R help - May 2010 - matrix cross product in R different from cross product in Matlab

Hi all,

I have been searching all sorts of documentation, reference cards, cheat 
sheets but can't find why R's
crossprod(A, B) which is identical to A%*%B
does not produce the same as Matlabs
cross(A, B)
Supposedly both calculate the cross product, and say so, or where do I 
go wrong?

R is only doing sums in the crossprod however, as indicated by

(z <- crossprod(1:4))    # = sum(1 + 2^2 + 3^2 + 4^2) 
in 

http://127.0.0.1:13073/library/base/html/crossprod.html

R's result of
g <- rbind(c(1, 2, 3), c( 4, 5, 6))
h <- rbind(c(4, 5, 6), c(1, 2, 3))
c <-  crossprod(g, h)
is

 > c
     [,1] [,2] [,3]
[1,]    8   13   18
[2,]   13   20   27
[3,]   18   27   36

because there are only sums involved, however, I cant work out ALL of 
them for the 3D example, something like
         [,1]                     [,2]                     [,3]
[1,]   1*4+4*1                 ?                   ?            # #sum 
of elementwise multiplication of first column of first matrix with first 
column of second matrix    of second matrix
[2,]   ?                            2*5+5*2      ?
? cant figure out how these were derived, definitely this is NOT 
identical to e.g. http://en.wikipedia.org/wiki/Cross_product

I can work it out for the tcrossprod
 > c <- tcrossprod(g, h)
 > c
     [,1] [,2]
[1,]   32   14
[2,]   77   32

because
            [,1]                     [,2]
 [1,]     1*4+2*5+3*6   1*1+2*2+3*3   #sum of elementwise multiplication 
of first line of first matrix with first line of second matrix   sum of 
elementwise multiplication of first line of first matrix with second 
line of second matrix
 [2,]     4*4+5*5+6*6   4*1+5*2+6*3   #sum of elementwise multiplication 
of second line of first matrix with first line of second matrix   sum of 
elementwise multiplication of second line of first matrix with second 
line of second matrix


outer product is something completely different again , no need to show 
it here


Matlab's result in contrast of
g = [1 2 3 ; 4 5 6]
h = [4 5 6; 1 2 3]
c = cross(g,h)

is
c 
    -3     6    -3
     3    -6     3


which is in accordance to
http://en.wikipedia.org/wiki/Cross_product
and any math text book

 >> d = dot(g, h)

d 
    32    50    72
which is of course something different again

What exactly does crossprod mean in R? and why does R's cross product 
not do the same as indicated in references for cross products?

base::crossprod
doesnt tell me much:
function (x, y = NULL)
.Internal(crossprod(x, y))
<environment: namespace:base>

Where exactly do I look up the core of the function on Windows ? sorry, 
I HAVE been trying to find this for hours now
Thanks in advance,
Susanne

Susanne Schmidt wrote:
> Hi all,
>
> I have been searching all sorts of documentation, reference cards, cheat 
> sheets but can't find why R's
> crossprod(A, B) which is identical to A%*%B
>   
If you read the help page ?crossprod, you'll see it is supposed to be 
identical to t(A) %*% B.
> does not produce the same as Matlabs
> cross(A, B)
> Supposedly both calculate the cross product, and say so, or where do I 
> go wrong?
>   
They are following different definitions for "cross product".  The R 
definition is the statistical one, e.g. what is described here:  
http://stattrek.com/matrix-algebra/sums-of-squares.aspx .  The one you 
describe below is the one from 3 dimensional vector geometry.  You can 
get that one in R in a few different packages, but it's not really used 
much in statistics, so it's not in base R.  (It's called xprod in RFOC 
and RSEIS, extprod3d in geometry.)

Duncan Murdoch
> R is only doing sums in the crossprod however, as indicated by
>
> (z <- crossprod(1:4))    # = sum(1 + 2^2 + 3^2 + 4^2) 
> in 
>
> http://127.0.0.1:13073/library/base/html/crossprod.html
>
> R's result of
> g <- rbind(c(1, 2, 3), c( 4, 5, 6))
> h <- rbind(c(4, 5, 6), c(1, 2, 3))
> c <-  crossprod(g, h)
> is
>
>  > c
>      [,1] [,2] [,3]
> [1,]    8   13   18
> [2,]   13   20   27
> [3,]   18   27   36
>
> because there are only sums involved, however, I cant work out ALL of 
> them for the 3D example, something like
>          [,1]                     [,2]                     [,3]
> [1,]   1*4+4*1                 ?                   ?            # #sum 
> of elementwise multiplication of first column of first matrix with first 
> column of second matrix    of second matrix
> [2,]   ?                            2*5+5*2      ?
> ? cant figure out how these were derived, definitely this is NOT 
> identical to e.g. http://en.wikipedia.org/wiki/Cross_product
>
> I can work it out for the tcrossprod
>  > c <- tcrossprod(g, h)
>  > c
>      [,1] [,2]
> [1,]   32   14
> [2,]   77   32
>
> because
>             [,1]                     [,2]
>  [1,]     1*4+2*5+3*6   1*1+2*2+3*3   #sum of elementwise multiplication 
> of first line of first matrix with first line of second matrix   sum of 
> elementwise multiplication of first line of first matrix with second 
> line of second matrix
>  [2,]     4*4+5*5+6*6   4*1+5*2+6*3   #sum of elementwise multiplication 
> of second line of first matrix with first line of second matrix   sum of 
> elementwise multiplication of second line of first matrix with second 
> line of second matrix
>
>
> outer product is something completely different again , no need to show 
> it here
>
>
> Matlab's result in contrast of
> g = [1 2 3 ; 4 5 6]
> h = [4 5 6; 1 2 3]
> c = cross(g,h)
>
> is
> c >
>     -3     6    -3
>      3    -6     3
>
>
> which is in accordance to
> http://en.wikipedia.org/wiki/Cross_product
> and any math text book
>
>  >> d = dot(g, h)
>
> d >
>     32    50    72
> which is of course something different again
>
> What exactly does crossprod mean in R? and why does R's cross product 
> not do the same as indicated in references for cross products?
>
> base::crossprod
> doesnt tell me much:
> function (x, y = NULL)
> .Internal(crossprod(x, y))
> <environment: namespace:base>
>
> Where exactly do I look up the core of the function on Windows ? sorry, 
> I HAVE been trying to find this for hours now
> Thanks in advance,
> Susanne
>   
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