9 p.m.
A question came up lately regarding addition (or subtraction) of an
m x n matrix and a 1 x 1 matrix. The manual said that this was
permitted (with the 1 x 1 matrix being treated as a scalar, and
added to each element of the m x n one). But in fact it was
supported only if the m x n matrix was on the left; and I responded
to the report by enabling the case where the 1 x 1 matrix is on the
left.
But I wonder... is this really a good idea? We have the "dot
operators", ".+" and friends, which are suitable for this purpose,
and I'm concerned that allowing plain '+' and '-' for
non-conformable operands may mask scripting errors.
I ran into this myself the other day: I got the dimensions of a
certain matrix wrong but didn't notice the problem at first, since a
subtraction that, in a sense, "should have" generated an error went
through apparently OK, producing a nonsense result.
Maybe we shouldn't change this for gretl 1.9.6, but my feeling is
that we probably ought to be more rigorous in insisting on use of
the dot operators where they are the right tool for the job.
Allin
9:21 p.m.
On Sun, 25 Sep 2011, Allin Cottrell wrote:
A question came up lately regarding addition (or subtraction) of
an m x n matrix and a 1 x 1 matrix. The manual said that this was
permitted (with the 1 x 1 matrix being treated as a scalar, and
added to each element of the m x n one). But in fact it was
supported only if the m x n matrix was on the left; and I
responded to the report by enabling the case where the 1 x 1
matrix is on the left.
On more thought on this. Maybe I'm being irrational, but it seems to
me that the status quo ante was in a way more defensible than the
new, "more consistent" state of things.
Proper addition is of course commutative, but the "extended
addition" that I'm talking about here maybe is not. I tend to think
of the left-hand operand as the "posit", so to speak, and the
right-hand operand as the increment (or decrement, in the case of
subtraction). And I reckon I can attach a good sense to the case
where an m x n matrix is the posit and the increment or decrement is
a scalar (applied to all elements of the posit). But I feel queasy
about the case where the posit is a scalar value and the
increment/decrement is an m x n matrix. This seems a step too far.
This may become moot if we decide to tighten up and insist on the
dot operators, but I thought I'd just mention it.
Allin
11:51 p.m.
Allin et al,
<quote>
Proper addition is of course commutative, but the "extended
addition" that I'm talking about here maybe is not. I tend to think
of the left-hand operand as the "posit", so to speak, and the
right-hand operand as the increment (or decrement, in the case of
subtraction). And I reckon I can attach a good sense to the case
where an m x n matrix is the posit and the increment or decrement is
a scalar (applied to all elements of the posit). But I feel queasy
about the case where the posit is a scalar value and the
increment/decrement is an m x n matrix. This seems a step too far.
This may become moot if we decide to tighten up and insist on the
dot operators, but I thought I'd just mention it.
</quote>
My first thought is that if the manual says (mxn) + scalar is allowed, then the order
shouldn't matter. Addition is addition. Plus (so to speak), the alternative you
suggest is afaik different from the treatments in Matlab, Gauss, etc. So I think if you
want to insist on left-vs-right positioning, that should be documented.
A second thought is that at least for me, the rigor you're suggesting would be another
stumbling block in switching completely from the above-mentioned programs to gretl.
It's one thing to say I can't add a 1xn matrix to a 1xn series, for example.
I've learned to be more careful about such things in gretl, but if now I have to start
worrying about which side of the + sign a scalar or matrix is on, well, that seems
excessive.
It makes more sense to me to insist on a dot operator any time you're combining a
matrix and scalar, but that wouldn't be my first choice.
fwiw,
PS
________________________________________
From: gretl-devel-bounces(a)lists.wfu.edu [gretl-devel-bounces(a)lists.wfu.edu] on behalf of
Allin Cottrell [cottrell(a)wfu.edu]
Sent: Sunday, September 25, 2011 5:21 PM
To: Gretl development
Subject: Re: [Gretl-devel] matrix multiplication question
On Sun, 25 Sep 2011, Allin Cottrell wrote:
A question came up lately regarding addition (or subtraction) of
an m x n matrix and a 1 x 1 matrix. The manual said that this was
permitted (with the 1 x 1 matrix being treated as a scalar, and
added to each element of the m x n one). But in fact it was
supported only if the m x n matrix was on the left; and I
responded to the report by enabling the case where the 1 x 1
matrix is on the left.
