Convert cell array of character vectors to evaluable expressions

I have a cell array of character vectors:

>> list
list =
  5×1 cell array
    {'10^{-4}'}
    {'10^{-3}'}
    {'10^{-2}'}
    {'10^{-1}'}
    {'10^{0}' }

I want to convert these vectors into the numbers they represent. I tried to use str2num, but it doesn't work with arrays or cell arrays. Using str2double, I get a cell array of NaNs because the character vectors are not only numbers, but rather expressions to evaluate. So I tried to use eval. This is my first attempt:

>> eval(list)
Error using eval
Must be a string scalar or character vector.

So I thought using cellfun would do the job because eval would be fed only one vector at a time, but instead I get this:

>> cellfun(eval, list)
Error using eval
Not enough input arguments.

After further tests, it seems like eval doesn't work with cellfun or arrayfun, which doesn't make sense to me. Is there any way to convert my expressions into numbers?

[Stephen23]

You have avoided mentioning the elephant in the room: none of the character vectors use valid MATLAB syntax, so none of your methods would ever work until you do something with those vectors to convert them into valid MATLAB syntax. Even better would be to avoid eval and friends and just parse the values yourself.

Answer 1

[Stephen23]

This is pretty easy with standard string parsing tools, e.g. sscanf:

>> C = {'10^{-4}';'10^{-3}';'10^{-2}';'10^{-1}';'10^{0}'};
>> V = sscanf([C{:}],'%d^{%d}');
>> Z = V(1:2:end).^V(2:2:end)
Z =
   0.00010000
   0.00100000
   0.01000000
   0.10000000
   1.00000000

You will find that this is quite fast too (1e4 iterations):

Elapsed time is 0.281599 seconds. % my answer
Elapsed time is 6.407189 seconds. % Fangjun Jiang's answer.

Also, because it does not use eval in any way (e.g. str2num), it is secure and does not impede MATLAB's JIT engine.

Answer 2

[Fangjun Jiang]

NewList=strrep(list,'{','(');
NewList=strrep(NewList,'}',')');
cellfun(@str2num,NewList)

[Stephen23]

Note that str2num calls eval, with all of its inherent disadvantages: slow, security risk, etc.

[Alec Poulin]

Can you talk a bit about these disadvantages?

[Stephen23]

"Can you talk a bit about these disadvantages"

Sure. The main disadvantages of eval (slow, security risk, etc) are covered here:

https://www.mathworks.com/matlabcentral/answers/304528-tutorial-why-variables-should-not-be-named-dynamically-eval