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hyperrogue/devmods/solv-error-analyze.cpp
2020-08-12 22:09:52 +02:00

594 lines
16 KiB
C++

#include "../hyper.h"
// This program generates the error table for Solv approxiations.
#define D3 1
#define D2 0
#if CAP_FIELD
namespace hr {
ld solerror(hyperpoint ok, hyperpoint chk) {
return geo_dist(chk, ok);
}
ld minz = -1e-9, maxz = 1e-9;
int max_iter = 999999;
bool isok;
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[6];
for(int a=0; a<3; a++) c[a] = point3(a==0, a==1, a==2);
for(int a=0; a<3; a++) c[3+a] = point3(-(a==0), -(a==1), -(a==2));
int iter = 0;
while(err > minerr) { again:
iter++; if(iter > max_iter) { isok = false; return at; }
// cands.push_back(at);
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, "imp ", err - solerror(xp, f(x)) );
auto y = at - c[a] * eps;
if(debug) println(hlog, "f(", y, ") = ", f(y), " = y + ", f(y)-ver, "imp ", err - solerror(xp, f(y)) );
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;
ld lbonus = hypot_d(3, bonus);
if(lbonus > 0.1) bonus = bonus * 0.1 / hypot_d(3, bonus);
if(false && lbonus > 1000) {
int best = -1;
ld besti = err;
for(int a=0; a<6; a++) {
auto x = at + c[a] * eps;
auto nerr = solerror(xp, f(x));
if(nerr < besti) best = a, besti = nerr;
}
if(best == -1) {
println(hlog, "local best");
for(int a=0; a<1000000; a++) {
auto x = at;
for(int i=0; i<3; i++) x[i] += (hrand(1000000) - hrand(1000000)) * 1e-5;
auto nerr = solerror(xp, f(x));
if(nerr < besti) { println(hlog, "moved to ", x); at = x; goto again; }
}
break;
}
bonus = c[best] * 1e-3;
}
int fixes = 0;
if(debug)
println(hlog, "\nU = ", U, "\ndiff = ", diff, "\nbonus = ", bonus, " of ", lbonus, "\n");
nextfix:
hyperpoint next = at + bonus;
hyperpoint nextver = f(next);
ld nexterr = solerror(xp, nextver);
if(debug) println(hlog, "f(", next, ") = ", nextver, ", imp = ", err - 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);
}
if(debug) println(hlog, "fixes = ", fixes, " : break");
isok = false;
return at;
}
goto nextfix;
}
nextiter: ;
}
if(debug) println(hlog, "\n\nsolution found: f(", at, ") = ", ver, " (error ", err, ")");
isok = true;
return at;
}
EX void geodesic_step_euler(hyperpoint& at, hyperpoint& velocity) {
auto acc = nisot::christoffel(at, velocity, velocity);
at = at + velocity + acc / 2;
velocity += acc;
}
EX void geodesic_step_poor(hyperpoint& at, hyperpoint& velocity) {
auto acc = nisot::christoffel(at, velocity, velocity);
at = at + velocity;
velocity += acc;
}
EX void geodesic_step_midpoint(hyperpoint& at, hyperpoint& velocity) {
// y(n+1) = y(n) + f(y(n) + 1/2 f(y(n)))
auto acc = nisot::christoffel(at, velocity, velocity);
auto at2 = at + velocity / 2;
auto velocity2 = velocity + acc / 2;
auto acc2 = nisot::christoffel(at2, velocity2, velocity2);
at = at + velocity + acc2 / 2;
velocity = velocity + acc2;
}
auto& chr = nisot::get_acceleration;
EX bool invalid_any(const hyperpoint h) {
return isnan(h[0]) || isnan(h[1]) || isnan(h[2]) || isinf(h[0]) || isinf(h[1]) || isinf(h[2]) ||
abs(h[0]) > 1e20 || abs(h[1]) > 1e20 || abs(h[2]) > 1e20;
}
EX void geodesic_step_rk4(hyperpoint& at, hyperpoint& vel) {
