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#cython: boundscheck=False
#(not slicing or indexing any numpy arrays)
#TODO:
# - extend to more then 3-dimensions (feature)
# - replace build_tree with non-recursive function (speed)
# - add the option to determine splitting planes based on point position spread
# (feature)
# - enable bottom-up algorithms by keeping track of ancestral node
# - common stack size constant, how?
cimport numpy as np
from numpy cimport NPY_DOUBLE, NPY_ULONGLONG, npy_intp
from stdlib cimport malloc, realloc, free
__version__ = "('1', '5', '3')"
cdef extern from "numpy/arrayobject.h":
cdef object PyArray_SimpleNewFromData(int nd, npy_intp *dims,\
int typenum, void *data)
cdef int import_array1(int ret)
cdef kdpoint *points(DTYPE_t *c_array, UTYPE_t points, UTYPE_t dims):
"""creates an array of kdpoints from c-array of numpy doubles."""
cdef kdpoint *pnts = <kdpoint *>malloc(sizeof(kdpoint)*points)
cdef UTYPE_t i
for 0 <= i < points:
pnts[i].index = i
pnts[i].coords = c_array+i*dims
return pnts
cdef inline void swap(kdpoint *a, kdpoint *b):
"""swaps two pointers to kdpoint structs."""
cdef kdpoint t
t = a[0]
a[0] = b[0]
b[0] = t
cdef inline DTYPE_t dist(kdpoint *a, kdpoint *b, UTYPE_t dims):
"""calculates the squared distance between two points."""
cdef UTYPE_t i
cdef DTYPE_t dif, dst = 0
for 0 <= i < dims:
dif = a.coords[i] - b.coords[i]
dst += dif * dif
return dst
cdef void qsort(kdpoint *A, UTYPE_t l, UTYPE_t r, UTYPE_t dim):
"""implements the quick sort algorithm on kdpoint arrays."""
cdef UTYPE_t i, j, jstack = 0
cdef DTYPE_t v
cdef UTYPE_t *istack = <UTYPE_t *>malloc(NSTACK * sizeof(UTYPE_t))
while True:
if r - l > 2:
i = (l + r) >> 1
if A[l].coords[dim] > A[i].coords[dim]: swap(&A[l], &A[i])
if A[l].coords[dim] > A[r].coords[dim]: swap(&A[l], &A[r])
if A[i].coords[dim] > A[r].coords[dim]: swap(&A[i], &A[r])
j = r - 1
swap(&A[i], &A[j])
i = l
v = A[j].coords[dim]
while True:
while A[i+1].coords[dim] < v: i+=1
i+=1
while A[j-1].coords[dim] > v: j-=1
j-=1
if j < i:
break
swap(&A[i], &A[j])
swap(&A[i], &A[r-1])
jstack += 2
if r - i >= j:
istack[jstack] = r
istack[jstack - 1] = i
r = j
else:
istack[jstack] = j
istack[jstack - 1] = l
l = i
else:
i = (l + r) >> 1
if A[l].coords[dim] > A[i].coords[dim]: swap(&A[l], &A[i])
if A[l].coords[dim] > A[r].coords[dim]: swap(&A[l], &A[r])
if A[i].coords[dim] > A[r].coords[dim]: swap(&A[i], &A[r])
if jstack == 0:
break
r = istack[jstack]
jstack-=1
l = istack[jstack]
jstack-=1
free(istack)
cdef kdnode *build_tree(kdpoint *point_list, UTYPE_t start, UTYPE_t end,\
UTYPE_t dims, UTYPE_t bucket_size, UTYPE_t depth):
"""recursive tree building function."""
# cannot make variable in if/else
cdef UTYPE_t split, i
cdef kdnode *node = <kdnode*>malloc(sizeof(kdnode))
node.dimension = depth % dims
node.start = start
node.end = end
if end - start <= bucket_size:
# make bucket node
node.bucket = 1
node.position = -1.0
node.left = NULL
node.right = NULL
else:
## make branch node
node.bucket = 0
split = (start + end) / 2
qsort(point_list, start, end, node.dimension)
node.position = point_list[split].coords[node.dimension]
# recurse
node.left = build_tree(point_list, start, split, dims , bucket_size , depth+1)
node.right = build_tree(point_list, split+1, end, dims , bucket_size , depth+1)
return node
cdef void *knn(kdnode *root, kdpoint *point_list, kdpoint point, DTYPE_t *dst,\
UTYPE_t *idx, UTYPE_t k, UTYPE_t dims):
"""finds the K-Nearest Neighbors."""
# arrays of pointers will be used as a stack for left and right nodes
# left nodes will be explored first.
cdef kdnode *lstack[100]
cdef UTYPE_t i, j, jold, ia, kmin # counter and index
cdef DTYPE_t a, i_dist, diff
cdef kdnode *node
# set helper variable to heap-queue
kmin = k - 1
# initialize stack
cdef int jstack = 1
lstack[jstack] = root
# initialize arrays
for 0 <= i < k:
dst[i] = 1000000000.00 # DBL_MAX
idx[i] = 2147483647 # INT_MAX
while jstack:
node = lstack[jstack]
jstack -= 1
if node.bucket:
for node.start <= i <= node.end:
i_dist = dist(&point_list[i], &point, dims)
if i_dist < dst[0]:
dst[0] = i_dist
idx[0] = i
if k > 1:
a = dst[0]
ia = idx[0]
jold = 0
j = 1
while j <= kmin:
if (j < kmin) and (dst[j] < dst[j+1]):
j+=1
if (a >= dst[j]):
break
dst[jold] = dst[j]
idx[jold] = idx[j]
jold = j
j = 2*j + 1
dst[jold] = a
idx[jold] = ia
else:
diff = point.coords[node.dimension] - node.position
if diff < 0:
if dst[0] >= diff * diff:
jstack+=1
lstack[jstack] = node.right
jstack+=1
lstack[jstack] = node.left
else:
if dst[0] >= diff * diff:
jstack+=1
lstack[jstack] = node.left
jstack+=1
lstack[jstack] = node.right
cdef UTYPE_t rn(kdnode *root, kdpoint *point_list, kdpoint point, DTYPE_t **dstptr,\
UTYPE_t **idxptr, DTYPE_t r, UTYPE_t dims, UTYPE_t buf):
"""finds points within radius of query."""
