# read arguments from endpoint calling subroutine
args = commandArgs(trailingOnly = TRUE)

N = as.numeric(args[1])
ToSelect = as.numeric(args[2])
BaseRate = as.numeric(args[3]) / 100
Validity = as.numeric(args[4])

# DISCLAIMER: The code below is not my original work. It was obtained from a third-party source and used for learning purposes. Credit goes to the original author.
# Adapted from: https://www.r-bloggers.com/2012/02/reflect-your-personnel-selection-r-taylor-russell-tables/

F1 = function(P) {
  SPLIT = 0.42
  A0 = 2.50662823884
  A1 = -18.61500062529
  A2 = 41.391199773534
  A3 = -25.44106049637
  B1 = -8.4735109309
  B2 = 23.08336743743
  B3 = -21.06224101826
  B4 = 3.13082909833
  C0 = -2.78718931138
  C1 = -2.29796479134
  C2 = 4.85014127135
  C3 = 2.32121276858
  D1 = 3.54388924762
  D2 = 1.63706781897 
  Q = P - 0.5
  if (abs(Q) <= SPLIT) {
    R = Q*Q
    PPN = Q * (((A3 * R + A2) * R + A1) * R + A0) / ((((B4 * R + B3) * R + B2) * R + B1)*R +1.0)
    return(PPN)
  }
  R = P
  if (Q > 0) {R =1.0-P}
  if (R <= 0) {
    print("You have entered a value that is not permitted. The result is false.")
    return(0)
  }
  R = sqrt(-log(R))
  PPN = (((C3 * R + C2) * R + C1) * R + C0) / ((D2 * R + D1) * R + 1.0)
  if (Q < 0) {PPN =-PPN}
  return(PPN)
}


F2 = function(X) {
  P1A = 242.667955230532
  P1B = 21.97926616182942
  P1C = 6.996383488661914
  P1D = -3.5609843701815E-02
  Q1A = 215.058875869861
  Q1B = 91.1649054045149
  Q1C = 15.0827976304078
  Q1D = 1.0
  P2A = 300.459261020162
  P2B = 451.918953711873
  P2C = 339.320816734344
  P2D = 152.98928504694
  P2E = 43.1622272220567
  P2F = 7.21175825088309
  P2G = .564195517478994
  P2H = -1.36864857382717E-07
  Q2A = 300.459260956983
  Q2B = 790.950925327898
  Q2C = 931.35409485061
  Q2D = 638.980264465631
  Q2E = 277.585444743988
  Q2F = 77.0001529352295
  Q2G = 12.7827273196294
  Q2H = 1.0
  P3A = -2.99610707703542E-03
  P3B = -4.94730910623251E-02
  P3C = -.226956593539687
  P3D = -.278661308609648
  P3E = -2.23192459734185E-02
  Q3A = 1.06209230528468E-02
  Q3B = .19130892610783
  Q3C = 1.05167510706793
  Q3D = 1.98733201817135
  Q3E = 1.0
  SQRT2 = 1.4142135623731
  SQRTPI = 1.77245385090552
  
  Y = X/SQRT2
  if (Y < 0) {
    Y = -Y
    SN = -1.0
  } else {
    SN = 1.0
  }
  Y2 = Y * Y
  if (Y < 0.46875) {
    R1 = ((P1D * Y2 + P1C) * Y2 + P1B) * Y2 + P1A
    R2 = ((Q1D * Y2 + Q1C) * Y2 + Q1B) * Y2 + Q1A
    ERFVAL = Y * R1 / R2
    if (SN == 1) LOAREA = 0.5 + 0.5 * ERFVAL
    else LOAREA = 0.5 - 0.5 * ERFVAL
  } else {
    if (Y < 4.0) {
      R1 = ((((((P2H * Y + P2G) * Y + P2F) * Y + P2E) * Y + P2D) * Y + P2C) * Y + P2B) * Y + P2A
      R2 = ((((((Q2H * Y + Q2G) * Y + Q2F) * Y + Q2E) * Y + Q2D) * Y + Q2C) * Y + Q2B) * Y + Q2A
      ERFCVAL = exp(-Y2) * R1 / R2
    } else {
      Z = Y2 * Y2
      R1 = (((P3E * Z + P3D) * Z + P3C) * Z + P3B) * Z + P3A
      R2 = (((Q3E * Z + Q3D) * Z + Q3C) * Z + Q3B) * Z + Q3A
      ERFCVAL = (exp(-Y2) / Y) * (1.0 / SQRTPI + R1 / (R2 * Y2))
    }
    if (SN == 1) LOAREA = 1.0 - 0.5 * ERFCVAL
    else LOAREA = 0.5 * ERFCVAL
  }
  UPAREA = 1.0 - LOAREA
  return(UPAREA)
}


