solv-error-analyze added
This commit is contained in:
Zeno Rogue
parent
f27c54596e
commit
c9e0529a88
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#include "../hyper.h"
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// This program generates the error table for Solv approxiations.
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#define D3 1
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#define D2 0
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#if CAP_FIELD
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namespace hr {
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ld solerror(hyperpoint ok, hyperpoint chk) {
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return geo_dist(chk, ok);
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}
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ld minz = -1e-9, maxz = 1e-9;
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int max_iter = 999999;
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bool isok;
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hyperpoint iterative_solve(hyperpoint xp, hyperpoint candidate, 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); }; // 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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hyperpoint c[6];
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for(int a=0; a<3; a++) c[a] = point3(a==0, a==1, a==2);
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for(int a=0; a<3; a++) c[3+a] = point3(-(a==0), -(a==1), -(a==2));
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int iter = 0;
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while(err > minerr) { again:
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iter++; if(iter > max_iter) { isok = false; return at; }
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// cands.push_back(at);
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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, "imp ", err - solerror(xp, f(x)) );
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auto y = at - c[a] * eps;
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if(debug) println(hlog, "f(", y, ") = ", f(y), " = y + ", f(y)-ver, "imp ", err - solerror(xp, f(y)) );
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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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ld lbonus = hypot_d(3, bonus);
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if(lbonus > 0.1) bonus = bonus * 0.1 / hypot_d(3, bonus);
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if(false && lbonus > 1000) {
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int best = -1;
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ld besti = err;
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for(int a=0; a<6; a++) {
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auto x = at + c[a] * eps;
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auto nerr = solerror(xp, f(x));
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if(nerr < besti) best = a, besti = nerr;
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}
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if(best == -1) {
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println(hlog, "local best");
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for(int a=0; a<1000000; a++) {
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auto x = at;
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for(int i=0; i<3; i++) x[i] += (hrand(1000000) - hrand(1000000)) * 1e-5;
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auto nerr = solerror(xp, f(x));
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if(nerr < besti) { println(hlog, "moved to ", x); at = x; goto again; }
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}
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break;
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}
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bonus = c[best] * 1e-3;
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}
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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, " of ", lbonus, "\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, ", imp = ", err - 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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if(debug) println(hlog, "fixes = ", fixes, " : break");
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isok = false;
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return at;
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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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if(debug) println(hlog, "\n\nsolution found: f(", at, ") = ", ver, " (error ", err, ")");
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isok = true;
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return at;
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}
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EX void geodesic_step_euler(hyperpoint& at, hyperpoint& velocity) {
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auto acc = nisot::christoffel(at, velocity, velocity);
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at = at + velocity + acc / 2;
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velocity += acc;
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}
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EX void geodesic_step_poor(hyperpoint& at, hyperpoint& velocity) {
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auto acc = nisot::christoffel(at, velocity, velocity);
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at = at + velocity;
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velocity += acc;
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}
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EX void geodesic_step_midpoint(hyperpoint& at, hyperpoint& velocity) {
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// y(n+1) = y(n) + f(y(n) + 1/2 f(y(n)))
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auto acc = nisot::christoffel(at, velocity, velocity);
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auto at2 = at + velocity / 2;
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auto velocity2 = velocity + acc / 2;
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auto acc2 = nisot::christoffel(at2, velocity2, velocity2);
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at = at + velocity + acc2 / 2;
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velocity = velocity + acc2;
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}
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auto& chr = nisot::get_acceleration;
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EX bool invalid_any(const hyperpoint h) {
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return isnan(h[0]) || isnan(h[1]) || isnan(h[2]) || isinf(h[0]) || isinf(h[1]) || isinf(h[2]) ||
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abs(h[0]) > 1e20 || abs(h[1]) > 1e20 || abs(h[2]) > 1e20;
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}
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EX void geodesic_step_rk4(hyperpoint& at, hyperpoint& vel) {
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auto acc1 = chr(at, vel);
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auto acc2 = chr(at + vel/2, vel + acc1/2);
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auto acc3 = chr(at + vel/2 + acc1/4, vel + acc2/2);
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auto acc4 = chr(at + vel + acc2/2, vel + acc3);
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at += vel + (acc1+acc2+acc3)/6;
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vel += (acc1+2*acc2+2*acc3+acc4)/6;
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}
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template<class T>
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hyperpoint numerical_exp(hyperpoint v, int steps, const T& gstep) {
