# utilities

## animation

 gif_from_images Create an animated GIF from a series of images.

## async

 await_callback Wait for the completion of an asynchronous code that uses callbacks to signal completion.

## decorators

 memoize Decorator to wrap a function with a memoizing callable.

## functions

 fibonacci binomial_coefficient Returns the binomial coefficient of the $$x^k$$ term in the polynomial expansion of the binomial power $$(1 + x)^n$$ [wikipedia2017j].

## itertools

 take Return first n items of the iterable as a list tabulate Return function(0), function(1), … tail Return an iterator over the last n items consume Advance the iterator n-steps ahead. nth Returns the nth item or a default value all_equal Returns True if all the elements are equal to each other quantify Count how many times the predicate is true padnone Returns the sequence elements and then returns None indefinitely. ncycles Returns the sequence elements n times dotproduct flatten Flatten one level of nesting repeatfunc Repeat calls to func with specified arguments. pairwise s -> (s0,s1), (s1,s2), (s2, s3), … window Returns a sliding window (of width n) over data from the iterable. roundrobin roundrobin(‘ABC’, ‘D’, ‘EF’) –> A D E B F C powerset unique_justseen List unique elements, preserving order. iter_except Call a function repeatedly until an exception is raised. first_true Returns the first true value in the iterable. random_permutation Random selection from itertools.permutations(iterable, r) random_combination Random selection from itertools.combinations(iterable, r) random_combination_with_replacement Random selection from itertools.combinations_with_replacement(iterable, r)

## maps

 geometric_key Convert XYZ coordinates to a string that can be used as a dict key. reverse_geometric_key Reverse a geometric key string into xyz coordinates. geometric_key2 Convert XY coordinates to a string that can be used as a dict key. normalize_values Normalize a list of numbers to the range between new_min and new_max.

## profiling

 print_profile Decorate a function with automatic profile printing.

## statistics

 average Average of a list. variance Variance of a list. standard_deviation Standard deviation of a list.

## xfunc

 XFunc Wrapper for functions that turns them into externally run processes.