/*=========================================================================
 *
 *  Copyright NumFOCUS
 *
 *  Licensed 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
 *
 *         https://www.apache.org/licenses/LICENSE-2.0.txt
 *
 *  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.
 *
 *=========================================================================*/

#include "itkTDistribution.h"
#include "itkTestingMacros.h"
#include "itkStdStreamStateSave.h"
#include "itkMath.h"

int
itkTDistributionTest(int, char *[])
{
  // Save the format stream variables for std::cout
  // They will be restored when coutState goes out of scope
  itk::StdStreamStateSave coutState(std::cout);

  std::cout << "itkTDistribution Test \n \n";

  using DistributionType = itk::Statistics::TDistribution;

  auto distributionFunction = DistributionType::New();

  std::cout << "GetNameOfClass() = " << distributionFunction->GetNameOfClass() << std::endl;
  std::cout << "HasMean()        = " << distributionFunction->HasMean() << std::endl;
  std::cout << "Number of parameters = " << distributionFunction->GetNumberOfParameters() << std::endl;

  distributionFunction->Print(std::cout);

  int    i;
  double x;
  double value;
  double diff;

  int status = EXIT_SUCCESS;

  // Tolerance for the values.
  double tol;

  // expected values for Student-t cdf with 1 degree of freedom at
  // values of -5:1:5
  double expected1[] = { 6.283295818900114e-002, 7.797913037736926e-002, 1.024163823495667e-001, 1.475836176504333e-001,
                         2.500000000000000e-001, 5.000000000000000e-001, 7.500000000000000e-001, 8.524163823495667e-001,
                         8.975836176504333e-001, 9.220208696226308e-001, 9.371670418109989e-001 };


  std::cout << "Testing distribution with 1 degree of freedom" << std::endl;

  std::cout << "Student-t CDF" << std::endl;
  tol = 1e-15;
  std::cout << "Tolerance used for test: ";
  std::cout.width(20);
  std::cout.precision(15);
  std::cout << tol << std::endl;
  distributionFunction->SetDegreesOfFreedom(1);
  for (i = -5; i <= 5; ++i)
  {
    x = static_cast<double>(i);

    value = distributionFunction->EvaluateCDF(x);

    diff = itk::Math::abs(value - expected1[i + 5]);

    std::cout << "Student-t cdf at ";
    std::cout.width(2);
    std::cout << x << " with ";
    std::cout.width(2);
    std::cout << distributionFunction->GetDegreesOfFreedom() << " degrees of freedom = ";
    std::cout.width(20);
    std::cout << value << ", expected value = ";
    std::cout.width(20);
    std::cout << expected1[i + 5] << ", error = ";
    std::cout.width(22);
    std::cout << diff;
    if (diff < tol)
    {
      std::cout << ", Passed." << std::endl;
    }
    else
    {
      std::cout << ", Failed." << std::endl;
      status = EXIT_FAILURE;
    }
  }
  std::cout << std::endl;

  std::cout << "Inverse Student-t CDF" << std::endl;
  tol = 1e-10;
  std::cout << "Tolerance used for test: ";
  std::cout.width(20);
  std::cout.precision(15);
  std::cout << tol << std::endl;
  for (i = -5; i <= 5; ++i)
  {

    value = distributionFunction->EvaluateInverseCDF(expected1[i + 5]);

    diff = itk::Math::abs(value - static_cast<double>(i));

    std::cout << "Student-t cdf at ";
    std::cout.width(20);
    std::cout << expected1[i + 5] << " with ";
    std::cout.width(2);
    std::cout << distributionFunction->GetDegreesOfFreedom() << " degrees of freedom = ";
    std::cout.width(22);
    std::cout << value << ", expected value = ";
    std::cout.width(22);
    std::cout << static_cast<double>(i) << ", error = ";
    std::cout.width(22);
    std::cout << diff;
    if (diff < tol)
    {
      std::cout << ", Passed." << std::endl;
    }
    else
    {
      std::cout << ", Failed." << std::endl;
      status = EXIT_FAILURE;
    }
  }
  std::cout << std::endl;


