Consider I have these lists:
l = [5,6,7,8,9,10,5,15,20]
m = [10,5]
I want to get the index of m in l. I used list comprehension to do that:
[(i,i+1) for i,j in enumerate(l) if m[0] == l[i] and m[1] == l[i+1]]
Output : [(5,6)]
But if I have more numbers in m, I feel its not the right way. So is there any easy approach in Python or with NumPy?
Another example:
l = [5,6,7,8,9,10,5,15,20,50,16,18]
m = [10,5,15,20]
The output should be:
[(5,6,7,8)]
The easiest way (using pure Python) would be to iterate over the items and first only check if the first item matches. This avoids doing sublist comparisons when not needed. Depending on the contents of your l this could outperform even NumPy broadcasting solutions:
def func(haystack, needle): # obviously needs a better name ...
if not needle:
return
# just optimization
lengthneedle = len(needle)
firstneedle = needle[0]
for idx, item in enumerate(haystack):
if item == firstneedle:
if haystack[idx:idx+lengthneedle] == needle:
yield tuple(range(idx, idx+lengthneedle))
>>> list(func(l, m))
[(5, 6, 7, 8)]
In case your interested in speed I checked the performance of the approaches (borrowing from my setup here):
import random
import numpy as np
# strided_app is from https://stackoverflow.com/a/40085052/
def strided_app(a, L, S ): # Window len = L, Stride len/stepsize = S
nrows = ((a.size-L)//S)+1
n = a.strides[0]
return np.lib.stride_tricks.as_strided(a, shape=(nrows,L), strides=(S*n,n))
def pattern_index_broadcasting(all_data, search_data):
n = len(search_data)
all_data = np.asarray(all_data)
all_data_2D = strided_app(np.asarray(all_data), n, S=1)
return np.flatnonzero((all_data_2D == search_data).all(1))
# view1D is from https://stackoverflow.com/a/45313353/
def view1D(a, b): # a, b are arrays
a = np.ascontiguousarray(a)
void_dt = np.dtype((np.void, a.dtype.itemsize * a.shape[1]))
return a.view(void_dt).ravel(), b.view(void_dt).ravel()
def pattern_index_view1D(all_data, search_data):
a = strided_app(np.asarray(all_data), L=len(search_data), S=1)
a0v, b0v = view1D(np.asarray(a), np.asarray(search_data))
return np.flatnonzero(np.in1d(a0v, b0v))
def find_sublist_indices(haystack, needle):
if not needle:
return
# just optimization
lengthneedle = len(needle)
firstneedle = needle[0]
restneedle = needle[1:]
for idx, item in enumerate(haystack):
if item == firstneedle:
if haystack[idx+1:idx+lengthneedle] == restneedle:
yield tuple(range(idx, idx+lengthneedle))
def Divakar1(l, m):
return np.squeeze(pattern_index_broadcasting(l, m)[:,None] + np.arange(len(m)))
def Divakar2(l, m):
return np.squeeze(pattern_index_view1D(l, m)[:,None] + np.arange(len(m)))
def MSeifert(l, m):
return list(find_sublist_indices(l, m))
# Timing setup
timings = {Divakar1: [], Divakar2: [], MSeifert: []}
sizes = [2**i for i in range(5, 20, 2)]
# Timing
for size in sizes:
l = [random.randint(0, 50) for _ in range(size)]
m = [random.randint(0, 50) for _ in range(10)]
larr = np.asarray(l)
marr = np.asarray(m)
for func in timings:
# first timings:
# res = %timeit -o func(l, m)
# second timings:
if func is MSeifert:
res = %timeit -o func(l, m)
else:
res = %timeit -o func(larr, marr)
timings[func].append(res)
%matplotlib notebook
import matplotlib.pyplot as plt
import numpy as np
fig = plt.figure(1)
ax = plt.subplot(111)
for func in timings:
ax.plot(sizes,
[time.best for time in timings[func]],
label=str(func.__name__))
ax.set_xscale('log')
ax.set_yscale('log')
ax.set_xlabel('size')
ax.set_ylabel('time [seconds]')
ax.grid(which='both')
ax.legend()
plt.tight_layout()
In case your l and m are lists my function outperforms the NumPy solutions for all sizes:
But in case you have these as numpy arrays you'll get faster results for large arrays (size > 1000 elements) when using Divakars NumPy solutions:
You are basically looking for the starting indices of a list in another list.
