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
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Dr. Gerrit Eichner Mathematical Institute, Room 212
gerrit.eich...@math.uni-giessen.de Justus-Liebig-University Giessen
Tel: +49-(0)641-99-32104 Arndtstr. 2, 35392 Giessen, Germany
Fax: +49-(0)641-99-32109 http://www.uni-giessen.de/cms/eichner
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