Auxiliary classes and methods for multi-dimensional interpolations and histograms. More...

Classes
struct	JAbstractCollection
	Abstract interface for abscissa values of a collection of elements. More...

struct	JAbstractHistogram
	Simple data structure for histogram binning. More...

struct	JAbstractMultiMap
	Abstract interface for abscissa values of a multidimensional map. More...

struct	JAbstractMultiMap< 0, JAbscissa_t >
	Terminator class of recursive class JAbstractMultiMap. More...

class	JArray
	One dimensional array of template objects with fixed length. More...

class	JArray< 1, T >
	One dimensional array of template objects with fixed length. More...

class	JArray< N, const T >
	One dimensional read-only array of template objects with fixed length. More...

class	JArray< 1, const T >
	One dimensional read-only array of template objects with fixed length. More...

struct	JAssembler
	Auxiliary class to check whether given template is a collection, i.e. has a defined type `collection_type`. More...

struct	JAssembler< T, typename JVoid< typename T::collection_type >::type >
	Template specialisation of class JAssembler for classes with a defined type `collection_type`. More...

class	JAutoMap
	Forward declaration of class JAutoMap for specialisation of class JAutomate. More...

struct	JAutomate
	Auxiliary class for automatic element creation. More...

struct	JAutomate< JAutoMap< JKey_t, JValue_t > >
	Specialisation of class JAutomate for class JAutoMap. More...

class	JCollection
	General purpose class for collection of elements, see: Collection of elements. . More...

class	JCombinatorics
	Auxiliary class to convert pair of indices to unique index and back. More...

class	JConstantFunction1D
	Template implementation of function object in one dimension returning a constant value. More...

struct	JDistance
	Template class for distance evaluation. More...

class	JDriver
	Auxiliary class to load and store objects. More...

struct	JElement2D
	2D Element. More...

struct	JSplineElement2D
	2D Element for spline interpolations. More...

struct	JSplineElement2S
	2D Element for spline interpolations. More...

struct	JPolintElement2S
	2D Element for polynomial interpolations. More...

struct	JBin2D
	2D Binned element. More...

struct	JElement3D
	3D Element. More...

struct	JGridSplineFunction1D
	Type definition of a spline interpolation based on a JGridCollection. More...

struct	JSplineFunction1D_t
	Type definition of a spline interpolation method based on a JCollection with double result type. More...

struct	JSplineFunction1H_t
	Type definition of a spline interpolation method based on a JCollection with JResultDerivative result type. More...

struct	JSplineFunction1S_t
	Type definition of a spline interpolation method based on a JCollection with JResultPDF result type. More...

struct	JGridSplineFunction1D_t
	Type definition of a spline interpolation based on a JGridCollection with result type double. More...

struct	JGridSplineFunction1H_t
	Type definition of a spline interpolation based on a JGridCollection with JResultDerivative result type. More...

struct	JGridSplineFunction1S_t
	Type definition of a spline interpolation based on a JGridCollection with JResultPDF result type. More...

struct	JGridHermiteSplineFunction1D
	Type definition of a spline interpolation based on a JGridCollection. More...

struct	JHermiteSplineFunction1D_t
	Type definition of a spline interpolation method based on a JCollection with double result type. More...

struct	JHermiteSplineFunction1H_t
	Type definition of a spline interpolation method based on a JCollection with JResultDerivative result type. More...

struct	JHermiteSplineFunction1S_t
	Type definition of a spline interpolation method based on a JCollection with JResultPDF result type. More...

struct	JGridHermiteSplineFunction1D_t
	Type definition of a spline interpolation based on a JGridCollection with result type double. More...

struct	JGridHermiteSplineFunction1H_t
	Type definition of a spline interpolation based on a JGridCollection with JResultDerivative result type. More...

struct	JPolint0Function1D
	Type definition of a zero degree polynomial interpolation. More...

struct	JPolint1Function1D
	Type definition of a 1st degree polynomial interpolation. More...

struct	JPolint2Function1D
	Type definition of a 2nd degree polynomial interpolation. More...

struct	JPolint3Function1D
	Type definition of a 3rd degree polynomial interpolation. More...

struct	JPolintFunction1D_t
	Polynomial interpolation method with result type double. More...

struct	JPolint0Function1D_t
	Type definition of a zero degree polynomial interpolation with result type double. More...

struct	JPolint1Function1D_t
	Type definition of a 1st degree polynomial interpolation with result type double. More...

struct	JPolint2Function1D_t
	Type definition of a 2nd degree polynomial interpolation with result type double. More...

struct	JPolint3Function1D_t
	Type definition of a 3rd degree polynomial interpolation with result type double. More...

struct	JPolintFunction1H_t
	Polynomial interpolation method with result type JResultDerivative. More...

struct	JPolint1Function1H_t
	Type definition of a 1st degree polynomial interpolation with result type JResultDerivative. More...

struct	JPolint2Function1H_t
	Type definition of a 2nd degree polynomial interpolation with result type JResultDerivative. More...

struct	JPolint3Function1H_t
	Type definition of a 3rd degree polynomial interpolation with result type JResultDerivative. More...

struct	JPolintFunction1S_t
	Polynomial interpolation method with result type JResultPDF. More...

struct	JPolint1Function1S_t
	Type definition of a 1st degree polynomial interpolation with result type JResultPDF. More...

struct	JPolint2Function1S_t
	Type definition of a 2nd degree polynomial interpolation with result type JResultPDF. More...

struct	JPolint3Function1S_t
	Type definition of a 3rd degree polynomial interpolation with result type JResultPDF. More...

struct	JGridPolintFunction1D_t
	Polynomial interpolation method based on a JGridCollection with result type double. More...

struct	JGridPolint0Function1D_t
	Type definition of a zero degree polynomial interpolation based on a JGridCollection with result type double. More...

struct	JGridPolint1Function1D_t
	Type definition of a 1st degree polynomial interpolation based on a JGridCollection with result type double. More...

struct	JGridPolint2Function1D_t
	Type definition of a 2nd degree polynomial interpolation based on a JGridCollection with result type double. More...

struct	JGridPolint3Function1D_t
	Type definition of a 3rd degree polynomial interpolation based on a JGridCollection with result type double. More...

struct	JGridPolintFunction1H_t
	Polynomial interpolation method based on a JGridCollection with result type JResultDerivative. More...

struct	JGridPolint1Function1H_t
	Type definition of a 1st degree polynomial interpolation with result type JResultDerivative. More...

struct	JGridPolint2Function1H_t
	Type definition of a 2nd degree polynomial interpolation with result type JResultDerivative. More...

struct	JGridPolint3Function1H_t
	Type definition of a 3rd degree polynomial interpolation with result type JResultDerivative. More...

struct	JGridPolintFunction1S_t
	Polynomial interpolation method with result type JResultPDF. More...

struct	JGridPolint1Function1S_t
	Type definition of a 1st degree polynomial interpolation with result type JResulPDF. More...

struct	JGridPolint2Function1S_t
	Type definition of a 2nd degree polynomial interpolation with result type JResulPDF. More...

struct	JGridPolint3Function1S_t
	Type definition of a 3rd degree polynomial interpolation with result type JResulPDF. More...

class	JFunctional
	Template definition of function object interface. More...

class	JFunctional< JNullType, JNullType >
	Template specialisation of compilable function object. More...

struct	JFunction
	Template definition of function object interface in multidimensions. More...

struct	JFunction1D
	Template definition of function object interface in one dimension. More...

struct	JCompiler
	Functional object compiler. More...

struct	JResultType
	Auxiliary class to evaluate result type. More...

struct	JResultType< JClass_t, typename JVoid< typename JClass_t::result_type >::type >
	Auxiliary class to evaluate result type. More...

struct	JFunctionalMap
	Auxiliary class to define corresponding one-dimensional function interpolator `function_type`. More...

struct	JFunctionalMap< JSplineFunctionalMap >
	Specialisation of JFunctionalMap for JSplineFunctionalMap. More...

struct	JFunctionalMap< JSplineFunctionalGridMap >
	Specialisation of JFunctionalMap for JSplineFunctionalGridMap. More...

struct	JFunctionalMap< JPolint0FunctionalMap >
	Specialisation of JFunctionalMap for JPolint0FunctionalMap. More...

struct	JFunctionalMap< JPolint1FunctionalMap >
	Specialisation of JFunctionalMap for JPolint1FunctionalMap. More...

struct	JFunctionalMap< JPolint2FunctionalMap >
	Specialisation of JFunctionalMap for JPolint2FunctionalMap. More...

