// See KmTree.cpp
//
// Author: David Arthur (darthur@gmail.com), 2009

// Includes
#include "KmTree.h"
#include <iostream>
#include <stdlib.h>
#include <stdio.h>
using namespace std;

KmTree::KmTree(int n, int d, Scalar *points): n_(n), d_(d), points_(points) {
// Initialize memory
// DD: need to cast to long otherwise malloc will fail
// if we need more than 2 gigabytes or so
int node_size = sizeof(Node) + d_ * 3 * sizeof(Scalar);
node_data_ = (char*)malloc((2*(long unsigned int)n-1) * node_size);
point_indices_ = (int*)malloc(n * sizeof(int));
for (int i = 0; i < n; i++)
point_indices_[i] = i;
KM_ASSERT(node_data_ != 0 && point_indices_ != 0);

// Calculate the bounding box for the points
Scalar *bound_v1 = PointAllocate(d_);
Scalar *bound_v2 = PointAllocate(d_);
KM_ASSERT(bound_v1 != 0 && bound_v2 != 0);
PointCopy(bound_v1, points, d_);
PointCopy(bound_v2, points, d_);
for (int i = 1; i < n; i++)
for (int j = 0; j < d; j++) {
if (bound_v1[j] > points[i*d_ + j]) bound_v1[j] = points[i*d_ + j];
if (bound_v2[j] < points[i*d_ + j]) bound_v1[j] = points[i*d_ + j];
}

// Build the tree
char *temp_node_data = node_data_;
top_node_ = BuildNodes(points, 0, n-1, &temp_node_data);

// Cleanup
PointFree(bound_v1);
PointFree(bound_v2);
}

KmTree::~KmTree() {
free(point_indices_);
free(node_data_);
}

Scalar KmTree::DoKMeansStep(int k, Scalar *centers, int *assignment) const {
// Create an invalid center for comparison purposes

// Allocate data
Scalar *sums = (Scalar*)calloc(k * d_, sizeof(Scalar));
int *counts = (int*)calloc(k, sizeof(int));
int num_candidates = 0;
int *candidates = (int*)malloc(k * sizeof(int));
KM_ASSERT(sums != 0 && counts != 0 && candidates != 0);
for (int i = 0; i < k; i++)
if (memcmp(centers + i*d_, bad_center, d_ * sizeof(Scalar)) != 0)
candidates[num_candidates++] = i;

// Find nodes
Scalar result = DoKMeansStepAtNode(top_node_, num_candidates, candidates, centers, sums,
counts, assignment);

// Set the new centers
for (int i = 0; i < k; i++) {
if (counts[i] > 0) {
PointScale(sums + i*d_, Scalar(1) / counts[i], d_);
PointCopy(centers + i*d_, sums + i*d_, d_);
} else {
memcpy(centers + i*d_, bad_center, d_ * sizeof(Scalar));
}
}

// Cleanup memory
free(candidates);
free(counts);
free(sums);
return result;
}

// Helper functions for constructor
// ================================

// Build a kd tree from the given set of points
KmTree::Node *KmTree::BuildNodes(Scalar *points, int first_index, int last_index,
char **next_node_data) {
// Allocate the node
Node *node = (Node*)(*next_node_data);
(*next_node_data) += sizeof(Node);
node->sum = (Scalar*)(*next_node_data);
(*next_node_data) += sizeof(Scalar) * d_;
node->median = (Scalar*)(*next_node_data);
(*next_node_data) += sizeof(Scalar) * d_;
(*next_node_data) += sizeof(Scalar) * d_;

// Fill in basic info
node->num_points = (last_index - first_index + 1);
node->first_point_index = first_index;

// Calculate the bounding box
Scalar *first_point = points + point_indices_[first_index] * d_;
Scalar *bound_p1 = PointAllocate(d_);
Scalar *bound_p2 = PointAllocate(d_);
KM_ASSERT(bound_p1 != 0 && bound_p2 != 0);
PointCopy(bound_p1, first_point, d_);
PointCopy(bound_p2, first_point, d_);
for (int i = first_index+1; i <= last_index; i++)
for (int j = 0; j < d_; j++) {
Scalar c = points[point_indices_[i]*d_ + j];
if (bound_p1[j] > c) bound_p1[j] = c;
if (bound_p2[j] < c) bound_p2[j] = c;
}

// Calculate bounding box stats and delete the bounding box memory
int split_d = -1;
for (int j = 0; j < d_; j++) {
node->median[j] = (bound_p1[j] + bound_p2[j]) / 2;
node->radius[j] = (bound_p2[j] - bound_p1[j]) / 2;
split_d = j;
}
}
PointFree(bound_p2);
PointFree(bound_p1);

