sumouter {spatstat} | R Documentation |
Calculates certain quadratic forms of matrices.
sumouter(x, w) quadform(x, v)
x |
A matrix, whose rows are the vectors in the quadratic form. |
w |
Vector of weights |
v |
Matrix determining the quadratic form |
The matrix x
will be interpreted as a collection of row vectors.
The command sumouter
computes the sum of the outer
products of these vectors, weighted by the entries of w
:
M = sum[i] (w[i] * outer(x[i,], x[i,]))
where the sum is over all rows of x
(after removing any rows containing NA
or other non-finite values).
The result is a p * p matrix where
p = ncol(x)
.
The command quadform
evaluates the quadratic form, defined by
the matrix v
, for each of the row vectors of x
:
y[i] = x[i,] %*% v %*% t(x[i,])
The result y
is a numeric vector of length n
where
n = nrow(x)
. If x[i,]
contains NA
or
other non-finite values, then y[i] = NA
.
A vector or matrix.
Adrian Baddeley Adrian.Baddeley@csiro.au http://www.maths.uwa.edu.au/~adrian/ and Rolf Turner r.turner@auckland.ac.nz
x <- matrix(1:12, 4, 3) dimnames(x) <- list(c("Wilma", "Fred", "Barney", "Betty"), letters[1:3]) x w <- 4:1 sumouter(x, w) v <- matrix(1, 3, 3) quadform(x, v) # See what happens with NA's x[3,2] <- NA sumouter(x, w) quadform(x, v)