struct	JFunctionalMap< JPolint3FunctionalMap >
	Specialisation of JFunctionalMap for JPolint3FunctionalMap. More...

struct	JFunctionalMap< JPolint0FunctionalGridMap >
	Specialisation of JFunctionalMap for JPolint0FunctionalGridMap. More...

struct	JFunctionalMap< JPolint1FunctionalGridMap >
	Specialisation of JFunctionalMap for JPolint1FunctionalGridMap. More...

struct	JFunctionalMap< JPolint2FunctionalGridMap >
	Specialisation of JFunctionalMap for JPolint2FunctionalGridMap. More...

struct	JFunctionalMap< JPolint3FunctionalGridMap >
	Specialisation of JFunctionalMap for JPolint3FunctionalGridMap. More...

struct	JSplineFunctionalMap
	Type definition of a spline interpolation based on a JMap implementation. More...

struct	JSplineFunctionalGridMap
	Type definition of a spline interpolation based on a JGridMap implementation. More...

struct	JPolint0FunctionalMap
	Type definition of a zero degree polynomial interpolation based on a JMap implementation. More...

struct	JPolint1FunctionalMap
	Type definition of a 1st degree polynomial interpolation based on a JMap implementation. More...

struct	JPolint2FunctionalMap
	Type definition of a 2nd degree polynomial interpolation based on a JMap implementation. More...

struct	JPolint3FunctionalMap
	Type definition of a 3rd degree polynomial interpolation based on a JMap implementation. More...

struct	JPolint0FunctionalGridMap
	Type definition of a zero degree polynomial interpolation based on a JGridMap implementation. More...

struct	JPolint1FunctionalGridMap
	Type definition of a 1st degree polynomial interpolation based on a JGridMap implementation. More...

struct	JPolint2FunctionalGridMap
	Type definition of a 2nd degree polynomial interpolation based on a JGridMap implementation. More...

struct	JPolint3FunctionalGridMap
	Type definition of a 3rd degree polynomial interpolation based on a JGridMap implementation. More...

struct	JSplineFunctionalMapH
	Type definition of a spline interpolation based on a JMap implementation. More...

struct	JSplineFunctionalGridMapH
	Type definition of a spline interpolation based on a JGridMap implementation. More...

struct	JPolint0FunctionalMapH
	Type definition of a zero degree polynomial interpolation based on a JMap implementation. More...

struct	JPolint1FunctionalMapH
	Type definition of a 1st degree polynomial interpolation based on a JMap implementation. More...

struct	JPolint2FunctionalMapH
	Type definition of a 2nd degree polynomial interpolation based on a JMap implementation. More...

struct	JPolint3FunctionalMapH
	Type definition of a 3rd degree polynomial interpolation based on a JMap implementation. More...

struct	JPolint0FunctionalGridMapH
	Type definition of a zero degree polynomial interpolation based on a JGridMap implementation. More...

struct	JPolint1FunctionalGridMapH
	Type definition of a 1st degree polynomial interpolation based on a JGridMap implementation. More...

struct	JPolint2FunctionalGridMapH
	Type definition of a 2nd degree polynomial interpolation based on a JGridMap implementation. More...

struct	JPolint3FunctionalGridMapH
	Type definition of a 3rd degree polynomial interpolation based on a JGridMap implementation. More...

class	JExternalFunction1D
	Template implementation of function object in one dimension using an external function. More...

class	JFunctionObject1D
	Template implementation of function object in one dimension. More...

class	JGarbageCollection
	Garbage collection. More...

struct	JGrid
	Simple data structure for an abstract collection of equidistant abscissa values. More...

class	JGridCollection
	General purpose class for collection of equidistant elements. More...

class	JGridMap
	Map of equidistant pair-wise elements. More...

struct	JMapCollection< JGridMap >
	Specialisation of JMapCollection for JGridMap. More...

class	JHashCollection
	General purpose class for hash collection of unique elements. More...

struct	JHashEvaluator
	Auxiliary class for default hash key evaluation. More...

struct	JHashMapEvaluator
	Auxiliary class for hash evaluation of map keys and elements. More...

struct	JHashMap
	General purpose class for hash map of unique keys. More...

struct	JHashMapToolkit
	Toolkit for JHashMap. More...

class	JHashSet
	General purpose class for hash set of elements. More...

class	JHermiteSplineCollection
	Template base class spline interpolations. More...

class	JHermiteSplineFunction
	Template definition for functional collection with spline interpolation. More...

class	JHermiteSplineFunction< JElement_t, JCollection_t, typename JResultType< typename JElement_t::ordinate_type >::result_type, JDistance_t >
	Template specialisation for functional collection with spline interpolation. More...

class	JHermiteSplineFunction< JElement_t, JCollection_t, JResultDerivative< typename JResultType< typename JElement_t::ordinate_type >::result_type >, JDistance_t >
	Template specialisation for spline interpolation method with returning JResultDerivative data structure. More...

class	JHermiteSplineFunction< JElement_t, JCollection_t, JResultPDF< typename JResultType< typename JElement_t::ordinate_type >::result_type >, JDistance_t >
	Template specialisation for spline interpolation method with returning JResultPDF data structure. More...

class	JHermiteSplineFunction1D
	Template class for spline interpolation in 1D. More...

class	JHermiteSplineMap
	Functional map with spline interpolation. More...

struct	JHesseMatrix
	Hessian matrix. More...

class	JHistogram
	Template definition of histogram object interface. More...

struct	JCumulator
	Functional histogram cumulator. More...

struct	JRebin
	Auxiliary class for merging of fixed number of consecutive bins. More...

struct	JContent
	Auxiliary class for merging of consecutive bins until minimal content is reached. More...

class	JHistogram1D
	Histogram in 1D. More...

class	JHistogram1D< JBin2D< JAbscissa_t, JContents_t >, JContainer_t, JDistance_t >
	Template specialisation if JHistogram1D class with bin centering. More...

class	JHistogramMap
	Histogram map. More...

struct	JHistogramMap_t
	Type definition of a JHistogramMap based on JMap implementation. More...

struct	JHistogramGridMap_t
	Type definition of a JHistogramMap based on JGridMap implementation. More...

class	JList
	Recursive template class. More...

class	JList< 1, T, JClass_t >
	Terminator class of recursive template class. More...

class	JList< 0, T, JClass_t >
	Template specialisation of obsolete JList<unsigned int, ...> class. More...

class	JMap
	Map of pair-wise elements. More...

struct	JMapCollection< JMap >
	Specialisation of JMapCollection for JMap. More...

struct	JMapCollection
	Template class to define the corresponding JCollection for a given template JMap. More...

struct	JMapList
	Map list. More...

struct	JMapList< JHead_t, JNullType >
	Terminator class of map list. More...

struct	JMapLength
	Length of map list. More...

struct	JMapLength< JMapList< JHead_t, JTail_t > >
	Recursive length of map list. More...

struct	JMapLength< JMapList< JHead_t, JNullType > >
	Terminator class of length of map list. More...

struct	JNullMap
	Auxiliary class for no map definition. More...

struct	JMAPLIST
	Auxiliary class for recursive map list generation. More...

struct	JMAPLIST< A, JNullMap, JNullMap, JNullMap, JNullMap, JNullMap, JNullMap, JNullMap, JNullMap, JNullMap, JNullMap, JNullMap, JNullMap, JNullMap, JNullMap, JNullMap, JNullMap, JNullMap, JNullMap, JNullMap, JNullMap, JNullMap, JNullMap, JNullMap, JNullMap, JNullMap >
	Template specialisation to terminate recursive map list generation. More...

struct	JMappableCollection
	Template interface definition for associative collection of elements. More...

struct	JMappable
	Auxiliary class to define JMappableCollection for given template. More...

class	JMergeSort
	This class implements a merge and sort algorithm based on the divide-and-conquer concept. More...

class	JMultiFunction
	Multidimensional interpolation method. More...

class	JMultiFunction< JConstantFunction1D< JArgument_t, JResult_t >, JMapList< JMap_t >, JDistance_t >
	Template specialisation of JMultiFunction for a JConstantFunction. More...

class	JMultiFunction< JConstantFunction1D< JArgument_t, JResult_t >, JMaplist_t, JDistance_t >
	Template specialisation of JMultiFunction for a JConstantFunction. More...

struct	JMultiGrid
	Simple data structure for an abstract multidimensional map of equidistant elements. More...

struct	JMultiGrid< 0, JAbscissa_t >
	Terminator class of recursive class JMultiGrid. More...

struct	JHashMap< JTypeList< JHead_t, JTail_t >, JValue_t, JEvaluator_t >
	Multi-dimensional hash map. More...

