# Licensed to the Apache Software Foundation (ASF) under one or more
# contributor license agreements.  See the NOTICE file distributed with
# this work for additional information regarding copyright ownership.
# The ASF licenses this file to You under the Apache License, Version 2.0
# (the "License"); you may not use this file except in compliance with
# the License.  You may obtain a copy of the License at
#
#      http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
#
#------------------------------------------------------------------------------
# R source file to validate Poisson distribution tests in
# org.apache.commons.math.distribution.PoissonDistributionTest
#
# To run the test, install R, put this file and testFunctions
# into the same directory, launch R from this directory and then enter
# source("<name-of-this-file>")
#
# R functions used
# dpois(x, lambda, log = FALSE) <-- density
# ppois(q, lambda, lower.tail = TRUE, log.p = FALSE) <-- distribution
# pnorm(q, mean=0, sd=1, lower.tail = TRUE, log.p = FALSE) <-- normal dist.
#------------------------------------------------------------------------------
tol <- 1E-10
#------------------------------------------------------------------------------
# Function definitions

source("testFunctions")           # utility test functions

# function to verify density computations

verifyDensity <- function(points, expected, lambda, tol) {
    rDensityValues <- rep(0, length(points))
    i <- 0
    for (point in points) {
        i <- i + 1
        rDensityValues[i] <- dpois(point, lambda, log = FALSE)
    }
    output <- c("Density test lambda = ", lambda)
    if (assertEquals(expected, rDensityValues, tol, "Density Values")) {
        displayPadded(output, SUCCEEDED, WIDTH)
    } else {
        displayPadded(output, FAILED, WIDTH)
    }       
}

# function to verify distribution computations

verifyDistribution <- function(points, expected, lambda, tol) {
    rDistValues <- rep(0, length(points))
    i <- 0
    for (point in points) {
        i <- i + 1
        rDistValues[i] <- ppois(point, lambda, log = FALSE)
    }
    output <- c("Distribution test lambda = ", lambda)
    if (assertEquals(expected, rDistValues, tol, "Distribution Values")) {
        displayPadded(output, SUCCEEDED, WIDTH)
    } else {
        displayPadded(output, FAILED, WIDTH)
    }       
}

# function to verify normal approximation

verifyNormalApproximation <- function(expected, lambda, lower, upper, tol) {
    rValue <- pnorm(upper, mean=lambda, sd=sqrt(lambda), lower.tail = TRUE,
               log.p = FALSE) - 
               pnorm(lower, mean=lambda, sd=sqrt(lambda), lower.tail = TRUE,
               log.p = FALSE)
    output <- c("Normal approx. test lambda = ", lambda, " upper = ",
               upper, " lower = ", lower)
    if (assertEquals(expected, rValue, tol, "Distribution Values")) {
        displayPadded(output, SUCCEEDED, WIDTH)
    } else {
        displayPadded(output, FAILED, WIDTH)
    }       
}

cat("Poisson distribution test cases\n")

# stock tests

lambda <- 4.0
densityPoints <- c(-1,0,1,2,3,4,5,10,20)
densityValues <- c(0, 0.0183156388887,  0.073262555555, 0.14652511111,
                   0.195366814813, 0.195366814813, 0.156293451851,
                   0.00529247667642, 8.27746364655e-09)
verifyDensity(densityPoints, densityValues, lambda, tol)


distributionPoints <- c(-1, 0, 1, 2, 3, 4, 5, 10, 20)
distributionValues <- c(0,  0.0183156388887, 0.0915781944437, 0.238103305554,
                        0.433470120367, 0.62883693518, 0.78513038703,
                        0.99716023388, 0.999999998077)
verifyDistribution(distributionPoints, distributionValues, lambda, tol)

# normal approximation tests

lambda <- 100
verifyNormalApproximation(0.706281887248, lambda, 89.5, 110.5, tol)

lambda <- 10000
verifyNormalApproximation(0.820070051552, lambda, 9899.5, 10200.5, tol)

displayDashes(WIDTH)