Matlab function handle workspace shenanigans

Question

In short: is there an elegant way to restrict the scope of anonymous functions, or is Matlab broken in this example?

I have a function that creates a function handle to be used in a pipe network solver. It takes as input a Network state which includes information about the pipes and their connections (or edges and vertices if you must), constructs a large string which will return a large matrix when in function form and "evals" that string to create the handle.

function [Jv,...] = getPipeEquations(Network)
... %// some stuff happens here

Jv_str = ['[listConnected(~endNodes,:)',...
    ' .* areaPipes(~endNodes,:);\n',...
    anotherLongString,']'];

Jv_str = sprintf(Jv_str); %// This makes debugging the string easier

eval(['Jv = @(v,f,rho)', Jv_str, ';']);

This function works as intended, but whenever I need to save later data structures that contain this function handle, it requires a ridiculous amount of memory (150MB) - coincidentally about as much as the entire Matlab workspace at the time of this function's creation (~150MB). The variables that this function handle requires from the getPipeEquations workspace are not particularly large, but what's even crazier is that when I examine the function handle:

>> f = functions(Network.jacobianFun)
f = 

     function: [1x8323 char]
         type: 'anonymous'
         file: '...\pkg\+adv\+pipe\getPipeEquations.m'
    workspace: {2x1 cell}

...the workspace field contains everything that getPipeEquations had (which, incidentally is not the entire Matlab workspace).

If I instead move the eval statement to a sub-function in an attempt to force the scope, the handle will save much more compactly (~1MB):

function Jv = getJacobianHandle(Jv_str,listConnected,areaPipes,endNodes,D,L,g,dz)
eval(['Jv = @(v,f,rho)', Jv_str, ';']);

Is this expected behavior? Is there a more elegant way to restrict the scope of this anonymous function?

As an addendum, when I run the simulation that includes this function several times, clearing workspaces becomes painfully slow, which may or may not be related to Matlab's handling of the function and its workspace.

Answer 1

I can reproduce: anonymous functions for me are capturing copies of all variables in the enclosing workspace, not just those referenced in the expression of the anonymous function.

Here's a minimal repro.

function fcn = so_many_variables()
a = 1;
b = 2;
c = 3;
fcn = @(x) a+x;
a = 42;

And indeed, it captures a copy of the whole enclosing workspace.

>> f = so_many_variables;
>> f_info = functions(f);
>> f_info.workspace{1}
ans = 
    a: 1
>> f_info.workspace{2}
ans = 
    fcn: @(x)a+x
      a: 1
      b: 2
      c: 3

This was a surprise to me at first. But it makes sense when you think about it: because of the presence of feval and eval, Matlab can't actually know at construction time what variables the anonymous function is actually going to end up referencing. So it has to capture everything in scope just in case they get referenced dynamically, like in this contrived example. This uses the value of foo but Matlab won't know that until you invoke the returned function handle.

function fcn = so_many_variables()
a = 1;
b = 2;
foo = 42;
fcn = @(x) x + eval(['f' 'oo']);

The workaround you're doing - isolating the function construction in a separate function with a minimal workspace - sounds like the right fix.

Here's a generalized way to get that restricted workspace to build your anonymous function in.

function eval_with_vars_out = eval_with_vars(eval_with_vars_expr, varargin)

% Assign variables to the local workspace so they can be captured
ewvo__reserved_names = {'varargin','eval_with_vars_out','eval_with_vars_expr','ewvo__reserved_names','ewvo_i'};
for ewvo_i = 2:nargin
    if ismember(inputname(ewvo_i), ewvo__reserved_names)
        error('variable name collision: %s', inputname(ewvo_i));
    end
    eval([ inputname(ewvo_i) ' = varargin{ewvo_i-1};']);
end
clear ewvo_i ewvo__reserved_names varargin;

% And eval the expression in that context
eval_with_vars_out = eval(eval_with_vars_expr);

The long variable names here hurt readability, but reduce the likelihood of collision with the caller's variables.

You just call eval_with_vars() instead of eval(), and pass in all the input variables as additional arguments. Then you don't have to type up a static function definition for each of your anonymous function builders. This'll work as long as you know up front what variables are actually going to be referenced, which is the same limitation as the approach with getJacobianHandle.

Jv = eval_with_vars_out(['@(v,f,rho) ' Jv_str],listConnected,areaPipes,endNodes,D,L,g,dz);

Answer 2

Anonymous functions capture everything within their scope and store them in the function workspace. See MATLAB documentation for anonymous functions

In particular:

"Variables specified in the body of the expression. MATLAB captures these variables and holds them constant throughout the lifetime of the function handle.

The latter variables must have a value assigned to them at the time you construct an anonymous function that uses them. Upon construction, MATLAB captures the current value for each variable specified in the body of that function. The function will continue to associate this value with the variable even if the value should change in the workspace or go out of scope."