struct	JHashMap< JTypeList< JHead_t, JNullType >, JValue_t, JEvaluator_t >
	Terminator class of recursive class JHashMap. More...

class	JMultiHistogram
	Multidimensional histogram. More...

class	JMultiKey
	Forward declaration of template JMultiKey class. More...

class	JMultiKey< 2, JKey_t >
	Two-dimensional key. More...

class	JMultiKey< 1, JKey_t >
	One-dimensional key. More...

class	JMultiKey< 0, JKey_t >
	Empty key. More...

class	JMultiMap
	Multidimensional map. More...

class	JMultiMap< JAbscissa_t, JOrdinate_t, JMapList< JHead_t, JTail_t >, JDistance_t >
	Template specialisation of JMultiMap for map list with at least one map. More...

class	JMultiMap< JAbscissa_t, JOrdinate_t, JMapList< JHead_t, JLANG::JNullType >, JDistance_t >
	Terminator class of recursive JMultiMap class. More...

class	JMultiMapTransformer
	Interface for weight application and coordinate transformation of function. More...

class	JMultiMapPutTransformer
	Auxiliary class to convert JMultiMapTransformer to JCollectionElementTransformer. More...

class	JMultiMapGetTransformer
	Auxiliary class to convert JMultiMapTransformer to JCollectionElementTransformer. More...

struct	JTransformable
	Abstract interface for transformable multidimensional map. More...

class	JMultiPair
	Multidimensional pair. More...

class	JMultiPair< 2, JKey_t, JValue_t >
	Two-dimensional pair. More...

class	JMultiPair< 1, JKey_t, JValue_t >
	One-dimensional pair. More...

class	JMultiPair< 0, JKey_t, JValue_t >
	Empty pair. More...

class	JMultiPDF
	General purpose class for multi-dimensional probability density function (PDF). More...

struct	JMultipleMap
	List of identical maps. More...

struct	JMultipleMap< 1, JMap_t >
	Terminator class of list of identical maps. More...

struct	JMultiSet
	Simple data structure for an abstract multidimensional map of equidistant elements. More...

struct	JMultiSet< 0, JAbscissa_t >
	Terminator class of recursive class JMultiSet. More...

class	JPair
	Template specialisation for a pair of values. More...

class	JPair< JKey_t &, JValue_t & >
	Template specialisation for a pair of references. More...

class	JPair< const JKey_t &, JValue_t & >
	Template specialisation for a mixed pair of const and non-const references. More...

class	JPair< const JKey_t &, const JValue_t & >
	Template specialisation for a pair of const references. More...

class	JPolintFunction
	Template definition for functional collection with polynomial interpolation. More...

class	JPolintFunction< N, JElement_t, JCollection_t, typename JResultType< typename JElement_t::ordinate_type >::result_type, JDistance_t >
	Template specialisation for functional collection with polynomial interpolation. More...

class	JPolintFunction< 0, JElement_t, JCollection_t, typename JResultType< typename JElement_t::ordinate_type >::result_type, JDistance_t >
	Template specialisation for zero-degree polynomial interpolation method. More...

class	JPolintFunction< 1, JElement_t, JCollection_t, typename JResultType< typename JElement_t::ordinate_type >::result_type, JDistance_t >
	Template specialisation for first-degree polynomial interpolation method. More...

class	JPolintFunction< N, JElement_t, JCollection_t, JResultPDF< typename JResultType< typename JElement_t::ordinate_type >::result_type >, JDistance_t >
	Template specialisation for polynomial interpolation method with returning JResultPDF data structure. More...

class	JPolintCollection
	Template definition of base class for polynomial interpolations with polynomial result. More...

class	JPolintFunction< N, JElement_t, JCollection_t, JResultPolynome< M, typename JResultType< typename JElement_t::ordinate_type >::result_type >, JDistance_t >
	Template specialisation for polynomial interpolation method with returning JResultPolynome data structure. More...

class	JPolintFunction< N, JElement_t, JCollection_t, JResultDerivative< typename JResultType< typename JElement_t::ordinate_type >::result_type >, JDistance_t >
	Template specialisation for polynomial interpolation method with returning JResultDerivative data structure. More...

class	JPolintFunction< N, JElement_t, JCollection_t, JResultHesse< typename JResultType< typename JElement_t::ordinate_type >::result_type >, JDistance_t >
	Template specialisation for polynomial interpolation method with returning JResultHesse data structure. More...

class	JPolintFunction1D
	Template class for polynomial interpolation in 1D. More...

class	JPolintMap
	Functional map with polynomial interpolation. More...

class	JQuadrature
	Type definition for numerical integration. More...

class	JGaussLegendre
	Numerical integrator for `W(x) = 1`. More...

class	JGaussLaguerre
	Numerical integrator for `W(x) = x^a e^(-x)`. More...

class	JGaussHermite
	Numerical integrator for `W(x) = e^-(x^2)`. More...

class	JHenyeyGreenstein
	Numerical integrator for `W(x) = (1 + g^2 - 2gx)^a`. More...

class	JRayleigh
	Numerical integrator for `W(x) = (1 + gxx)`. More...

class	JCotangent
	Numerical integrator for `W(x) = \|x\| / sqrt(1 - x*x)` More...

class	JBitangent
	Numerical integrator for `W(x) = \|x\| / sqrt(1 - x*x), x > 0` and `W(x) = 1, x <= 0`. More...

struct	JQuantile_t
	Auxiliary data structure for quantiles. More...

struct	JQuantile
	Quantile calculator. More...

class	JQuantiles
	Quantile calculator for a given function. More...

class	JRange
	Range of values. More...

struct	JResultDerivative
	Data structure for result including value and first derivative of function. More...

struct	JResultHesse
	Data structure for result including value and first derivative of function. More...

struct	JResultPDF
	Data structure for result including value, first derivative and integrals of function. More...

struct	JResultPolynome
	Data structure for result including value and `N` derivatives of function. More...

struct	JResultEvaluator
	Auxiliary class to recursively evaluate to a result. More...

struct	JResultEvaluator< JResultDerivative< T > >
	Template specialisation of JResultEvaluator for JResultDerivative. More...

struct	JResultEvaluator< JResultHesse< T > >
	Template specialisation of JResultEvaluator for JResultHesse. More...

struct	JResultEvaluator< JResultPDF< T > >
	Template specialisation of JResultEvaluator for JResultPDF. More...

struct	JResultEvaluator< JResultPolynome< N, T > >
	Template specialisation of JResultEvaluator for JResultPolynome. More...

struct	JResultEvaluator< JResultPolynome< 0, T > >
	Template specialisation of JResultEvaluator for JResultPolynome. More...

struct	JResultTransformer
	Auxiliary class to handle multidimensional map transformations for given result type. More...

struct	JResultTransformer< JResultHesse< JResult_t > >
	Auxiliary class to handle multidimensional map transformations for given result type. More...

struct	JResultTransformer< JResultPDF< JResult_t > >
	Auxiliary class to handle multidimensional map transformations for given result type. More...

class	JRouter
	Direct addressing of elements with unique identifiers. More...

class	JRouter< JAddress_t, false >
	Template specialisation of JRouter without default address comparison. More...

class	JRouter< JAddress_t, true >
	Template specialisation of JRouter with default address comparison. More...

class	JAbstractAutoPointer
	Abstract class of an automatic pointer. More...

class	JAutoPointer
	Template class for loading and storing of objects. More...

class	JAutoElement
	Handler class for automatic pointer. More...

class	JSelector
	Template selector class. More...

struct	JSet
	Simple data structure for an abstract collection of non-equidistant abscissa values. More...

class	JSplineBounds
	Auxiliary class to define first derivates of the spline function at the two extrema. More...

class	JSplineCollection
	Template base class for spline interpolations. More...

class	JSplineFunction
	Template definition for functional collection with spline interpolation. More...

class	JSplineFunction< JElement_t, JCollection_t, typename JResultType< typename JElement_t::ordinate_type >::result_type, JDistance_t >
	Template specialisation for functional collection with spline interpolation. More...

class	JSplineFunction< JElement_t, JCollection_t, JResultDerivative< typename JResultType< typename JElement_t::ordinate_type >::result_type >, JDistance_t >
	Template specialisation for spline interpolation method with returning JResultDerivative data structure. More...

class	JSplineFunction< JElement_t, JCollection_t, JResultPDF< typename JResultType< typename JElement_t::ordinate_type >::result_type >, JDistance_t >
	Template specialisation for spline interpolation method with returning JResultPDF data structure. More...

class	JSplineFunction1D
	Template class for spline interpolation in 1D. More...

class	JSplineMap
	Functional map with spline interpolation. More...

struct	JTable2D
	2D table with arithmetic capabilities. More...

class	JTransformableMultiFunction
	Transformable multidimensional function. More...

class	JTransformableMultiHistogram
	Transformable multidimensional histogram. More...

struct	JCollectionElementTransformer
	Interface for transformation of collection of elements. More...

struct	JTuple
	Template data structure. More...

struct	JTuple< JTypeList< JHead_t, JTail_t > >
	Template specialisation of JTuple for multiple data types. More...

struct	JTuple< JTypeList< JHead_t, JTypeList< JTail_t, JNullType > > >
	Template specialisation of JTuple for two data types. More...

struct	JTuple< JTypeList< JHead_t, JNullType > >
	Terminator class of recursive JTuple class. More...

class	JWeight
	Weight calculator. More...

struct	JGetElement
	Auxiliary class to convert value to element. More...