On more thought on this. Maybe I'm being irrational, but it seems to
me that the status quo ante was in a way more defensible than the
new, "more consistent" state of things.
Proper addition is of course commutative, but the "extended
addition" that I'm talking about here maybe is not. I tend to think
of the left-hand operand as the "posit", so to speak, and the
right-hand operand as the increment (or decrement, in the case of
subtraction). And I reckon I can attach a good sense to the case
where an m x n matrix is the posit and the increment or decrement is
a scalar (applied to all elements of the posit). But I feel queasy
about the case where the posit is a scalar value and the
increment/decrement is an m x n matrix. This seems a step too far.
This may become moot if we decide to tighten up and insist on the
dot operators, but I thought I'd just mention it.
Allin
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1:09 a.m.
On Sun, 25 Sep 2011, Summers, Peter wrote:
Allin et al,
<quote>
Proper addition is of course commutative, but the "extended
addition" that I'm talking about here maybe is not. I tend to think
of the left-hand operand as the "posit", so to speak, and the
right-hand operand as the increment (or decrement, in the case of
subtraction). And I reckon I can attach a good sense to the case
where an m x n matrix is the posit and the increment or decrement is
a scalar (applied to all elements of the posit). But I feel queasy
about the case where the posit is a scalar value and the
increment/decrement is an m x n matrix. This seems a step too far.
This may become moot if we decide to tighten up and insist on the
dot operators, but I thought I'd just mention it.
</quote>
My first thought is that if the manual says (mxn) + scalar is
allowed, then the order shouldn't matter. Addition is addition.
Plus (so to speak), the alternative you suggest is afaik different
from the treatments in Matlab, Gauss, etc. So I think if you want
to insist on left-vs-right positioning, that should be documented.
Thanks, Peter, that's a useful perspective: what other software does
is certainly relevant.
BTW, I realize that my posting was wrongly titled: it's not
multiplication that I find possibly questionable, but rather
addition/subtraction of m x n and 1 x 1 matrices.
Allin
4:48 a.m.
On 26-09-2011, at 03:09, Allin Cottrell wrote:
On Sun, 25 Sep 2011, Summers, Peter wrote:
> Allin et al,
>
> <quote>
> Proper addition is of course commutative, but the "extended
> addition" that I'm talking about here maybe is not. I tend to think
> of the left-hand operand as the "posit", so to speak, and the
> right-hand operand as the increment (or decrement, in the case of
> subtraction). And I reckon I can attach a good sense to the case
> where an m x n matrix is the posit and the increment or decrement is
> a scalar (applied to all elements of the posit). But I feel queasy
> about the case where the posit is a scalar value and the
> increment/decrement is an m x n matrix. This seems a step too far.
>
> This may become moot if we decide to tighten up and insist on the
> dot operators, but I thought I'd just mention it.
> </quote>
>
> My first thought is that if the manual says (mxn) + scalar is
> allowed, then the order shouldn't matter. Addition is addition.
> Plus (so to speak), the alternative you suggest is afaik different
> from the treatments in Matlab, Gauss, etc. So I think if you want
> to insist on left-vs-right positioning, that should be documented.
Thanks, Peter, that's a useful perspective: what other software does
is certainly relevant.
Both R and Octave accept <Matrix>+<scalar> and <scalar>+<Matrix>
and also <Matrix>-<scalar> and <scalar>-<Matrix>
Berend
7:41 a.m.
Am 09/26/2011 06:48 AM, schrieb Berend Hasselman:
On 26-09-2011, at 03:09, Allin Cottrell wrote:
> On Sun, 25 Sep 2011, Summers, Peter wrote:
>
>> Allin et al,
>>
>> <quote>
>> Proper addition is of course commutative, but the "extended
>> addition" that I'm talking about here maybe is not. I tend to think
>> of the left-hand operand as the "posit", so to speak, and the
>> right-hand operand as the increment (or decrement, in the case of
>> subtraction). And I reckon I can attach a good sense to the case
>> where an m x n matrix is the posit and the increment or decrement is
>> a scalar (applied to all elements of the posit). But I feel queasy
>> about the case where the posit is a scalar value and the
>> increment/decrement is an m x n matrix. This seems a step too far.