auto acc1 = chr(at, vel);
auto acc2 = chr(at + vel/2, vel + acc1/2);
auto acc3 = chr(at + vel/2 + acc1/4, vel + acc2/2);
auto acc4 = chr(at + vel + acc2/2, vel + acc3);
at += vel + (acc1+acc2+acc3)/6;
vel += (acc1+2*acc2+2*acc3+acc4)/6;
}
template<class T>
hyperpoint numerical_exp(hyperpoint v, int steps, const T& gstep) {
hyperpoint at = point31(0, 0, 0);
v /= steps;
v[3] = 0;
for(int i=0; i<steps; i++) {
if(invalid_any(at)) return at;
gstep(at, v);
}
return at;
}
ld x_to_scr(ld x) { return 150 + 100 * x; }
ld y_to_scr(ld x) { return 950 - log(x * 1e9) / log(10) * 80; }
hyperpoint pt(ld x, ld y) { return tC0(atscreenpos(x, y, 1)); };
map<pair<string, color_t>, map<double, double>> maxerr;
bool scatterplot;
void queueline1(hyperpoint a, hyperpoint b, color_t c) {
queueline(shiftless(a), shiftless(b), c);
}
void draw_graph() {
vid.linewidth *= 2;
queueline1(pt(0, 950), pt(1500, 950), 0xFF);
queueline1(pt(150, 0), pt(150, 1000), 0xFF);
vid.linewidth /= 2;
for(int i=1; i<=9; i++) {
queueline1(pt(x_to_scr(i), 950), pt(x_to_scr(i), 960), 0xFF);
queuestr(x_to_scr(i), 980, 0, 60, its(i), 0, 0, 8);
}
for(int i=-8; i<=2; i++) {
ld v = pow(10, i);
queueline1(pt(140, y_to_scr(v)), pt(150, y_to_scr(v)), 0xFF);
queuestr(70, y_to_scr(v), 0, 60, "1e"+its(i), 0, 0, 8);
vid.linewidth /= 2;
queueline1(pt(1100, y_to_scr(v)), pt(150, y_to_scr(v)), 0xFF);
vid.linewidth *= 2;
}
vid.linewidth *= 2;
for(auto& [id, graph]: maxerr) {
auto& [name, col] = id;
ld last = 1e-9;
ld lastx = 0;
for(auto [x, y]: graph) {
if(scatterplot) {
curvepoint(pt(x_to_scr(x)+2, y_to_scr(y)));
curvepoint(pt(x_to_scr(x)-2, y_to_scr(y)));
queuecurve(shiftless(Id), col, 0, PPR::LINE);
curvepoint(pt(x_to_scr(x), y_to_scr(y)+2));
curvepoint(pt(x_to_scr(x), y_to_scr(y)-2));
queuecurve(shiftless(Id), col, 0, PPR::LINE);
}
if(y_to_scr(y) > y_to_scr(last) - x_to_scr(lastx) + x_to_scr(x)) continue;
if(y > 100) y = 100;
last = y;
lastx = x;
ld xx = x;
if(xx > 9) xx = 9;
if(!scatterplot) curvepoint(pt(x_to_scr(x), y_to_scr(y)));
if(xx == 9) break;
}
if(!scatterplot) {
queuestr(1100, y_to_scr(last), 0, 60, name, col >> 8, 0, 0);
queuecurve(shiftless(Id), col, 0, PPR::LINE);
}
}
vid.linewidth /= 2;
drawqueue();
}
void draw_sol_diffeq_graph() {
}
void make_graph(string fname) {
start_game();
flat_model_enabler fme;
shot::shotx = 1500;
shot::shoty = 1000;
shot::format = shot::screenshot_format::svg;
svg::divby = 1;
shot::take(fname, draw_graph);
}
void sol_diffeq_graph() {
auto& s = sn::get_tabled();
s.load();
for(int x=0; x<s.PRECX-1; x++)
for(int y=0; y<s.PRECY-1; y++)
for(int z=0; z<s.PRECZ-1; z++) {
println(hlog, tie(x,y,z));
auto ax = sn::ix_to_x(x / (s.PRECX-1.));
auto ay = sn::ix_to_x(y / (s.PRECY-1.));
auto az = sn::iz_to_z(z / (s.PRECZ-1.));
ld d = hypot(ax, hypot(ay, az));
hyperpoint h = point31(ax, ay, az);
hyperpoint v = inverse_exp(shiftless(h)); // , pfNO_INTERPOLATION);
hyperpoint actual = numerical_exp(v, 2000, geodesic_step_rk4);
if(invalid_any(actual)) continue;
auto test = [&] (string name, color_t col, int iter, auto method) {
hyperpoint res = numerical_exp(v, iter, method);
if(invalid_any(res)) return;
ld err = geo_dist(actual, res);
