mirror of
https://github.com/zenorogue/hyperrogue.git
synced 2024-11-17 10:44:48 +00:00
337 lines
9.5 KiB
C++
337 lines
9.5 KiB
C++
// This generates the 'solv-geodesics.dat' file.
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// You may change the _PREC* values for more precise geodesics.
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#include "../hyper.h"
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#include <thread>
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#include <mutex>
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namespace hr {
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const int _PRECX = 64;
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const int _PRECY = 64;
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const int _PRECZ = 64;
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transmatrix parabolic1(ld u);
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namespace solv {
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typedef hyperpoint pt;
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typedef array<float, 3> ptlow;
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ptlow be_low(pt x) { return ptlow({float(x[0]), float(x[1]), float(x[2])}); }
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template<class T> void parallelize(int threads, int Nmin, int Nmax, T action) {
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std::vector<std::thread> v;
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for(int k=0; k<threads; k++)
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v.emplace_back([&,k] () {
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for(int i=Nmin+k; i < Nmax; i += threads) action(k, i);
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});
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for(std::thread& t:v) t.join();
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}
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hyperpoint sol1(pt v) {
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auto [x,y,z,t] = (array<ld,4>&) v;
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if(x == 0 && z == 0) return C0;
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hyperpoint h = parabolic1(x) * xpush(-z) * C0;
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ld d = acosh(h[2]) / sqrt(h[0] * h[0] + h[1] * h[1]);
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return hyperpoint({h[1]*d, 0, -h[0]*d,1});
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}
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hyperpoint sol2(pt v) {
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auto [x,y,z,t] = (array<ld,4>&) v;
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if(y == 0 && z == 0) return C0;
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hyperpoint h = parabolic1(y) * xpush(z) * C0;
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ld d = acosh(h[2]) / sqrt(h[0] * h[0] + h[1] * h[1]);
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return hyperpoint({0, h[1]*d, +h[0]*d,1});
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}
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ld x_to_ix(ld u);
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ld solerror(pt ok, pt chk) {
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auto zok = point3( x_to_ix(ok[0]), x_to_ix(ok[1]), tanh(ok[2]) );
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auto zchk = point3( x_to_ix(chk[0]), x_to_ix(chk[1]), tanh(chk[2]) );
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return hypot_d(3, zok - zchk);
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}
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ld eucerror(pt ok, pt chk) {
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return pow(ok[0]-chk[0], 2) + pow(ok[1]-chk[1], 2) + pow(ok[2]-chk[2], 2);
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}
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pt iterative_solve(pt xp, pt 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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auto f = [&] (hyperpoint x) { return nisot::numerical_exp(x, prec); }; // T * x; };
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auto ver = f(candidate);
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ld err = solerror(xp, ver);
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auto at = candidate;
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ld eps = 1e-6;
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pt 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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while(err > minerr) {
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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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auto x = at + c[a] * eps;
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if(debug) println(hlog, "f(", x, ") = ", f(x), " = y + ", f(x)-ver );
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pnear[a] = (f(x) - ver) / eps; // (direct_exp(at + c[a] * eps, prec) - ver) / eps;
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}
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transmatrix U = Id;
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for(int a=0; a<3; a++)
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for(int b=0; b<3; b++)
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U[a][b] = pnear[b][a];
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hyperpoint diff = (xp - ver);
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hyperpoint bonus = inverse(U) * diff;
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if(hypot_d(3, bonus) > 0.1) bonus = bonus * 0.1 / hypot_d(3, bonus);
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int fixes = 0;
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if(debug)
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println(hlog, "\nU = ", U, "\ndiff = ", diff, "\nbonus = ", bonus, "\n");
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nextfix:
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hyperpoint next = at + bonus;
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hyperpoint nextver = f(next);
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ld nexterr = solerror(xp, nextver);
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if(debug) println(hlog, "f(", next, ") = ", nextver, ", error = ", nexterr);
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if(nexterr < err) {
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// println(hlog, "reduced error ", err, " to ", nexterr);
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at = next;
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ver = nextver;
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err = nexterr;
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continue;
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}
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else {
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bonus /= 2;
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fixes++;
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if(fixes > 10) {
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if(err > 999) {
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for(ld s = 1; abs(s) > 1e-9; s *= 0.5)
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for(int k=0; k<27; k++) {
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int kk = k;
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next = at;
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for(int i=0; i<3; i++) { if(kk%3 == 1) next[i] += s; if(kk%3 == 2) next[i] -= s; kk /= 3; }
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// next = at + c[k] * s;
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nextver = f(next);
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nexterr = solerror(xp, nextver);
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// println(hlog, "f(", next, ") = ", nextver, ", error = ", nexterr);
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if(nexterr < err) { at = next; ver = nextver; err = nexterr; goto nextiter; }
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}
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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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}
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goto nextfix;
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}
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nextiter: ;
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}
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return at;
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}
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ptlow solution[_PRECZ][_PRECY][_PRECX];
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ptlow mlow(ld x, ld y, ld z) { return ptlow({float(x), float(y), float(z)}); }
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pt atxyz(ld x, ld y, ld z) { return hyperpoint({x, y, z, 1}); }
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ptlow operator +(ptlow a, ptlow b) { return mlow(a[0]+b[0], a[1]+b[1], a[2]+b[2]); }
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ptlow operator -(ptlow a, ptlow b) { return mlow(a[0]-b[0], a[1]-b[1], a[2]-b[2]); }
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ptlow operator *(ptlow a, ld x) { return mlow(a[0]*x, a[1]*x, a[2]*x); }
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ptlow can(pt x) {
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// azimuthal equidistant to Klein
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ld r = sqrt(x[0] * x[0] + x[1] * x[1] + x[2] * x[2]);
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if(r == 0) return mlow(0,0,0);
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ld make_r = tanh(r);
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ld d = make_r / r;
