General-purpose mathematical functions and function templates. More...

#include <cmtkMathUtil.h>

Classes
class	BitInitializer
	Helper class to initialize a constant 64bit field. More...
Static Public Member Functions
template<class T >
static bool	IsNaN (const T value)
	Portable test for "not a number" values.
static double	GetDoubleNaN ()
	Get double-precision not-a-number (NaN) value.
static float	GetFloatNaN ()
	Get single-precision not-a-number (NaN) value.
static double	GetDoubleInf ()
	Get double-precision infinite (Inf) value.
static float	GetFloatInf ()
	Get single-precision infinite (Inf) value.
static double	Sin (const Units::Radians &radians)
	Unit-safe sin() function.
static double	Cos (const Units::Radians &radians)
	Unit-safe cos() function.
static double	Tan (const Units::Radians &radians)
	Unit-safe tan() function.
static const Units::Radians	ArcSin (const double value)
	Unit-safe asin() function.
static const Units::Radians	ArcCos (const double value)
	Unit-safe acos() function.
static const Units::Radians	ArcTan (const double value)
	Unit-safe aten() function.
static const Units::Radians	ArcTan2 (const double y, const double x)
	Unit-safe atan2() function.
template<class T >
static T	Square (const T a)
	Return square of a float value.
template<class T >
static T	Min (const int nValues, const T *Values)
	Return minimum of an array of ordered values.
template<class T >
static T	Max (const int nValues, const T *Values)
	Return minimum of an array of ordered values.
template<class T >
static T	Intersect (const T aMin, const T aMax, const T bMin, const T bMax)
	Return length of intersection of two intervals.
template<class T >
static int	Round (const T a)
	Round float value to the nearest integer.
template<class T >
static int	Sign (const T a)
	Return sign of float value.
template<class T >
static int	CheckRange (const T value, const T a, const T b)
	Check if some float value is within a range.
template<class T >
static double	plogp (const T p)
	Compute p*log(p) for a single value.
template<class T >
static T	Mean (const unsigned int nValues, const T *values)
	Computes average of an array of float values.
template<class T >
static T	Mean (const std::vector< T > &values)
	Computes average of a vector of float values.
template<class T >
static T	Variance (const unsigned int nValues, const T *values, T mean, const bool unbiased=false)
	Computes variance of an array of float values.
template<class T >
static T	Variance (const std::vector< T > &values, T mean, const bool unbiased=false)
	Computes variance of a vector of float values.
template<class T >
static T	Correlation (const std::vector< T > &x, const std::vector< T > &y)
	Normalized correlation coefficient between two float vectors.
static double	TStatFromCorrelation (const double r, const size_t df)
	Compute t-statistic from coefficient of correlation.
static double	ProbabilityFromTStat (const double t, const size_t df)
	Compute probability from T-statistic.
template<class T >
static T	TTest (const std::vector< T > &valuesX, const std::vector< T > &valuesY, T &t)
	Performs two-tailed unpaired t-test on two distributions.
template<class T >
static T	TTest (const std::vector< T > &valuesX, const std::vector< T > &valuesY, T &t, T &avgX, T &avgY)
	Performs two-tailed unpaired t-test on two distributions.
template<class T >
static T	PairedTTest (const std::vector< T > &valuesX, const std::vector< T > &valuesY, T &t, T &avgX, T &avgY)
	Performs two-tailed paired t-test on two distributions.
template<class T >
static T	TTest (const std::vector< T > &valuesX, T &t, T &avgX)
	Performs one-sample t-test on distribution to test for zero mean.
static double	Betai (const double a, const double b, const double x)
	Beta-i function.
static double	BetaCf (const double a, const double b, const double x)
	Beta-Cf function.
static double	GammaLn (const double xx)
	GammaLn function.
static void	SVD (Matrix2D< double > U, size_t m, size_t n, std::vector< double > W, Matrix2D< double > *V)
	Singular Value Decomposition.
static void	SVDLinearRegression (Matrix2D< double > U, size_t m, size_t n, std::vector< double > W, Matrix2D< double > V, double b, std::vector< double > &lm_params)
	Linear Regression using SVD results.
static int	CompareFloat (const void a, const void b)
	Function that compares two floats; to be used in qsort().
static int	CompareDouble (const void a, const void b)
	Function that compares two doubles; to be used in qsort().
static double	NormalRandom (const double sigma)
	Generate normally distributed random numbers.
static double	NormalRandom (const double sigma, const unsigned int seed)
	Generate normally distributed random numbers with explicit seed.
static double	UniformRandom ()
	Uniform random number generator.
template<class T >
static void	ComputeEigensystem (const Matrix2D< T > &matrix, Matrix2D< T > &eigensystem, std::vector< T > &eigenvalues)
	Compute eigensystem and eigenvalues for square real matrix using Jacobi rotation.
template<class T >
static void	ComputeEigenvalues (const Matrix2D< T > &matrix, std::vector< T > &eigenvalues)
	Compute eigenvalues for square real matrix using Jacobi rotation.
template<class T >
static T	CholeskyDeterminant (const Matrix2D< T > &matrix, int n)
	Determinant of an n x n square matrix.
Public Attributes
const FPInitializeUnion	FPInitializeNaN
const FPInitializeUnion	FPInitializeInf
const void *	FPInitializeNaN_P = &FPInitializeNaN
const void *	FPInitializeInf_P = &FPInitializeInf
const void *	FPInitializeNaN_fP = &FPInitializeNaN.f[1]
const void *	FPInitializeInf_fP = &FPInitializeInf.f[1]
Private Types
typedef MathUtil	Self
	This class.
Static Private Member Functions
static const Self::BitInitializer &	GetInternalNaN ()
	Get reference to internal representation of NaN.
static const Self::BitInitializer &	GetInternalInf ()
	Get reference to internal representation of Inf.

