102 lines
2.4 KiB
C++
102 lines
2.4 KiB
C++
#include <vector>
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#include <cstdio>
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#include <cmath>
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#include <array>
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namespace lsq {
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using namespace std;
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typedef double val;
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struct inverse_error {};
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template<size_t N> array<array<val, N>, N> invert(const array<array<val, N>, N>& T) {
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int iN = N;
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auto T1 = T, T2 = T;
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for(int y=0; y<iN; y++)
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for(int x=0; x<iN; x++)
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T2[y][x] = (x==y);
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for(int a=0; a<iN; a++) {
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int best = a;
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for(int b=a+1; b<iN; b++)
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if(abs(T1[b][a]) > abs(T1[best][a]))
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best = b;
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int b = best;
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if(b != a)
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for(int c=0; c<iN; c++)
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swap(T1[b][c], T1[a][c]), swap(T2[b][c], T2[a][c]);
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if(abs(T1[a][a]) < 1e-6) throw inverse_error();
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for(int b=a+1; b<iN; b++) {
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val co = -T1[b][a] / T1[a][a];
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for(int c=0; c<iN; c++) T1[b][c] += T1[a][c] * co, T2[b][c] += T2[a][c] * co;
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}
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}
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for(int a=N-1; a>=0; a--) {
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for(int b=0; b<a; b++) {
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val co = -T1[b][a] / T1[a][a];
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for(int c=0; c<iN; c++) T1[b][c] += T1[a][c] * co, T2[b][c] += T2[a][c] * co;
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}
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val co = 1 / T1[a][a];
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for(int c=0; c<iN; c++) T1[a][c] *= co, T2[a][c] *= co;
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}
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return T2;
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}
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template<size_t N> struct leastsquare_solution : public array<val, N> {
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val operator() (const array<val, N> X) {
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int iN = N;
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val res = 0;
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for(int j=0; j<iN; j++) res += X[j] * (*this)[j];
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return res;
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}
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};
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template<size_t N> struct leastsquare_solver {
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array<array<val, N>, N> toinvert;
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array<val, N> Xty;
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static constexpr int iN = N;
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leastsquare_solver() {
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for(int y=0; y<iN; y++) Xty[y] = 0;
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for(int y=0; y<iN; y++)
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for(int x=0; x<iN; x++)
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toinvert[y][x] = 0;
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}
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void add_data(const array<val, N> X, val y) {
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for(int j=0; j<iN; j++)
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for(int k=0; k<iN; k++)
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toinvert[j][k] += X[j] * X[k];
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for(int j=0; j<iN; j++)
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Xty[j] += X[j] * y;
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}
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void operator += (const leastsquare_solver<iN> other) {
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for(int j=0; j<iN; j++)
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for(int k=0; k<iN; k++)
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toinvert[j][k] += other.toinvert[j][k];
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for(int j=0; j<iN; j++)
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Xty[j] += other.Xty[j];
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}
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leastsquare_solution<iN> solve() {
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auto res = invert(toinvert);
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leastsquare_solution<iN> s;
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for(int i=0; i<iN; i++) {
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s[i] = 0;
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for(int j=0; j<iN; j++)
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s[i] += res[i][j] * Xty[j];
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}
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return s;
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}
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};
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}
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