Typedefs
typedef JRange< double >	JAngleRange
	Type definition for angle range. More...

typedef JHistogram1D < JElement2D< double, double > , JCollection >	JHistogram1D_t
	Type definition of a 1 dimensional histogram based on a JCollection. More...

typedef JHistogram1D < JElement2D< double, double > , JGridCollection >	JGridHistogram1D_t
	Type definition of a 1 dimensional histogram based on a JGridCollection. More...

typedef JHistogram1D< JBin2D < double, double > , JCollection >	JHistogram1B_t
	Type definition of a 1 dimensional histogram with bin centering based on a JCollection. More...

typedef JHistogram1D< JBin2D < double, double > , JGridCollection >	JGridHistogram1B_t
	Type definition of a 1 dimensional histogram with bin centering based on a JGridCollection. More...

typedef JElement2D< double, double >	JElement2D_t
	Type definition of basic element for quadratures. More...

typedef JRange< double >	JTimeRange
	Type definition for time range. More...

Functions
template<class JAbscissa_t >
JAbstractHistogram< JAbscissa_t >	make_histogram (const int nx, const JAbscissa_t xmin, const JAbscissa_t xmax)
	Helper method for JAbstractHistogram. More...

template<class JElement_t , class JDistance_t >
JElement_t::ordinate_type	integrate (const JCollection< JElement_t, JDistance_t > &input, typename JMappable< JElement_t >::map_type &output)
	Conversion of data points to integral values. More...

const double	getSpeedOfLight ()
	Number of bytes in a gigabyte. More...

const double	getInverseSpeedOfLight ()
	Get inverse speed of light. More...

double	getIndexOfRefraction ()
	Get average index of refraction of water. More...

double	getIndexOfRefractionPhase ()
	Get average index of refraction of water. More...

double	getTanThetaC ()
	Get average tangent of Cherenkov angle of water. More...

double	getCosThetaC ()
	Get average cosine of Cherenkov angle of water. More...

double	getSinThetaC ()
	Get average sine of Cherenkov angle of water. More...

double	getKappaC ()
	Get average kappa of Cherenkov light in water. More...

template<class JAbscissa_t >
JGrid< JAbscissa_t >	make_grid (const int nx, const JAbscissa_t Xmin, const JAbscissa_t Xmax)
	Helper method for JGrid. More...

template<class JElement_t , template< class, class > class JCollection_t, class JResult_t , class JDistance_t >
JElement_t::ordinate_type	integrate (const JHermiteSplineFunction1D< JElement_t, JCollection_t, JResult_t, JDistance_t > &input, typename JMappable< JElement_t >::map_type &output)
	Conversion of data points to integral values. More...

template<class JElement_t , template< class, class > class JCollection_t, class JDistance_t >
JElement_t::ordinate_type	integrate (const JHermiteSplineFunction1D< JElement_t, JCollection_t, JResultPDF< typename JElement_t::ordinate_type >, JDistance_t > &input, typename JMappable< JElement_t >::map_type &output)
	Conversion of data points to integral values. More...

template<class JElement_t , template< class, class > class JContainer_t, class JDistance_t >
void	makePDF (const JHistogram1D< JElement_t, JContainer_t, JDistance_t > &input, typename JMappable< JElement_t >::map_type &output)
	Conversion of histogram to probability density function (PDF). More...

template<class JAbscissa_t , class JContents_t , template< class, class > class JContainer_t, class JDistance_t >
void	makePDF (const JHistogram1D< JBin2D< JAbscissa_t, JContents_t >, JContainer_t, JDistance_t > &input, JMappableCollection< JAbscissa_t, JContents_t > &output)
	Conversion of histogram to probability density function (PDF). More...

template<class JElement_t , template< class, class > class JContainer_t, class JDistance_t >
JElement_t::ordinate_type	integrate (const JHistogram1D< JElement_t, JContainer_t, JDistance_t > &input, typename JMappable< JElement_t >::map_type &output)
	Conversion of data points to integral values. More...

template<class JHistogram_t , class JHistogramMaplist_t , class JHistogramDistance_t , class JFunction_t , class JFunctionMaplist_t , class JFunctionDistance_t >
void	makePDF (const JMultiHistogram< JHistogram_t, JHistogramMaplist_t, JHistogramDistance_t > &input, JMultiFunction< JFunction_t, JFunctionMaplist_t, JFunctionDistance_t > &output)
	Conversion of multidimensional histogram to multidimensional function. More...

template<unsigned int N, class JAbscissa_t >
JMultiGrid< N, JAbscissa_t >	make_multigrid (const JGrid< JAbscissa_t > &bounds)
	Helper method for JMultiGrid. More...

template<class JHistogram_t , class JHistogramMaplist_t , class JHistogramDistance_t , class JFunction_t , class JFunctionMaplist_t , class JFunctionDistance_t >
void	makePDF (const JMultiHistogram< JHistogram_t, JHistogramMaplist_t, JHistogramDistance_t > &input, JMultiPDF< JFunction_t, JFunctionMaplist_t, JFunctionDistance_t > &output)
	Conversion of multi-dimensional histogram to multi-dimensional PDF. More...

template<unsigned int N, class JAbscissa_t >
JMultiSet< N, JAbscissa_t >	make_multiset (const JSet< JAbscissa_t > &bounds)
	Helper method for JMultiSet. More...

template<class T , class JComparator_t >
bool	next_permutation (T __begin, T __last, T __end, JComparator_t compare, std::bidirectional_iterator_tag)
	Implementation of method next_permutation for bidirectional iterators. More...

template<class T , class JComparator_t >
bool	next_permutation (T __begin, T __last, T __end, JComparator_t compare)
	Permutations of sub-set of data. More...

template<unsigned int N, class JElement_t , template< class, class > class JCollection_t, class JDistance_t , unsigned int M>
	if ((p==this->begin()&&this->getDistance(x,(p++) ->getX()) > distance_type::precision)\|\|(p==this->end()&&this->getDistance((--p) ->getX(), x) > distance_type::precision))
	Template base class for polynomial interpolations with polynomial result. More...

	for (int i=n/2;i!=0 &&p!=this->end();--i,++p)

	for (int i=n;i!=0 &&p!=this->begin();--i,--p)

	for (unsigned int k=0;k!=M+1;++k)

	for (int m=1;m!=n;++m)

virtual void	do_compile ()
	Function compilation. More...

template<unsigned int N, class JElement_t , template< class, class > class JCollection_t, class JResult_t , class JDistance_t >
JElement_t::ordinate_type	integrate (const JPolintFunction1D< N, JElement_t, JCollection_t, JResult_t, JDistance_t > &input, typename JMappable< JElement_t >::map_type &output)
	Conversion of data points to integral values. More...

template<unsigned int N, class JElement_t , template< class, class > class JCollection_t, class JResult_t , class JDistance_t >
JElement_t::ordinate_type	integrate (const JPolintFunction1D< N, JElement_t, JCollection_t, JResult_t, JDistance_t > &input, typename JMappable< JElement_t >::map_type &output, const JLANG::JBool< false > &option)
	Conversion of data points to integral values. More...

template<class JElement_t , template< class, class > class JCollection_t, class JResult_t , class JDistance_t >
JElement_t::ordinate_type	integrate (const JPolintFunction1D< 0, JElement_t, JCollection_t, JResult_t, JDistance_t > &input, typename JMappable< JElement_t >::map_type &output, const JLANG::JBool< true > &option)
	Conversion of data points to integral values. More...