// If the max spread is 0, make this a leaf node
node->lower_node = node->upper_node = 0;
PointCopy(node->sum, first_point, d_);
if (last_index != first_index)
PointScale(node->sum, Scalar(last_index - first_index + 1), d_);
node->opt_cost = 0;
return node;
}

// Partition the points around the midpoint in this dimension. The partitioning is done in-place
// by iterating from left-to-right and right-to-left in the same way that partioning is done for
// quicksort.
Scalar split_pos = node->median[split_d];
int i1 = first_index, i2 = last_index, size1 = 0;
while (i1 <= i2) {
bool is_i1_good = (points[point_indices_[i1]*d_ + split_d] < split_pos);
bool is_i2_good = (points[point_indices_[i2]*d_ + split_d] >= split_pos);
if (!is_i1_good && !is_i2_good) {
int temp = point_indices_[i1];
point_indices_[i1] = point_indices_[i2];
point_indices_[i2] = temp;
is_i1_good = is_i2_good = true;
}
if (is_i1_good) {
i1++;
size1++;
}
if (is_i2_good) {
i2--;
}
}

// Create the child nodes
KM_ASSERT(size1 >= 1 && size1 <= last_index - first_index);
node->lower_node = BuildNodes(points, first_index, first_index + size1 - 1, next_node_data);
node->upper_node = BuildNodes(points, first_index + size1, last_index, next_node_data);

// Calculate the new sum and opt cost
PointCopy(node->sum, node->lower_node->sum, d_);
Scalar *center = PointAllocate(d_);
KM_ASSERT(center != 0);
PointCopy(center, node->sum, d_);
PointScale(center, Scalar(1) / node->num_points, d_);
node->opt_cost = GetNodeCost(node->lower_node, center) + GetNodeCost(node->upper_node, center);
PointFree(center);
return node;
}

// Returns the total contribution of all points in the given kd-tree node, assuming they are all
// assigned to a center at the given location. We need to return:
//
//   sum_{x \in node} ||x - center||^2.
//
// If c denotes the center of mass of the points in this node and n denotes the number of points in
// it, then this quantity is given by
//
//   n * ||c - center||^2 + sum_{x \in node} ||x - c||^2
//
// The sum is precomputed for each node as opt_cost. This formula follows from expanding both sides
Scalar KmTree::GetNodeCost(const Node *node, Scalar *center) const {
Scalar dist_sq = 0;
for (int i = 0; i < d_; i++) {
Scalar x = (node->sum[i] / node->num_points) - center[i];
dist_sq += x*x;
}
return node->opt_cost + node->num_points * dist_sq;
}

// Helper functions for DoKMeans step
// ==================================

// A recursive version of DoKMeansStep. This determines which clusters all points that are rooted
// node will be assigned to, and updates sums, counts and assignment (if not null) accordingly.
// candidates maintains the set of cluster indices which could possibly be the closest clusters
// for points in this subtree.
Scalar KmTree::DoKMeansStepAtNode(const Node *node, int k, int *candidates, Scalar *centers,
Scalar *sums, int *counts, int *assignment) const {
// Determine which center the node center is closest to
Scalar min_dist_sq = PointDistSq(node->median, centers + candidates[0]*d_, d_);
int closest_i = candidates[0];
for (int i = 1; i < k; i++) {
Scalar dist_sq = PointDistSq(node->median, centers + candidates[i]*d_, d_);
if (dist_sq < min_dist_sq) {
min_dist_sq = dist_sq;
closest_i = candidates[i];
}
}

// If this is a non-leaf node, recurse if necessary
if (node->lower_node != 0) {
// Build the new list of candidates
int new_k = 0;
int *new_candidates = (int*)malloc(k * sizeof(int));
KM_ASSERT(new_candidates != 0);
for (int i = 0; i < k; i++)
if (!ShouldBePruned(node->median, node->radius, centers, closest_i, candidates[i]))
new_candidates[new_k++] = candidates[i];

// Recurse if there's at least two
if (new_k > 1) {
Scalar result = DoKMeansStepAtNode(node->lower_node, new_k, new_candidates, centers,
sums, counts, assignment) +
DoKMeansStepAtNode(node->upper_node, new_k, new_candidates, centers,
sums, counts, assignment);
free(new_candidates);
return result;
} else {
free(new_candidates);
}
}

