I've the following numpy ndarray.
[ -0.54761371 17.04850603 4.86054302]
I want to apply this function to all elements of the array
def sigmoid(x):
return 1 / (1 + math.exp(-x))
probabilities = np.apply_along_axis(sigmoid, -1, scores)
This is the error that I get.
TypeError: only length-1 arrays can be converted to Python scalars
What am I doing wrong.
Function numpy.apply_along_axis is not good for this purpose.
Try to use numpy.vectorize to vectorize your function: https://docs.scipy.org/doc/numpy/reference/generated/numpy.vectorize.html
This function defines a vectorized function which takes a nested sequence of objects or numpy arrays as inputs and returns an single or tuple of numpy array as output.
import numpy as np
import math
# custom function
def sigmoid(x):
return 1 / (1 + math.exp(-x))
# define vectorized sigmoid
sigmoid_v = np.vectorize(sigmoid)
# test
scores = np.array([ -0.54761371, 17.04850603, 4.86054302])
print sigmoid_v(scores)
Output: [ 0.36641822 0.99999996 0.99231327]
Performance test which shows that the scipy.special.expit is the best solution to calculate logistic function and vectorized variant comes to the worst:
import numpy as np
import math
import timeit
def sigmoid_(x):
return 1 / (1 + math.exp(-x))
sigmoidv = np.vectorize(sigmoid_)
def sigmoid(x):
return 1 / (1 + np.exp(x))
print timeit.timeit("sigmoidv(scores)", "from __main__ import sigmoidv, np; scores = np.random.randn(100)", number=25),\
timeit.timeit("sigmoid(scores)", "from __main__ import sigmoid, np; scores = np.random.randn(100)", number=25),\
timeit.timeit("expit(scores)", "from scipy.special import expit; import numpy as np; scores = np.random.randn(100)", number=25)
print timeit.timeit("sigmoidv(scores)", "from __main__ import sigmoidv, np; scores = np.random.randn(1000)", number=25),\
timeit.timeit("sigmoid(scores)", "from __main__ import sigmoid, np; scores = np.random.randn(1000)", number=25),\
timeit.timeit("expit(scores)", "from scipy.special import expit; import numpy as np; scores = np.random.randn(1000)", number=25)
print timeit.timeit("sigmoidv(scores)", "from __main__ import sigmoidv, np; scores = np.random.randn(10000)", number=25),\
timeit.timeit("sigmoid(scores)", "from __main__ import sigmoid, np; scores = np.random.randn(10000)", number=25),\
timeit.timeit("expit(scores)", "from scipy.special import expit; import numpy as np; scores = np.random.randn(10000)", number=25)
Results:
size vectorized numpy expit
N=100: 0.00179314613342 0.000460863113403 0.000132083892822
N=1000: 0.0122890472412 0.00084114074707 0.000464916229248
N=10000: 0.109477043152 0.00530695915222 0.00424313545227
scipy.special.expit, that will certainly be faster!Use np.exp and that will work on numpy arrays in a vectorized fashion:
>>> def sigmoid(x):
... return 1 / (1 + np.exp(-x))
...
>>> sigmoid(scores)
array([ 6.33581776e-01, 3.94391811e-08, 7.68673281e-03])
>>>
You will likely not get any faster than this. Consider:
>>> def sigmoid(x):
... return 1 / (1 + np.exp(-x))
...
And:
>>> def sigmoidv(x):
... return 1 / (1 + math.exp(-x))
...
>>> vsigmoid = np.vectorize(sigmoidv)
Now, to compare the timings. With a small (size 100) array:
>>> t = timeit.timeit("vsigmoid(arr)", "from __main__ import vsigmoid, np; arr = np.random.randn(100)", number=100)
>>> t
0.006894525984534994
>>> t = timeit.timeit("sigmoid(arr)", "from __main__ import sigmoid, np; arr = np.random.randn(100)", number=100)
>>> t
0.0007238480029627681
So, still an order-of-magnitude difference with small arrays. This performance differences stays relatively constant, with a 10,000 size array:
>>> t = timeit.timeit("vsigmoid(arr)", "from __main__ import vsigmoid, np; arr = np.random.randn(10000)", number=100)
>>> t
0.3823414359940216
>>> t = timeit.timeit("sigmoid(arr)", "from __main__ import sigmoid, np; arr = np.random.randn(10000)", number=100)
>>> t
0.011259705002885312
And finally with a size 100,000 array:
>>> t = timeit.timeit("vsigmoid(arr)", "from __main__ import vsigmoid, np; arr = np.random.randn(100000)", number=100)
>>> t
3.7680041620042175
>>> t = timeit.timeit("sigmoid(arr)", "from __main__ import sigmoid, np; arr = np.random.randn(100000)", number=100)
>>> t
0.09544878199812956
Just to clarify what apply_along_axis is doing, or not doing.
def sigmoid(x):
print(x) # show the argument
return 1 / (1 + math.exp(-x))
In [313]: np.apply_along_axis(sigmoid, -1,np.array([ -0.54761371 ,17.04850603 ,4.86054302]))
[ -0.54761371 17.04850603 4.86054302] # the whole array
...
TypeError: only length-1 arrays can be converted to Python scalars
The reason you get the error is that apply_along_axis passes a whole 1d array to your function. I.e. the axis. For your 1d array this is the same as
sigmoid(np.array([ -0.54761371 ,17.04850603 ,4.86054302]))
The apply_along_axis does nothing for you.
As others noted,switching to np.exp allows sigmoid to work with the array (with or without the apply_along_axis wrapper).
scipy already implements the function Luckily, Python allows us to rename things upon import:
from scipy.special import expit as sigmoid
math.expwithnp.expwill solve the issue