template<class JElement_t , template< class, class > class JCollection_t, class JResult_t , class JDistance_t >
JElement_t::ordinate_type	integrate (const JPolintFunction1D< 1, JElement_t, JCollection_t, JResult_t, JDistance_t > &input, typename JMappable< JElement_t >::map_type &output, const JLANG::JBool< true > &option)
	Conversion of data points to integral values. More...

template<class JFunction1D_t >
double	search (const double xa, const double xb, const double xc, const JFunction1D_t &f, const int is, const double eps=1.0e-6)
	Locate maximum or minimun of function. More...

template<class T , class JComparator_t >
JRange< T, JComparator_t >	operator+ (const JRange< T, JComparator_t > &first, const JRange< T, JComparator_t > &second)
	Add ranges. More...

template<class T , class JComparator_t >
JRange< T, JComparator_t >	operator- (const JRange< T, JComparator_t > &first, const JRange< T, JComparator_t > &second)
	Subtract ranges. More...

template<class T , class JComparator_t >
bool	overlap (const JRange< T, JComparator_t > &first, const JRange< T, JComparator_t > &second)
	Test overlap between ranges. More...

template<class T , class JComparator_t >
JRange< T, JComparator_t >	join (const JRange< T, JComparator_t > &first, const JRange< T, JComparator_t > &second)
	Join ranges. More...

template<class T , class JComparator_t >
JRange< T, JComparator_t >	combine (const JRange< T, JComparator_t > &first, const JRange< T, JComparator_t > &second)
	Combine ranges. More...

template<class T >
JRange< T >	make_range (T x, T y)
	Auxiliary method to create range of values. More...

template<class JResult_t >
JResultEvaluator< JResult_t > ::result_type	get_value (const JResult_t &value)
	Helper method to recursively evaluate a to function value. More...

template<class JResult_t >
JResultEvaluator< JResult_t > ::result_type	get_derivative (const JResult_t &value)
	Helper method to convert function value to derivative value. More...

template<class JResult_t >
JResultEvaluator< JResult_t > ::result_type	get_integral (const JResult_t &value)
	Helper method to convert function value to partial integral value. More...

template<class T >
JSet< typename std::iterator_traits< T > ::value_type >	make_set (T __begin, T __end)
	Helper method for JSet. More...

template<class JAbscissa_t >
JSet< JAbscissa_t >	make_set (const JAbstractCollection< JAbscissa_t > &input)
	Helper method for JSet. More...

template<class JOrdinate_t >
JSplineBounds< JOrdinate_t >	make_spline_bounds (const JOrdinate_t fpAtXmin, const JOrdinate_t fpAtXmax)
	Helper method for JSplineBounds. More...

template<class JElement_t , template< class, class > class JCollection_t, class JResult_t , class JDistance_t >
JElement_t::ordinate_type	integrate (const JSplineFunction1D< JElement_t, JCollection_t, JResult_t, JDistance_t > &input, typename JMappable< JElement_t >::map_type &output)
	Conversion of data points to integral values. More...

template<class JElement_t , template< class, class > class JCollection_t, class JDistance_t >
JElement_t::ordinate_type	integrate (const JSplineFunction1D< JElement_t, JCollection_t, JResultPDF< typename JElement_t::ordinate_type >, JDistance_t > &input, typename JMappable< JElement_t >::map_type &output)
	Conversion of data points to integral values. More...

template<class JContainer_t , class JKey_t , class JValue_t >
JContainer_t::ordinate_type	makeCDF (const JContainer_t &input, JMappableCollection< JKey_t, JValue_t > &output, const typename JContainer_t::ordinate_type eps=JMATH::zero)
	Conversion of data points to cumulative probability distribition (CDF). More...

template<class JContainer_t >
JContainer_t::ordinate_type	getIntegral (const JContainer_t &input)
	Get integral of input data points. More...

template<class JFunction_t , template< class, class, class > class JMap_t, class JTail_t >
JFunction_t::ordinate_type	getIntegral (const JMultiMap< typename JFunction_t::abscissa_type, JFunction_t, JMapList< JMap_t, JTail_t >, typename JFunction_t::distance_type > &input)
	Auxiliary method to get integral of input data points. More...

template<class JFunction_t , template< class, class, class > class JMap_t, class JTail_t >
JFunction_t::ordinate_type	getIntegral (const JMultiFunction< JFunction_t, JMapList< JMap_t, JTail_t >, typename JFunction_t::distance_type > &input)
	Get integral of input data points. More...

template<class T >
void	reset (T &value)
	Reset value. More...

template<class JElement_t , class JDistance_t >
void	reset (JCollection< JElement_t, JDistance_t > &collection)
	Recursive reset of collection. More...

template<class T >
void	copy (const T &input, T &output)
	Copy of input to output. More...

template<class JElement_t , class JDistance_t , class JKey_t , class JValue_t >
void	copy (const JCollection< JElement_t, JDistance_t > &input, JMappableCollection< JKey_t, JValue_t > &output)
	Recursive copy of input collection to output collection. More...

template<class T , class JAbscissa_t >
void	configure (const T &value, const JAbstractCollection< JAbscissa_t > &bounds, JBool< false > option)
	Configuration of value. More...

template<class JElement_t , class JDistance_t >
void	configure (JCollection< JElement_t, JDistance_t > &collection, const JAbstractCollection< typename JElement_t::abscissa_type > &bounds, JBool< true > option=JBool< true >())
	Recursive configuration of collection. More...

template<class T >
void	accumulate (T &value, JBool< false > option)
	Accumulation of value. More...

template<class JElement_t , class JDistance_t >
void	accumulate (JCollection< JElement_t, JDistance_t > &collection, JBool< true > option=JBool< true >())
	Recursive accumulation of collection. More...

template<class JHistogram_t , class JHistogramMaplist_t , class JHistogramDistance_t , class JFunction_t , class JFunctionMaplist_t , class JFunctionDistance_t >
void	makePDF (const JTransformableMultiHistogram< JHistogram_t, JHistogramMaplist_t, JHistogramDistance_t > &input, JTransformableMultiFunction< JFunction_t, JFunctionMaplist_t, JFunctionDistance_t > &output)
	Conversion of multidimensional histogram to multidimensional function. More...

template<class JObject_t , class JHead_t , class JTail_t , class T >
JObject_t &	for_each (JObject_t &object, JType< JTypeList< JHead_t, JTail_t > > typelist, const JTuple< T > &tuple)
	For each data type method. More...

template<class JObject_t , class JTypelist_t , class T >
JObject_t &	for_each (JObject_t &object, JType< JTypelist_t > type, const JTuple< T > &tuple)
	For each data type method. More...

template<class... Args>
JTuple< typename JTYPELIST < Args...>::typelist >	make_tuple (const Args &...args)
	Helper method for tuple. More...

template<class JObject_t , class T >
JObject_t &	for_each (JObject_t &object, JType< JNullType > type, const JTuple< T > &tuple)
	Termination method of for each data type method. More...

template<class T >
void	inplace_merge (T __begin, const size_t N, const size_t *delimiter)
	Merge multiple sorted ranges. More...

template<class T >
bool	is_sorted (T __begin, T __end)
	Test whether range is sorted. More...

Variables
static const double	PI = 3.1415927
	Constants. More...

static const double	EULER = 0.577215664901533
	Euler number. More...

static const double	C = 0.299792458
	Speed of light in vacuum [m/ns]. More...

static const double	C_INVERSE = 1.0/C
	Inverse speed of light in vacuum [ns/m]. More...

static const double	AVOGADRO = 6.0221415e23
	Avogadro's number [gr^-1]. More...

static const double	H = 4.13566733e-15
	Planck constant [eV s]. More...

static const double	HBAR = H/(2*PI)
	Planck constant [eV s]. More...

static const double	HBARC = HBARC1.0e9
	Planck constant [eV m]. More...

static const double	ALPHA_ELECTRO_MAGNETIC = 1.0/137.036
	Electro-Magnetic coupling constant. More...

static const double	THETA_MCS = 13.6e-3
	Multiple Coulomb scattering constant [GeV]. More...

static const double	DENSITY_SEA_WATER = 1.038
	Fixed environment values. More...

static const double	DENSITY_ROCK = 2.65
	Density of rock [g/cm^3]. More...

static const double	SALINITY_SEA_WATER = 0.035
	Salinity of sea water. More...

static const double	INDEX_OF_REFRACTION_WATER = 1.3800851282
	average index of refraction of water More...

static const double	X0_WATER_M = 0.36
	Radiation length pure water [m]. More...

static const double	TAN_THETA_C_WATER = sqrt((INDEX_OF_REFRACTION_WATER - 1.0) * (INDEX_OF_REFRACTION_WATER + 1.0))
	Derived quantities of optical medium. More...