ld& me = maxerr[{name, col}][d];
me = max(me, err);
};
test("RK2 5", 0xB0E0B0FF, 5, geodesic_step_rk4);
test("RK2 10", 0x8AD0A0FF, 10, geodesic_step_rk4);
test(" ", 0x90E090FF, 20, geodesic_step_rk4);
test("RK2 30", 0x80C080FF, 30, geodesic_step_rk4);
test("RK4 100", 0x408040FF, 100, geodesic_step_rk4);
test("RK4 300", 0x306030FF, 300, geodesic_step_rk4);
test("RK4 1000", 0x204020FF, 1000, geodesic_step_rk4);
test("mid 100", 0x8080C0FF, 100, geodesic_step_midpoint);
test("mid 1000", 0x404080FF, 1000, geodesic_step_midpoint);
}
make_graph("sol-diff-graph.svg");
}
void sol_numerics_out() {
hyperpoint v = inverse_exp(shiftless(point31(2, 1, 0)));
// point3(0.1, 0, 10);
hyperpoint result = numerical_exp(v, 1000000, geodesic_step_rk4);
println(hlog, "exp(", v, ") = ", result);
for(int steps: {1, 2, 10, 20, 50, 100, 200, 500, 1000, 2000, 5000, 10000, 20000, 50000, 100000}) {
shstream ss;
auto experiment = [&] (string name, auto f) {
print(ss, name, lalign(30, hdist0(numerical_exp(v, steps, f) - result)));
};
experiment(" P ", geodesic_step_poor);
experiment(" E ", geodesic_step_euler);
experiment(" M ", geodesic_step_midpoint);
experiment(" R ", geodesic_step_rk4);
println(hlog, " steps=", lalign(6, steps), ss.s);
}
println(hlog, "timing M");
numerical_exp(v, 10000000, geodesic_step_midpoint);
println(hlog, "timing R");
numerical_exp(v, 10000000, geodesic_step_rk4);
println(hlog, "ok");
}
vector<ld> quantiles(vector<ld> data) {
sort(data.begin(), data.end());
if(isize(data) <= 20) return data;
vector<ld> q;
for(int i=0; i<=20; i++)
q.push_back(data[(isize(data)-1)*i/20]);
return q;
}
auto smax(auto& tab, ld& i, ld x) { if(x) tab[i] = max(tab[i], x); }
ld median(vector<ld> v) {
sort(v.begin(), v.end());
return v[isize(v)/2];
}
void sol_table_test() {
// auto& length_good = maxerr[{"length/good", 0x408040FF}];
// auto& angle_good = maxerr[{"angle/good", 0x404080FF}];
// auto& length_good2 = maxerr[{"length/mid", 0x808040FF}];
// auto& angle_good2 = maxerr[{"angle/mid", 0x804080FF}];
// auto& length_bad = maxerr[{"length/bad", 0xC08040FF}];
// auto& angle_bad = maxerr[{"angle/bad", 0xC04080FF}];
// map<string, int> wins;
auto& s = sn::get_tabled();
s.load();
map<double, double> maxerr;
int good = 0, bad = 0;
vector<ld> length_errors;
vector<ld> angle_errors;
vector<ld> split;
vector<ld> lerrs[4][4][4], aerrs[4][4][4];
for(int a: {16, 32, 48, 60})
println(hlog, "xy_", a, " : ", sn::ix_to_x(a / (s.PRECX-1.)));
for(int a: {16, 32, 48, 60})
println(hlog, "z_", a, " : ", sn::iz_to_z(a / (s.PRECZ-1.)));
FILE *g = fopen("solv-error-data.csv", "wt");
for(ld x=0; x<s.PRECX-4; x+=.25)
for(ld y=0; y<s.PRECY-4; y+=.25)
for(ld z=0; z<s.PRECZ-4; z+=.25) {
int xp = x * 4 / s.PRECX;
int yp = y * 4 / s.PRECY;
int zp = z * 4 / s.PRECZ;
if(y == 0.5 && z== 0.5) println(hlog, x, " : ", good, " vs ", bad);
int a0 = 0, b0 = 0;
for(ld x1: {floor(x), ceil(x)})
for(ld y1: {floor(y), ceil(y)})
for(ld z1: {floor(z), ceil(z)}) {
auto ax = sn::ix_to_x(x1 / (s.PRECX-1.));
auto ay = sn::ix_to_x(y1 / (s.PRECY-1.));
auto az = sn::iz_to_z(z1 / (s.PRECZ-1.));
hyperpoint h = point31(ax, ay, az);
