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/*
* Copyright (C) Andrew Helmer 2020.
* Licensed under MIT Open-Source License: see LICENSE.
*
* This file implements different methods of selecting the subquadrants in
* between odd and even powers of 4 for the PMJ and PMJ02 algorithms. Compared
* to random, they make a big difference for the overall error!
*/
#ifndef SAMPLE_GENERATION_SELECT_SUBQUAD_H_
#define SAMPLE_GENERATION_SELECT_SUBQUAD_H_
#include <iostream>
#include <utility>
#include <vector>
#include "util.h"
namespace pmj {
typedef std::vector<std::pair<int, int>> (*subquad_fn)(
const Point samples[], const int dim, random_gen& rng);
/*
* This will randomly choose once to swap X or swap Y, and will always swap
* X or Y for all subquadrants. For PMJ02, this ensures that the next set of
* samples are themselves a (0,2) sequence. Based off some basic analysis,
* it seems like this is the only way to maintain this property.
*
* Credit goes to Simon Brown for discovering this method with his Rust
* implementation: https://github.com/sjb3d/pmj
*/
std::vector<std::pair<int, int>> GetSubQuadrantsSwapXOrY(
const Point samples[],
const int dim, random_gen& rng);
/*
* Pick which subquadrants to use, using the ox-plowing technique from
* Christensen et al.
*/
std::vector<std::pair<int, int>> GetSubQuadrantsOxPlowing(
const Point samples[],
const int dim, random_gen& rng);
/*
* Pick which subquadrants to use randomly. No reason to actually use this:
* OxPlowing is better for pmj and ShuffleSwap is better for pmj(0,2).
*/
std::vector<std::pair<int, int>> GetSubQuadrantsRandomly(
const Point samples[],
const int dim, random_gen& rng);
std::vector<std::pair<int, int>> GetSubQuadrantsRandomly(
const Point samples[],
const int dim, random_gen& rng) {
const int quad_dim = dim / 2;
const int n = quad_dim*quad_dim;
std::vector<std::pair<int, int>> choices(n);
for (int i = 0; i < n; i++) {
const auto& sample = samples[i];
int x_pos = sample.x * dim;
int y_pos = sample.y * dim;
if (UniformRand(0,1,rng) < 0.5) {
choices[i] = {x_pos ^ 1, y_pos};
} else {
choices[i] = {x_pos, y_pos ^ 1};
}
}
return choices;
}
std::vector<std::pair<int, int>> GetSubQuadrantsSwapXOrY(
const Point samples[],
const int dim, random_gen& rng) {
const int quad_dim = dim / 2;
const int n = quad_dim*quad_dim;
std::vector<std::pair<int, int>> choices(n);
const bool swap_x = UniformRand(0,1,rng) < 0.5;
for (int i = 0; i < n; i++) {
const Point& sample = samples[i];
int x_pos = sample.x * dim;
int y_pos = sample.y * dim;
if (swap_x) x_pos = x_pos ^ 1;
else
y_pos = y_pos ^ 1;
choices[i] = {x_pos, y_pos};
}
return choices;
}
std::vector<std::pair<int, int>> GetSubQuadrantsOxPlowing(
const Point samples[],
const int dim, random_gen& rng) {
const int quad_dim = dim / 2;
const int n = quad_dim*quad_dim;
std::vector<std::pair<int, int>> choices(n);
// First we want to get the subquadrant positions, and also the sampling order
// from the original samples.
std::vector<int> first_cells(n*2);
std::vector<int> quadrant_order(n);
for (int i = 0; i < n; i++) {
const auto& sample = samples[i];
int x_pos = sample.x * dim;
int y_pos = sample.y * dim;
const int quadrant_index = (y_pos / 2)*(quad_dim) + (x_pos / 2);
first_cells[2*quadrant_index] = x_pos;
first_cells[2*quadrant_index+1] = y_pos;
quadrant_order[quadrant_index] = i;
}
// This method doesn't always work successfully, so we try a few times. In
// the worst case, we'll always give a valid selection at the end anyway. In
// practice, it virtually always succeeds within 10 attempts.
for (int attempt = 0; attempt < 10; attempt++) {
std::vector<int> choice_balance_x(quad_dim);
std::vector<int> choice_balance_y(quad_dim);
bool up = true;
for (int col = 0; col < quad_dim; col++) {
up = !up;
for (int i = 0; i < quad_dim; i++) {
const int row = up ? i : quad_dim - i - 1;
const int quadrant_index = row*quad_dim + col;
int x_pos = first_cells[2*quadrant_index];
int y_pos = first_cells[2*quadrant_index+1];
const bool last = (i == quad_dim - 1);
const int balance_y = choice_balance_y[row];
const int balance_x = choice_balance_x[col];
bool swap_x = false;
if (balance_y != 0 && !last) {
swap_x = (balance_y > 0) != (y_pos & 1);
} else if (balance_x != 0) {
swap_x = (balance_x > 0) == (x_pos & 1);
} else {
swap_x = UniformRand(0,1,rng) < 0.5;
}
x_pos = swap_x ? x_pos ^ 1 : x_pos;
y_pos = (!swap_x) ? y_pos ^ 1 : y_pos;
choices[quadrant_order[quadrant_index]].first = x_pos;
choices[quadrant_order[quadrant_index]].second = y_pos;
choice_balance_x[col] += (x_pos & 1) ? 1 : -1;
choice_balance_y[row] += (y_pos & 1) ? 1 : -1;
}
}
// Always unbalanced, just return.
if (n == 1) {
return choices;
}
bool is_balanced = true;
for (int row = 0; row < quad_dim; row++) {
if (choice_balance_y[row] != 0) {
is_balanced = false;
break;
}
}
if (is_balanced) break;
}
return choices;
}
} // namespace pmj
#endif // SAMPLE_GENERATION_SELECT_SUBQUAD_H_
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