static const double	COS_THETA_C_WATER = 1.0 / INDEX_OF_REFRACTION_WATER

static const double	SIN_THETA_C_WATER = TAN_THETA_C_WATER * COS_THETA_C_WATER

static const double	KAPPA_WATER = 0.96

static const double	MASS_PHOTON = 0.0
	Particle masses. More...

static const double	MASS_ELECTRON_NEUTRINO = 0.0
	electron neutrino mass [GeV] More...

static const double	MASS_MUON_NEUTRINO = 0.0
	muon neutrino mass [GeV] More...

static const double	MASS_TAU_NEUTRINO = 0.0
	tau neutrino mass [GeV] More...

static const double	MASS_ELECTRON = 0.510998946e-3
	electron mass [GeV] More...

static const double	MASS_MUON = 0.1056583745
	muon mass [GeV] More...

static const double	MASS_TAU = 1.77682
	tau mass [GeV] More...

static const double	MASS_NEUTRAL_PION = 0.1349766
	pi_0 mass [GeV] More...

static const double	MASS_CHARGED_PION = 0.13957018
	pi^+/- mass [GeV] More...

static const double	MASS_NEUTRAL_KAON = 0.497614
	K_0 mass [GeV]. More...

static const double	MASS_CHARGED_KAON = 0.493677
	K^+/- mass [GeV]. More...

static const double	MASS_PROTON = 0.9382720813
	proton mass [GeV] More...

static const double	MASS_NEUTRON = 0.9395654133
	neutron mass [GeV] More...

static const double	MASS_LAMBDA = 1.115683
	Lambda mass [GeV]. More...

static const double	MASS_NEUTRAL_SIGMA = 1.192642
	Sigma_0 mass [GeV]. More...

static const double	MASS_CHARGED_SIGMA = 1.18937
	Sigma^+/- mass [GeV]. More...

static const double	MASS_NEUTRAL_XI = 1.31486
	Xi_0 mass [GeV]. More...

static const double	MASS_CHARGED_XI = 1.32171
	Xi^+/- mass [GeV]. More...

static const double	MASS_CHARGED_OMEGA = 1.67245
	Omega^+/- mass [GeV]. More...

static const long long int	KILOBYTE = 1024
	Computing quantities. More...

static const long long int	MEGABYTE = KILOBYTE*KILOBYTE
	Number of bytes in a kilobyte. More...

static const long long int	GIGABYTE = KILOBYTEKILOBYTEKILOBYTE
	Number of bytes in a megabyte. More...

static const JCompiler	compiler
	Function object for functional object compilation. More...

static const JCumulator	cumulator
	Function object for functional object compilation. More...

	pX

const int	n = std::min((int) (N + 1), (int) this->size())

int	j = 0

return	result

double	u [N+1]

data_type	v [N+1][M+1]

data_type	w [N+1][M+1]

data_type	r [M+1]

Detailed Description

Auxiliary classes and methods for multi-dimensional interpolations and histograms.

Author: mdejong

Typedef Documentation

typedef JRange<double> JTOOLS::JAngleRange

Type definition for angle range.

Definition at line 19 of file JAngleRange.hh.

typedef JHistogram1D<JElement2D<double, double>, JCollection> JTOOLS::JHistogram1D_t

Type definition of a 1 dimensional histogram based on a JCollection.

Definition at line 22 of file JHistogram1D_t.hh.

typedef JHistogram1D<JElement2D<double, double>, JGridCollection> JTOOLS::JGridHistogram1D_t

Type definition of a 1 dimensional histogram based on a JGridCollection.

Definition at line 28 of file JHistogram1D_t.hh.

typedef JHistogram1D<JBin2D<double, double>, JCollection> JTOOLS::JHistogram1B_t

Type definition of a 1 dimensional histogram with bin centering based on a JCollection.

Definition at line 34 of file JHistogram1D_t.hh.

typedef JHistogram1D<JBin2D<double, double>, JGridCollection> JTOOLS::JGridHistogram1B_t

Type definition of a 1 dimensional histogram with bin centering based on a JGridCollection.

Definition at line 40 of file JHistogram1D_t.hh.

typedef JElement2D<double, double> JTOOLS::JElement2D_t

Type definition of basic element for quadratures.

Definition at line 25 of file JQuadrature.hh.

typedef JRange<double> JTOOLS::JTimeRange

Type definition for time range.

Definition at line 19 of file JTools/JTimeRange.hh.

Function Documentation

template<class JAbscissa_t >

JAbstractHistogram<JAbscissa_t> JTOOLS::make_histogram	(	const int	nx,
		const JAbscissa_t	xmin,
		const JAbscissa_t	xmax
	)

inline

Helper method for JAbstractHistogram.

Parameters

nx	number of bins
xmin	lower limit
xmax	upper limit

Returns: histogram

Definition at line 158 of file JAbstractHistogram.hh.

   {
     return JAbstractHistogram<JAbscissa_t>(nx, xmin, xmax);
   }

template<class JElement_t , class JDistance_t >

JElement_t::ordinate_type JTOOLS::integrate	(	const JCollection< JElement_t, JDistance_t > &	input,
		typename JMappable< JElement_t >::map_type &	output
	)

inline

Conversion of data points to integral values.

The integration is based on the trapezoidal rule applied to the input data points.

Parameters

input	collection
output	mappable collection

Returns: integral

Definition at line 812 of file JCollection.hh.

   {
     typedef typename JElement_t::ordinate_type                             ordinate_type;
     typedef typename JCollection<JElement_t, JDistance_t>::const_iterator  const_iterator;
 
     ordinate_type V(JMATH::zero);
 
     if (input.getSize() > 1) {
 
       output.put(input.begin()->getX(), V);
 
       for (const_iterator j = input.begin(), i = j++; j != input.end(); ++i, ++j) {
 
         V += 0.5 * input.getDistance(i->getX(), j->getX()) * (i->getY() + j->getY());
 
         output.put(j->getX(), V);
       }
     }
 
     return V;
   }

const double JTOOLS::getSpeedOfLight ( )

inline

Number of bytes in a gigabyte.

Get speed of light.

return speed of light [m/ns]

Definition at line 89 of file JConstants.hh.

   {
     return C;
   }

const double JTOOLS::getInverseSpeedOfLight ( )

inline

Get inverse speed of light.

return inverse speed of light [ns/m]

Definition at line 100 of file JConstants.hh.

   { 
     return C_INVERSE; 
   }

double JTOOLS::getIndexOfRefraction ( )

inline

Get average index of refraction of water.

Returns: index of refraction

Definition at line 111 of file JConstants.hh.

   {
     return INDEX_OF_REFRACTION_WATER;
   }

double JTOOLS::getIndexOfRefractionPhase ( )

inline

Get average index of refraction of water.

Returns: index of refraction

Definition at line 122 of file JConstants.hh.

   {
     return 1.35;
   }

double JTOOLS::getTanThetaC ( )

inline

Get average tangent of Cherenkov angle of water.

Returns: tan(theta_C)

Definition at line 133 of file JConstants.hh.

   {
     return TAN_THETA_C_WATER;
   }

double JTOOLS::getCosThetaC ( )

inline

Get average cosine of Cherenkov angle of water.

Returns: cos(theta_C)

Definition at line 144 of file JConstants.hh.

   {
     return COS_THETA_C_WATER;
   }

double JTOOLS::getSinThetaC ( )

inline

Get average sine of Cherenkov angle of water.

Returns: sin(theta_C)

Definition at line 155 of file JConstants.hh.

   {
     return SIN_THETA_C_WATER;
   }

double JTOOLS::getKappaC ( )

inline

Get average kappa of Cherenkov light in water.

Returns: kappa

Definition at line 166 of file JConstants.hh.

   {
     return KAPPA_WATER;
   }

template<class JAbscissa_t >

JGrid<JAbscissa_t> JTOOLS::make_grid	(	const int	nx,
		const JAbscissa_t	Xmin,
		const JAbscissa_t	Xmax
	)

inline

Helper method for JGrid.

Parameters

nx	number of elements
Xmin	lower limit
Xmax	upper limit

Returns: grid

Definition at line 177 of file JGrid.hh.

   {
     return JGrid<JAbscissa_t>(nx, Xmin, Xmax);
   }

template<class JElement_t , template< class, class > class JCollection_t, class JResult_t , class JDistance_t >

JElement_t::ordinate_type JTOOLS::integrate	(	const JHermiteSplineFunction1D< JElement_t, JCollection_t, JResult_t, JDistance_t > &	input,
		typename JMappable< JElement_t >::map_type &	output
	)

inline

Conversion of data points to integral values.