  // expected values for Student-t cdf with 11 degrees of freedom at
  // values of -5:1:5
  double expected11[] = { 2.012649090622596e-004, 1.043096783487477e-003, 6.039919735960683e-003,
                          3.540197753401686e-002, 1.694003480981013e-001, 5.000000000000000e-001,
                          8.305996519018988e-001, 9.645980224659831e-001, 9.939600802640394e-001,
                          9.989569032165125e-001, 9.997987350909378e-001 };

  std::cout << "-----------------------------------------------" << std::endl << std::endl;
  std::cout << "Testing distribution with 11 degrees of freedom" << std::endl;

  std::cout << "Student-t CDF" << std::endl;
  tol = 1e-15;
  std::cout << "Tolerance used for test: ";
  std::cout.width(20);
  std::cout.precision(15);
  std::cout << tol << std::endl;
  distributionFunction->SetDegreesOfFreedom(11);
  for (i = -5; i <= 5; ++i)
  {
    x = static_cast<double>(i);

    value = distributionFunction->EvaluateCDF(x);

    diff = itk::Math::abs(value - expected11[i + 5]);

    std::cout << "Student-t cdf at ";
    std::cout.width(2);
    std::cout << x << " with ";
    std::cout.width(2);
    std::cout << distributionFunction->GetDegreesOfFreedom() << " degrees of freedom = ";
    std::cout.width(20);
    std::cout << value << ", expected value = ";
    std::cout.width(20);
    std::cout << expected11[i + 5] << ", error = ";
    std::cout.width(22);
    std::cout << diff;
    if (diff < tol)
    {
      std::cout << ", Passed." << std::endl;
    }
    else
    {
      std::cout << ", Failed." << std::endl;
      status = EXIT_FAILURE;
    }
  }
  std::cout << std::endl;

  std::cout << "Inverse Student-t CDF" << std::endl;
  tol = 1e-13;
  std::cout << "Tolerance used for test: ";
  std::cout.width(20);
  std::cout.precision(15);
  std::cout << tol << std::endl;
  for (i = -5; i <= 5; ++i)
  {

    value = distributionFunction->EvaluateInverseCDF(expected11[i + 5]);

    diff = itk::Math::abs(value - static_cast<double>(i));

    std::cout << "Student-t cdf at ";
    std::cout.width(20);
    std::cout << expected11[i + 5] << " with ";
    std::cout.width(2);
    std::cout << distributionFunction->GetDegreesOfFreedom() << " degrees of freedom = ";
    std::cout.width(22);
    std::cout << value << ", expected value = ";
    std::cout.width(22);
    std::cout << static_cast<double>(i) << ", error = ";
    std::cout.width(22);
    std::cout << diff;
    if (diff < tol)
    {
      std::cout << ", Passed." << std::endl;
    }
    else
    {
      std::cout << ", Failed." << std::endl;
      status = EXIT_FAILURE;
    }
  }


  // Same test but with the parameter vector API
  std::cout << "-----------------------------------------------" << std::endl << std::endl;
  std::cout << "Testing distribution with 11 degrees of freedom"
            << " (parameter vector API)" << std::endl;

  std::cout << "Student-t CDF" << std::endl;
  tol = 1e-15;
  std::cout << "Tolerance used for test: ";
  std::cout.width(20);
  std::cout.precision(15);
  std::cout << tol << std::endl;

  distributionFunction->SetDegreesOfFreedom(1); // clear settings
  DistributionType::ParametersType params(1);
  params[0] = 11;

  for (i = -5; i <= 5; ++i)
  {
    x = static_cast<double>(i);

    value = distributionFunction->EvaluateCDF(x, params);

    diff = itk::Math::abs(value - expected11[i + 5]);

    std::cout << "Student-t cdf at ";
    std::cout.width(2);
    std::cout << x << " with ";
    std::cout.width(2);
    std::cout << " 11 "
              << " degrees of freedom = ";
    std::cout.width(20);
    std::cout << value << ", expected value = ";
    std::cout.width(20);
    std::cout << expected11[i + 5] << ", error = ";
    std::cout.width(22);
    std::cout << diff;
    if (diff < tol)
    {
      std::cout << ", Passed." << std::endl;
    }
    else
    {
      std::cout << ", Failed." << std::endl;
      status = EXIT_FAILURE;
    }
  }
  std::cout << std::endl;

  std::cout << "Inverse Student-t CDF" << std::endl;
  tol = 1e-13;
  std::cout << "Tolerance used for test: ";
  std::cout.width(20);
  std::cout.precision(15);
  std::cout << tol << std::endl;
  for (i = -5; i <= 5; ++i)
  {

    value = distributionFunction->EvaluateInverseCDF(expected11[i + 5], params);

    diff = itk::Math::abs(value - static_cast<double>(i));

    std::cout << "Student-t cdf at ";
    std::cout.width(20);
    std::cout << expected11[i + 5] << " with ";
    std::cout.width(2);
    std::cout << " 11 "
              << " degrees of freedom = ";
    std::cout.width(22);
    std::cout << value << ", expected value = ";
    std::cout.width(22);
    std::cout << static_cast<double>(i) << ", error = ";
    std::cout.width(22);
    std::cout << diff;
    if (diff < tol)
    {
      std::cout << ", Passed." << std::endl;
    }
    else
    {
      std::cout << ", Failed." << std::endl;
      status = EXIT_FAILURE;
    }
  }