Approach #1 : One approach to solve it would be to create sliding windows of the elements in list in which we are searching, giving us a 2D array and then simply use NumPy broadcasting to perform broadcasted comparison against the search list against each row of the 2D sliding window version obtained earlier. Thus, one method would be -
# strided_app is from https://stackoverflow.com/a/40085052/
def strided_app(a, L, S ): # Window len = L, Stride len/stepsize = S
nrows = ((a.size-L)//S)+1
n = a.strides[0]
return np.lib.stride_tricks.as_strided(a, shape=(nrows,L), strides=(S*n,n))
def pattern_index_broadcasting(all_data, search_data):
n = len(search_data)
all_data = np.asarray(all_data)
all_data_2D = strided_app(np.asarray(all_data), n, S=1)
return np.flatnonzero((all_data_2D == search_data).all(1))
out = np.squeeze(pattern_index_broadcasting(l, m)[:,None] + np.arange(len(m)))
Sample runs -
In [340]: l = [5,6,7,8,9,10,5,15,20,50,16,18]
...: m = [10,5,15,20]
...:
In [341]: np.squeeze(pattern_index_broadcasting(l, m)[:,None] + np.arange(len(m)))
Out[341]: array([5, 6, 7, 8])
In [342]: l = [5,6,7,8,9,10,5,15,20,50,16,18,10,5,15,20]
...: m = [10,5,15,20]
...:
In [343]: np.squeeze(pattern_index_broadcasting(l, m)[:,None] + np.arange(len(m)))
Out[343]:
array([[ 5, 6, 7, 8],
[12, 13, 14, 15]])
Approach #2 : Another method would be to get the sliding window and then get the row-wise scalar view into the data to be search data and the data to be search for, giving us 1D data to work with, like so -
# view1D is from https://stackoverflow.com/a/45313353/
def view1D(a, b): # a, b are arrays
a = np.ascontiguousarray(a)
void_dt = np.dtype((np.void, a.dtype.itemsize * a.shape[1]))
return a.view(void_dt).ravel(), b.view(void_dt).ravel()
def pattern_index_view1D(all_data, search_data):
a = strided_app(np.asarray(all_data), L=len(search_data), S=1)
a0v, b0v = view1D(np.asarray(a), np.asarray(search_data))
return np.flatnonzero(np.in1d(a0v, b0v))
out = np.squeeze(pattern_index_view1D(l, m)[:,None] + np.arange(len(m)))
In search of more easy/compact approaches, we could look into scikit-image's view_as_windows for getting sliding windows with a built-in. I am assuming arrays as inputs for less messy code. For lists as input, we have to use np.asarray() as shown earlier.
Approach #3 : Basically a derivative of pattern_index_broadcasting with view_as_windows for a one-liner with a as the larger data and b is the array to be searched -
from skimage.util import view_as_windows
np.flatnonzero((view_as_windows(a,len(b))==b).all(1))[:,None]+np.arange(len(b))
Approach #4 : For a small number of matches from b in a, we could optimize, by looking for first element match from b to reduce the dataset size for searches -
mask = a[:-len(b)+1]==b[0]
mask[mask] = (view_as_windows(a,len(b))[mask]).all(1)
out = np.flatnonzero(mask)[:,None]+np.arange(len(b))
Approach #5 : For a small sized b, we could simply run a loop for each of the elements in b and perform bitwise and-reduction -
mask = np.bitwise_and.reduce([a[i:len(a)-len(b)+1+i]==b[i] for i in range(len(b))])
out = np.flatnonzero(mask)[:,None]+np.arange(len(b))
Just making the point that @MSeifert's approach can, of course, also be implemented in numpy:
def pp(h,n):
nn = len(n)
NN = len(h)
c = (h[:NN-nn+1]==n[0]).nonzero()[0]
if c.size==0: return
for i,l in enumerate(n[1:].tolist(),1):
c = c[h[i:][c]==l]
if c.size==0: return
return np.arange(c[0],c[0]+nn)
def get_data(l1,l2):
d=defaultdict(list)
[d[item].append(index) for index,item in enumerate(l1)]
print(d)
Using defaultdict to store indices of elements from other list.