The integration includes the use of 2nd derivatives of the data points of the input spline interpolating function.

Parameters

input	collection
output	mappable collection

Returns: integral

Definition at line 642 of file JHermiteSpline.hh.

   {
     typedef typename JElement_t::ordinate_type                                                             ordinate_type;
     typedef typename JHermiteSplineFunction1D<JElement_t, JCollection_t, JResult_t, JDistance_t>::const_iterator  const_iterator;
     
     ordinate_type V(JMATH::zero);
     
     if (input.getSize() > 1) {
       
       output.put(input.begin()->getX(), V);
       
       for (const_iterator j = input.begin(), i = j++; j != input.end(); ++i, ++j) {
         
         const double        dx = input.getDistance(i->getX(), j->getX());
         const ordinate_type y  = i->getY() + j->getY();
         const ordinate_type z  = i->getU() - j->getU();
         
         const ordinate_type v = dx * 0.50 * y;
         const ordinate_type w = dx * 1.00 * z*dx/12.0;
         
         V += v + w;
         
         output.put(j->getX(), V);
       }
     }
     
     return V;
   }

template<class JElement_t , template< class, class > class JCollection_t, class JDistance_t >

JElement_t::ordinate_type JTOOLS::integrate	(	const JHermiteSplineFunction1D< JElement_t, JCollection_t, JResultPDF< typename JElement_t::ordinate_type >, JDistance_t > &	input,
		typename JMappable< JElement_t >::map_type &	output
	)

inline

Conversion of data points to integral values.

The integration directly uses the integral values of the input spline interpolating function.

Parameters

input	collection
output	mappable collection

Returns: integral

Definition at line 686 of file JHermiteSpline.hh.

   {
     typedef typename JElement_t::ordinate_type                                                                      ordinate_type;
     typedef JResultPDF<ordinate_type>                                                                               result_type;
     typedef typename JHermiteSplineFunction1D<JElement_t, JCollection_t, result_type, JDistance_t>::const_iterator  const_iterator;
     
     if (input.getSize() > 1) {
       
       for (const_iterator i = input.begin(); i != input.end(); ++i) {
         output.put(i->getX(), i->getIntegral());
       }
 
       return input.rbegin()->getIntegral();
     }
     
     return JMATH::zero;
   }

template<class JElement_t , template< class, class > class JContainer_t, class JDistance_t >

void JTOOLS::makePDF	(	const JHistogram1D< JElement_t, JContainer_t, JDistance_t > &	input,
		typename JMappable< JElement_t >::map_type &	output
	)

inline

Conversion of histogram to probability density function (PDF).

The PDF abscissa and contents are set to the bin center and contents divided the bin width, respectively.

Parameters

input	histogram
output	mappable collection

Definition at line 545 of file JHistogram1D.hh.

   {
     typedef typename JElement_t::abscissa_type                                            abscissa_type;
     typedef typename JElement_t::ordinate_type                                            ordinate_type;
     typedef typename JHistogram1D<JElement_t, JContainer_t, JDistance_t>::const_iterator  const_iterator;
     
     if (input.getSize() > 1) {
       
       for (const_iterator j = input.begin(), i = j++; j != input.end(); ++i, ++j) {
         
         const abscissa_type x = 0.5 * (i->getX() + j->getX());
         const ordinate_type y = i->getY();
         const double        w = input.getDistance(i->getX(), j->getX());
         
         output.put(x, y/w);
       }
     }
   }

template<class JAbscissa_t , class JContents_t , template< class, class > class JContainer_t, class JDistance_t >

void JTOOLS::makePDF	(	const JHistogram1D< JBin2D< JAbscissa_t, JContents_t >, JContainer_t, JDistance_t > &	input,
		JMappableCollection< JAbscissa_t, JContents_t > &	output
	)

inline

Conversion of histogram to probability density function (PDF).

The PDF abscissa and contents are set to the bin center and contents divided the bin width, respectively.

Parameters

input	histogram
output	mappable collection

Definition at line 578 of file JHistogram1D.hh.

   {
     typedef JAbscissa_t                                                                                         abscissa_type;
     typedef JContents_t                                                                                         contents_type;
     typedef typename JHistogram1D<JBin2D<JAbscissa_t, JContents_t>, JContainer_t, JDistance_t>::const_iterator  const_iterator;
     
     if (input.getSize() > 1) {
       
       for (const_iterator j = input.begin(), i = j++; j != input.end(); ++i, ++j) {
         
         const abscissa_type x = i->getBinCenter();
         const contents_type y = i->getY();
         const double        w = input.getDistance(i->getX(), j->getX());
         
         output.put(x, y/w);
       }
     }
   }

template<class JElement_t , template< class, class > class JContainer_t, class JDistance_t >

JElement_t::ordinate_type JTOOLS::integrate	(	const JHistogram1D< JElement_t, JContainer_t, JDistance_t > &	input,
		typename JMappable< JElement_t >::map_type &	output
	)

inline

Conversion of data points to integral values.

The integration is based on the sum of bin contents of the input data points.

Parameters

input	histogram
output	mappable collection

Returns: integral

Definition at line 612 of file JHistogram1D.hh.

   {
     typedef typename JElement_t::ordinate_type                                            ordinate_type;
     typedef typename JHistogram1D<JElement_t, JContainer_t, JDistance_t>::const_iterator  const_iterator;
     
     ordinate_type V(JMATH::zero);
     
     if (input.getSize() > 1) {
       
       output.put(input.begin()->getX(), V);
       
       for (const_iterator j = input.begin(), i = j++; j != input.end(); ++i, ++j) {
         
         V += i->getY();
 
         output.put(j->getX(), V);
       }
     }
     
     return V;
   }

template<class JHistogram_t , class JHistogramMaplist_t , class JHistogramDistance_t , class JFunction_t , class JFunctionMaplist_t , class JFunctionDistance_t >

void JTOOLS::makePDF	(	const JMultiHistogram< JHistogram_t, JHistogramMaplist_t, JHistogramDistance_t > &	input,
		JMultiFunction< JFunction_t, JFunctionMaplist_t, JFunctionDistance_t > &	output
	)

inline

Conversion of multidimensional histogram to multidimensional function.

Parameters

input	multidimensional histogram
output	multidimensional function

Definition at line 347 of file JMultiFunction.hh.

   {
     output.insert(input);
   }

template<unsigned int N, class JAbscissa_t >

JMultiGrid<N, JAbscissa_t> JTOOLS::make_multigrid ( const JGrid< JAbscissa_t > & bounds )

inline

Helper method for JMultiGrid.

Parameters

bounds bounds

Returns: multidimensional grid

Definition at line 150 of file JMultiGrid.hh.

   {
     return JMultiGrid<N, JAbscissa_t>(bounds);
   }

template<class JHistogram_t , class JHistogramMaplist_t , class JHistogramDistance_t , class JFunction_t , class JFunctionMaplist_t , class JFunctionDistance_t >

void JTOOLS::makePDF	(	const JMultiHistogram< JHistogram_t, JHistogramMaplist_t, JHistogramDistance_t > &	input,
		JMultiPDF< JFunction_t, JFunctionMaplist_t, JFunctionDistance_t > &	output
	)

inline

Conversion of multi-dimensional histogram to multi-dimensional PDF.

Parameters

input	multi-dimensional histogram
output	multi-dimensional PDF

Definition at line 185 of file JMultiPDF.hh.

   {
     output.insert(input);
   }

template<unsigned int N, class JAbscissa_t >

JMultiSet<N, JAbscissa_t> JTOOLS::make_multiset ( const JSet< JAbscissa_t > & bounds )

inline

Helper method for JMultiSet.

Parameters

bounds bounds

Returns: multidimensional set

Definition at line 151 of file JMultiSet.hh.

   {
     return JMultiSet<N, JAbscissa_t>(bounds);
   }

template<class T , class JComparator_t >

bool JTOOLS::next_permutation	(	T	__begin,
		T	__last,
		T	__end,
		JComparator_t	compare,
		std::bidirectional_iterator_tag
	)

inline

Implementation of method next_permutation for bidirectional iterators.

Definition at line 20 of file JPermutation.hh.

