sumouter {spatstat}R Documentation

Compute Quadratic Forms

Description

Calculates certain quadratic forms of matrices.

Usage

  sumouter(x, w)
  quadform(x, v)

Arguments

x

A matrix, whose rows are the vectors in the quadratic form.

w

Vector of weights

v

Matrix determining the quadratic form

Details

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.

Value

A vector or matrix.

Author(s)

Adrian Baddeley Adrian.Baddeley@csiro.au http://www.maths.uwa.edu.au/~adrian/ and Rolf Turner r.turner@auckland.ac.nz

Examples

  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)

[Package spatstat version 1.25-3 Index]