Column wise matrix multiplication

Hi all,
I am trying to multiply each column of a matrix such to have a unique resulting vector with length equal to the number of rows of the original matrix. In short I would like to do what prod(.) function in Matlab does, i.e.

A<-matrix(c(1:10),5,2)

V = A[,1]*A[,2]

Thank you

Graziano



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Hi all,
I am trying to multiply each column of a matrix such to have
a unique resulting vector with length equal to the number of
rows of the original matrix. In short I would like to do what
prod(.) function in Matlab does, i.e.

A <-matrix(c(1:10),5,2)

V = A[,1]*A[,2]

Thank you

Graziano

On 20-Feb-2012 Graziano Mirata wrote:

Hi all,
I am trying to multiply each column of a matrix such to have
a unique resulting vector with length equal to the number of
rows of the original matrix. In short I would like to do what
prod(.) function in Matlab does, i.e.

A <-matrix(c(1:10),5,2)

V = A[,1]*A[,2]

Thank you

Graziano

The Matlab prod(A,2) function computes the products along the
rows of the matrix A and returns the result as a column vector,
of length equal to the number of rows in A, which seems to be
what you describe.

Your code above does this for your 2-column example, but the
result is a simple "R vector" which is not an array (and in
particular is not a column vector):

  A[,1]*A[,2]
  # [1]  6 14 24 36 50

  dim(A[,1]*A[,2])
  # NULL

For a matrix A with arbitrary number of columns, if you wanted
the row sums rather than the row products, you could use the
R function rowSums():

  rowSums(A)
  # [1]  7  9 11 13 15

This is still a dimensionless "simple R vector":

  dim(rowSums(A))
  # NULL

Unfortunately, there seems to be no equivalent for products
(e.g. "rowProds"). But you can define one:

  rowProds <- function(X){ apply(X,1,FUN="prod") }

  rowProds(A)
  # [1]  6 14 24 36 50

Even then, the result is a "simple R vector", without dimensions:

  dim(rowProds(A))
  # NULL

If you need an array (row) vector then you can apply t():

  t(rowProds(A))
  #      [,1] [,2] [,3] [,4] [,5]
  # [1,]    6   14   24   36   50

or t(t()) for a column vector:

  t(t(rowProds(A)))
  #      [,1]
  # [1,]    6
  # [2,]   14
  # [3,]   24
  # [4,]   36
  # [5,]   50

Ted.

-------------------------------------------------

Unfortunately, there seems to be no equivalent for products
(e.g. "rowProds"). But you can define one:

  rowProds <- function(X){ apply(X,1,FUN="prod") }

  rowProds(A)
  # [1]  6 14 24 36 50

Even then, the result is a "simple R vector", without dimensions:

  dim(rowProds(A))
  # NULL

If you need an array (row) vector then you can apply t():

  t(rowProds(A))
  #      [,1] [,2] [,3] [,4] [,5]
  # [1,]    6   14   24   36   50

or t(t()) for a column vector:

  t(t(rowProds(A)))
  #      [,1]
  # [1,]    6
  # [2,]   14
  # [3,]   24
  # [4,]   36
  # [5,]   50

Ted.

-------------------------------------------------

Further to the above: I have managed to track down a
function rowProds in the "matrixStats" package:

http://finzi.psych.upenn.edu/R/library/matrixStats/html/rowProds.html

http://www.stats.bris.ac.uk/R/web/packages/matrixStats/matrixStats.pdf

Note that:

  "Details
   Internally the product is calculated via the logarithmic
   transform, treating zeros and negative values specially."

In view of this, which strikes me as potentially getting
close to thin ice, plus the overhead of loading a whole
package just for one function, it may be more straightforward
(and perhaps safer) to define one's own function (as above).
Also (see the PDF reference manual) it is apparently "work
in progress" and also has dependencies on other packages:
see the description at

http://www.stats.bris.ac.uk/R/web/packages/matrixStats/index.html