>>
>> This may become moot if we decide to tighten up and insist on the
>> dot operators, but I thought I'd just mention it.
>> </quote>
>>
>> My first thought is that if the manual says (mxn) + scalar is
>> allowed, then the order shouldn't matter. Addition is addition.
I strongly agree here; introducing some notion of pre- or post-addition
is certainly creative, but not helpful here IMHO.
Apart from that, given that matrix plus scalar is a case of
"broadcasting" (a term borrowed from numerical Python) as documented in
the gretl user guide also for more general cases, and given that gretl
in general uses ".+" as an operator to indicate the programmer's wish to
do that, I tend to agree with Allin to require the use of ".+" also for
the matrix plus scalar case.
Certainly not for 1.9.6, but a good case for 2.0 IMHO.
cheers,
sven
8:17 a.m.
Allin et al,
95/95 votes from russian students for "Addition is addition" (matrix +
scalar is allowed, order does not matter)
Best,
Boris Demeshev,
teaching assistant
26.09.2011 11:41, Sven Schreiber пишет:
Am 09/26/2011 06:48 AM, schrieb Berend Hasselman:
> On 26-09-2011, at 03:09, Allin Cottrell wrote:
>
>> On Sun, 25 Sep 2011, Summers, Peter wrote:
>>
>>> Allin et al,
>>>
>>> <quote>
>>> Proper addition is of course commutative, but the "extended
>>> addition" that I'm talking about here maybe is not. I tend to think
>>> of the left-hand operand as the "posit", so to speak, and the
>>> right-hand operand as the increment (or decrement, in the case of
>>> subtraction). And I reckon I can attach a good sense to the case
>>> where an m x n matrix is the posit and the increment or decrement is
>>> a scalar (applied to all elements of the posit). But I feel queasy
>>> about the case where the posit is a scalar value and the
>>> increment/decrement is an m x n matrix. This seems a step too far.
>>>
>>> This may become moot if we decide to tighten up and insist on the
>>> dot operators, but I thought I'd just mention it.
>>> </quote>
>>>
>>> My first thought is that if the manual says (mxn) + scalar is
>>> allowed, then the order shouldn't matter. Addition is addition.
I strongly agree here; introducing some notion of pre- or post-addition
is certainly creative, but not helpful here IMHO.
Apart from that, given that matrix plus scalar is a case of
"broadcasting" (a term borrowed from numerical Python) as documented in
the gretl user guide also for more general cases, and given that gretl
in general uses ".+" as an operator to indicate the programmer's wish to
do that, I tend to agree with Allin to require the use of ".+" also for
the matrix plus scalar case.
Certainly not for 1.9.6, but a good case for 2.0 IMHO.
cheers,
sven
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9:16 a.m.
On Mon, 26 Sep 2011, Boris Demeshev wrote:
Allin et al,
95/95 votes from russian students for "Addition is addition" (matrix +
scalar is allowed, order does not matter)
I believe that the crux of the matter, as Allin pointed out, is: assume
that the sum between a matrix and a scalar is defined in the obvious way.
Then, is it possible to find cases when the operaton is _not_ commutative?
After some thinking about it, I believe it isn't possible (but then again,
neutrinos may be faster than light [http://operaweb.lngs.infn.it/], so you
should never say never). As a consequence, IMO (a \pm b) should be ok for
any matrix/scalar combination.
Actually, I believe that most matrix-oriented languages work more or less
like this: use "§" to indicate an arbitrary binary operator which can
operate elementwise on matrices. Then
A § B
is well defined as long as
[ rows(A) == rows(B) || rows(A) == 1 || rows(B) == 1 ]
&&
[ cols(A) == cols(B) || cols(A) == 1 || cols(B) == 1 ]
which makes it legal, for example, to add a (nx1) column vector to a (1xm)
row vector and obtain an (nxm) matrix (which we cannot do at present, we
need ".+" for that).
Riccardo (Jack) Lucchetti
Dipartimento di Economia
Università Politecnica delle Marche
r.lucchetti(a)univpm.it
http://www.econ.univpm.it/lucchetti
4847
days inactive
4848
days old
7 comments
6 participants
participants (6)
-
Allin Cottrell -
Berend Hasselman -
Boris Demeshev -
Riccardo (Jack) Lucchetti -
Summers, Peter -
Sven Schreiber