Given a simple Gaussian kernel

UnscaledKernel[a_, b_, sigma_] := 
 Exp[-(((a - b)/sigma).((a - b)/sigma))/2]

and un-normalized smoothing function

Smooth[valCountLst_, val_, sigma_] := 
    UnscaledKernel[{valCountLst[[i]][[1]]}, {val}, sigma], {i, 1, 

and a normalization constant so that the integral on the defined domain is 1:

ScalingFactor[valCountLst_, sigma_, lower_, upper_] := 
  Smooth[valCountLst, everyVal, sigma], {everyVal, lower, upper}]

From this unsmoothed data (that is, 1000 items at value 0 and 10 items at value 1):

testList = {{0, 1000}, {1, 10}};

I'm plotting smoothed (un-normalized) data takes 0.024 seconds:

Plot[N[Log[Smooth[testList, x, 0.2]]], {x, 0, 1.0}] // Timing

(output is {0.024, THEFIGURE}).

When plotting the smoothed, normalized data, it takes much longer, 13.09 seconds:

    Smooth[testList, x, 0.2]/ScalingFactor[testList, 0.2]]], {x, 0, 
   1.0}] // Timing

This seems strange since the scaling factor takes only 0.044 seconds to compute.

My conclusion is that Mathematica is computing the scaling factor for every point, even though it does not depend on the point value x.

Is there a way to help Mathematica compute this expression once and factor it out (or memoize it)?

Thanks a lot.


2 Answers 2


You could also use the Evaluated -> True undocumented option:

Plot[N[Log[Smooth[testList, x, 0.2]/ScalingFactor[testList, 0.2]]], 
      {x, 0, 1.0}, Evaluated -> True] 

Please note that I had modified your definition of ScalingFactor to

ScalingFactor[valCountLst_, sigma_] := Integrate[ Smooth[valCountLst, x, sigma], {x, 0, 1}]

because you're calling it with the wrong number of parameters in your question


Is there a way to help Mathematica compute this expression once and factor it out (or memoize it)?

I'd use With[], like so:

With[{sc = ScalingFactor[testList, 0.2]},
     Plot[Log[Smooth[testList, x, 0.2]/sc], {x, 0, 1}]

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.