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Can EvaluationMonitor Give FiniteDifference Gradients in FindMinimum?

Frank Kampas

Frank Kampas, Physicist at Large Consulting

Posted 11 years ago

I'd like to use EvaluationMonitor to see what values for the gradients FindMinimum is calculating when I set Gradient :> {"FiniteDifference", "DifferenceOrder" -> 1} as that seems to work better than gradients I calculate symbolically.

POSTED BY: Frank Kampas

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Frank Kampas

Frank Kampas, Physicist at Large Consulting

Posted 11 years ago

?Experimental`CreateNumericalFunction Experimental`CreateNumericalFunction Attributes[Experimental`CreateNumericalFunction]={Protected} Options[Experimental`CreateNumericalFunction]={Compiled->Automatic,ErrorReturn->Automatic,Evaluated->Automatic,EvaluationMonitor->None,Gradient->Automatic,Hessian->Automatic,Jacobian->Automatic,Message->Automatic,SampleArgument->False,StepMonitor->None,WorkingPrecision->MachinePrecision} Based on an error message about a dimension list, I was able to calculate a Jacobian, as follows: In[39]:= nf2 = Experimental`CreateNumericalFunction[{x, y}, {x^2 + 2 y^4, x*y}, {2}]; In[40]:= nf2["Jacobian"[{1, 2}]] Out[40]= {{2., 64.}, {2., 1.}} Am I correct in assuming that the third argument is the dimensions of the function?

?Experimental`CreateNumericalFunction

Experimental`CreateNumericalFunction

Attributes[Experimental`CreateNumericalFunction]={Protected}

Options[Experimental`CreateNumericalFunction]={Compiled->Automatic,ErrorReturn->Automatic,Evaluated->Automatic,EvaluationMonitor->None,Gradient->Automatic,Hessian->Automatic,Jacobian->Automatic,Message->Automatic,SampleArgument->False,StepMonitor->None,WorkingPrecision->MachinePrecision}

Based on an error message about a dimension list, I was able to calculate a Jacobian, as follows:

In[39]:= nf2 = 
  Experimental`CreateNumericalFunction[{x, y}, {x^2 + 2 y^4, 
    x*y}, {2}];

In[40]:= nf2["Jacobian"[{1, 2}]]

Out[40]= {{2., 64.}, {2., 1.}}

Am I correct in assuming that the third argument is the dimensions of the function?

POSTED BY: Frank Kampas

Ilian Gachevski

Ilian Gachevski, Wolfram Research

Posted 11 years ago

Sure, for example `nf @ "Hessian"[{1, 1}]`

POSTED BY: Ilian Gachevski

Frank Kampas

Frank Kampas, Physicist at Large Consulting

Posted 11 years ago

Thanks. That looks like a useful technique. Can a Hessian be calculated numerically in a similar fashion?

POSTED BY: Frank Kampas

Ilian Gachevski

Ilian Gachevski, Wolfram Research

Posted 11 years ago

In FindMinimum, it's possible to use Gradient -> {"FiniteDifference", "DifferenceOrder" -> 1, EvaluationMonitor :> Sow[{x, y}]} to find out where the gradient is being evaluated and then compute the gradient at each of these points, for example In[4]:= nf = Experimental`CreateNumericalFunction[{x, y}, x^2 + 2 y^4, {}, Gradient -> {"FiniteDifference", "DifferenceOrder" -> 1}]; nf["Gradient"[{1, 1}]] Out[4]= {2., 8.}

In FindMinimum, it's possible to use

 Gradient -> {"FiniteDifference", "DifferenceOrder" -> 1, EvaluationMonitor :> Sow[{x, y}]}

to find out where the gradient is being evaluated and then compute the gradient at each of these points, for example

In[4]:= nf = Experimental`CreateNumericalFunction[{x, y}, x^2 + 2 y^4, {}, 
               Gradient -> {"FiniteDifference", "DifferenceOrder" -> 1}];
        nf["Gradient"[{1, 1}]]

Out[4]= {2., 8.}

POSTED BY: Ilian Gachevski

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