[Gretl-devel] matrix transposition/multiplication operator precedence

Sven Schreiber svetosch at gmx.net
Fri Jul 1 19:51:34 EDT 2016


Am 01.07.2016 um 20:37 schrieb Allin Cottrell:
> On Fri, 1 Jul 2016, Sven Schreiber wrote:

>>
>> <hansl>
>> matrix a = zeros(3,1)
>> matrix b = ones(2,3)
>>
>> matrix hu = a' * b'
>> hu = a'(b')
>> hu = a'b'    # fails
>> </hansl>
>>
>> Apparently gretl interprets the last line as "(a'b)'" which kind of
>> implies that the implicit multiplication with the transpose sign has
>> higher precedence than the actual transposition of b.
>
> "Kind of". But couldn't this be interpreted as a case of simple
> left-to-right evaluation in the absence of another deciding criterion?

Well, I admit that according to table 3.1 in the command reference the 
unary transpose and the binary transpose-multiply have the same 
priority, and so it would boil down to left-to-right.

But I'm not sure that's right. Semantically it's clear that 
transpose-multiply just exists to mimick mathematical handwriting (on 
the blackboard or on paper). So wherever it's meaningful, "'" must be 
replaced by "'*". And then in the expression "a'*b'" the right 
precedence kicks in.

Or to put it differently: Nobody would ever write "(a'b)'" on the 
blackboard as "a'b'", because I think it's a broad consensus that the 
two expressions are different.

thanks,
sven


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