I was working today and had to calculate the Hessian of a matrix, then I wondered a Hessian function might already exist. I typed Hessian and it does exist, but there's no documentation (neither online nor software embedded) that explains what the heck this function is. ?Hessian confirms the tag is protected and that it must do something. I'm curious now... Does anyone know what's going on?

P.S.: I'm using Mathematica 10.

P.S.2: I know how to calculate an Hessian.

  • $\begingroup$ Maybe it is a function that will be included in later versions (or has already been included in some 10.x version?). At the moment there is the name... $\endgroup$ – mattiav27 Aug 29 '16 at 19:12
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    $\begingroup$ No predefined function. Assuming your function f is a function of a vector (i.e., f[x1, x2, ..., xn] use D[f[x1, x2, ...,xn], {{x1, x2, ..., xn}, 2}]` $\endgroup$ – Jack LaVigne Aug 29 '16 at 19:17
  • $\begingroup$ Thanks, but defining a function for calculating an Hessian was never the problem. I was interested in the existence of a phantom function I found by accident =) $\endgroup$ – QuantumBrick Aug 29 '16 at 19:18
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    $\begingroup$ Apart for simply being a Protected symbol, PrintDefinitions (from GeneralUtilities package) shows no other definitions attached to it (not even <<kernel function>>). So it does nothing. $\endgroup$ – QuantumDot Aug 29 '16 at 19:52
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    $\begingroup$ Hessian (alternatively "Hessian") is an option name. Related: (91628), (98501), Newton's method tutorial, derivative tutorial $\endgroup$ – Michael E2 Aug 30 '16 at 12:30

The Mathematica documentation for FindMaxValue includes the example

FindMaxValue[Sin[x] Sin[2 y], {x, y}, 
 Gradient -> {Cos[x] Sin[2 y], 2 Cos[2 y] Sin[x]}, 
 Method -> {"Newton", 
   Hessian -> {{-Sin[x] Sin[2 y], 
      2 Cos[x] Cos[2 y]}, {2 Cos[x] Cos[2 y], -4 Sin[x] Sin[2 y]}}}]

which includes a reference to Hessian as part of the Method. I believe that this (and probably other similar usages) will cause it to appear as a symbol in the "System" context.


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