On Apr 3, 2009, at 1:36 AM, Kutlwano Ramaboa wrote:
Agree, it is ambiguous. Will try again....
Suppose I have the following
X<-matrix(c(1:20),nrow=4,byrow=T), hence this is a 4 by 5 matrix
Y<-matrix(c(2,4,6,8),ncol=1), and this is a 4 by 1 vector, each
value denote y1, y2,y3, y4
Step 1 - write each row of X as a vector, so I have vectors t(x_1),
t(x_2), t(x_3) and t(x_4)
Not necessary to form the transpose of the row vectors because the %*%
infix operator implicitly forms the transpose of the first argument.
Step 2 (inner product) ---- [prod(t(x_1) *x_2) + prod(t(x_1) *x_3) +
prod(t(x_1) *x_4) ] *y1
For the first row, you can get all cross-products with:
apply(X, 1, function(x) x %*% X[1,] )
# [1] 55 130 205 280
Now form a matrix to hold the 4 sets:
xx <- matrix(NA, nrow=4,ncol=4)
for (i in 1:nrow(X) ) {xx[i, ] <- apply(X, 1, function(x) x %*% X[i,] )}
# Since you don't want the diagonal X[i, ]%*%X[i, ], zero them out:
diag(xx) <- 0
> xx
[,1] [,2] [,3] [,4]
[1,] 0 130 205 280
[2,] 130 0 530 730
[3,] 205 530 0 1180
[4,] 280 730 1180 0
sum(Y[1:4]*xx[1:4,])
# [1] 35800
You still have not really specified what your expectation was, so
there is no way to assess success at this end of the email-breathing-
straw
--
David Winsemius
Repeat for each row of X, that is
[prod(t(x_2) *x_1) + prod(t(x_2) *x_3) + prod(t(x_2) *x_4)] *y2
[prod(t(x_3) *x_1) + prod(t(x_3) *x_2) + prod(t(x_3) *x_4)] *y3
[prod(t(x_4) *x_1) + prod(t(x_4) *x_2) + prod(t(x_4) *x_3)] *y4
Hope this makes better sense ...
> by the remaining j rows
"remaining j rows" ==? What is "j", Is it nrow(X)-1 ? An what sort of
"multiplication by rows" do you mean? The inner product?
> multiplied by j y values (i.e sum( t(x_i) x_j y_j) )
"multiplied by j y values" ==? You defined Y but not y. Assuming that
you meant Y values, then we are still left to speculate about which of
the 5 Y values are suppose to be matched to the 3 rows of X.
>>> David Winsemius <dwinsem...@comcast.net> 2009/04/03 04:24 AM >>>
Generally unambiguous questions get answered quickly. Perhaps other
readers are having the same difficulties I am experiencing. So let's
try to parse what you are asking:
On Apr 2, 2009, at 8:26 AM, Kutlwano Ramaboa wrote:
> Hello
>
> This may have been answered elsewhere, and I have looked on the web,
> but nothing helps. I am trying to do the following:
>
> X<-matrix(c(1:15),nrow=3,byrow=T)
> Y<-matrix(c(2,4,6,8,10),ncol=1)
>
> I need to sum the product of each row of X
"sum the product of each row" ==? sum( prod(x[i, ] * ?
> by the remaining j rows
"remaining j rows" ==? What is "j", Is it nrow(X)-1 ? An what sort of
"multiplication by rows" do you mean? The inner product?
> multiplied by j y values (i.e sum( t(x_i) x_j y_j) )
"multiplied by j y values" ==? You defined Y but not y. Assuming that
you meant Y values, then we are still left to speculate about which of
the 5 Y values are suppose to be matched to the 3 rows of X.
>
>
> Hope this makes sense.
Not to me.
>
>
> Thanks in advance.
>
> Ps: how do I reference all the help that I have had from the R:
team?
?citation
>
>
> [[alternative HTML version deleted]]
David Winsemius, MD
Heritage Laboratories
West Hartford, CT
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David Winsemius, MD
Heritage Laboratories
West Hartford, CT
______________________________________________
R-help@r-project.org mailing list
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PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.