// Assigns all points within this node to a single center
counts[closest_i] += node->num_points;
if (assignment != 0) {
for (int i = node->first_point_index; i < node->first_point_index + node->num_points; i++)
assignment[point_indices_[i]] = closest_i;
}
return GetNodeCost(node, centers + closest_i*d_);
}

// Determines whether every point in the box is closer to centers[best_index] than to
// centers[test_index].
//
// If x is a point, c_0 = centers[best_index], c = centers[test_index], then:
//       (x-c).(x-c) < (x-c_0).(x-c_0)
//   <=> (c-c_0).(c-c_0) < 2(x-c_0).(c-c_0)
//
// The right-hand side is maximized for a vertex of the box where for each dimension, we choose
// the low or high value based on the sign of x-c_0 in that dimension.
bool KmTree::ShouldBePruned(Scalar *box_median, Scalar *box_radius, Scalar *centers,
int best_index, int test_index) const {
if (best_index == test_index)
return false;

Scalar *best = centers + best_index*d_;
Scalar *test = centers + test_index*d_;
Scalar lhs = 0, rhs = 0;
for (int i = 0; i < d_; i++) {
Scalar component = test[i] - best[i];
lhs += component * component;
if (component > 0)
rhs += (box_median[i] + box_radius[i] - best[i]) * component;
else
rhs += (box_median[i] - box_radius[i] - best[i]) * component;
}
return (lhs >= 2*rhs);
}

Scalar KmTree::SeedKMeansPlusPlus(int k, Scalar *centers) const {
Scalar *dist_sq = (Scalar*)malloc(n_ * sizeof(Scalar));
KM_ASSERT(dist_sq != 0);

// Choose an initial center uniformly at random
SeedKmppSetClusterIndex(top_node_, 0);
int i = GetRandom(n_);
memcpy(centers, points_ + point_indices_[i]*d_, d_*sizeof(Scalar));
Scalar total_cost = 0;
for (int j = 0; j < n_; j++) {
dist_sq[j] = PointDistSq(points_ + point_indices_[j]*d_, centers, d_);
total_cost += dist_sq[j];
}

// Repeatedly choose more centers
for (int new_cluster = 1; new_cluster < k; new_cluster++) {
while (1) {
Scalar cutoff = (rand() / Scalar(RAND_MAX)) * total_cost;
Scalar cur_cost = 0;
for (i = 0; i < n_; i++) {
cur_cost += dist_sq[i];
if (cur_cost >= cutoff)
break;
}
if (i < n_)
break;
}
memcpy(centers + new_cluster*d_, points_ + point_indices_[i]*d_, d_*sizeof(Scalar));
total_cost = SeedKmppUpdateAssignment(top_node_, new_cluster, centers, dist_sq);
}

// Clean up and return
free(dist_sq);
}

// Helper functions for SeedKMeansPlusPlus
// =======================================

// Sets kmpp_cluster_index to 0 for all nodes
void KmTree::SeedKmppSetClusterIndex(const Node *node, int value) const {
node->kmpp_cluster_index = value;
if (node->lower_node != 0) {
SeedKmppSetClusterIndex(node->lower_node, value);
SeedKmppSetClusterIndex(node->upper_node, value);
}
}

Scalar KmTree::SeedKmppUpdateAssignment(const Node *node, int new_cluster, Scalar *centers,
Scalar *dist_sq) const {
// See if we can assign all points in this node to one cluster
if (node->kmpp_cluster_index >= 0) {
if (ShouldBePruned(node->median, node->radius, centers, node->kmpp_cluster_index, new_cluster))
return GetNodeCost(node, centers + node->kmpp_cluster_index*d_);
node->kmpp_cluster_index)) {
SeedKmppSetClusterIndex(node, new_cluster);
for (int i = node->first_point_index; i < node->first_point_index + node->num_points; i++)
dist_sq[i] = PointDistSq(points_ + point_indices_[i]*d_, centers + new_cluster*d_, d_);
return GetNodeCost(node, centers + new_cluster*d_);
}

// It may be that the a leaf-node point is equidistant from the new center or old
if (node->lower_node == 0)
return GetNodeCost(node, centers + node->kmpp_cluster_index*d_);
}

// Recurse
Scalar cost = SeedKmppUpdateAssignment(node->lower_node, new_cluster, centers, dist_sq) +
SeedKmppUpdateAssignment(node->upper_node, new_cluster, centers, dist_sq);
int i1 = node->lower_node->kmpp_cluster_index, i2 = node->upper_node->kmpp_cluster_index;
if (i1 == i2 && i1 != -1)
node->kmpp_cluster_index = i1;
else
node->kmpp_cluster_index = -1;
return cost;
}