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/*=========================================================================
Program: Insight Segmentation & Registration Toolkit
Module: itkChiSquareDistribution.cxx
Language: C++
Date: $Date$
Version: $Revision$
Copyright (c) Insight Software Consortium. All rights reserved.
See ITKCopyright.txt or http://www.itk.org/HTML/Copyright.htm for details.
This software is distributed WITHOUT ANY WARRANTY; without even
the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR
PURPOSE. See the above copyright notices for more information.
=========================================================================*/
#include "itkChiSquareDistribution.h"
#include "itkGaussianDistribution.h"
#include "itkNumericTraits.h"
#include "vnl/vnl_math.h"
#include "vnl/vnl_erf.h"
extern "C" double dgami_(double *a, double *x);
extern "C" double dgamma_(double *x);
namespace itk {
namespace Statistics {
ChiSquareDistribution
::ChiSquareDistribution()
{
m_Parameters = ParametersType(1);
m_Parameters[0] = 1.0;
}
void
ChiSquareDistribution
::SetDegreesOfFreedom(long dof)
{
bool modified = false;
if (m_Parameters.GetSize() > 0)
{
if (m_Parameters[0] != static_cast<double>(dof) )
{
modified = true;
}
}
if (m_Parameters.GetSize() != 1)
{
m_Parameters = ParametersType(1);
}
m_Parameters[0] = static_cast<double>(dof);
if (modified)
{
this->Modified();
}
}
long
ChiSquareDistribution
::GetDegreesOfFreedom() const
{
if (m_Parameters.GetSize() != 1)
{
itkGenericExceptionMacro(
"Invalid number of parameters to describe distribution. Expected 1 parameter, but got "
<< m_Parameters.size()
<< " parameters.");
}
return static_cast<long>(m_Parameters[0]);
}
double
ChiSquareDistribution
::PDF(double x, long degreesOfFreedom)
{
double dof = static_cast<double>(degreesOfFreedom);
double dofon2 = 0.5*dof;
double pdf = 0.0;
if (x >= 0.0)
{
pdf = vcl_exp(-0.5*x) * vcl_pow(x, dofon2 - 1.0)
/ (vcl_pow(2.0, dofon2) * dgamma_(&dofon2));
}
return pdf;
}
double
ChiSquareDistribution
::PDF(double x, const ParametersType& p)
{
if (p.GetSize() != 1)
{
itkGenericExceptionMacro(
"Invalid number of parameters to describe distribution. Expected 1 parameter, but got "
<< p.size()
<< " parameters.");
}
return ChiSquareDistribution::PDF(x, static_cast<long>(p[0]));
}
double
ChiSquareDistribution
::CDF(double x, long degreesOfFreedom)
{
// Based on Abramowitz and Stegun 26.4.19 which relates the
// cumulative of the chi-square to incomplete (and complete) gamma
// function.
if (x < 0)
{
return 0.0;
}
double dofon2 = 0.5*degreesOfFreedom;
double xon2 = 0.5*x;
return dgami_(&dofon2, &xon2) / dgamma_(&dofon2);
}
double
ChiSquareDistribution
::CDF(double x, const ParametersType& p)
{
if (p.GetSize() != 1)
{
itkGenericExceptionMacro(
"Invalid number of parameters to describe distribution. Expected 1 parameter, but got "
<< p.size()
<< " parameters.");
}
return ChiSquareDistribution::CDF(x, (long) p[0]);
}
double
ChiSquareDistribution
::InverseCDF(double p, long degreesOfFreedom)
{
if (p <= 0.0)
{
return itk::NumericTraits<double>::Zero;
}
else if (p >= 1.0)
{
return itk::NumericTraits<double>::max();
}
double x;
double dof;
double nx;
// Based on Abramowitz and Stegun 26.4.17
dof = static_cast<double>(degreesOfFreedom);
nx = GaussianDistribution::InverseCDF(p);
double f = 2.0 / (9.0*dof);
x = dof*vcl_pow(1.0 - f + nx*vcl_sqrt(f), 3.0);
// The approximation above is only accurate for large degrees of
// freedom. We'll improve the approximation by a few Newton iterations.
