Why does fplot think my function is not vectorized

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Matt J 2019-5-30

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https://ww2.mathworks.cn/matlabcentral/answers/464826-why-does-fplot-think-my-function-is-not-vectorized

编辑： Matt J 2019-6-25

采纳的回答： Walter Roberson

在 MATLAB Online 中打开

Executing the following as a script in R2018a

a=ones(1,10);
b=a;
b0=1;
fun=@(x) myFourier(x,a,b,b0);
fplot(fun);
function f=myFourier(x,a,b,b0)
   n=numel(a);
   arg=x(:).*(1:n);
   
   f=b0+sin(arg)*a(:)+cos(arg)*b(:);
   f=reshape(f,size(x));
   
end

results successfully in a plot, but throws warnings (EDIT: and results in non-vectorized execution!!!)

Warning: Function behaves unexpectedly on array inputs. To improve performance, properly vectorize your
function to return an output with the same size and shape as the input arguments. 
> In matlab.graphics.function.FunctionLine>getFunction
  In matlab.graphics.function.FunctionLine/updateFunction
  In matlab.graphics.function.FunctionLine/set.Function_I
  In matlab.graphics.function.FunctionLine/set.Function
  In matlab.graphics.function.FunctionLine
  In fplot>singleFplot (line 234)
  In fplot>@(f)singleFplot(cax,{f},limits,extraOpts,args) (line 193)
  In fplot>vectorizeFplot (line 193)
  In fplot (line 163)
  In test (line 7) 

But the input function is properly vectorized as is easily verified in simple tests,

 >> fun(rand(1,5))
  
  
 ans =
    3.4371    2.5677   14.1698    2.4490    1.0828
    
  
 >> fun(rand(5,1))
 
 ans =
   14.1745
    8.3619
   -0.2579
    1.7024
    1.5748

Why the warnings, then?

采纳的回答

Walter Roberson 2019-5-31

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https://ww2.mathworks.cn/matlabcentral/answers/464826-why-does-fplot-think-my-function-is-not-vectorized#answer_377297

在 MATLAB Online 中打开

f1 = fun(1);
f2 = fun([1 2]);
f1 - f2(1)
ans =
      4.44089209850063e-16
      

Your code produces different outputs for the same input, which violates the rule that the calculations must be independent.

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Walter Roberson 2019-6-1

在 MATLAB Online 中打开

fplot(@(x) x .* (1 + (length(x)>1)*eps))

generates the warning, so regardless of whether it "should", it does check for equality.

Matt J 2019-6-5

编辑：Matt J 2019-6-5

Tech support got back to me and confirmed Walter's explanation of the problem, and said they will look into remedies for future releases. I passed on to them my suggestions for fixes as well.

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dpb 2019-5-31

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Because fplot is just looking at the source code, not the output and it doesn't recognize the reshape operation at the end--only that there are no "dot" operators in the evaluation from which it infers (usually correctly, but as you've shown not infallibly) that the function isn't "vectorized".

Whether there's any chance of being able to get this one right without way more parsing logic than would want to use for performance is, I'm guessing, pretty small. You can't just presume that if the user has a reshape call in the function that always works correctly, either.

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Matt J 2019-6-2

编辑：Matt J 2019-6-2

Worse than that, because fplot incorrectly judges the function to be nonvectorized, it forms the plot by executing the function in non-vectorized fashion forcing the user to endure slow behavior. I think they should let fplot() operate like integral() already does. Let the user specify whether execution will be vectorized or not, and take responsibility for the result.

dpb 2019-6-2

This could well be the basis for an enhancement/quality of implemenation improvement request.

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Catalytic 2019-6-7

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Here's a workaround to trick fplot into doing the right thing.

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Yair Altman 2019-6-22

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https://ww2.mathworks.cn/matlabcentral/answers/464826-why-does-fplot-think-my-function-is-not-vectorized#answer_380374

在 MATLAB Online 中打开

As far as I can tell (never mind exactly how), internally a check is made whether the output of fun(1:3) is exactly equaln to the output of [fun(1),fun(2),fun(3)]. Even a tiny FP eps difference will cause the warning to be evoked. If you want to disable the error in run-time, run the following command:

warning off MATLAB:fplot:NotVectorized

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Matt J 2019-6-25

编辑：Matt J 2019-6-25

Thanks, Yair. But disabling the warning still leaves the bigger problem of execution efficiency. fplot will still go ahead and evaluate fun in non-vectorized (therefore slow) fashion based on the fun(1:3) test, even with the warning disabled.

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