  // Same test but with the separate parameter API
  std::cout << "-----------------------------------------------" << std::endl << std::endl;
  std::cout << "Testing distribution with 11 degrees of freedom"
            << " (separate parameter API)" << std::endl;

  std::cout << "Student-t CDF" << std::endl;
  tol = 1e-15;
  std::cout << "Tolerance used for test: ";
  std::cout.width(20);
  std::cout.precision(15);
  std::cout << tol << std::endl;

  for (i = -5; i <= 5; ++i)
  {
    x = static_cast<double>(i);

    value = distributionFunction->EvaluateCDF(x, static_cast<itk::SizeValueType>(params[0]));

    diff = itk::Math::abs(value - expected11[i + 5]);

    std::cout << "Student-t cdf at ";
    std::cout.width(2);
    std::cout << x << " with ";
    std::cout.width(2);
    std::cout << " 11 "
              << " degrees of freedom = ";
    std::cout.width(20);
    std::cout << value << ", expected value = ";
    std::cout.width(20);
    std::cout << expected11[i + 5] << ", error = ";
    std::cout.width(22);
    std::cout << diff;
    if (diff < tol)
    {
      std::cout << ", Passed." << std::endl;
    }
    else
    {
      std::cout << ", Failed." << std::endl;
      status = EXIT_FAILURE;
    }
  }
  std::cout << std::endl;

  std::cout << "Inverse Student-t CDF" << std::endl;
  tol = 1e-13;
  std::cout << "Tolerance used for test: ";
  std::cout.width(20);
  std::cout.precision(15);
  std::cout << tol << std::endl;
  for (i = -5; i <= 5; ++i)
  {

    value = distributionFunction->EvaluateInverseCDF(expected11[i + 5], static_cast<itk::SizeValueType>(params[0]));
    diff = itk::Math::abs(value - static_cast<double>(i));

    std::cout << "Student-t cdf at ";
    std::cout.width(20);
    std::cout << expected11[i + 5] << " with ";
    std::cout.width(2);
    std::cout << " 11 "
              << " degrees of freedom = ";
    std::cout.width(22);
    std::cout << value << ", expected value = ";
    std::cout.width(22);
    std::cout << static_cast<double>(i) << ", error = ";
    std::cout.width(22);
    std::cout << diff;
    if (diff < tol)
    {
      std::cout << ", Passed." << std::endl;
    }
    else
    {
      std::cout << ", Failed." << std::endl;
      status = EXIT_FAILURE;
    }
  }


  DistributionType::ParametersType parameters(distributionFunction->GetNumberOfParameters());
  parameters[0] = 5.0;
  distributionFunction->SetParameters(parameters);

  unsigned long dof = 5;

  std::cout << "Variance() = " << distributionFunction->GetVariance() << std::endl;
  std::cout << "PDF(x,p) = " << distributionFunction->PDF(x, parameters) << std::endl;
  std::cout << "PDF(x,dof) = " << distributionFunction->PDF(x, dof) << std::endl;
  std::cout << "EvaluatePDF(x) = " << distributionFunction->EvaluatePDF(x) << std::endl;
  std::cout << "EvaluatePDF(x,p) = " << distributionFunction->EvaluatePDF(x, parameters) << std::endl;
  std::cout << "EvaluatePDF(x,dof) = " << distributionFunction->EvaluatePDF(x, dof) << std::endl;
  std::cout << "CDF(x,p) = " << distributionFunction->CDF(x, parameters) << std::endl;
  std::cout << "CDF(x,dof) = " << distributionFunction->CDF(x, dof) << std::endl;
  std::cout << "EvaluateCDF(x,p) = " << distributionFunction->EvaluateCDF(x, parameters) << std::endl;
  std::cout << "EvaluateCDF(x,dof) = " << distributionFunction->EvaluateCDF(x, dof) << std::endl;
  std::cout << "InverseCDF(x,p) = " << distributionFunction->InverseCDF(x, parameters) << std::endl;
  std::cout << "InverseCDF(x,dof) = " << distributionFunction->InverseCDF(x, dof) << std::endl;


