lfe (version 1.7-1416)

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'))

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

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.

Examples

oldopts <- options(lfe.threads=1)
## 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 <- t(rBind(as(f1,'sparseMatrix'),as(f2,'sparseMatrix'),
as(f3,'sparseMatrix'), as(f4,'sparseMatrix')))
  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
  res <- D %*% sol - R
  sqrt(sum(res^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))
  options(oldopts)