F3 = function(H1, HK, R) {
  X = c(0.04691008, 0.23076534, 0.5, 0.76923466, 0.95308992)
  W = c(0.018854042, 0.038088059, 0.0452707394, 0.038088059, 0.018854042)
  H2 = HK
  H12 = (H1*H1 + H2*H2)/2.0
  BV = 0
  if (abs(R) >= 0.7) {
    R2 = 1.0-R*R
    R3 = sqrt(R2)
    if (R < 0) H2 = -H2
    H3 = H1*H2
    H7 = exp(-H3 / 2.0)
    if (R2 != 0) {
      H6 = abs(H1 - H2)
      H5 = H6 * H6 / 2.0
      H6 = H6 / R3
      AA = 0.5 - (H3 / 8.0)
      AB = 3.0 - (2.0 * AA * H5)
      BV = 0.13298076 * H6 * AB * F2(H6) - exp(-H5 / R2) * (AB + AA * R2) * 0.053051647
      for (i in 1:5) {
        R1 = R3 * X[i]
        RR = R1 * R1
        R2 = sqrt( 1.0- RR)
        BV = BV - W[i] * exp(-H5 / RR) * (exp(-H3 / (1.0 + R2)) / R2 / H7 - 1.0 - AA    * RR)
      }
    }
    if (R > 0 & H1 > H2) {
      BV = BV * R3 * H7 + F2(H1)
      return(BV)
    }
    if (R > 0 & H1 <= H2) {
      BV = BV * R3 * H7 + F2(H2)
      return(BV)
    }
    if (R < 0 & (F2(H1) - F2(H2)) < 0) {
      BV = 0 - BV * R3 * H7
      return(BV)
    }
    if (R < 0 & (F2(H1) - F2(H2)) >= 0) {
      BV = (F2(H1) - F2(H2)) - BV * R3 * H7
      return(BV)
    }
  }
  H3 = H1 * H2
  for (i in 1:5)
  {
    R1 = R * X[i]
    RR2 = 1.0 - R1 * R1
    BV = BV + W[i] * exp((R1 * H3 - H12) / RR2) / sqrt(RR2)
  }
  BV = F2(H1) * F2(H2) + R * BV
  return(BV)
}


true_positives = function(N, ToSelect,BaseRate, Validity) {round(F3(F1(1.0-ToSelect/N), F1(1.0-BaseRate), Validity)/(ToSelect/N)*ToSelect,1)}
false_positives = function(N, ToSelect,BaseRate, Validity) {round(ToSelect-F3(F1(1.0-ToSelect/N), F1(1.0-BaseRate), Validity)/(ToSelect/N)*ToSelect,1)}
false_negatives = function(N, ToSelect,BaseRate, Validity) {round(N*BaseRate - F3(F1(1.0-ToSelect/N), F1(1.0-BaseRate), Validity)/(ToSelect/N)*ToSelect,1)}
true_negatives = function(N, ToSelect,BaseRate, Validity) {N - true_positives(N, ToSelect,BaseRate, Validity) - false_positives(N, ToSelect,BaseRate, Validity) - false_negatives(N, ToSelect,BaseRate, Validity)}

payload = list(
    "true_positives" = true_positives(N, ToSelect,BaseRate, Validity),
    "false_positives" = false_positives(N, ToSelect,BaseRate, Validity),
    "false_negatives" = false_negatives(N, ToSelect,BaseRate, Validity),
    "true_negatives" = true_negatives(N, ToSelect,BaseRate, Validity)
)

# export results as JSON for the endpoint
library(jsonlite)
cat(toJSON(payload, auto_unbox = TRUE))