How to make a matrix of derivatives?

Question

For example I can construct:

  row1 = D[f(x,y),x,#]&/@{x,y}
  row2 = D[f(x,y),x,#]&/@{x,y}

then:

matrix = {row1,row2}

That yields a matrix like:

$$\left(\matrix{\frac{\partial^2 f}{\partial x^2} \quad\frac{\partial^2 f}{\partial x\partial y}\\ \frac{\partial^2 f}{\partial y\partial x}\quad \frac{\partial^2f}{\partial y^2}}\right)$$

Question: how to construct such matrix in a single line of code?

Related: http://mathematica.stackexchange.com/questions/123403/compute-hessian-of-function-symbolically — Michael E2, Oct 16 '16 at 20:32

score 10 · Accepted Answer · answered Oct 16 '16 at 20:30

10

See D (search for Hessian):

D[f[x, y], {{x, y}, 2}]

Mathematica graphics

answered Oct 16 '16 at 20:30

Michael E2

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Ok that works, but when I do that I cannot perform matrix summation, Mathematica don't evaluate the operation (even if I use Evaluate). – rsaavedra Oct 16 '16 at 20:44
For example, for D[f[x, y], {{x, y}, 2}]+D[g[x, y], {{x, y}, 2}] – rsaavedra Oct 16 '16 at 20:44
Ok, I solved that, I was placing a //MatrixForm that was messing the evaluation, thank you for your helpful answer – rsaavedra Oct 16 '16 at 21:09
@Saavestro You can find out more about the MatrixForm problem here. -- And you're welcome! Thanks, – Michael E2 Oct 16 '16 at 21:19

score 3 · Answer 2 · answered Oct 16 '16 at 20:18

3

I think Tuples is the missing element for you:

TraditionalForm[
 Partition[D[f[x, y], Sequence @@ #] & /@ Tuples[{x, y}, 2], 2]
]

answered Oct 16 '16 at 20:18

Johu

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Outer is more elegant solution. – Johu Oct 16 '16 at 20:23

How to make a matrix of derivatives?

2 Answers2