I have a list of 2 by 2 matrices and I want the list of their traces. I have been using
Map[Tr,mylistofmatrices] But I wonder if there is a way to make Tr Listable so I can just call
Tr[mylistofmatrices] $\begingroup$ $\endgroup$
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- $\begingroup$ Related: (6588), (15749), (26686) (in my interpretation of this question) $\endgroup$Mr.Wizard– Mr.Wizard2015-05-21 16:04:49 +00:00Commented May 21, 2015 at 16:04
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2 Answers
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0 No, there isn't. There are several reasons for that:
Troperates on tensors of arbitrary rank, not just matricesListablefunctions will automatically thread to the deepest level of lists, so if you setTrto beListable, it'll individually wrap each deepest element of a nested list, e.g.Tr[{{1,2},{3,4}}]would transform to{{Tr[1], Tr[2]}, {Tr[3], Tr[4]}}.
Just use Map, which is unambiguous and takes just one extra character to type ... Tr /@ list vs Tr @ list.
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5 If you have version 10 or later you can use operators forms, i.e. Map[Tr] acts as a function:
mylistofmatrices = {{{a, b}, {c, d}}, {{q, r, s}, {t, u, v}}}; Map[Tr][mylistofmatrices] {a + d, q + u}
This is a subtle difference but it may be useful nevertheless.
If you always want the trace of a tensor with a specific array depth you can check for that. If you want only a two-dimensional tensor (which is what you state in your question) you can use MatrixQ; otherwise look at ArrayDepth and TensorRank. One implementation:
myTr[m_?MatrixQ] := Tr[m] myTr[{m__?MatrixQ}] := Tr /@ {m} Now:
myTr @ foo myTr @ {1, 2, 3} myTr @ {{a, b}, {c, d}} myTr @ mylistofmatrices myTr[foo] myTr[{1, 2, 3}] a + d {a + d, q + u}
- 1$\begingroup$ Re:
TensorRank[], how very odd. "Introduced in 2012 (9.0)", and yet it's been around since the first version, and at one point "replaced byArrayDepth". $\endgroup$J. M.'s missing motivation– J. M.'s missing motivation2015-05-21 16:48:22 +00:00Commented May 21, 2015 at 16:48 - $\begingroup$ @Guess The poor developers are run every which direction. Rube Goldberg would love the present state of affairs. :o) $\endgroup$Mr.Wizard– Mr.Wizard2015-05-21 16:50:13 +00:00Commented May 21, 2015 at 16:50
- $\begingroup$ I am slightly frightened whenever I get into a situation where it turns out that I know even slightly more than the supposed experts… :o $\endgroup$J. M.'s missing motivation– J. M.'s missing motivation2015-05-21 16:56:37 +00:00Commented May 21, 2015 at 16:56
- $\begingroup$ @Guess I wouldn't jump to that conclusion in this case; I imagine the developers are well aware that this was a v1 function but someone probably told them to pretend that it was a new function in v9 as that has better publicity than "oops, we deprecated that but now see value in reintroducing it and applying it to this shiny new tensor stuff we'd like you to upgrade for" ;-) $\endgroup$Mr.Wizard– Mr.Wizard2015-05-21 16:59:02 +00:00Commented May 21, 2015 at 16:59
- $\begingroup$ Good point; but then, I spent some amount of time bitching about why they renamed
TensorRank[], so reading that "new" bit gave mixed emotions. :) Oh well, glad that it's "back". $\endgroup$J. M.'s missing motivation– J. M.'s missing motivation2015-05-21 17:06:26 +00:00Commented May 21, 2015 at 17:06