hyperpoint v = inverse_exp(shiftless(h), pfNO_INTERPOLATION);
if(v[2] > 0) a0++;
else b0++;
}
bool bad_region = x > s.PRECX/2 && y > s.PRECY/2 && z < s.PRECZ/2;
bool bad_break = bad_region && a0 && b0;
auto ax = sn::ix_to_x(x / (s.PRECX-1.));
auto ay = sn::ix_to_x(y / (s.PRECY-1.));
auto az = sn::iz_to_z(z / (s.PRECZ-1.));
hyperpoint h = point31(ax, ay, az);
hyperpoint v = inverse_exp(shiftless(h), bad_break ? pfNO_INTERPOLATION : pNORMAL);
// println(hlog, "looking for ", h);
// println(hlog, "exp(", v, ") = ", nisot::numerical_exp(v));
hyperpoint v1 = iterative_solve(h, v, 1e-9, false);
// println(hlog, "exp(", v1, ") = ", nisot::numerical_exp(v1));
hyperpoint h2 = nisot::numerical_exp(v1);
if(sqhypot_d(3, h-h2) > 1e-6) {
bad++;
continue;
}
else good++;
ld dv = hypot_d(3, v);
ld dv1 = hypot_d(3, v1);
ld lerr = abs(dv - dv1);
ld aerr = asin(hypot_d(3, v^v1) / dv / dv1);
ld d = hypot_d(3, v1);
if(dv == 0 || dv1 == 0) continue;
if(invalid_any(v1) || invalid_any(v)) {
println(hlog, "invalid");
continue;
}
if(isnan(aerr)) println(hlog, "v = ", v, " v1 = ", v1, "aerr");
else fprintf(g, "%lf;%lf;%lf;%lf;%lf;%lf;%lf;%lf;%d\n",
x, y, z,
ax, ay, az,
lerr, aerr,
bad_break
);
lerrs[zp][yp][xp].push_back(lerr);
aerrs[zp][yp][xp].push_back(aerr);
}
fclose(g);
/*
if(d >= 3 && d <= 3.1 && !bad_region) {
println(hlog, tie(x,y,z), " : ", lerr);
split.push_back(lerr);
}
if(bad_break)
smax(length_bad, d, lerr),
smax(angle_bad, d, aerr),
0;
else if(bad_region)
smax(length_good2, d, lerr),
smax(angle_good2, d, aerr),
0;
else
smax(length_good, d, lerr),
smax(angle_good, d, aerr),
0;
length_errors.push_back(lerr);
ld cross = hypot_d(3, v^v1) / dv / dv1;
angle_errors.push_back(cross);
}
// println(hlog, quantiles(length_errors));
println(hlog, quantiles(split)); */
// for(auto p: angle_good) println(hlog, p);
// make_graph("sol-la-errors.svg");
FILE *f = fopen("devmods/graph.tex", "wt");
fprintf(f, "\\documentclass{article}\n\\begin{document}\n");
fprintf(f, "\\small\\setlength{\\tabcolsep}{3pt}\n");
fprintf(f, "\\begin{tabular}{|c|cccc|cccc|cccc|cccc|}\n\\hline\n");
for(int z=0; z<4; z++) {
fprintf(f, " & ");
fprintf(f, "\\multicolumn{4}{|c%s}{$z_%d$}", z==3?"|":"", z);
}
fprintf(f, "|\\\\\n");
for(int z=0; z<4; z++) {
for(int x=0; x<4; x++) {
fprintf(f, " & ");
fprintf(f, "$x_%d$", x);
}
}
fprintf(f, "\\\\\n\\hline");
for(int y=0; y<4; y++) {
fprintf(f, "$y_%d$ ", y);
for(int z=0; z<4; z++) {
for(int x=0; x<4; x++) {
fprintf(f, " & ");
fprintf(f, "%4.2g", log10(median(lerrs[z][y][x])));
}
}
fprintf(f, "\\\\\n");
}
fprintf(f, "\\hline \n");
for(int y=0; y<4; y++) {
fprintf(f, "$y_%d$ ", y);
for(int z=0; z<4; z++) {
for(int x=0; x<4; x++) {
fprintf(f, " & ");
fprintf(f, "%4.2g", log10(median(aerrs[z][y][x])));
}
}
fprintf(f, "\\\\\n");
}
fprintf(f, "\\hline\n");
fprintf(f, "\\end{tabular}\n");
fprintf(f, "\\end{document}\n");
fclose(f);
}
int readArgs() {
using namespace arg;
if(0) ;
else if(argis("-sol-diff-graph")) {
sol_diffeq_graph();
}
else if(argis("-sol-tabletest")) {
sol_table_test();
}
else if(argis("-sol-numerics")) {
sol_numerics_out();
}
else return 1;
return 0;
}
auto nhook = addHook(hooks_args, 100, readArgs);
}
#endif