Detailed Description

General-purpose mathematical functions and function templates.

Definition at line 83 of file cmtkMathUtil.h.

Member Typedef Documentation

typedef MathUtil cmtk::MathUtil::Self [private]

This class.

Definition at line 87 of file cmtkMathUtil.h.

Member Function Documentation

static const Units::Radians cmtk::MathUtil::ArcCos ( const double value ) [inline, static]

Unit-safe acos() function.

Definition at line 154 of file cmtkMathUtil.h.

Referenced by cmtk::ParametricPlane::SetNormal().

static const Units::Radians cmtk::MathUtil::ArcSin ( const double value ) [inline, static]

Unit-safe asin() function.

Definition at line 148 of file cmtkMathUtil.h.

Referenced by cmtk::ParametricPlane::SetNormal().

static const Units::Radians cmtk::MathUtil::ArcTan ( const double value ) [inline, static]

Unit-safe aten() function.

Definition at line 160 of file cmtkMathUtil.h.

static const Units::Radians cmtk::MathUtil::ArcTan2	(	const double	y,
		const double	x
	)		`[inline, static]`

Unit-safe atan2() function.

Definition at line 166 of file cmtkMathUtil.h.

Referenced by cmtk::ParametricPlane::GetAlignmentXform().

static double cmtk::MathUtil::BetaCf	(	const double	a,
		const double	b,
		const double	x
	)		`[static]`

Beta-Cf function.

static double cmtk::MathUtil::Betai	(	const double	a,
		const double	b,
		const double	x
	)		`[static]`

Beta-i function.

template<class T >

static int cmtk::MathUtil::CheckRange	(	const T	value,
		const T	a,
		const T	b
	)		`[inline, static]`

Check if some float value is within a range.

Returns:: 0 if value is in range, -1 if value is below minumum, 1 if value is above maximum.

Definition at line 214 of file cmtkMathUtil.h.

static int cmtk::MathUtil::CompareDouble	(	const void *	a,
		const void *	b
	)		`[inline, static]`

Function that compares two doubles; to be used in qsort().

Definition at line 323 of file cmtkMathUtil.h.

Referenced by cmtk::ScalarImage::GetMedianFiltered().

static int cmtk::MathUtil::CompareFloat	(	const void *	a,
		const void *	b
	)		`[inline, static]`

Function that compares two floats; to be used in qsort().

Definition at line 313 of file cmtkMathUtil.h.

Referenced by cmtk::ScalarImage::GetMedianFiltered().

static double cmtk::MathUtil::Cos ( const Units::Radians & radians ) [inline, static]

Unit-safe cos() function.

Definition at line 136 of file cmtkMathUtil.h.

References cmtk::Units::UnitBase::Value().

Referenced by cmtk::AffineXform::RotateWXYZ(), and cmtk::ParametricPlane::Update().

static double cmtk::MathUtil::GammaLn ( const double xx ) [static]

GammaLn function.

static double cmtk::MathUtil::GetDoubleInf ( ) [inline, static]

Get double-precision infinite (Inf) value.

Definition at line 114 of file cmtkMathUtil.h.

static double cmtk::MathUtil::GetDoubleNaN ( ) [inline, static]

Get double-precision not-a-number (NaN) value.

Definition at line 98 of file cmtkMathUtil.h.

static float cmtk::MathUtil::GetFloatInf ( ) [inline, static]

Get single-precision infinite (Inf) value.

Definition at line 120 of file cmtkMathUtil.h.

static float cmtk::MathUtil::GetFloatNaN ( ) [inline, static]

Get single-precision not-a-number (NaN) value.