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hyperpoint at = point31(0, 0, 0);
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v /= steps;
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v[3] = 0;
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for(int i=0; i<steps; i++) {
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if(invalid_any(at)) return at;
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gstep(at, v);
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}
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return at;
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}
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ld x_to_scr(ld x) { return 150 + 100 * x; }
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ld y_to_scr(ld x) { return 950 - log(x * 1e9) / log(10) * 80; }
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hyperpoint pt(ld x, ld y) { return tC0(atscreenpos(x, y, 1)); };
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map<pair<string, color_t>, map<double, double>> maxerr;
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bool scatterplot;
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void queueline1(hyperpoint a, hyperpoint b, color_t c) {
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queueline(shiftless(a), shiftless(b), c);
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}
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void draw_graph() {
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vid.linewidth *= 2;
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queueline1(pt(0, 950), pt(1500, 950), 0xFF);
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queueline1(pt(150, 0), pt(150, 1000), 0xFF);
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vid.linewidth /= 2;
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for(int i=1; i<=9; i++) {
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queueline1(pt(x_to_scr(i), 950), pt(x_to_scr(i), 960), 0xFF);
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queuestr(x_to_scr(i), 980, 0, 60, its(i), 0, 0, 8);
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}
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for(int i=-8; i<=2; i++) {
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ld v = pow(10, i);
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queueline1(pt(140, y_to_scr(v)), pt(150, y_to_scr(v)), 0xFF);
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queuestr(70, y_to_scr(v), 0, 60, "1e"+its(i), 0, 0, 8);
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vid.linewidth /= 2;
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queueline1(pt(1100, y_to_scr(v)), pt(150, y_to_scr(v)), 0xFF);
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vid.linewidth *= 2;
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}
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vid.linewidth *= 2;
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for(auto& [id, graph]: maxerr) {
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auto& [name, col] = id;
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ld last = 1e-9;
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ld lastx = 0;
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for(auto [x, y]: graph) {
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if(scatterplot) {
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curvepoint(pt(x_to_scr(x)+2, y_to_scr(y)));
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curvepoint(pt(x_to_scr(x)-2, y_to_scr(y)));
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queuecurve(shiftless(Id), col, 0, PPR::LINE);
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curvepoint(pt(x_to_scr(x), y_to_scr(y)+2));
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curvepoint(pt(x_to_scr(x), y_to_scr(y)-2));
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queuecurve(shiftless(Id), col, 0, PPR::LINE);
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}
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if(y_to_scr(y) > y_to_scr(last) - x_to_scr(lastx) + x_to_scr(x)) continue;
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if(y > 100) y = 100;
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last = y;
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lastx = x;
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ld xx = x;
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if(xx > 9) xx = 9;
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if(!scatterplot) curvepoint(pt(x_to_scr(x), y_to_scr(y)));
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if(xx == 9) break;
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}
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if(!scatterplot) {
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queuestr(1100, y_to_scr(last), 0, 60, name, col >> 8, 0, 0);
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queuecurve(shiftless(Id), col, 0, PPR::LINE);
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}
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}
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vid.linewidth /= 2;
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drawqueue();
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}
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void draw_sol_diffeq_graph() {
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}
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void make_graph(string fname) {
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start_game();
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flat_model_enabler fme;
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shot::shotx = 1500;
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shot::shoty = 1000;
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shot::format = shot::screenshot_format::svg;
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svg::divby = 1;
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shot::take(fname, draw_graph);
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}
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void sol_diffeq_graph() {
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auto& s = sn::get_tabled();
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s.load();
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for(int x=0; x<s.PRECX-1; x++)
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for(int y=0; y<s.PRECY-1; y++)
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for(int z=0; z<s.PRECZ-1; z++) {
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println(hlog, tie(x,y,z));
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auto ax = sn::ix_to_x(x / (s.PRECX-1.));
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auto ay = sn::ix_to_x(y / (s.PRECY-1.));
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auto az = sn::iz_to_z(z / (s.PRECZ-1.));
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ld d = hypot(ax, hypot(ay, az));
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hyperpoint h = point31(ax, ay, az);
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hyperpoint v = inverse_exp(shiftless(h)); // , pfNO_INTERPOLATION);
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hyperpoint actual = numerical_exp(v, 2000, geodesic_step_rk4);
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if(invalid_any(actual)) continue;
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auto test = [&] (string name, color_t col, int iter, auto method) {
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hyperpoint res = numerical_exp(v, iter, method);
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if(invalid_any(res)) return;
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ld err = geo_dist(actual, res);
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ld& me = maxerr[{name, col}][d];
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me = max(me, err);
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};
