# sumouter

0th

Percentile

##### Compute Quadratic Forms

Calculates certain quadratic forms of matrices.

Keywords
array
##### 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: $$M = \sum_i w_i x_i x_i^\top$$ where the sum is over all rows of x (after removing any rows containing NA or other non-finite values). 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.

##### Value

• A vector or matrix.

• sumouter
##### 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)