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return mlow(x[0]*d, x[1]*d, x[2]*d);
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}
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pt uncan(ptlow x) {
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ld r = sqrt(x[0] * x[0] + x[1] * x[1] + x[2] * x[2]);
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if(r == 0) return atxyz(0,0,0);
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ld make_r = atanh(r);
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if(r == 1) make_r = 30;
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ld d = make_r / r;
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return atxyz(x[0]*d, x[1]*d, x[2]*d);
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}
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pt uncan_info(ptlow x) {
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ld r = sqrt(x[0] * x[0] + x[1] * x[1] + x[2] * x[2]);
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println(hlog, "r = ", r);
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if(r == 0) return atxyz(0,0,0);
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ld make_r = atanh(r);
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println(hlog, "make_r = ", make_r);
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ld d = make_r / r;
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println(hlog, "d = ", d);
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return atxyz(x[0]*d, x[1]*d, x[2]*d);
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}
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void fint(FILE *f, int x) { fwrite(&x, sizeof(x), 1, f); }
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void ffloat(FILE *f, float x) { fwrite(&x, sizeof(x), 1, f); }
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void write_table(const char *fname) {
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FILE *f = fopen(fname, "wb");
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fint(f, _PRECX);
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fint(f, _PRECY);
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fint(f, _PRECZ);
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fwrite(solution, sizeof(solution), 1, f);
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fclose(f);
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}
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void load_table(const char *fname) {
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int s;
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FILE *f = fopen(fname, "rb");
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fread(&s, 4, 1, f);
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fread(&s, 4, 1, f);
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fread(&s, 4, 1, f);
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fread(solution, sizeof(solution), 1, f);
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fclose(f);
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}
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ld ix_to_x(ld ix) {
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ld minx = 0, maxx = 1;
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for(int it=0; it<100; it++) {
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ld x = (minx + maxx) / 2;
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if(x_to_ix(atanh(x)) < ix) minx = x;
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else maxx = x;
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}
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return atanh(minx);
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}
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ld iz_to_z(ld z) {
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return atanh(z); // atanh(z * 2 - 1);
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}
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ld z_to_iz(ld z) {
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return tanh(z); // (tanh(z) + 1) / 2;
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}
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int last_x = _PRECX-1, last_y = _PRECY-1, last_z = _PRECZ-1;
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ld ptd(ptlow p) {
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return p[0]*p[0] + p[1]*p[1] + p[2] * p[2];
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}
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ptlow zflip(ptlow x) { return mlow(x[1], x[0], -x[2]); }
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void build_sols() {
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std::mutex file_mutex;
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ld max_err = 0;
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auto act = [&] (int tid, int iz) {
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auto solve_at = [&] (int ix, int iy) {
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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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auto v = hyperpoint ({x,y,z,1});
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vector<pt> candidates;
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pt cand;
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candidates.push_back(atxyz(0,0,0));
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static constexpr int prec = 100;
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// sort(candidates.begin(), candidates.end(), [&] (pt a, pt b) { return solerror(v, direct_exp(a, prec)) > solerror(v, direct_exp(b, prec)); });
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// cand_best = candidates.back();
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vector<pt> 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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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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sort(solved_candidates.begin(), solved_candidates.end(), [&] (pt a, pt b) { return solerror(v, nisot::numerical_exp(a, prec)) > solerror(v, nisot::numerical_exp(b, prec)); });
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cand = solved_candidates.back();
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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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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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println(hlog, "error = ", xerr);
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println(hlog, "canned = ", can(cand));
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max_err = xerr;
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hyperpoint h1 = uncan(solution[iz][iy-1][ix]);
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hyperpoint h2 = uncan(solution[iz][iy][ix-1]);
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hyperpoint h3 = uncan(solution[iz][iy-1][ix-1]);
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hyperpoint h4 = h1 + h2 - h3;
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solution[iz][iy][ix] = can(h4);
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return;
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}
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solution[iz][iy][ix] = can(cand);
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for(int z=0; z<3; z++) if(isnan(solution[iz][iy][ix][z]) || isinf(solution[iz][iy][ix][z])) {
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println(hlog, cand, "canned to ", solution[iz][iy][ix]);
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exit(4);
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}
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};
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for(int it=0; it<max(last_x, last_y); it++) {
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for(int a=0; a<it; a++) {
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if(it < last_x && a < last_y) solve_at(it, a);
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if(a < last_x && it < last_y) solve_at(a, it);
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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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}
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};
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parallelize(last_z, 0, last_z, 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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solution[z][y][x] = solution[z-1][y][x] * 2 - solution[z-2][y][x];
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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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solution[z][y][x] = solution[z][y-1][x] * 2 - solution[z][y-2][x];
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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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solution[z][y][x] = solution[z][y][x-1] * 2 - solution[z][y][x-2];
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}
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int main(int argc, char **argv) {
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println(hlog);
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geometry = gSol;
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build_sols();
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write_table("solv-geodesics-generated.dat");
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exit(0);
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}
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int phooks = addHook(hooks_main, 0, main);
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}
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}
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