Is it possible to change an anonymous function keeping the workspace? - matlab

Question

What I would like to be able to do is programmatically change an anonymous function for example by changing all the plus signs to multiplication signs in the function. This example can in many cases this can be done as follows:
function f2 = changefunction(f1)
fs = func2str(f1);
fs(fs=='+') = '*';
f2 = str2func(fs);
end
But consider the example
f = #(x) x+5;
a = 5;
g = #(x) x+a;
Both f and g will be anonymous functions that adds 5 to whatever you plug into it; however only f will be changed correctly by the changefunction function, whereas g will be changed into a function that will err on any input.
So my question is is it possible to extract the workspace from the function handle and retain it in the new function handle created? I need to do it programmatically and preferably without using the built-in function functions!

Answer 1

One naive implementation is to replace str2func with eval so you are not running into str2func's roadblock of not allowing access to local variables. We can use functions to obtain the workspace information for the input function handle.
For example:
a = 5;
f = #(x) x+a;
finfo = functions(f)
Yields:
finfo =
struct with fields:
function: '#(x)x+a'
type: 'anonymous'
file: 'X:\testcode-matlab\testcode.m'
workspace: {[1×1 struct]}
within_file_path: 'testcode'
Where workspace is a cell array containing a structure (come on MathWorks...) containing all of the variables in your function handle's namespace:
>> wspace = finfo.workspace{1}
wspace =
struct with fields:
a: 5
Using this functionality, the naive solution is to loop through the variables in this workspace, assign them in the namespace of changefunction, then use eval to generate the new function handle.
For example:
function f2 = changefunction_new(f1)
tmp = functions(f1);
workspacevars = tmp.workspace{1};
varnames = fieldnames(workspacevars);
for ii = 1:length(varnames)
evalstr = sprintf('%s = %d;', varnames{ii}, workspacevars.(varnames{ii}));
eval(evalstr);
end
fs = func2str(f1);
fs(fs=='+') = '*';
f2 = eval(fs);
end
Here I'm assuming that the variables are going to be strictly numeric. You can add logic to check the class of the data to be generated if this is not always the case.
With this we have:
a = 5;
g = #(x) x+a;
test1 = changefunction(g);
test2 = changefunction_new(g);
>> g(1)
ans =
6
>> test1(1)
Undefined function or variable 'a'.
Error in testcode>#(x)x*a
>> test2(1)
ans =
5
All that being said, the best solution really is to just explicitly define your function handles. It may be a pain but it's much easier to understand and debug.
A few caveats:
Because eval arbitrarily executes all code passed to it, it can be a very dangerous function that must be used with care.
The documentation for functions warns against using it programmatically, so take care to check behavior as MATLAB versions change:
Use the functions function for querying and debugging purposes only.
Note: Do not use functions programmatically because its behavior could change in subsequent MATLAB® releases.

Answer 2

One possible way to do this is to save the function handle to a .mat file (using the -v7.3 flag so that it creates an easily-modifiable HDF5 file), modify the struct within the file that contains the workspace data for the anonymous function (using the HDF5 tools built into MATLAB), and then load the anonymous function again from the file.
Here is a little function which does exactly that (and it works for relatively simple variable types)
function result = modifyfunc(f, varname, value)
% modifyfunc - Modify the workspace of an anonymous function
%
% INPUTS:
% f: Function Handle, Anonymous function to modify
% varname: String, Name of the variable to modify
% value: Data to replace the specified variable
% If the value is a struct, recursively modify the function handle
if isstruct(value)
fields = fieldnames(value);
result = f;
% Modify each field separately
for k = 1:numel(fields)
% Append the fieldname to the variable name and modify
name = [varname, '.', fields{k}];
result = modifyfunc(result, name, value.(fields{k}));
end
return;
end
% Write the anonymous function to an HDF5 file
fname = tempname;
save(fname, 'f', '-mat', '-v7.3');
% Replace any "." in the variable name with "/" to construct the HDF5 path
varname = strrep(varname, '.' , '/');
% Now modify the data in the file
h5write(fname, ['/#refs#/e/' varname], value);
% Load the modified function handle from the file
result = load(fname, '-mat');
result = result.f;
% Remove the temporary file
delete(fname);
end
And you can use it like:
a = 1;
b = struct('field', 2);
f = #(x)disp(a + b.field + x);
f(10)
% 13
f2 = modifyfunc(f, 'a', 2);
f2(10)
% 14
f3 = modifyfunc(f2, 'b.field', 3);
f3(10)
% 15
b.field = 4;
f4 = modifyfunc(f3, 'b', b);
f4(10)
% 16
Some caveats include:
The replacement data must be the same size as the original data
This relies upon the format of the .mat file which for anonymous functions is completely undocumented so it could fail in future releases.
This currently doesn't work for variables in the function workspace that are cell arrays.