问题描述:

I'm desperately searching for an efficient way to check if two 2D numpy Arrays intersect.

So what I have is two arrays with an arbitrary amount of 2D arrays like:

`A=np.array([[2,3,4],[5,6,7],[8,9,10]])`

B=np.array([[5,6,7],[1,3,4]])

C=np.array([[1,2,3],[6,6,7],[10,8,9]])

All I need is a True if there is at least one vector intersecting with another one of the other array, otherwise a false. So it should give results like this:

`f(A,B) -> True`

f(A,C) -> False

I'm kind of new to python and at first I wrote my program with Python lists, which works but of course is very inefficient. The Program takes days to finish so I am working on a `numpy.array`

solution now, but these arrays really are not so easy to handle.

Here's Some Context about my Program and the Python List Solution:

What i'm doing is something like a self-avoiding random walk in 3 Dimensions. http://en.wikipedia.org/wiki/Self-avoiding_walk. But instead of doing a Random walk and hoping that it will reach a desirable length (e.g. i want chains build up of 1000 beads) without reaching a dead end i do the following:

I create a "flat" Chain with the desired length N:

`X=[]`

for i in range(0,N+1):

X.append((i,0,0))

Now i fold this flat chain:

- randomly choose one of the elements ("pivotelement")
- randomly choose one direction ( either all elements to the left or to the right of the pivotelment)
- randomly choose one out of 9 possible rotations in space (3 axes * 3 possible rotations 90°,180°,270°)
- rotate all the elements of the chosen direction with the chosen rotation
- Check if the new elements of the chosen direction intersect with the other direction
- No intersection -> accept the new configuration, else -> keep the old chain.

Steps 1.-6. have to be done a large amount of times (e.g. for a chain of length 1000, ~5000 Times) so these steps have to be done efficiently. My List-based solution for this is the following:

`def PivotFold(chain):`

randPiv=random.randint(1,N) #Chooses a random pivotelement, N is the Chainlength

Pivot=chain[randPiv] #get that pivotelement

C=[] #C is going to be a shifted copy of the chain

intersect=False

for j in range (0,N+1): # Here i shift the hole chain to get the pivotelement to the origin, so i can use simple rotations around the origin

C.append((chain[j][0]-Pivot[0],chain[j][1]-Pivot[1],chain[j][2]-Pivot[2]))

rotRand=random.randint(1,18) # rotRand is used to choose a direction and a Rotation (2 possible direction * 9 rotations = 18 possibilitys)

#Rotations around Z-Axis

if rotRand==1:

for j in range (randPiv,N+1):

C[j]=(-C[j][1],C[j][0],C[j][2])

if C[0:randPiv].__contains__(C[j])==True:

intersect=True

break

elif rotRand==2:

for j in range (randPiv,N+1):

C[j]=(C[j][1],-C[j][0],C[j][2])

if C[0:randPiv].__contains__(C[j])==True:

intersect=True

break

...etc

if intersect==False: # return C if there was no intersection in C

Shizz=C

else:

Shizz=chain

return Shizz

The Function PivotFold(chain) will be used on the initially flat chain X a large amount of times. it's pretty naivly written so maybe you have some protips to improve this ^^ I thought that numpyarrays would be good because i can efficiently shift and rotate entire chains without looping over all the elements ...

This should do it:

```
In [11]:
def f(arrA, arrB):
return not set(map(tuple, arrA)).isdisjoint(map(tuple, arrB))
In [12]:
f(A, B)
Out[12]:
True
In [13]:
f(A, C)
Out[13]:
False
In [14]:
f(B, C)
Out[14]:
False
```

To find intersection? OK, `set`

sounds like a logical choice.
But `numpy.array`

or `list`

are not hashable? OK, convert them to `tuple`

.
That is the idea.

A `numpy`

way of doing involves very unreadable boardcasting:

```
In [34]:
(A[...,np.newaxis]==B[...,np.newaxis].T).all(1)
Out[34]:
array([[False, False],
[ True, False],
[False, False]], dtype=bool)
In [36]:
(A[...,np.newaxis]==B[...,np.newaxis].T).all(1).any()
Out[36]:
True
```

Some timeit result:

```
In [38]:
#Dan's method
%timeit set_comp(A,B)
10000 loops, best of 3: 34.1 µs per loop
In [39]:
#Avoiding lambda will speed things up
%timeit f(A,B)
10000 loops, best of 3: 23.8 µs per loop
In [40]:
#numpy way probably will be slow, unless the size of the array is very big (my guess)
%timeit (A[...,np.newaxis]==B[...,np.newaxis].T).all(1).any()
10000 loops, best of 3: 49.8 µs per loop
```

Also the `numpy`

method will be RAM hungry, as `A[...,np.newaxis]==B[...,np.newaxis].T`

step creates a 3D array.

Using the same idea outlined here, you could do the following:

```
def make_1d_view(a):
a = np.ascontiguousarray(a)
dt = np.dtype((np.void, a.dtype.itemsize * a.shape[1]))
return a.view(dt).ravel()
def f(a, b):
return len(np.intersect1d(make_1d_view(A), make_1d_view(b))) != 0
>>> f(A, B)
True
>>> f(A, C)
False
```

This doesn't work for floating point types (it will not consider +0.0 and -0.0 the same value), and `np.intersect1d`

uses sorting, so it is has linearithmic, not linear, performance. You may be able to squeeze some performance by replicating the source of `np.intersect1d`

in your code, and instead of checking the length of the return array, calling `np.any`

on the boolean indexing array.

This should be much faster it is not O(n^2) like the for-loop solution, but it isn't fully numpythonic. Not sure how better to leverage numpy here

```
def set_comp(a, b):
sets_a = set(map(lambda x: frozenset(tuple(x)), a))
sets_b = set(map(lambda x: frozenset(tuple(x)), b))
return not sets_a.isdisjoint(sets_b)
```

You can also get the job done with some `np.tile`

and `np.swapaxes`

business!

```
def intersect2d(X, Y):
"""
Function to find intersection of two 2D arrays.
Returns index of rows in X that are common to Y.
"""
X = np.tile(X[:,:,None], (1, 1, Y.shape[0]) )
Y = np.swapaxes(Y[:,:,None], 0, 2)
Y = np.tile(Y, (X.shape[0], 1, 1))
eq = np.all(np.equal(X, Y), axis = 1)
eq = np.any(eq, axis = 1)
return np.nonzero(eq)[0]
```

To answer the question more specifically, you'd only need to check if the returned array is empty.

i think you want true if tow arrays have subarray set ! you can use this :

```
def(A,B):
for i in A:
for j in B:
if i==j
return True
return False
```

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