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Re: addressing matrix elements

  • To: mathgroup at
  • Subject: [mg3580] Re: addressing matrix elements
  • From: rjfrey at (Robert J. Frey)
  • Date: Wed, 27 Mar 1996 03:25:22 -0500
  • Organization: Renaissance Technologies Corp.
  • Sender: owner-wri-mathgroup at

David Cabana (drc at wrote:
: More generally, I would like to be able to apply a function f to each
: element in a matrix of arbitrary size and dimensions, without worrying
: about the particulars of the matrix representation via lists.

This function is quite general:

	pervade[f_, a_] := If[ListQ[a], Map[pervade[f,#]&,

It applies the function f to the leaves of a.

For example, pervade[Length, {{1,2},3}] gives {{0,0},0} and
pervade[Range, {{1,2},3}] gives {{{1},{1,2}},{1,2,3}}. Write
out the input as a tree and apply the function in question to
the leaves to see why this is so.

Nested lists are essentially trees. As any good book on data
structures will tell you, recursive functions are a natural
way to traverse such objects.

I hope this is clear.
Robert (rjfrey at


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