Definition at line 104 of file cmtkMathUtil.h.

static const Self::BitInitializer& cmtk::MathUtil::GetInternalInf ( ) [inline, static, private]

Get reference to internal representation of Inf.

Definition at line 425 of file cmtkMathUtil.h.

static const Self::BitInitializer& cmtk::MathUtil::GetInternalNaN ( ) [inline, static, private]

Get reference to internal representation of NaN.

Definition at line 414 of file cmtkMathUtil.h.

template<class T >

static T cmtk::MathUtil::Intersect	(	const T	aMin,
		const T	aMax,
		const T	bMin,
		const T	bMax
	)		`[inline, static]`

Return length of intersection of two intervals.

Definition at line 197 of file cmtkMathUtil.h.

template<class T >

static bool cmtk::MathUtil::IsNaN ( const T value ) [inline, static]

Portable test for "not a number" values.

Definition at line 92 of file cmtkMathUtil.h.

template<class T >

static T cmtk::MathUtil::Max	(	const int	nValues,
		const T *	Values
	)		`[inline, static]`

Return minimum of an array of ordered values.

Definition at line 187 of file cmtkMathUtil.h.

template<class T >

static T cmtk::MathUtil::Min	(	const int	nValues,
		const T *	Values
	)		`[inline, static]`

Return minimum of an array of ordered values.

Definition at line 176 of file cmtkMathUtil.h.

Referenced by cmtk::ReformatVolume::GetTransformedReferenceGrey(), cmtk::ReformatVolume::GetTransformedReferenceJacobianAvgThread(), and cmtk::ReformatVolume::GetTransformedReferenceLabel().

static double cmtk::MathUtil::NormalRandom ( const double sigma ) [inline, static]

Generate normally distributed random numbers.

This function uses the Box-Muller method to transform a pair of uniformly distributed random numbers into a pair of normally (ie., Gaussian) distributed random numbers. One of the two generated numbers is returned while the other is stored so that, when this function is called the next time, the previously computed value can be returned without further computational expense.

Parameters:

sigma Standard deviation of the resulting distribution.

Definition at line 341 of file cmtkMathUtil.h.

static double cmtk::MathUtil::NormalRandom	(	const double	sigma,
		const unsigned int	seed
	)		`[inline, static]`

Generate normally distributed random numbers with explicit seed.

Parameters:

sigma	Standard deviation of the resulting distribution.
seed	Random seed given to srandom() function.

Definition at line 367 of file cmtkMathUtil.h.

template<class T >

static double cmtk::MathUtil::plogp ( const T p ) [inline, static]

Compute p*log(p) for a single value.

Definition at line 221 of file cmtkMathUtil.h.

template<class T >

static int cmtk::MathUtil::Round ( const T a ) [inline, static]

Round float value to the nearest integer.

Definition at line 203 of file cmtkMathUtil.h.

Referenced by cmtk::ScalarImage::ProjectPixel().

template<class T >

static int cmtk::MathUtil::Sign ( const T a ) [inline, static]

Return sign of float value.

Returns:: -1 if a<0, 1 if a>0, 0 if a==0.

Definition at line 208 of file cmtkMathUtil.h.

Referenced by cmtk::ParametricPlane::GetAlignmentXform().

static double cmtk::MathUtil::Sin ( const Units::Radians & radians ) [inline, static]

Unit-safe sin() function.

Definition at line 130 of file cmtkMathUtil.h.

References cmtk::Units::UnitBase::Value().

Referenced by cmtk::AffineXform::RotateWXYZ(), cmtk::ParametricPlane::SetNormal(), and cmtk::ParametricPlane::Update().

template<class T >

static T cmtk::MathUtil::Square ( const T a ) [inline, static]

Return square of a float value.

Definition at line 172 of file cmtkMathUtil.h.

Referenced by cmtk::CongealingFunctional< TXform >::CreateGaussianKernels(), cmtk::ScalarImage::GetGaussFiltered(), cmtk::AffineXform::GetParamStep(), and cmtk::ScalarImage::GetSobel2DFiltered().

static double cmtk::MathUtil::Tan ( const Units::Radians & radians ) [inline, static]

Unit-safe tan() function.

Definition at line 142 of file cmtkMathUtil.h.

References cmtk::Units::UnitBase::Value().

Member Data Documentation

const FPInitializeUnion cmtk::MathUtil::FPInitializeNaN

Initial value:

{
}

Definition at line 47 of file cmtkMathUtil_NaNInf.cxx.

The documentation for this class was generated from the following files:

cmtk::MathUtil Class Reference [cmtkBase Library]

Classes

Static Public Member Functions

Public Attributes

Private Types

Static Private Member Functions

Detailed Description

Member Typedef Documentation

Member Function Documentation

Member Data Documentation

cmtk::MathUtil Class Reference
[cmtkBase Library]