Getting back to 2 months old considerations [more inline]:
>>>>> Martin Maechler <maech...@stat.math.ethz.ch>
>>>>> on Tue, 24 Jun 2014 15:08:09 +0200 writes:
>>>>> Radford Neal <radf...@cs.toronto.edu>
>>>>> on Mon, 23 Jun 2014 11:24:35 -0400 writes:
>> A new version of pqR is now available at pqR-project.org, which fixes
>> several bugs that are also present in the latest R Core patch release
>> (r66002). A number of bugs found previously during pqR development
>> are also unfixed in the latest R Core release. Here is the list of
>> these bugs that are unfixed in r66002 (including documentation
>> deficiencies), taken from the pqR bug fix and documentation update
>> sections of the pqR NEWS file (pqR-project.org/NEWS.txt):
> Duncan Murdoch has already mentioned that "unfixed bugs" is a
> strong wording...
> I'm commenting on one subtopic only:
> [.........]
>> o Fixed the following bug (also present in R-2.15.0 and R-3.0.2):
>> x <- t(5)
>> print (x %*% c(3,4))
>> print (crossprod(5,c(3,4)))
>> The call of crossprod produced an error, whereas the
>> corresponding use of %*% does not.
>> In pqR-2013-12-29, this bug also affected the expression t(5) %*%
>> c(3,4), since it is converted to the equivalent of
>> crossprod(5,c(3,4)).
> (I'm not getting this last para... but that may be unimportant)
> [........]
>> o Fixed the following bug (also present in R-2.15.0 and R-3.0.2):
>> v <- c(1,2)
>> m <- matrix(c(3,4),1,2)
>> print(t(m)%*%v)
>> print(crossprod(m,v))
>> in which crossprod gave an error rather than produce the answer
>> for the corresponding use of %*%.
> Both cases above concern %*%, crossprod() {and also
> tcrossprod()}, and always when one at least one operand is a
> vector...
> As S and R's terminology has always been mathematically correct and
> "knows" that a vector is not a 1-row matrix or 1-column matrix
> (which some people call row-vector and column-vector), R has
> indeed much more freedom to be lenient in how to promote vectors
> to matrices, and it has always done so tolerantly for some cases
> of "%*%", but even there is room for discussion, see below.
> Since about January, I have a corresponding entry in the TODO
> file of the Matrix package (which I maintain), and I (at least
> partly) agree with you, that we should *consider* changing the
> current behavior.
> The following is from my corresponding R script :
> ### NOTA BENE: vector %*% Matrix _and_ Matrix %*% vector :
> ### --------- ----------------- -----------------
> ## The k-vector is treated as (1,k)-matrix *or* (k,1)-matrix
> ## on both sides whenever it "helps fit" the matrix dimensions:
> and one kind of reasoning would go to say that
> crossprod() and tcrossprod() should do the same. This would
> even make more cases work than (I think) your proposal.
Yes, more cases, indeed:
I've just (svn rev 66495) committed changes to R-devel (aka "the trunk"),
with the following regression tests:
## Radford (R-devel, June 24, 2014); M.Maechler
m <- matrix(1:2, 1,2); v <- 1:3
stopifnot(identical(crossprod(2, v), t(2) %*% v),
identical(crossprod(m, v), t(m) %*% v),
identical(5 %*% v, 5 %*% t(v)),
identical(tcrossprod(m, 1:2), m %*% 1:2) )
## gave error "non-conformable arguments" in R <= 3.2.0
Note that the first two correspond to your "bugs" and the other two
follow the principle of promoting a vector to that (column or
row) matrix which "makes it work".
I did not label these as bug fixes, but new features, and for
this reason -- and for a longer review period and RFC --
these are *not* planned to be part of the next R release
(R 3.1.2, no release date planned yet), but only of the next
yearly ".0" release next spring, (probably) version 3.2.0.
Comments are welcome, (particularly praises ;-)
Martin
> However, one can argue that the current behavior is quite
> consistent {there is more than one kind of consistency here; in
> this case it's the consistency of underlying C code IIRC}, and
> not strictly a bug.
> It is something which I am grateful you bring up for discussion,
> and I'm happy to settle here.
> Note that the Matrix package and many other packages that
> implement matrix multiplication methods, should then also follow
> the new semantic, and so this is typically rather for R-devel
> than R-patched.
> Note that from your first case example, one could also argue
> -- at least from my 'NOTA BENE' rule above --
> that 5 %*% 3:4
> should work, since
> 5 %*% rbind(3:4)
> does work, but
> 5 %*% cbind(3:4)
> does not. So you see, there are quite a few cases one could
> discuss, and have reasons pro and contra some of the changes.
> I will be too busy till the end of 'useR! 2014' and would want
> quite a bit of further thoughts before making a quick decision,
> notably about the cases I have in the appended products.Rout
> Martin Maechler,
> (ETH Zurich and R Core team)
> ---------------
> ### NOTA BENE: vector %*% Matrix _and_ Matrix %*% vector :
> ### --------- ----------------- -----------------
> ## The k-vector is treated as (1,k)-matrix *or* (k,1)-matrix
> ## on both sides whenever it "helps fit" the matrix dimensions:
> ## --------------- %*% ---------------------------------------------
> ## --------- v . v -----------------------------
> ## We *could* consider allowing more even here: could argue
> ## from the 'NOTA BENE' above that
>> 5 %*% 3:4 ## should work, since
>> 5 %*% rbind(3:4) ## does work, but
>> 5 %*% cbind(3:4) ## does not.