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test("RK2 5", 0xB0E0B0FF, 5, geodesic_step_rk4);
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test("RK2 10", 0x8AD0A0FF, 10, geodesic_step_rk4);
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test(" ", 0x90E090FF, 20, geodesic_step_rk4);
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test("RK2 30", 0x80C080FF, 30, geodesic_step_rk4);
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test("RK4 100", 0x408040FF, 100, geodesic_step_rk4);
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test("RK4 300", 0x306030FF, 300, geodesic_step_rk4);
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test("RK4 1000", 0x204020FF, 1000, geodesic_step_rk4);
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test("mid 100", 0x8080C0FF, 100, geodesic_step_midpoint);
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test("mid 1000", 0x404080FF, 1000, geodesic_step_midpoint);
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}
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make_graph("sol-diff-graph.svg");
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}
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void sol_numerics_out() {
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hyperpoint v = inverse_exp(shiftless(point31(2, 1, 0)));
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// point3(0.1, 0, 10);
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hyperpoint result = numerical_exp(v, 1000000, geodesic_step_rk4);
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println(hlog, "exp(", v, ") = ", result);
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for(int steps: {1, 2, 10, 20, 50, 100, 200, 500, 1000, 2000, 5000, 10000, 20000, 50000, 100000}) {
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shstream ss;
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auto experiment = [&] (string name, auto f) {
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print(ss, name, lalign(30, hdist0(numerical_exp(v, steps, f) - result)));
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};
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experiment(" P ", geodesic_step_poor);
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experiment(" E ", geodesic_step_euler);
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experiment(" M ", geodesic_step_midpoint);
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experiment(" R ", geodesic_step_rk4);
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println(hlog, " steps=", lalign(6, steps), ss.s);
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}
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println(hlog, "timing M");
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numerical_exp(v, 10000000, geodesic_step_midpoint);
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println(hlog, "timing R");
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numerical_exp(v, 10000000, geodesic_step_rk4);
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println(hlog, "ok");
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}
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vector<ld> quantiles(vector<ld> data) {
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sort(data.begin(), data.end());
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if(isize(data) <= 20) return data;
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vector<ld> q;
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for(int i=0; i<=20; i++)
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q.push_back(data[(isize(data)-1)*i/20]);
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return q;
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}
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auto smax(auto& tab, ld& i, ld x) { if(x) tab[i] = max(tab[i], x); }
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ld median(vector<ld> v) {
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sort(v.begin(), v.end());
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return v[isize(v)/2];
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}
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void sol_table_test() {
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// auto& length_good = maxerr[{"length/good", 0x408040FF}];
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// auto& angle_good = maxerr[{"angle/good", 0x404080FF}];
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// auto& length_good2 = maxerr[{"length/mid", 0x808040FF}];
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// auto& angle_good2 = maxerr[{"angle/mid", 0x804080FF}];
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// auto& length_bad = maxerr[{"length/bad", 0xC08040FF}];
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// auto& angle_bad = maxerr[{"angle/bad", 0xC04080FF}];
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// map<string, int> wins;
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auto& s = sn::get_tabled();
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s.load();
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map<double, double> maxerr;
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int good = 0, bad = 0;
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vector<ld> length_errors;
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vector<ld> angle_errors;
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vector<ld> split;
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vector<ld> lerrs[4][4][4], aerrs[4][4][4];
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for(int a: {16, 32, 48, 60})
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println(hlog, "xy_", a, " : ", sn::ix_to_x(a / (s.PRECX-1.)));
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for(int a: {16, 32, 48, 60})
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println(hlog, "z_", a, " : ", sn::iz_to_z(a / (s.PRECZ-1.)));
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FILE *g = fopen("solv-error-data.csv", "wt");
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for(ld x=0; x<s.PRECX-4; x+=.25)
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for(ld y=0; y<s.PRECY-4; y+=.25)
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for(ld z=0; z<s.PRECZ-4; z+=.25) {
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int xp = x * 4 / s.PRECX;
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int yp = y * 4 / s.PRECY;
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int zp = z * 4 / s.PRECZ;
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if(y == 0.5 && z== 0.5) println(hlog, x, " : ", good, " vs ", bad);
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int a0 = 0, b0 = 0;
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for(ld x1: {floor(x), ceil(x)})
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for(ld y1: {floor(y), ceil(y)})
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for(ld z1: {floor(z), ceil(z)}) {
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auto ax = sn::ix_to_x(x1 / (s.PRECX-1.));
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auto ay = sn::ix_to_x(y1 / (s.PRECY-1.));
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auto az = sn::iz_to_z(z1 / (s.PRECZ-1.));
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hyperpoint h = point31(ax, ay, az);
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hyperpoint v = inverse_exp(shiftless(h), pfNO_INTERPOLATION);
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if(v[2] > 0) a0++;
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else b0++;
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}
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bool bad_region = x > s.PRECX/2 && y > s.PRECY/2 && z < s.PRECZ/2;
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bool bad_break = bad_region && a0 && b0;
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||||
|
||||
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
|
||||
Loading…
Reference in New Issue