  const unsigned int               wrongNumberOfParameters = distributionFunction->GetNumberOfParameters() * 42;
  DistributionType::ParametersType wrongParameters(wrongNumberOfParameters);
  wrongParameters.Fill(1.0);
  std::cout << "new number of parameters = " << wrongParameters.Size() << std::endl;
  std::cout << "current number of parameters = " << distributionFunction->GetParameters().Size() << std::endl;
  distributionFunction->SetParameters(wrongParameters);
  std::cout << "new set number of parameters = " << distributionFunction->GetParameters().Size() << std::endl;

  ITK_TRY_EXPECT_NO_EXCEPTION(distributionFunction->HasMean());
  ITK_TRY_EXPECT_EXCEPTION(distributionFunction->HasVariance());
  ITK_TRY_EXPECT_EXCEPTION(distributionFunction->GetVariance());
  ITK_TRY_EXPECT_EXCEPTION(distributionFunction->GetDegreesOfFreedom());
  ITK_TRY_EXPECT_EXCEPTION(distributionFunction->PDF(x, wrongParameters));
  ITK_TRY_EXPECT_EXCEPTION(distributionFunction->EvaluatePDF(x));
  ITK_TRY_EXPECT_EXCEPTION(distributionFunction->EvaluatePDF(x, wrongParameters));
  ITK_TRY_EXPECT_EXCEPTION(distributionFunction->CDF(x, wrongParameters));
  ITK_TRY_EXPECT_EXCEPTION(distributionFunction->InverseCDF(x, wrongParameters));
  ITK_TRY_EXPECT_EXCEPTION(distributionFunction->PDF(x, wrongParameters));
  ITK_TRY_EXPECT_EXCEPTION(distributionFunction->EvaluatePDF(x));
  ITK_TRY_EXPECT_EXCEPTION(distributionFunction->EvaluatePDF(x, wrongParameters));
  ITK_TRY_EXPECT_EXCEPTION(distributionFunction->EvaluateCDF(x));
  ITK_TRY_EXPECT_EXCEPTION(distributionFunction->EvaluateCDF(x, wrongParameters));
  ITK_TRY_EXPECT_EXCEPTION(distributionFunction->EvaluateInverseCDF(x));
  ITK_TRY_EXPECT_EXCEPTION(distributionFunction->EvaluateInverseCDF(x, wrongParameters));
  ITK_TRY_EXPECT_EXCEPTION(distributionFunction->CDF(x, wrongParameters));
  ITK_TRY_EXPECT_EXCEPTION(distributionFunction->InverseCDF(x, wrongParameters));

  DistributionType::ParametersType parameters1(1);
  parameters1[0] = 3.0;

  distributionFunction->SetParameters(parameters1);

  ITK_TRY_EXPECT_NO_EXCEPTION(distributionFunction->HasMean());
  ITK_TRY_EXPECT_NO_EXCEPTION(distributionFunction->HasVariance());
  ITK_TRY_EXPECT_NO_EXCEPTION(distributionFunction->GetMean());
  ITK_TRY_EXPECT_NO_EXCEPTION(distributionFunction->GetVariance());

  parameters1[0] = 1.5;

  distributionFunction->SetParameters(parameters1);

  ITK_TRY_EXPECT_NO_EXCEPTION(distributionFunction->HasMean());
  ITK_TRY_EXPECT_NO_EXCEPTION(distributionFunction->HasVariance());
  ITK_TRY_EXPECT_NO_EXCEPTION(distributionFunction->GetMean());
  ITK_TRY_EXPECT_NO_EXCEPTION(distributionFunction->GetVariance());

  std::cout << "Exercise negative argument " << std::endl;
  std::cout << "InverseCDF(x,p) = " << distributionFunction->InverseCDF(-1.0, dof) << std::endl;

  unsigned long newdof = 17;
  distributionFunction->SetDegreesOfFreedom(newdof);
  ITK_TEST_SET_GET_VALUE(newdof, distributionFunction->GetDegreesOfFreedom());


  DistributionType::ParametersType parameters2(2);
  parameters2[0] = 3.0;
  distributionFunction->SetParameters(parameters2);
  distributionFunction->SetDegreesOfFreedom(16);

  DistributionType::ParametersType parameters0(0);
  distributionFunction->SetParameters(parameters0);
  distributionFunction->Print(std::cout);

  return status;
}