# Marja de eroare pentru comparatii pe numere reale.
EPSILON <- 10e-9

CONST_DISP <- 5

# De cate ori verificam sa fie PDF pe fiecare interval al functiei date.
TESTS <- 500

equalToOne <- function (x)
{
  return (x < 1 + EPSILON & x > 1 - EPSILON)
}

calcIntegralSum <- function (myFunc, domain)
{
  sum <- 0
  for (i in domain)
    sum <- sum + integrate (Vectorize (myFunc), i[1], i[2])$value
  return (sum)
}

# Ca o functie sa fie densitate de probabilitate trebuie sa fie pozitiva, iar integrala ei pe R sa fie 1.
checkDensProb <- function (myFunc, domain = list (c (-Inf, Inf)), constNorm = 1)
{
  tryCatch (
    {
      # Calculam suma integralelor, similar cu cerinta 1.
      integralSum <- calcIntegralSum (myFunc, domain)

      # Comparam cu 1 folosindu-ne de EPSILON.
      if (equalToOne (integralSum / constNorm))
      {
        # Pentru fiecare interval al functiei, verificam daca este PDF.
        for (i in domain)
        {
          # Verificam intervalul [st, dr].
          st <- max(i[1], -2e9)
          dr <- min(i[2], 2e9)

          length <- dr / CONST_DISP - st / CONST_DISP
          nrs <- runif (TESTS, st, dr-length)

          # Testam TESTS subintervale de lungime egala.
          for (mn in nrs)
          {
            mx = mn + length
            # Daca integrala este negativa, functia nu este PDF.
            if (integrate (Vectorize (myFunc), mn, mx)$value < 0) return (FALSE)
          }
        }
        return (TRUE)
      }
      return (FALSE)
    },
    error = function (e)
    {
      # Daca integrarea a esuat, returnam false.
      return (FALSE)
    })
}

isPdf <- function(f, suport = list(c(-Inf, Inf)), normCt = 1, TCNT = 1000){

  tryCatch({

    integratedVal <- 0

    for(interval in suport){

      integratedVal <- integratedVal + integrate(Vectorize(f), lower = interval[1], upper = interval[2])$value
    }

    if((integratedVal / normCt) < 1 + 10e-9 & (integratedVal / normCt) > 1 - 10e-9){

      cnt <- TCNT / length(suport)

      for(interval in suport){

        lowRand <- 0
        upperRand <- 0

        if(interval[1] == -Inf){
          lowRand <- -.Machine$integer.max
        }
        else{
          lowRand <- interval[1]
        }

        if(interval[2] == Inf){
          upperRand <- .Machine$integer.max
        }
        else{
          upperRand <- interval[2]
        }

        testLen <- upperRand / 10 - lowRand / 10

        rands <- runif(cnt, lowRand, upperRand - testLen)

        for(x in c(1:cnt)){

          lowerBound <- rands[x]
          upperBound = lowerBound + testLen

          if(lowerBound > upperBound){

            swapAux <- upperBound
            upperBound <- lowerBound
            lowerBoud <- swapAux
          }

          if(integrate(Vectorize(f), lower = lowerBound, upper = upperBound)$value < 0)
            return(FALSE)
        }

      }

      return(TRUE)
    }
    else
      return(FALSE)

  },
  error = function(err){

    message(paste("eroare a functiei isPdf: ", err))
    return(FALSE)
  })

}