tests/testthat/test_CubicRoot.R

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

library(FixedPoint)
library(testthat)
context("Testing cubic root in 6 dimensions.")

Test_Of_Convergence = function(Function = function(x){ sign(x) * abs(x)^(1/3) }, 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 = 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 cubic root case to within tolerance", {
  expect_true(Test_Of_Convergence(Method = "Anderson")) # This takes 12  iterations.
  expect_true(Test_Of_Convergence(Method = "Simple"))   # This takes 22  iterations.
  expect_true(Test_Of_Convergence(Method = "Aitken"))   # This takes 9   iterations.
  expect_true(Test_Of_Convergence(Method = "Newton"))   # This takes 9   iterations.
  expect_true(Test_Of_Convergence(Method = "MPE"))      # This takes 9   iterations.
  expect_true(Test_Of_Convergence(Method = "RRE"))      # This takes 10  iterations.
  expect_true(Test_Of_Convergence(Method = "VEA"))      # This takes 13  iterations.
  expect_true(Test_Of_Convergence(Method = "SEA"))      # This takes 13  iterations.
})

Test_Of_FullDampening = function(Function = function(x){ sqrt(0.5*x) }, Inputs = c(0.3, 0.4,0.5,0.6,0.7,0.8), Outputs = c(), ConvergenceMetric  = function(Resids){max(abs(Resids))} , ConvergenceMetricThreshold = 1e-07, MaxIter = 1e3, MaxM = 10, PrintReports = TRUE, ReportingSigFig = 5){
  # Under full dampening (Dampening = 0) all methods in fact use the simple method. Thus convergence vectors from all should be equal.
  A = FixedPoint(Function = Function, Inputs = Inputs, Outputs = Outputs, Method = "Anderson", ConvergenceMetric = ConvergenceMetric, ConvergenceMetricThreshold = ConvergenceMetricThreshold, MaxIter = MaxIter, MaxM = MaxM, Dampening = 0, PrintReports = PrintReports, ReportingSigFig = ReportingSigFig)
  B = FixedPoint(Function = Function, Inputs = Inputs, Outputs = Outputs, Method = "Simple", ConvergenceMetric = ConvergenceMetric, ConvergenceMetricThreshold = ConvergenceMetricThreshold, MaxIter = MaxIter, MaxM = MaxM, Dampening = 0, PrintReports = PrintReports, ReportingSigFig = ReportingSigFig)
  C = FixedPoint(Function = Function, Inputs = Inputs, Outputs = Outputs, Method = "Aitken", ConvergenceMetric = ConvergenceMetric, ConvergenceMetricThreshold = ConvergenceMetricThreshold, MaxIter = MaxIter, MaxM = MaxM, Dampening = 0, PrintReports = PrintReports, ReportingSigFig = ReportingSigFig)
  D = FixedPoint(Function = Function, Inputs = Inputs, Outputs = Outputs, Method = "Newton", ConvergenceMetric = ConvergenceMetric, ConvergenceMetricThreshold = ConvergenceMetricThreshold, MaxIter = MaxIter, MaxM = MaxM, Dampening = 0, PrintReports = PrintReports, ReportingSigFig = ReportingSigFig)
  E = FixedPoint(Function = Function, Inputs = Inputs, Outputs = Outputs, Method = "MPE", ConvergenceMetric = ConvergenceMetric, ConvergenceMetricThreshold = ConvergenceMetricThreshold, MaxIter = MaxIter, MaxM = MaxM, Dampening = 0, PrintReports = PrintReports, ReportingSigFig = ReportingSigFig)
  G = FixedPoint(Function = Function, Inputs = Inputs, Outputs = Outputs, Method = "RRE", ConvergenceMetric = ConvergenceMetric, ConvergenceMetricThreshold = ConvergenceMetricThreshold, MaxIter = MaxIter, MaxM = MaxM, Dampening = 0, PrintReports = PrintReports, ReportingSigFig = ReportingSigFig)
  H = FixedPoint(Function = Function, Inputs = Inputs, Outputs = Outputs, Method = "VEA", ConvergenceMetric = ConvergenceMetric, ConvergenceMetricThreshold = ConvergenceMetricThreshold, MaxIter = MaxIter, MaxM = MaxM, Dampening = 0, PrintReports = PrintReports, ReportingSigFig = ReportingSigFig)
  I = FixedPoint(Function = Function, Inputs = Inputs, Outputs = Outputs, Method = "SEA", ConvergenceMetric = ConvergenceMetric, ConvergenceMetricThreshold = ConvergenceMetricThreshold, MaxIter = MaxIter, MaxM = MaxM, Dampening = 0, PrintReports = PrintReports, ReportingSigFig = ReportingSigFig)
  return(all(abs(A$Convergence - C$Convergence) < 1e-10, abs(B$Convergence - C$Convergence) < 1e-10, abs(C$Convergence - D$Convergence) < 1e-10,  abs(D$Convergence - E$Convergence) < 1e-10,  abs(E$Convergence - G$Convergence) < 1e-10,  abs(G$Convergence - H$Convergence) < 1e-10,  abs(H$Convergence - I$Convergence) < 1e-10 ))
}

test_that("Testing that full dampening means that all methods are same as simple iteration", {
  expect_true(Test_Of_FullDampening())
})