_to_x(ix / (PRECX-1.));
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ld y = ix_to_x(iy / (PRECY-1.));
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ld z = iz_to_z(iz / (PRECZ-1.));
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hyperpoint p = point31(x, y, z);
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// hyperpoint h1 = inverse_exp(p, iTable, false);
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hyperpoint h2 = find_optimal_geodesic(p);
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std::lock_guard<std::mutex> fm(file_mutex_global);
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if(ix == last_x-1) println(hlog, "solved ", tie(ix, iy, iz));
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if(h2 != fail) {
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auto& so = tab.get_int(ix, iy, iz);
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so = can(h2);
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// println(hlog, "can: ", can(h2), " @ ", so[0]*so[0]+so[1]*so[1]+so[2]*so[2]);
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// println(hlog, h2, " vs ", uncan(can(h2)));
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}
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}
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};
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max_iter = 1000000;
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parallelize(PRECZ, 0, PRECZ, act);
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if(deb) exit(7);
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fix_boundaries(tab, last_x, last_y, last_z);
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}
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int dimX=64, dimY=64, dimZ=64;
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int readArgs() {
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using namespace arg;
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@ -333,11 +596,30 @@ int readArgs() {
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PHASEFROM(2);
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build_sols(dimX, dimY, dimZ);
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}
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else if(argis("-load-old")) {
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sn::get_tabled().load();
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}
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else if(argis("-improve")) {
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sn::get_tabled().load();
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improve(sn::get_tabled());
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}
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else if(argis("-write")) {
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PHASEFROM(2);
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shift();
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build_sols(dimX, dimY, dimZ);
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write_table(solnihv::get_tabled(), argcs());
|
||||
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<63; iz++)
|
||||
println(hlog, "iz=", iz, " z=", iz_to_z(iz / (sn::get_tabled().PRECZ-1.)));
|
||||
}
|
||||
else if(argis("-visualize")) {
|
||||
shift();
|
||||
sn::get_tabled().load();
|
||||
visualize_table(sn::get_tabled(), argcs());
|
||||
}
|
||||
|
||||
else return 1;
|
||||
|
|
|
|||
Loading…
Reference in New Issue