tests/testthat/test_LinearRoot.R

In FixedPoint: Algorithms for Finding Fixed Point Vectors of Functions

library(FixedPoint)
library(testthat)
library(SQUAREM)
context("Testing all convergence methods for a simple linear fixed point problem.")

Test_Of_Convergence = function(Function = function(x){ 95*(18-x) }, Inputs = c(0.3, 0.4,0.5,0.6,0.7,0.8), Outputs = c(), Method = c("Newton") , ConvergenceMetric  = function(Resids){max(abs(Resids))} , ConvergenceMetricThreshold = 1e-10, MaxIter = 1e3, MaxM = 10, Dampening = 1, PrintReports = FALSE, ReportingSigFig = 5, ConditionNumberThreshold = 1e10){

  A = FixedPoint(Function = Function, Inputs = Inputs, Outputs = Outputs, Method = Method, ConvergenceMetric = ConvergenceMetric, ConvergenceMetricThreshold = ConvergenceMetricThreshold, MaxIter = MaxIter, MaxM = MaxM, Dampening = Dampening, PrintReports = PrintReports, ReportingSigFig = ReportingSigFig)
  cat(paste0("The ", Method, " method took ", length(A$Convergence), " iterations and finished with ", A$Finish, "\n"))
  return((A$Convergence[length(A$Convergence)] < ConvergenceMetricThreshold))
}

test_that("Testing that each method converges in the linear case to within tolerance", {
  expect_true(Test_Of_Convergence(Method = "Anderson")) # This takes 5   iterations.
  #expect_true(Test_Of_Convergence(Method = "Simple"))  # Does not converge.
  expect_true(Test_Of_Convergence(Method = "Aitken"))   # This takes 3   iterations.
  expect_true(Test_Of_Convergence(Method = "Newton"))   # This takes 3   iterations.
  expect_true(Test_Of_Convergence(Method = "VEA"))      # This takes 25  iterations.
  #expect_true(Test_Of_Convergence(Method = "SEA"))     # Does not converge.
  expect_true(Test_Of_Convergence(Method = "MPE"))     # This takes 19  iterations. Fails in OpenBLAS
  expect_true(Test_Of_Convergence(Method = "RRE"))     # This takes 7   iterations.
})
#Function = function(x){ 95*(18-x) }
#Inputs = c(0.3, 0.4,0.5,0.6,0.7,0.8)
#sqm = SQUAREM::squarem(Inputs,Function, control=list(tol= 1e-10*4 )) # This throws an error. Does not converge.
#convergence = sum(abs(sqm$par - Function(sqm$par) ))
#cat(paste0("The squarem method took ", sqm$fpevals, " iterations and finished with convergence of ", convergence, "\n"))