sumouter {spatstat} | R Documentation |
Calculates certain quadratic forms of matrices.
sumouter(x, w=NULL, y=x) quadform(x, v) bilinearform(x, v, y)
x,y |
A matrix, whose rows are the vectors in the quadratic form. |
w |
Optional vector of weights |
v |
Matrix determining the quadratic form |
The matrices x
and y
will be interpreted as
collections of row vectors. They must have the same number of rows.
The entries of x
and y
may be
numeric, integer, logical or complex values.
The command sumouter
computes the sum of the outer
products of corresponding row vectors, weighted by the entries of w
:
M = sum[i] (w[i] * outer(x[i,], y[i,]))
where x[i,] is the i
-th row of x
and y[i,] is the i
-th row of y
(after removing any rows containing NA
or other non-finite
values).
If w
is missing, the weights will be taken as 1.
The result is a p * q matrix where
p = ncol(x)
and q = ncol(y)
.
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
.
The command bilinearform
evaluates the more general bilinear
form defined by the matrix v
. Here x
and y
must
be matrices of the same dimensions. For each row vector of
x
and corresponding row vector of y
, the bilinear form is
z[i] = x[i,] %*% v %*% t(y[i,])
The result z
is a numeric vector of length n
where
n = nrow(x)
. If x[i,]
or y[i,]
contains NA
or
other non-finite values, then z[i] = NA
.
A vector or matrix.
Adrian Baddeley Adrian.Baddeley@curtin.edu.au 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 sumouter(x) w <- 4:1 sumouter(x, w) v <- matrix(1, 3, 3) quadform(x, v) # should be the same as quadform(x, v) bilinearform(x, v, x) # See what happens with NA's x[3,2] <- NA sumouter(x, w) quadform(x, v)