# How to detect a sign change for elements in a numpy array

## Question:

I have a numpy array with positive and negative values in.

```
a = array([1,1,-1,-2,-3,4,5])
```

I want to create another array which contains a value at each index where a sign change occurs (For example, if the current element is positive and the previous element is negative and vice versa).

For the array above, I would expect to get the following result

```
array([0,0,1,0,0,1,0])
```

Alternatively, a list of the positions in the array where the sign changes occur or list of booleans instead of 0’s and 1’s is fine.

## Answers:

Something like

```
a = array([1,1,-1,-2,-3,4,5])
asign = np.sign(a)
signchange = ((np.roll(asign, 1) - asign) != 0).astype(int)
print signchange
array([0, 0, 1, 0, 0, 1, 0])
```

Now, numpy.roll does a circular shift, so if the last element has different sign than the first, the first element in the signchange array will be 1. If this is not desired, one can of course do a simple

```
signchange[0] = 0
```

Also, np.sign considers 0 to have it’s own sign, different from either positive or negative values. E.g. the “signchange” array for [-1,0,1] would be [0,1,1] even though the zero line was “crossed” only once. If this is undesired, one could insert the lines

```
sz = asign == 0
while sz.any():
asign[sz] = np.roll(asign, 1)[sz]
sz = asign == 0
```

between lines 2 and 3 in the first example.

How about

```
[0 if x == 0 else 1 if numpy.sign(a[x-1]) != numpy.sign(y) else 0 for x, y in enumerate(a)]
```

numpy.sign assigns 0 its own sign, so 0s will be sign changes from anything except other 0s, which is probably what you want.

The answers above use list comprehensions and some numpy magic to get the result you want. Here is a very straight forward, if a little convoluted, way of doing the same:

```
import numpy as np
arr = np.array([1,1,-1,-2,-3,4,5])
result = []
for i, v in enumerate(arr):
if i == 0:
change = False
elif v < 0 and arr[i-1] > 0:
change = True
elif v > 0 and arr[i-1] < 0:
change = True
else:
change = False
result.append(change)
print result
```

For the direct interpretation of this question, where 0’s aren’t their own case, it’s probably easier to use `greater`

than `sign`

. Here’s an example:

```
a = array([1, 1, -1, -2, -3, 0, 4, 0, 5, 6])
x = greater_equal(a, 0)
sign_change = x[:-1]-x[1:]
```

Which gives, when printed with `T`

or `F`

to indicate the sign change between different numbers:

```
1 F 1 T -1 F -2 F -3 T 0 F 4 F 0 F 5 F 6
```

when printed using:

```
print `a[0]`+"".join([(" T" if sign_change[i] else " F")+" "+`a[i+1]` for i in range(len(sign_change))])
```

Also note that this is one element shorter than the original array, which makes sense since you’re asking for the change of sign. If you want to include the change between the last and first element, you can use `roll`

, as others have suggested.

```
(numpy.diff(numpy.sign(a)) != 0)*1
```

### Three methods to determine the location of sign change occurrences

```
import numpy as np
a = np.array([1,1,-1,-2,-3,4,5])
```

#### Method 1: Multiply adjacent items in array and find negative

```
idx1 = np.where(a[:-1] * a[1:] < 0 )[0] +1
idx1
Out[2]: array([2, 5], dtype=int64)
%timeit np.where(a[:-1] * a[1:] < 0 )[0] + 1
4.31 µs ± 15.1 ns per loop (mean ± std. dev. of 7 runs, 100000 loops each)
```

#### Method 2 (fastest): Where adjacent signs are not equal

```
idx2 = np.where(np.sign(a[:-1]) != np.sign(a[1:]))[0] + 1
idx2
Out[4]: array([2, 5], dtype=int64)
%timeit np.where(np.sign(a[:-1]) != np.sign(a[1:]))[0] + 1
3.94 µs ± 20.4 ns per loop (mean ± std. dev. of 7 runs, 100000 loops each)
```

#### Method 3: As proposed by ianalis. Most IMO elegant but a little slower

```
idx3 = np.where(np.diff(np.sign(a)) != 0)[0] + 1
idx3
Out[6]: array([2, 5], dtype=int64)
%timeit np.where(np.diff(np.sign(a)) != 0)[0] + 1
9.7 µs ± 36.2 ns per loop (mean ± std. dev. of 7 runs, 100000 loops each)
```

#### Edit:

For large arrays method 1 is the best.

Another idea on getting the ‘strict’ sign changes from positive to negative and negative to positive (excluding zeros):

```
a = np.array([0.4, 0.5, -0.2, -0.6, 5, 0, 0, 5, 0,-2])
# Get associated index
ind =np.arange(len(a))
# remove zero from array but keep original index
a2 =a[a!=0.]
ind2 =ind[a!=0.]
# Detect sign changes in reduced array
idx=np.where(np.diff(np.sign(a2)) != 0)[0] + 1
# Get sign changes index for original array
ind2[idx]
```

```
array([2, 4, 9])
```