> ## --------- v . M -----------------------------
>> 1:3 %*% matrix(1:12, 3,4) ## (1, n) if n == nrow(.)
> [,1] [,2] [,3] [,4]
> [1,] 14 32 50 68
>> 1:4 %*% matrix(1:12, 3,4)
> Error in 1:4 %*% matrix(1:12, 3, 4) : non-conformable arguments
> No suitable frames for recover()
>> 1:4 %*% matrix(1:5, 1,5) ## (n, 1) if nrow(.) == 1
> [,1] [,2] [,3] [,4] [,5]
> [1,] 1 2 3 4 5
> [2,] 2 4 6 8 10
> [3,] 3 6 9 12 15
> [4,] 4 8 12 16 20
> ## --------- M . v -----------------------------
>> matrix(1:4, 3,4) %*% 1:4 ## (n, 1) if n == ncol(.)
> [,1]
> [1,] 26
> [2,] 28
> [3,] 26
>> matrix(1:4, 3,4) %*% 1:3
> Error in matrix(1:4, 3, 4) %*% 1:3 : non-conformable arguments
> No suitable frames for recover()
>> matrix(1:3, 3,1) %*% 1:3 ## (1, n) if ncol(.) == 1
> [,1] [,2] [,3]
> [1,] 1 2 3
> [2,] 2 4 6
> [3,] 3 6 9
>>
> ## --------------- crossprod -------------------------------------
> ## --------- M . v -----------------------------
>> crossprod(matrix(1:4, 3,4), 1:3) ## (n, 1) if n == nrow(.)
> [,1]
> [1,] 14
> [2,] 12
> [3,] 14
> [4,] 20
>> crossprod(matrix(1:4, 3,4), 1:4)
> Error in crossprod(matrix(1:4, 3, 4), 1:4) : non-conformable arguments
>> m <- matrix(1:2, 1,2); v <- 1:3
>> crossprod(m,v) ##>>> *could* be nice and use (1,n) as nrow(.)==1 <<<
> Error in crossprod(m, v) : non-conformable arguments
> ##>> after all, crossprod(m,v) "should"== t(m) %*% v and that does work:
>> t(m) %*% v
> [,1] [,2] [,3]
> [1,] 1 2 3
> [2,] 2 4 6
>>
> ## --------- v . M -----------------------------
>> crossprod(1:3, matrix(1:4, 3,4)) ## (1, n) if n == nrow(.)
> [,1] [,2] [,3] [,4]
> [1,] 14 12 14 20
>> crossprod(1:4, matrix(1:4, 3,4))
> Error in crossprod(1:4, matrix(1:4, 3, 4)) : non-conformable arguments
>> crossprod(1:3, matrix(1:3, 1,3)) ##>>> *could* be nice and use (n,1) as
nrow(.)==1 <<<
> Error in crossprod(1:3, matrix(1:3, 1, 3)) : non-conformable arguments
>> crossprod(v,m)
> Error in crossprod(v, m) : non-conformable arguments
> ##>> "as" v %*% m does work and v could have been A[1,] instead of
A[1, , drop=TRUE]
>> ## --------------- tcrossprod -------------------------------------
> ## --------- M . v -----------------------------
>> tcrossprod(matrix(1:4, 3,4), 1:3)
> Error in tcrossprod(matrix(1:4, 3, 4), 1:3) : non-conformable arguments
>> tcrossprod(matrix(1:4, 3,4), 1:4)
> Error in tcrossprod(matrix(1:4, 3, 4), 1:4) : non-conformable arguments
>> tcrossprod(matrix(1:4, 1,4), 1:4)##>>> *could* be nice and use (n,1) as
ncol(.) == 1 <<<
> Error in tcrossprod(matrix(1:4, 1, 4), 1:4) : non-conformable arguments
> ##>> "as" m %*% v does work and v could have been A[1,] instead of
A[1, , drop=TRUE]
>> matrix(1:4, 1,4) %*% 1:4
> [,1]
> [1,] 30
>> tcrossprod(matrix(1:2, 2,1), 1:5) # v -> c(1, n) as ncol(.) == 1
> [,1] [,2] [,3] [,4] [,5]
> [1,] 1 2 3 4 5
> [2,] 2 4 6 8 10
>>
> ## --------- v . M -----------------------------
>> tcrossprod(1:4, matrix(1:4, 3,4)) # v -> c(1, n) as n == ncol(.)
> [,1] [,2] [,3]
> [1,] 26 28 26
>> tcrossprod(1:3, matrix(1:4, 3,4))
> Error in tcrossprod(1:3, matrix(1:4, 3, 4)) : non-conformable arguments
>> tcrossprod(1:3, matrix(1:3, 3,1)) # v -> c(n, 1) as ncol(.) == 1
> [,1] [,2] [,3]
> [1,] 1 2 3
> [2,] 2 4 6
> [3,] 3 6 9
>>
> ##--------------------------- vector x vector -----------------
>> 1:3 %*% 1:3 ## must have same n
> [,1]
> [1,] 14
>> crossprod(1:3, 1:3) ## must have same n
> [,1]
> [1,] 14
>> tcrossprod(1:3, 1:4) ## can have different length
> [,1] [,2] [,3] [,4]
> [1,] 1 2 3 4
> [2,] 2 4 6 8
> [3,] 3 6 9 12
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