[R] Strange Matrix Multiplication Behaviour

[Gavin Simpson]

Wayne Jones wrote:
> Hi there fellow R-users, 
> 
> Im seeing some strange behaviour when I multiply a vector by a matrix
> 
> Here is my script: 
> 

"*" does array or element-wise multiplication. %*% is Matrix multiplication.

In the first case, you are multiplying tr by the first row of ex1

 > tr * ex1[1, ]
            a          b           c          d          e          f
1 0.05122422 -0.5117032 -0.09961093 -0.1842568 0.03664727 -0.2285117

In the second, you are extracting the first row of the result of 
multiplying tr by ex1, which as we see below returns a 2x6 matrix:

 > tr * ex1
             a          b           c           d           e           f
1  0.05122422 -0.4878917 -0.10648873 -0.24451059  0.03428033 -0.24698556
2 -0.04471461 -0.4211459 -0.01675805 -0.05573933 -0.44671804 -0.04852005
 > (tr * ex1)[1, ]
            a          b          c          d          e          f
1 0.05122422 -0.4878917 -0.1064887 -0.2445106 0.03428033 -0.2469856

Note that tr gets recycled in the tr * ex1 and (tr * ex1)[1, ] as tr is 
not as long as ex1.

Element 1b in (tr * ex1)[1, ] is formed by multiplying element 1b of ex1 
(-3.279045) by the third element of the vector tr (0.1487908):

 > tr[3] * ex1[1,2]
[1] -0.4878917

the second value of the vector tr was used to multiply against element 
2a in matrix ex1:

but in the tr * ex1[1, ] case tr and ex1[1, ] both contain 6 elements 
and the element 1b in the results is formed by multiplying element 1b of 
ex1[1, ] (-3.279045) by the second element of vector tr (0.1560525)

 > tr[2] * ex1[1,2]
[1] -0.5117032

> 
> Notice that the output from tr * ex[1,] is different from (tr* ex1)[1,]
> Especially element number 4. 

The difference is due to recycling of tr and of where you are doing your 
sub setting

> I would naturally expect both vectors to be equivalent. 
> 

Hopefully my longwinded explanation helps.

Gav
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Gavin Simpson                     [T] +44 (0)20 7679 5522
ENSIS Research Fellow             [F] +44 (0)20 7679 7565
ENSIS Ltd. & ECRC                 [E] gavin.simpson at ucl.ac.uk
UCL Department of Geography       [W] http://www.ucl.ac.uk/~ucfagls/cv/
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