# arrays of pointers will be used as a stack for left and right nodes
# left nodes will be explored first.
cdef kdnode *lstack[100]
dstptr[0] = <DTYPE_t *>malloc(buf * sizeof(DTYPE_t))
idxptr[0] = <UTYPE_t *>malloc(buf * sizeof(UTYPE_t))
cdef UTYPE_t i, count # counter and index
cdef DTYPE_t i_dist, diff
cdef kdnode *node
# initialize stack
cdef int jstack = 1
lstack[jstack] = root
count = 0
while jstack:
node = lstack[jstack]
jstack -= 1
if node.bucket:
for node.start <= i <= node.end:
i_dist = dist(&point_list[i], &point, dims)
if i_dist < r:
dstptr[0][count] = i_dist
idxptr[0][count] = i
count += 1
if count % buf == 0:
dstptr[0] = <DTYPE_t *>realloc(dstptr[0], (count + buf) * sizeof(DTYPE_t))
idxptr[0] = <UTYPE_t *>realloc(idxptr[0], (count + buf) * sizeof(UTYPE_t))
else:
diff = point.coords[node.dimension] - node.position
if diff < 0:
if r >= diff * diff:
jstack+=1
lstack[jstack] = node.right
jstack+=1
lstack[jstack] = node.left
else:
if r >= diff * diff:
jstack+=1
lstack[jstack] = node.left
jstack+=1
lstack[jstack] = node.right
dstptr[0] = <DTYPE_t *>realloc(dstptr[0], count * sizeof(DTYPE_t))
idxptr[0] = <UTYPE_t *>realloc(idxptr[0], count * sizeof(UTYPE_t))
return count
cdef class KDTree:
"""Implements the KDTree data structure for fast neares neighbor queries."""
cdef np.ndarray n_array
cdef DTYPE_t *c_array
cdef kdpoint *kdpnts
cdef kdnode *tree
cdef readonly UTYPE_t dims
cdef readonly UTYPE_t pnts
cdef readonly UTYPE_t bucket_size
def __init__(self, np.ndarray[DTYPE_t, ndim =2] n_array, \
UTYPE_t bucket_size =5):
self.bucket_size = bucket_size
self.pnts = n_array.shape[0]
self.dims = n_array.shape[1]
self.n_array = n_array
self.c_array = <DTYPE_t *> n_array.data
self.kdpnts = points(self.c_array, \
self.pnts, self.dims)
self.tree = build_tree(self.kdpnts, 0, self.pnts-1, \
self.dims,self.bucket_size,0)
import_array1(0)
def knn(self, np.ndarray[DTYPE_t, ndim =1] point, npy_intp k):
"""Finds the K-Nearest Neighbors of given point.
Arguments:
- point: 1-d numpy array (query point).
- k: number of neighbors to find."""
if self.pnts < k:
return 1
cdef UTYPE_t i
cdef kdpoint pnt
pnt.coords = <DTYPE_t *>point.data
cdef UTYPE_t size = point.size
cdef DTYPE_t *dst = <DTYPE_t *>malloc(k * sizeof(DTYPE_t))
cdef UTYPE_t *idx = <UTYPE_t *>malloc(k * sizeof(UTYPE_t))
cdef UTYPE_t *ridx = <UTYPE_t *>malloc(k * sizeof(UTYPE_t))
knn(self.tree, self.kdpnts, pnt, dst, idx, k, self.dims)
cdef np.ndarray dist = PyArray_SimpleNewFromData(1, &k, NPY_DOUBLE, <void*>dst)
for 0 <= i < k:
ridx[i] = self.kdpnts[idx[i]].index
cdef np.ndarray index = PyArray_SimpleNewFromData(1, &k, NPY_ULONGLONG, <void*>ridx)
free(idx)
return (index, dist)
def rn(self, np.ndarray[DTYPE_t, ndim =1] point, DTYPE_t r):
"""Returns Radius Neighbors i.e. within radius from query point."""
cdef UTYPE_t i
cdef npy_intp j
cdef kdpoint pnt
pnt.coords = <DTYPE_t *>point.data
cdef UTYPE_t size = point.size
cdef DTYPE_t **dstptr = <DTYPE_t **>malloc(sizeof(DTYPE_t*))
cdef UTYPE_t **idxptr = <UTYPE_t **>malloc(sizeof(UTYPE_t*))
j = <npy_intp>rn(self.tree, self.kdpnts, pnt, dstptr, idxptr, r, self.dims, 100)
cdef np.ndarray dist = PyArray_SimpleNewFromData(1, &j, NPY_DOUBLE, <void*>dstptr[0])
cdef UTYPE_t *ridx = <UTYPE_t *>malloc(j * sizeof(UTYPE_t))
for 0 <= i < j:
ridx[i] = self.kdpnts[idxptr[0][i]].index
cdef np.ndarray index = PyArray_SimpleNewFromData(1, &j, NPY_ULONGLONG, <void*>ridx)
free(idxptr[0])
free(idxptr)
free(dstptr)
return (index, dist)
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