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vp_tree.go
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vp_tree.go
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package search
import (
"container/heap"
"math"
"math/rand"
"runtime"
"sort"
"sync"
)
// VPTreeDistancer interface compares two items to be sorted in the VP-Tree
type VPTreeDistancer interface {
// Distance returns the distance between two items satisfying the triangle
// inequality
Distance(a, b VPTreeItem) float64
}
// VPTreeItem interface provides a generic interface to support indexing
// different types
type VPTreeItem interface {
SetNode(*VPTreeNode)
GetNode() *VPTreeNode
ShouldSkip(VPTreeItem) bool
ApplyAffinity(float64, VPTreeItem) float64
}
type vpTreeComparator struct {
Distancer VPTreeDistancer
}
func (v *vpTreeComparator) Less(a, b *VPTreeNode) bool {
return a.dist < b.dist
}
type VPTreeNode struct {
index int
threshold, m, M, dist float64
left, right *VPTreeNode
children []int
isLeaf bool
_dead bool
}
// IsDead returns if the node has been marked for deletion
func (v *VPTreeNode) IsDead() bool {
return v._dead
}
type vpHeapItem struct {
index int
dist float64
node, parent *VPTreeNode
}
func (v *vpHeapItem) Priority() float64 {
return v.dist
}
func (v *vpHeapItem) Less(other *vpHeapItem) bool {
return v.dist < other.dist
}
// VPTree is an instance of a vp-tree index
type VPTree struct {
// Distancer will be invoked to calculate the distance between items
Distancer VPTreeDistancer
comparator vpTreeComparator
root *VPTreeNode
items []VPTreeItem
_deadIdx []int
mutex sync.Mutex
// MaxChildren int
}
// SetItems will (re)build the index for the slice of items
func (v *VPTree) SetItems(items []VPTreeItem) {
v.items = items
v._deadIdx = make([]int, 0)
nodes := make([]*VPTreeNode, len(items))
for i := 0; i < len(nodes); i++ {
var n VPTreeNode
item := items[i]
n.index = i
nodes[i] = &n
item.SetNode(&n)
}
v.root = v.buildFromPoints(nodes)
}
// ItemCount returns the number of items in the tree
func (v *VPTree) ItemCount() int {
return len(v.items)
}
// Search returns the nearest k items to the target. The items are sorted with
// by distance ascending. The second parameter is the repective distances to the
// target
func (v *VPTree) Search(target VPTreeItem, k int) ([]VPTreeItem, []float64) {
tau := new(float64)
*tau = math.MaxFloat64
pq := &PriorityQueue{}
heap.Init(pq)
v.search(v.root, target, k, pq, tau, math.MaxFloat64, true)
results := make([]VPTreeItem, pq.Len())
distances := make([]float64, pq.Len())
for i := pq.Len() - 1; i >= 0; i-- {
item := heap.Pop(pq).(*vpHeapItem)
results[i] = v.items[item.index]
distances[i] = item.Priority()
}
return results, distances
}
// SearchInRange returns the nearest k items to the target sorted by distance
// ascending with no result being more that maxDistance away from the target.
