Using Map in a function definition

Question

I want to calculate the hessian of a matrix. So each element gets replaced by a 2 by 2 matrix.

hessian[im_, s_] := 
  {{gD[im, 2, 0, 2], gD[im, 1, 1, 2]}, {gD[im, 1, 1, 2], gD[im, 0, 2, 2]}};

Now im = My matrix.

I want to modify my hessian function in some way (using Map) such that when I calculate the hessian of im, 1 element at a time is calculated by gD. At this time gD works on the entire im matrix.

How do I do this? Any help (preferable code) will be very helpful. I am new to Mathematica, struggling, and very frustrated.

Answer 1

This might be what you're after (although some more details would indeed help):

hessian[im_] := Map[
  {
    {gD[#, 2, 0, 2], gD[#, 1, 1, 2]},
    {gD[#, 1, 1, 2], gD[#, 0, 2, 2]}
  } &,
  im,
  {2}
];

This is almost Karsten's suggestion, the difference being the third argument to Map, {2}. It tells Map to only map on elements at level 2 of the input expression. Here it is in action on a generic 2x2 matrix:

hessian[ Array[m, {2, 2}] ] // MatrixForm