lfe (version 2.9-0)

kaczmarz: Solve a linear system defined by factors

Description

Uses the Kaczmarz method to solve a system of the type Dx = R, where D is the matrix of dummies created from a list of factors.

Usage

kaczmarz(
  fl,
  R,
  eps = getOption("lfe.eps"),
  init = NULL,
  threads = getOption("lfe.threads")
)

Value

A vector x of length equal to the sum of the number of levels of the factors in fl, which solves the system \(Dx=R\). If the system is inconsistent, the algorithm may not converge, it will give a warning and return something which may or may not be close to a solution. By setting eps=0, maximum accuracy (with convergence warning) will be achieved.

Arguments

fl

A list of arbitrary factors of the same length

R

numeric. A vector, matrix or list of such of the same length as the factors

eps

a tolerance for the method

init

numeric. A vector to use as initial value for the Kaczmarz iterations. The algorithm converges to the solution closest to this

threads

integer. The number of threads to use when R is more than one vector

See Also

cgsolve()

Examples

## create factors
f1 <- factor(sample(24000, 100000, replace = TRUE))
f2 <- factor(sample(20000, length(f1), replace = TRUE))
f3 <- factor(sample(10000, length(f1), replace = TRUE))
f4 <- factor(sample(8000, length(f1), replace = TRUE))
## the matrix of dummies
D <- makeDmatrix(list(f1, f2, f3, f4))
dim(D)
## an x
truex <- runif(ncol(D))
## and the right hand side
R <- as.vector(D %*% truex)
## solve it
sol <- kaczmarz(list(f1, f2, f3, f4), R)
## verify that the solution solves the system Dx = R
sqrt(sum((D %*% sol - R)^2))
## but the solution is not equal to the true x, because the system is
## underdetermined
sqrt(sum((sol - truex)^2))
## moreover, the solution from kaczmarz has smaller norm
sqrt(sum(sol^2)) < sqrt(sum(truex^2))