# sumouter

0th

Percentile

Calculates certain quadratic forms of matrices.

Keywords
array
##### Usage
sumouter(x, w=NULL)
bilinearform(x, v, y)
##### Arguments
x,y
A matrix, whose rows are the vectors in the quadratic form.
w
Optional vector of weights
v
##### 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: $$M = \sum_i w_i x_i x_i^\top$$ where the sum is over all rows of x (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 $p \times p$ 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: $$y_i = x_i V x_i^\top$$ 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 dimensins. For each of the row vectors of x and corresponding row vector of y, the bilinear form is $$z_i = x_i V y_i^\top$$ 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.

##### Value

• A vector or matrix.

• sumouter
• bilinearform
##### Examples
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)