tests/testthat/test_SimpleCrossVectorDependent.R

In s-baumann/FixedPoint: Algorithms for Finding Fixed Point Vectors of Functions

library(FixedPoint)
library(testthat)
context("Testing all convergence methods for a simple vector dependent fixed point problem. This means x[2] depends directly on previous x[1]s and x[2]s and similarly for x[1].")

# Note that this has three fixed points. (0,0) and (1,3) and (-1,3).
# If we remove the absolute value function from inside the sqrt then there are only the first two. If this were our actual function
# only simple iteration would work while the other two would eventually return a negative in the square root and cause an error.

Test_Of_Convergence = function(Function = function(x){c(0.5*sqrt(abs(x[1] + x[2])), 1.5*x[1] + 0.5*x[2])}, Inputs = c(0.3,900), Outputs = c(), Method = c("Newton") , ConvergenceMetric  = function(Resids){max(abs(Resids))} , ConvergenceMetricThreshold = 1e-10, MaxIter = 1e3, MaxM = 10, Dampening = 1, PrintReports = TRUE, 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)

  return((A$Convergence[length(A$Convergence)] < ConvergenceMetricThreshold))
}

test_that("Testing that each method converges in the quadratic case to within tolerance", {
  expect_true(Test_Of_Convergence(Method = "Anderson")) # This takes 14  iterations.
  expect_true(Test_Of_Convergence(Method = "Simple"))   # This takes 105 iterations.
  expect_true(Test_Of_Convergence(Method = "Aitken"))   # This takes 67  iterations.
  expect_true(Test_Of_Convergence(Method = "Newton"))   # This takes 239 iterations.
  expect_true(Test_Of_Convergence(Method = "VEA"))      # This takes 20  iterations.
  expect_true(Test_Of_Convergence(Method = "SEA"))      # This takes 25  iterations.
  expect_true(Test_Of_Convergence(Method = "MPE"))      # This takes 31  iterations.
  expect_true(Test_Of_Convergence(Method = "RRE"))      # This takes 31  iterations.
})