func (v *VPTree) SearchInRange(target VPTreeItem, k int, maxDist float64) ([]VPTreeItem, []float64) {
tau := new(float64)
*tau = maxDist
pq := &PriorityQueue{}
heap.Init(pq)
v.search(v.root, target, k, pq, tau, maxDist, true)
results := make([]VPTreeItem, pq.Len())
distances := make([]float64, pq.Len())
for i := pq.Len() - 1; i >= 0; i-- {
item := heap.Pop(pq).(*vpHeapItem)
results[i] = v.items[item.index]
distances[i] = item.Priority()
}
return results, distances
}
func (v *VPTree) search(node *VPTreeNode, target VPTreeItem, k int, pq *PriorityQueue, tau *float64, maxDist float64, applyAffinity bool) {
if node == nil {
return
}
// if node.isLeaf {
// for _, idx := range node.children {
// dist := v.Distancer.Distance(v.items[idx], target)
// if dist < v.tau {
// if pq.Len() == k {
// heap.Pop(pq)
// }
// heap.Push(pq, &vpHeapItem{idx, dist, nil, node})
// if pq.Len() == k {
// v.tau = (*pq)[0].Priority()
// }
// }
// }
// return
// }
if node._dead || v.items[node.index].ShouldSkip(target) {
v.search(node.left, target, k, pq, tau, maxDist, applyAffinity)
v.search(node.right, target, k, pq, tau, maxDist, applyAffinity)
return
}
dist := v.Distancer.Distance((v.items)[node.index], target)
var priority float64
if applyAffinity && dist < maxDist {
priority = (v.items)[node.index].ApplyAffinity(dist, target)
} else {
priority = dist
}
t := *tau
// This Vantage-point is close enough
if priority < t {
if pq.Len() == k {
heap.Pop(pq)
}
heap.Push(pq, &vpHeapItem{
index: node.index,
dist: priority,
node: node,
parent: nil})
if pq.Len() == k {
item := heap.Pop(pq).(*vpHeapItem)
*tau = item.Priority()
heap.Push(pq, item)
}
}
if node.left == nil && node.right == nil {
return
}
if dist < node.threshold {
if node.left != nil && node.m-t <= dist {
v.search(node.left, target, k, pq, tau, maxDist, applyAffinity)
}
if node.right != nil && node.threshold-t < dist && dist < node.M+t {
v.search(node.right, target, k, pq, tau, maxDist, applyAffinity)
}
} else {
if node.right != nil && node.m-t < dist {
v.search(node.right, target, k, pq, tau, maxDist, applyAffinity)
}
if node.left != nil && node.m-t < dist && dist < node.threshold+t {
v.search(node.left, target, k, pq, tau, maxDist, applyAffinity)
}
}
}
func (v *VPTree) medianOf3(list []*VPTreeNode, a int, b int, c int) int {
A, B, C := list[a], list[b], list[c]
if v.comparator.Less(A, B) {
if v.comparator.Less(B, C) {
return b
}
if v.comparator.Less(A, C) {
return c
}
return a
}
if v.comparator.Less(A, C) {
return a
}
if v.comparator.Less(B, C) {
return c
}
return b
}
func (v *VPTree) partition(list []*VPTreeNode, left, right, pivotIndex int) int {
pivotValue := list[pivotIndex]
list[pivotIndex], list[right] = list[right], list[pivotIndex]
storeIndex := left
for i := left; i < right; i++ {
if v.comparator.Less(list[i], pivotValue) {
list[storeIndex], list[i] = list[i], list[storeIndex]
storeIndex++
}
}
list[right], list[storeIndex] = list[storeIndex], list[right]
return storeIndex
}
func (v *VPTree) nthElement(list []*VPTreeNode, left, nth, right int) *VPTreeNode {
var pivotIndex, pivotNewIndex, pivotDist int
for {
pivotIndex = v.medianOf3(list, left, right, (left+right)>>1)
pivotNewIndex = v.partition(list, left, right, pivotIndex)
pivotDist = pivotNewIndex - left + 1
if pivotDist == nth {
return list[pivotNewIndex]
} else if nth < pivotDist {
right = pivotNewIndex - 1
} else {
nth -= pivotDist
left = pivotNewIndex + 1
}
}
}
func (v *VPTree) buildFromPoints(nodes []*VPTreeNode) *VPTreeNode {
listLength := len(nodes)
if listLength == 0 {
return nil
}
// // Is this a leaf node
// if tree.MaxChildren > 1 && delta <= tree.MaxChildren {
// node.children = make([]int, delta)
// node.isLeaf = true
// for i := 0; i < delta-1; i++ {
// node.children[i] = lower + i + 1
// }
// return &node
// }
vpIndex := rand.Intn(listLength)
node := nodes[vpIndex]
nodes = append(nodes[0:vpIndex], nodes[vpIndex+1:]...)
