What is memoization?
Memoization is a way to optimize code by storing the return values of functions called with a specific set of arguments. Memoization is a specific type of caching.
When (not) to memoize?
Memoization is only valid for functions that are referentially transparent: functions that always return the same result for the same set of arguments, and that do not affect the state of the program.
Therefore, you should not memoize a function that returns random numbers, because it will end up returning the same set of random numbers over and over again. And you should also not memoize a function that depends on the state of the program, for example because it relies on the command-line arguments that were passed to a script.
But you could memoize a function that performs some time consuming operation that is always done in exactly the same way, such as a function that performs time-consuming operations on a large dataset.
Memoization is done with the
memoize decorator, which is part of
datamatrix.functional. Let's take a time-consuming function that determines the highest prime number below a certain value, and measure the performance improvement that memoization gives us when we call the function twice with same argument.
import time from itertools import dropwhile from datamatrix import functional as fnc @fnc.memoize def prime_below(x): """Returns the highest prime that is lower than X.""" print('Calculating the highest prime number below %d' % x) return next( dropwhile( lambda x: any(not x % i for i in range(x-1, 2, -1)), range(x-1, 0, -1) ) ) t0 = time.time() prime_below(10000) t1 = time.time() prime_below(10000) t2 = time.time() print('Fresh: %.2f ms' % (1000*(t1-t0))) print('Memoized: %.2f ms' % (1000*(t2-t1)))
Calculating the highest prime number below 10000 Fresh: 19.29 ms Memoized: 0.08 ms
Chaining memoized functions and lazy evaluation
When you call a function, Python automatically evaluates the function arguments. This happens even if a function has been memoized. In some cases, this is undesirable because evaluating the arguments may be time-consuming in itself, for example because one of the arguments is a call to another time-consuming function.
Ideally, evaluation of the arguments occurs only when the memoized function actually needs to be executed. To approximate this behavior in Python, the
memoize decorator accepts the
lazy keyword. When
lazy=True is specified, all callable objects that are passed to the memoized function are evaluated automatically, but only when the memoized function is actually executed.
@fnc.memoize(lazy=True) def prime_below(x): print('Calculating the highest prime number below %d' % x) return next( dropwhile( lambda x: any(not x % i for i in range(x-1, 2, -1)), range(x-1, 0, -1) ) ) def thousand(): print('Returning a thousand!') return 1000 print(prime_below(thousand)) print(prime_below(thousand))
Returning a thousand! Calculating the highest prime number below 1000 997 997
A slightly more complicated situation arises when you want to pass arguments to a function that is itself passed as argument, without evaluating the function. To accomplish this, you can first bind the argument to the function using
functools.partial and then pass the resulting partial function as an argument. Like so:
from functools import partial print(prime_below(partial(prime_below, 1000))) print(prime_below(partial(prime_below, 1000)))
Calculating the highest prime number below 1000 Calculating the highest prime number below 997 991 991
You can also implement this behavior with the
>> operator, in which the resulting of one function call is fed into the next function call, etc. The result is a
chain object that needs to be explicitly called. The
>> only works
with lazy memoization.
chain = 1000 >> prime_below >> prime_below print(chain()) print(chain())
Persistent memoization, memoization keys, and cache clearing
If you pass
persistent=True to the
memoize decorator, the cache will be written to disk, by default to a subfolder
.memoize of the current working directory. The filename will correspond to the memoization key, which by default is derived from the function name and the arguments.
If you want to change the cache folder, you can either pass a
folder keyword to the
memoize decorator, or change the
memoize.folder class property before applying the
memoize decorator to any functions.
You can also specify a custom memoization key through the
key keyword. If you specify a custom key,
memoize will no longer distinguish between different arguments (and thus no longer be real
To re-execute a memoized function, you can clear the memoization cache by calling the
.clear() method on the memoized function, as shown below. If memoization is persistent, this will clear all files in the cache folder. Otherwise, this will only clear the in-memory cache.
@fnc.memoize(persistent=True, key='custom-key') def prime_below(x): print('Calculating the highest prime number below %d' % x) return next( dropwhile( lambda x: any(not x % i for i in range(x-1, 2, -1)), range(x-1, 0, -1) ) ) print(prime_below(1000)) print(prime_below(1000)) prime_below.clear() # Clear the cache print(prime_below(1000))
Calculating the highest prime number below 1000 997 997 Calculating the highest prime number below 1000 997
Memoization only works for functions with:
- Arguments and keywords that:
- Can be serialized by
json_tricks, which includes simple data types, DataMatrix objects, and numpy array; or
- Are callable, which includes regular functions,
- Can be serialized by
- Return values that can be pickled.