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solver.h
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#include <cmath>
#include <iostream>
#include <type_traits>
//#include <omp.h>
#include <utility>
using Real = double;
constexpr size_t _NUMSTEPS = 20;
constexpr size_t _NUMSLASH = 50;
constexpr size_t _LEVELS = 5;
//constexpr Real _THRESH = 1e-16;
template<typename T, size_t D1, size_t D2, size_t D3>
class grid{
using self_t = grid<T, D1, D2, D3>;
static constexpr size_t data_count = D1 * D2 * D3;
public:
inline T& at(int i, int j, int k){
return data[((i + D1) % D1) * D2 * D3 + ((j + D2) % D2) * D3 + ((k + D3) % D3)];
}
inline const T& at(int i, int j, int k) const{
return data[((i + D1) % D1) * D2 * D3 + ((j + D2) % D2) * D3 + ((k + D3) % D3)];
}
void setZero(){
#pragma omp parallel for
for(u_int i = 0; i < D1; ++i){
for(u_int j = 0; j < D2; ++j){
for(u_int k = 0; k < D3; ++k){
at(i,j,k) = 0;
}
}
}
}
grid(){
setZero();
}
private:
T data[data_count];
};
template<typename T, size_t D1, size_t D2, size_t D3>
std::ostream & operator<<(std::ostream &os, const grid<T, D1, D2, D3> &gr){
for(u_int i = 0; i < D1; ++i){
os << "{ ";
for(u_int j = 0; j < D2; ++j){
os << std::endl << " { ";
for(u_int k = 0; k < D3; ++k){
os << gr.at(i, j, k) << " ";
}
os << "} ";
}
os << "}" << std::endl;
}
return os;
}
template<typename T, size_t D1, size_t D2, size_t D3, size_t depth>
struct level{
using self_t = level<T, D1, D2, D3, depth>;
grid<T, D1, D2, D3> dat;
void coarsen();
void refine();
static_assert(!(D1 % 2) && !(D2 % 2) && !(D3 % 2), "Parity issue!");
level<T, D1 / 2, D2 / 2, D3 / 2, depth - 1> down;
};
template<typename T, size_t D1, size_t D2, size_t D3>
struct level<T, D1, D2, D3, 0> {
grid<T, D1, D2, D3> dat;
};
template<typename T, size_t D1, size_t D2, size_t D3>
void StepRed(const grid<T, D1, D2, D3>& b, grid<T, D1, D2, D3>& x, int steps){
if(steps <= 0){
return;
} else{
#pragma omp parallel for
for(u_int i = 0; i < D1; ++i){
for(u_int j = 0; j < D2; ++j){
for(u_int k= (i+j) % 2; k < D3; k += 2){
x.at(i,j,k) = (b.at(i,j,k)
+ x.at(i+1,j,k) + x.at(i-1,j,k)
+ x.at(i,j+1,k) + x.at(i,j-1,k)
+ x.at(i,j,k+1) + x.at(i,j,k-1)) / 6;
}
}
}
StepBlack(b, x, steps - 1);
}
}
template<typename T, size_t D1, size_t D2, size_t D3>
void StepBlack(const grid<T, D1, D2, D3>& b, grid<T, D1, D2, D3>& x, int steps){
if(steps <= 0){
return;
} else{
#pragma omp parallel for
for(u_int i = 0; i < D1; ++i){
for(u_int j = 0; j < D2; ++j){
for(u_int k= (i+j+1) % 2; k < D3; k += 2){
x.at(i,j,k) = (b.at(i,j,k)
+ x.at(i+1,j,k) + x.at(i-1,j,k)
+ x.at(i,j+1,k) + x.at(i,j-1,k)
+ x.at(i,j,k+1) + x.at(i,j,k-1)) / 6;
}
}
}
StepRed(b, x, steps - 1);
}
}
template<typename T, size_t D1, size_t D2, size_t D3>
auto GetStatus(const grid<T, D1, D2, D3>& b, const grid<T, D1, D2, D3>& x) -> T{
T record = 0;
T dist = 0;
#pragma omp parallel for reduction(+: dist) reduction(max: record)
for(u_int i = 0; i < D1; ++i){
for(u_int j = 0; j < D2; ++j){
for(u_int k = 0; k < D3; ++k){
T val = std::abs(6 * x.at(i,j,k)
- x.at(i+1,j,k) - x.at(i-1,j,k)
- x.at(i,j+1,k) - x.at(i,j-1,k)
- x.at(i,j,k+1) - x.at(i,j,k-1) - b.at(i,j,k));
dist += val;
if(val > record){
record = val;
}
}
}
}
//std::cout << "L1: " << dist << " Linfty: " << record << std::endl;
return record;
}
template<typename T, size_t D1, size_t D2, size_t D3>
void GetRemainder(const grid<T, D1, D2, D3>& b, const grid<T, D1, D2, D3>& x, grid<T, D1, D2, D3>& rem){
#pragma omp parallel for
