You are using a np function, so I can safely guess that you are working on a numpy array?
Then the most efficient way to do this is to use the where function instead of a for loop
myarray= np.random.randint(10,size=10)
result = np.where(myarray>0, np.log(myarray), 0)
otherwise you can simply use the log function and then patch the hole:
myarray= np.random.randint(10,size=10)
result = np.log(myarray)
result[result==-np.inf]=0
The np.log function return correctly -inf when used on a value of 0, so are you sure that you want to return a 0? if somewhere you have to revert to the original value, you are going to experience some problem, changing zeros into ones...
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