//
// 0 iterations, error = 10^-1 at 1 degree of freedom
// 3 iterations, error = 10^-11 at 1 degree of freedom
// 10 iterations, erorr = 10^-13 at 1 degree of freedom
// 20 iterations, erorr = 10^-13 at 1 degree of freedom
//
// 0 iterations, error = 10^-1 at 11 degrees of freedom
// 3 iterations, error = 10^-8 at 11 degrees of freedom
// 10 iterations, erorr = 10^-13 at 11 degrees of freedom
// 20 iterations, erorr = 10^-13 at 11 degrees of freedom
//
// 0 iterations, error = 10^-1 at 100 degrees of freedom
// 3 iterations, error = 10^-9 at 100 degrees of freedom
// 10 iterations, erorr = 10^-10 at 100 degrees of freedom
// 20 iterations, erorr = 10^-9 at 100 degrees of freedom
// We are trying to find the zero of
//
// f(x) = p - chisquarecdf(x) = 0;
//
// So,
//
// x(n+1) = x(n) - f(x(n)) / f'(x(n))
// = x(n) + (p - chisquarecdf(x)) / chisquarepdf(x)
//
// Note that f'(x) = - chisquarepdf(x)
//
double delta;
for (unsigned int newt = 0; newt < 10; ++newt)
{
delta = (p - ChiSquareDistribution::CDF(x, degreesOfFreedom))
/ ChiSquareDistribution::PDF(x, degreesOfFreedom);
x += delta;
}
return x;
}
double
ChiSquareDistribution
::InverseCDF(double p, const ParametersType& params)
{
if( params.GetSize() != 1 )
{
itkGenericExceptionMacro(
"Invalid number of parameters to describe distribution. Expected 1 parameter, but got "
<< params.size()
<< " parameters.");
}
return ChiSquareDistribution::InverseCDF(p, static_cast<long>(params[0]));
}
double
ChiSquareDistribution
::EvaluatePDF(double x) const
{
if( m_Parameters.GetSize() != 1 )
{
itkGenericExceptionMacro(
"Invalid number of parameters to describe distribution. Expected 1 parameter, but got "
<< m_Parameters.size()
<< " parameters.");
}
return ChiSquareDistribution::PDF(x, static_cast<long>(m_Parameters[0]));
}
double
ChiSquareDistribution
::EvaluatePDF(double x, const ParametersType& p) const
{
if( p.GetSize() != 1 )
{
itkGenericExceptionMacro(
"Invalid number of parameters to describe distribution. Expected 1 parameter, but got "
<< p.size()
<< " parameters.");
}
return ChiSquareDistribution::PDF(x, static_cast<long>(p[0]));
}
double
ChiSquareDistribution
::EvaluatePDF(double x, long degreesOfFreedom) const
{
return ChiSquareDistribution::PDF(x, degreesOfFreedom);
}
double
ChiSquareDistribution
::EvaluateCDF(double x) const
{
if( m_Parameters.GetSize() != 1 )
{
itkGenericExceptionMacro(
"Invalid number of parameters to describe distribution. Expected 1 parameter, but got "
<< m_Parameters.size()
<< " parameters.");
}
return ChiSquareDistribution::CDF(x, static_cast<long>(m_Parameters[0]));
}
double
ChiSquareDistribution
::EvaluateCDF(double x, const ParametersType& p) const
{
if( p.GetSize() != 1 )
{
itkGenericExceptionMacro(
"Invalid number of parameters to describe distribution. Expected 1 parameter, but got "
<< p.size()
<< " parameters.");
}
return ChiSquareDistribution::CDF(x, static_cast<long>(p[0]));
}
double
ChiSquareDistribution
::EvaluateCDF(double x, long degreesOfFreedom) const
{
return ChiSquareDistribution::CDF(x, degreesOfFreedom);
}
double
ChiSquareDistribution
::EvaluateInverseCDF(double p) const
{
if( m_Parameters.GetSize() != 1 )
{
itkGenericExceptionMacro(
"Invalid number of parameters to describe distribution. Expected 1 parameter, but got "
<< m_Parameters.size()
<< " parameters.");
}
return ChiSquareDistribution::InverseCDF(p, static_cast<long>(m_Parameters[0]));
}
double
ChiSquareDistribution
::EvaluateInverseCDF(double p, const ParametersType& params) const
{
if( params.GetSize() != 1 )
{
itkGenericExceptionMacro(
"Invalid number of parameters to describe distribution. Expected 1 parameter, but got "
<< params.size()
<< " parameters.");
}
return ChiSquareDistribution::InverseCDF(p, static_cast<long>(params[0]));
}
double
ChiSquareDistribution
::EvaluateInverseCDF(double p, long degreesOfFreedom) const
{
return ChiSquareDistribution::InverseCDF(p, degreesOfFreedom);
}
double
ChiSquareDistribution
::GetMean() const
{
if( m_Parameters.GetSize() != 1 )
{
itkGenericExceptionMacro(
"Invalid number of parameters to describe distribution. Expected 1 parameter, but got "
<< m_Parameters.size()
<< " parameters.");
}
return m_Parameters[0];
}
double
ChiSquareDistribution
::GetVariance() const
{
if( m_Parameters.GetSize() != 1 )
{
itkGenericExceptionMacro(
"Invalid number of parameters to describe distribution. Expected 1 parameter, but got "
<< m_Parameters.size()
<< " parameters.");
}
return 2.0 * m_Parameters[0];
}
void
ChiSquareDistribution
::PrintSelf(std::ostream& os, Indent indent) const
{
Superclass::PrintSelf(os,indent);
if (m_Parameters.GetSize() > 0)
{
os << indent << "Degrees of freedom: "
<< static_cast<long>(m_Parameters[0]) << std::endl;
}
else
{
os << indent << "Degrees of freedom: (unknown)"
<< std::endl;
}
}
} // end of namespace Statistics
} // end namespace itk
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