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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.
801
If you are using List as an array, you can use its append(), insert(), and extend() functions. You can read more about it at Python add to List. If you are using array module, you can use the concatenation using the + operator, append(), insert(), and extend() functions to add elements to the array.
Map a Function in NumPy With the numpy. vectorize() function maps functions on data structures that contain a sequence of objects like arrays in Python. It successively applies the input function on each element of the sequence or array.
To create you own ufunc, you have to define a function, like you do with normal functions in Python, then you add it to your NumPy ufunc library with the frompyfunc() method. The frompyfunc() method takes the following arguments: function - the name of the function. inputs - the number of input arguments (arrays).
In numpy, += is implemented to do in memory changes, while + returns a new array.
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 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 If you love us? You can donate to us via Paypal or buy me a coffee so we can maintain and grow! Thank you!
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