[R] Product of certain rows in a matrix without loop

[Gerrit Eichner]

Ok, here is a bandmatrix solution "by hand":

leftmatrix <- matrix( c( rep( 1, k), rep( 0, nrow(A) - k + 1)),
                       byrow = TRUE, ncol = nrow(A), nrow = nrow(A) - k + 1)


  Gerrit

>> Thank you very much for your answer. Unfortunately, I cannot use any 
>> package...
> Er, ... this is quite unusual! (Is this is homework?)
>
>> Do you have a solution ?
> Well, take a look at the resulting bandmatrix leftmatrix. Yould can certainly 
> build it yourself "by hand" somehow. I used the Matrix package just for 
> convenience.
>
> Regards -- Gerrit
>
>> Thank you in advance
>> 
>> 
>> Edouard Hardy
>> 
>> 
>> On Tue, Sep 3, 2013 at 11:49 AM, Gerrit Eichner <
>> Gerrit.Eichner at math.uni-giessen.de> wrote:
>> 
>>> Hello, Edouard,
>>> 
>>> taking logs of A's elements (so that * turns into +, so to say), using a
>>> left-multiplication with a certain band matrix of the package Matrix, and
>>> exponentiating the result again could provide a solution (see below).
>>> 
>>>
>>>  I know have the following problem:
>>>> I have a matrix :
>>>> A =
>>>> 1  2  3
>>>> 4  5  6
>>>> 7  8  9
>>>> 9  8  7
>>>> 4  5  6
>>>> 3  2  1
>>>> 
>>>> And I would like to have :
>>>> B =
>>>> 1*4*7  2*5*8  3*6*9
>>>> 4*7*9  5*8*8  6*9*7
>>>> 7*9*4  8*8*5  9*7*6
>>>> 9*4*3  8*5*2  7*6*1
>>>> 
>>>> Here I took the product of 3 rows each time. And 3 needs to be a
>>>> parameter.
>>>> 
>>>> Is it possible to do so without any loop ?
>>>> 
>>> 
>>> 
>>> Caveat: Not very carefully tested!
>>> 
>>> library( Matrix)
>>> 
>>> k <- 3
>>> ones <- lapply( 1:k, function( j) rep( 1, nrow( A) - j + 1)))
>>> leftmatrix <- bandSparse( n = nrow(A) - k + 1, m = nrow(A),
>>>                           k = 0:(k-1), diagonals = ones)
>>> 
>>> exp( leftmatrix %*% log(A))
>>>
>>>  Hth  --  Gerrit