listLength--
if listLength == 0 {
return node
}
vp := v.items[node.index]
// Ensure Distance calculations are only done once per sort
S := v.items
var wg sync.WaitGroup
distances := make([]float64, listLength)
batchSize := int(math.Ceil(float64(listLength) / float64(runtime.NumCPU())))
for i := 0; i < listLength; i += batchSize {
wg.Add(batchSize)
go func(idx int) {
var batch []*VPTreeNode
if idx+batchSize < listLength {
batch = nodes[idx:(idx + batchSize)]
} else {
batch = nodes[idx:listLength]
}
for j, item := range batch {
dist := v.Distancer.Distance(vp, S[item.index])
item.dist = dist
distances[j] = dist
}
wg.Add(-batchSize)
}(i)
}
wg.Wait()
sort.Float64s(distances)
node.m = distances[0]
node.M = distances[listLength-1]
medianIndex := listLength >> 1
median := v.nthElement(nodes, 0, medianIndex+1, listLength-1)
leftItems := nodes[0:medianIndex]
rightItems := nodes[medianIndex:]
node.threshold = median.dist
node.left = v.buildFromPoints(leftItems)
node.right = v.buildFromPoints(rightItems)
return node
}
// Insert adds a new item to the index
func (v *VPTree) Insert(item VPTreeItem) {
if (len(v.items) - len(v._deadIdx)) <= 0 {
v.SetItems([]VPTreeItem{item})
return
}
tau := new(float64)
*tau = math.MaxFloat64
pq := &PriorityQueue{}
heap.Init(pq)
v.mutex.Lock()
defer v.mutex.Unlock()
v.search(v.root, item, 1, pq, tau, math.MaxFloat64, false)
heapItem := (*pq)[0].(*vpHeapItem)
var match *VPTreeNode
if heapItem.node != nil {
match = heapItem.node
} else {
match = heapItem.parent
}
var node VPTreeNode
node.index = len(v.items)
items := append(v.items, item)
v.items = items
node.isLeaf = false
item.SetNode(&node)
for {
dist := v.Distancer.Distance(v.items[match.index], item)
if dist <= match.threshold {
if dist < match.m {
match.m = dist
}
if match.left == nil {
match.m = dist
match.left = &node
return
}
match = match.left
} else {
if dist > match.M {
match.M = dist
}
if match.right == nil {
match.M = dist
match.right = &node
return
}
match = match.right
}
}
}
// Remove marks that an item should no longer be included in search results. The
// item will be removed from the index when the index rebuilds
func (v *VPTree) Remove(item VPTreeItem) {
if v.root == nil {
return
}
if node := item.GetNode(); node != nil {
node._dead = true
v.mutex.Lock()
v._deadIdx = append(v._deadIdx, node.index)
v.mutex.Unlock()
return
}
tau := new(float64)
*tau = math.MaxFloat64
pq := &PriorityQueue{}
heap.Init(pq)
v.search(v.root, item, 1, pq, tau, math.MaxFloat64, false)
if pq.Len() >= 1 {
heapItem := (*pq)[0].(*vpHeapItem)
var match *VPTreeNode
if heapItem.node != nil {
match = heapItem.node
} else {
match = heapItem.parent
}
match._dead = true
v.mutex.Lock()
v._deadIdx = append(v._deadIdx, match.index)
v.mutex.Unlock()
}
}
// Rebuild will trigger a rebuild on the index over the same items. All items
// marked for removal will be removed from the item list at this stage
func (v *VPTree) Rebuild() {
v.mutex.Lock()
defer v.mutex.Unlock()
sort.Ints(v._deadIdx)
l := v.items
for i := len(v._deadIdx) - 1; i >= 0; i-- {
didx := v._deadIdx[i]
l = append(l[0:didx], l[didx+1:]...)
}
v.SetItems(l)
}
func (v *VPTree) Items() []VPTreeItem {
return v.items
}