for(u_int i = 0; i < D1; ++i){
for(u_int j = 0; j < D2; ++j){
for(u_int k = 0; k < D3; ++k){
rem.at(i,j,k) = b.at(i,j,k) - 6 * x.at(i,j,k)
+ x.at(i+1,j,k) + x.at(i-1,j,k)
+ x.at(i,j+1,k) + x.at(i,j-1,k)
+ x.at(i,j,k+1) + x.at(i,j,k-1);
}
}
}
}
template<typename T, size_t D1, size_t D2, size_t D3>
void Accumulate(grid<T, D1, D2, D3>& x, const grid<T, D1, D2, D3>& y){
#pragma omp parallel for
for(u_int i = 0; i < D1; ++i){
for(u_int j = 0; j < D2; ++j){
for(u_int k = 0; k < D3; ++k){
x.at(i,j,k) += y.at(i,j,k);
}
}
}
}
template<typename T, size_t D1, size_t D2, size_t D3, size_t depth>
void level<T, D1, D2, D3, depth>::coarsen(){
#pragma omp parallel for
for(u_int i = 0; i < D1; i += 2){
for(u_int j = 0; j < D2; j += 2){
for(u_int k = 0; k < D3; k += 2){
down.dat.at(i / 2, j / 2, k / 2) = 0;
for(int dx = -1; dx < 2; ++dx){
for(int dy = -1; dy < 2; ++dy){
for(int dz = -1; dz < 2; ++dz){
down.dat.at(i / 2, j / 2, k / 2)
+= dat.at(i + dx, j + dy, k + dz) * (dx ? 1 : 2) * (dy ? 1 : 2) * (dz ? 1 : 2);
}
}
}
down.dat.at(i / 2, j / 2, k / 2) /= 64 / 4;
}
}
}
}
template<typename T, size_t D1, size_t D2, size_t D3, size_t depth>
void level<T, D1, D2, D3, depth>::refine(){
#pragma omp parallel for
for(u_int i = 0; i < D1 / 2; ++i){
for(u_int j = 0; j < D2 / 2; ++j){
for(u_int k = 0; k < D3 / 2; ++k){
dat.at(2*i, 2*j, 2*k) = down.dat.at(i,j,k);
dat.at(2*i+1, 2*j, 2*k) = (down.dat.at(i,j,k) + down.dat.at(i+1,j,k)) / 2;
dat.at(2*i, 2*j+1, 2*k) = (down.dat.at(i,j,k) + down.dat.at(i,j+1,k)) / 2;
dat.at(2*i, 2*j, 2*k+1) = (down.dat.at(i,j,k) + down.dat.at(i,j,k+1)) / 2;
dat.at(2*i, 2*j+1, 2*k+1) = (down.dat.at(i,j,k) + down.dat.at(i,j+1,k) + down.dat.at(i,j,k+1) + down.dat.at(i,j+1,k+1)) / 4;
dat.at(2*i+1, 2*j, 2*k+1) = (down.dat.at(i,j,k) + down.dat.at(i+1,j,k) + down.dat.at(i,j,k+1) + down.dat.at(i+1,j,k+1)) / 4;
dat.at(2*i+1, 2*j+1, 2*k) = (down.dat.at(i,j,k) + down.dat.at(i,j+1,k) + down.dat.at(i+1,j,k) + down.dat.at(i+1,j+1,k)) / 4;
dat.at(2*i+1, 2*j+1, 2*k+1) = (
down.dat.at(i,j,k) + down.dat.at(i,j+1,k) + down.dat.at(i+1,j,k) + down.dat.at(i,j,k+1)
+ down.dat.at(i,j+1,k+1) + down.dat.at(i+1,j,k+1) + down.dat.at(i+1,j+1,k) + down.dat.at(i+1,j+1,k+1)
) / 8;
}
}
}
}
template<typename T, size_t D1, size_t D2, size_t D3>
void Solve(level<T, D1, D2, D3, 0>& b, level<T, D1, D2, D3, 0>& x, int steps){
//NB: I'm setting x to zero at the bottom.
x.dat.setZero();
StepRed(b.dat, x.dat, steps);
//std::cout << "Level: 0 ";
GetStatus(b.dat, x.dat);
}
template<typename T, size_t D1, size_t D2, size_t D3, size_t depth>
void Solve(level<T, D1, D2, D3, depth>& b, level<T, D1, D2, D3, depth>& x, int steps){
b.coarsen();
Solve(b.down, x.down, steps);
x.refine();
StepRed(b.dat, x.dat, steps);
//std::cout << "Level: " << depth << " ";
GetStatus(b.dat, x.dat);
}
template<typename T, size_t D1, size_t D2, size_t D3, size_t depth>
int Slash(const level<T, D1, D2, D3, depth>& b, level<T, D1, D2, D3, depth>& x, int steps, int times, T thresh = 1e-15){
using level_t = level<T, D1, D2, D3, depth>;
level_t& x_scrap = *(new level_t);
level_t& b_scrap = *(new level_t);
GetRemainder(b.dat, x.dat, b_scrap.dat);
int K = 0;
T error;
do{
//std::cout << "Slash: " << K << std::endl;
Solve(b_scrap, x_scrap, steps);
Accumulate(x.dat, x_scrap.dat);
GetRemainder(b.dat, x.dat, b_scrap.dat);
//std::cout << "Overall: ";
error = GetStatus(b.dat, x.dat);
++K;
} while((K < times) && (error > thresh));
delete &x_scrap;
delete &b_scrap;
return K;
}