Add memoization semantics to function handle
Memoization is an optimization technique used to speed up programs by caching the results of expensive function calls and returning the cached result when the program is called with the same inputs.
Consider memoizing a function call if all of the following are true:
Performance is important.
The function is time consuming.
The function has return values that are determined entirely by the input values, and has no side effects.
System memory is adequate to store unique input and output combinations.
memoizedFcn = memoize( adds
memoization semantics to the input function handle, and returns a
memoizedFcn as you would invoke
memoizedFcn is not a function handle.
MemoizedFunction object maintains the
cache of inputs and the corresponding outputs. When it is invoked, MATLAB® returns
the associated cached output values if the following conditions are
The input arguments are numerically equal to cached inputs. When comparing input values, MATLAB treats
NaNs as equal.
The number of requested output arguments matches the number of cached outputs associated with the inputs.
The memoization of a function is associated with the input function
and not with the
MemoizedFunction object. Therefore,
keep the following in mind.
Constructing a new
MemoizedFunctionobject to the same function creates another reference to the same data. Two variables that memoize the same function share a cache and object property values, such as cache size. In the following example, the variables
bshare a cache and have the same value for cache size.Similarly, clearing the cache for
a = memoize(@svd); b = memoize(@svd);
b.clearCache) also clears the cache for
a, and any other variables that memoize the
MemoizedFunctionobject to a new variable creates another reference to the same data. In the following example, the variables
c = memoize(@svd); d = c;
Clearing a variable does not clear the cache associated with the input function. To clear the cache for a
MemoizedFunctionobject that no longer exists in the workspace, create a new
MemoizedFunctionobject to the same function, and use the
clearCachefunction on the new object. Alternatively, you can clear caches for all
MemoizedFunctionobjects using the
MemoizedFunction object is not aware of
updates to the underlying function. If you modify the function associated
with the memoized function, clear the cache with the
clearCache object function.
Cache Results from MATLAB Built-in Function
To speed up performing a singular value decomposition when you could be operating on the same inputs multiple times, memoize the
fh = @svd; memoizedFcn = memoize(fh);
Create a matrix and cache the results of the singular value decomposition. Time the function call.
X = magic(1234); tic [U,S,V]= memoizedFcn(X); preCachedTime = toc
preCachedTime = 0.7954
Call the memoized function again using the same inputs. To observe the speed improvement using cached results, time the function call again.
tic [U,S,V]= memoizedFcn(X); postCachedTime = toc
postCachedTime = 0.0066
Cache Results from User-Defined Function
In your current working folder, create a file
computeNumberCombinations.m that contains the following function to compute the number of combinations of
n items taken
k at a time.
function c = computeNumberCombinations(n,k) % Calculate number of combinations of n items taken k at a time c = fact(n)/(fact(n-k)*fact(k)); end function f = fact(n) f = 1; for m = 2:n f = f*m; end end
Clear the cache for any
MemoizedFunction objects in your workspace.
computeNumberCombinations function to speed up computation for repeated input values.
fh = @computeNumberCombinations; memoizedFcn = memoize(fh);
Call the memoized function and time the function call. This function call caches the results for the specified inputs.
tic c = memoizedFcn(42e5,137); preCachedTime = toc
preCachedTime = 0.0343
Call the memoized function and time the function call again. This function call uses the cached results and does not execute the function.
tic c = memoizedFcn(42e5,137); postCachedTime = toc
postCachedTime = 0.0077
fh — Function to memoize
Function to memoize, specified as a function handle.
memoizedEigs = memoize(@eigs)
Multiple calls to
memoizewith the same function handle return the same
MemoizedFunctionobject. For example:
x = memoize(@plus); y = memoize(@plus); x == y
ans = logical 1
You should not memoize a function with side effects such as setting some global state or performing I/O operations. Side effects are not repeated on subsequent calls to the memoized function with the same inputs. For example, if you memoize the
randifunction, the memoized function always returns the same value when called with the same input argument.
fh = @randi; memoized_fh = memoize(fh); fh_result = [fh(100) fh(100) fh(100)] memoized_result = [memoized_fh(100) memoized_fh(100) memoized_fh(100)]
fh_result = 18 71 4 memoized_result = 28 28 28