It means that the thing in question (usually running time) scales in a manner that is consistent with the logarithm of its input size. Big-O notation doesn’t mean an exact equation, but rather a bound. For instance, the output of the following functions is all O(n): Because as you increase x, their outputs all increase linearly – if there’s … Read more
Any function whose runtime has the form (log n)k is O((log n)k). This expression isn’t reducable to any other primitive function using simple transformations, and it’s fairly common to see algorithms with runtimes like O(n (log n)2). Functions with this growth rate are called polylogarithmic. By the way, typically (log n)k is written as logk n, so the above … Read more
O( log* N ) is “iterated logarithm“: In computer science, the iterated logarithm of n, written log* n (usually read “log star”), is the number of times the logarithm function must be iteratively applied before the result is less than or equal to 1.
It’s good to know that but also know that math.log takes an optional second argument which allows you to specify the base:
You can use the Axes.set_yscale method. That allows you to change the scale after the Axes object is created. That would also allow you to build a control to let the user pick the scale if you needed to. The relevant line to add is: You can use ‘linear’ to switch back to a linear scale. Here’s what your code would … Read more
np.log is ln, whereas np.log10 is your standard base 10 log. Relevant documentation: http://docs.scipy.org/doc/numpy/reference/generated/numpy.log.html http://docs.scipy.org/doc/numpy/reference/generated/numpy.log10.html