transposition operator for string arrays

[aviks]

julia> a=["X" "Y"; "A" "B"]
2x2 Array{ASCIIString,2}:
 "X"  "Y"
 "A"  "B"

julia> a'
ERROR: no method conj(ASCIIString)
 in ctranspose at array.jl:1332

julia> transpose(a)
2x2 Array{ASCIIString,2}:
 "X"  "A"
 "Y"  "B"

It is not that big a deal to explicitly call the transpose function from non numeric matrices, but since this is a change from 0.2, I thought I'd ask. Is this intended?

Version 0.3.0-prerelease+2306 (2014-03-31 07:12 UTC)

[carlobaldassi]

Actually, ' is the conjugate transpose operator; the transpose operator is .':

julia> a=["X" "Y"; "A" "B"]
2x2 Array{ASCIIString,2}:
 "X"  "Y"
 "A"  "B"

julia> a.'
2x2 Array{ASCIIString,2}:
 "X"  "A"
 "Y"  "B"

[aviks]

Ah right, thanks.

Note to self: RTFM: http://docs.julialang.org/en/latest/manual/functions/?highlight=transpose#operators-with-special-names

[StefanKarpinski]

The conjugate of a non-numeric value should fall back on the identity. In transit or I would do it.

[JeffBezanson]

I'm not sure if this should be part of the behavior of conj or of ctranspose.

[simonster]

See also #5449.

[StefanKarpinski]

Yeah, probably the ctranspose come to think of it.

[JeffBezanson]

The only thing I can think of doing is defining

ctrans_conj(x) = x
ctrans_conj(x::Number) = conj(x)

and using this instead of conj in ctranspose, but it seems strange to me.
I also don't think it should depend on the container type, since ctransposing a Matrix{Any} with various types of numbers in it should still apply conj.

[JeffBezanson]

I think conj just doesn't make sense on arbitrary types, and conjugate transpose is defined correctly. This should just stay as-is.

[StefanKarpinski]

This is annoying every time I trip over it. I really don't see the problem with making conj the identity on non-numbers.

[JeffBezanson]

I think what's going on here is that people don't want to type the extra
dot, but that is just an unavoidable consequence of making single quote a
conjugate transpose operator. If, for example, the functions were called
trans and ctrans, I don't think anybody would argue that ctrans should work
on non-numbers.
On Apr 4, 2014 9:02 PM, "Stefan Karpinski" [email protected] wrote:

This is annoying every time I trip over it. I really don't see the problem
with making conj the identity on non-numbers.

Reply to this email directly or view it on GitHubhttps://github.com//issues/6395#issuecomment-39624751
.

[pygy]

I'm with Stefan on this one, but if Jeff prevails, it would be nice to add conj(x::Any) to deprecated.jl, and remove it in v0.4.

[JeffBezanson]

Could you explain your reasoning? Do you think conj(x::Any) = x is actually correct?

[timholy]

Can we define

conj(x) = error("conj not defined for ", typeof(x), ". Did you mean to take the transpose (.')?")

[StefanKarpinski]

My reasoning is that conj is the identity on anything that doesn't have an imaginary part – and strings clearly don't have an imaginary part. Obviously it's silly to take the conjugate of a string, but it seems pedantic to force using .' – what's the harm that could come from just ignoring the conjugation of a non-number?

[JeffBezanson]

Well, a string can't be negative either, so maybe abs(x)=x should be defined too.

[StefanKarpinski]

Touché. I'd be fine with making this part of the behavior of ctranspose, but I think it's obnoxious to make people use .'. The key thing is that the conjugate transpose is the right generic transpose most of the time for complex numbers – it's the unconjugated transpose that is weird for complexes.

[pygy]

It's a matter of practicality and user friendliness. There's no syntactic construct that involves abs.

Julia is not about correctness and consistency above everything else, and, in this case, I think it's worth it to define conj as the identity for non-complex types, even if it does not make sense mathematically.

[StefanKarpinski]

I'm actually convinced now that this should be a behavior of ctranspose. The realization I had is that transpose is, despite the name, not the generic array transposition operator – ctranspose is. It just happens that the correct generic transposition for complex arrays also conjugates elements. If you want to do a transpose that doesn't conjugate, that is really a more special operation, as you can tell from the fact that A.' is a longer, less obvious syntax than A'. As Jeff pointed out, conjugating a string or other non-number still doesn't make sense and should be an error.

[pygy]

Indeed. To be honest I hadn't checked the nitty gritty of the transposition implementation, as long as A' works for all types, I'm fine :-).

How would you handle {0.0+1.0im}'? Define ctranspose(a::Array{Any}) based on maybeconj?

maybeconj(x) = x
maybeconj(z::Complex) = conj(z)

[JeffBezanson]

No; all methods of ctranspose would use maybeconj. And the one that calls conj should apply for all Numbers.

[JeffBezanson]

What worries me here is we're introducing a name for the concept "what you do to an element during generic transposition". In math, as far as I know, that's conj. Is there some other name that would make sense? Would you sometimes overload maybeconj (or whatever it should be called) instead of conj?

[StefanKarpinski]

Well, this is what led me to the notion that conj should just be the identity on non-numbers.

[JeffBezanson]

It's still possible I could be convinced that that is the correct generic meaning of conj. Wikipedia says "Usually one includes α itself in the set of conjugates." (http://en.wikipedia.org/wiki/Conjugate_element_(field_theory)).

[cmey]

Isn't the .op syntax meant to be an element-wise application of the op ?
I wouldn't expect .' to transpose the matrix (moving elements). Instead I would expect it to apply ' on each element of the matrix (without moving them).

[StefanKarpinski]

That's the general trend, but happens not to be what this operator means. This is a traditional meaning inherited from Matlab.