   {
     using namespace std;
 
     T __rend = __begin;
     --__rend;
 
     for (T __i = __last; --__i != __rend; ) {
 
       T __j;
 
       for (__j = __last; __j != __end && !compare(*__i,*__j); ++__j) {}
 
       if (__j != __end) {
 
         iter_swap(__i,__j);
 
         if (++__i != __last && ++__j != __end) {
 
           reverse(__i,__last);
           reverse(__j,__end);
 
           T __k = __end;
 
           while (__k != __j && __i != __last)
             iter_swap(__i++,--__k);
 
           reverse(__i,__last);
           reverse(__j,__k);
         }
 
         return true;
       }
     }
 
     reverse(__begin, __last);
     reverse(__last,  __end);
     reverse(__begin, __end);
 
     return false;
   }

template<class T , class JComparator_t >

bool JTOOLS::next_permutation	(	T	__begin,
		T	__last,
		T	__end,
		JComparator_t	compare
	)

inline

Permutations of sub-set of data.

The first template argument refers to a bidirectional iterator and the second template argument to the comparator.

Parameters

__begin	begin of input data
__last	end of output data
__end	end of input data
compare	comparison operator

Returns: true if another permutation exists; else false

Definition at line 79 of file JPermutation.hh.

   {
     return next_permutation(__begin, __last, __end, compare, typename std::iterator_traits<T>::iterator_category());
   }

template<unsigned int N, class JElement_t , template< class, class > class JCollection_t, class JDistance_t , unsigned int M>

JTOOLS::if ( (p==this->begin()&&this->getDistance(x,(p++) ->getX()) > distance_type::precision)||(p==this->end()&&this->getDistance((--p) ->getX(), x) > distance_type::precision) )

Template base class for polynomial interpolations with polynomial result.

This class partially implements the JFunctional interface.

Definition at line 619 of file JPolint.hh.

                                                                                                 {
 
         THROW(JValueOutOfRange, "JPolintFunction::evaluate() x out of range.");
       }

JTOOLS::for	(	int	i = `n/2; i != 0 && p != this->end(); --i`,
		++	p
	)

Definition at line 630 of file JPolint.hh.

630 {} // move p to begin of data

JTOOLS::for	(	int	i = `n ; i != 0 && p != this->begin(); --i`,
		--	p
	)

Definition at line 631 of file JPolint.hh.

631 {}

JTOOLS::for ( unsigned int k = 0; k != M+1; ++k )

Definition at line 652 of file JPolint.hh.

                                               {
         result.y[k] = v[j][k];
       }

JTOOLS::for ( int m = 1; m != n; ++m )

Definition at line 658 of file JPolint.hh.

                                    {
 
         for (int i = 0; i != n-m; ++i) {
 
           const double ho = u[ i ];
           const double hp = u[i+m];
           const double dx = ho - hp;
 
           for (int k = 0; k != M+1; ++k) {
             r[k] = (v[i+1][k] - w[i][k]) / dx;
           }
 
           v[i][0] = ho * r[0];
           w[i][0] = hp * r[0];
 
           for (int k = 1; k != M+1; ++k) {
             v[i][k] = ho * r[k]  -  k * r[k-1];
             w[i][k] = hp * r[k]  -  k * r[k-1];
           }
         }
 
         if (2*(j+1) < n - m) {
 
           for (int k = 0; k != M+1; ++k) {
             result.y[k] += v[j+1][k];
           }
 
         } else {
 
           for (int k = 0; k != M+1; ++k) {
             result.y[k] += w[j][k];
           }
 
           --j;
         }
       }

virtual void JTOOLS::do_compile ( )

privatevirtual

Function compilation.

Definition at line 702 of file JPolint.hh.

703 {}

template<unsigned int N, class JElement_t , template< class, class > class JCollection_t, class JResult_t , class JDistance_t >

JElement_t::ordinate_type JTOOLS::integrate	(	const JPolintFunction1D< N, JElement_t, JCollection_t, JResult_t, JDistance_t > &	input,
		typename JMappable< JElement_t >::map_type &	output
	)

inlineprivate

Conversion of data points to integral values.

This method transfers the integration to the corresponding specialised function.

Parameters

input	collection
output	mappable collection

Returns: integral

Definition at line 1029 of file JPolint.hh.

   {
     return integrate(input, output, JLANG::JBool<N == 0 || N == 1>());
   }

template<unsigned int N, class JElement_t , template< class, class > class JCollection_t, class JResult_t , class JDistance_t >

JElement_t::ordinate_type JTOOLS::integrate	(	const JPolintFunction1D< N, JElement_t, JCollection_t, JResult_t, JDistance_t > &	input,
		typename JMappable< JElement_t >::map_type &	output,
		const JLANG::JBool< false > &	option
	)

inlineprivate

Conversion of data points to integral values.

The integration uses the Gauss-Legendre quadratures with the number of points set to the degree of the input polynomial interpolating function.

Parameters

input	collection
output	mappable collection
option	false

Returns: integral

Definition at line 1053 of file JPolint.hh.

   {
     typedef typename JElement_t::abscissa_type                                                                abscissa_type;
     typedef typename JElement_t::ordinate_type                                                                ordinate_type;
     typedef typename JPolintFunction1D<N, JElement_t, JCollection_t, JResult_t, JDistance_t>::const_iterator  const_iterator;
     
     ordinate_type V(JMATH::zero);
 
     if (input.getSize() > 1) {
       
       output.put(input.begin()->getX(), V);
       
       const JGaussLegendre engine(N);
       
       for (const_iterator j = input.begin(), i = j++; j != input.end(); ++i, ++j) {
         
         const abscissa_type xmin = i->getX();
         const abscissa_type xmax = j->getX();
         
         for (JGaussLegendre::const_iterator m = engine.begin(); m != engine.end(); ++m) {
           
           const abscissa_type x = 0.5 * (xmax + xmin  +  m->getX() * (xmax - xmin));
           const ordinate_type v = 0.5 * (xmax - xmin) *  m->getY() * get_value(input(x));
           
           V += v;
         }
         
         output.put(xmax, V);
       }
     }
     
     return V;
   }

template<class JElement_t , template< class, class > class JCollection_t, class JResult_t , class JDistance_t >

JElement_t::ordinate_type JTOOLS::integrate	(	const JPolintFunction1D< 0, JElement_t, JCollection_t, JResult_t, JDistance_t > &	input,
		typename JMappable< JElement_t >::map_type &	output,
		const JLANG::JBool< true > &	option
	)

inlineprivate

Conversion of data points to integral values.

The integration is based on the sum of ordinates of the input data points.

Parameters

input	collection
output	mappable collection
option	true

Returns: integral

Definition at line 1105 of file JPolint.hh.

   {
     typedef typename JElement_t::ordinate_type                                                                ordinate_type;
     typedef typename JPolintFunction1D<0, JElement_t, JCollection_t, JResult_t, JDistance_t>::const_iterator  const_iterator;
     
     ordinate_type V(JMATH::zero);
     
     if (input.getSize() > 1) {
       
       output.put(input.begin()->getX(), V);
       
       for (const_iterator j = input.begin(), i = j++; j != input.end(); ++i, ++j) {
         
         V += input.getDistance(i->getX(), j->getX()) * j->getY();
         
         output.put(j->getX(), V);
       }
     }
     
     return V;
   }

template<class JElement_t , template< class, class > class JCollection_t, class JResult_t , class JDistance_t >

JElement_t::ordinate_type JTOOLS::integrate	(	const JPolintFunction1D< 1, JElement_t, JCollection_t, JResult_t, JDistance_t > &	input,
		typename JMappable< JElement_t >::map_type &	output,
		const JLANG::JBool< true > &	option
	)

inlineprivate

Conversion of data points to integral values.

The integration is based on the trapezoidal rule applied to the input data points.

Parameters

input	collection
output	mappable collection
option	true

Returns: integral

Definition at line 1145 of file JPolint.hh.

   {
     typedef typename JElement_t::ordinate_type                                                                ordinate_type;
     typedef typename JPolintFunction1D<1, JElement_t, JCollection_t, JResult_t, JDistance_t>::const_iterator  const_iterator;
     
     ordinate_type V(JMATH::zero);
     
     if (input.getSize() > 1) {
       
       output.put(input.begin()->getX(), V);
       
       for (const_iterator j = input.begin(), i = j++; j != input.end(); ++i, ++j) {
         
         V += 0.5 * input.getDistance(i->getX(), j->getX()) * (i->getY() + j->getY());
         
         output.put(j->getX(), V);
       }
     }
     
     return V;
   }

template<class JFunction1D_t >

double JTOOLS::search	(	const double	xa,
		const double	xb,
		const double	xc,
		const JFunction1D_t &	f,
		const int	is,
		const double	eps = `1.0e-6`
	)

Locate maximum or minimun of function.

Golden section search code is taken from reference: Numerical Recipes in C++, W.H. Press, S.A. Teukolsky, W.T. Vetterling and B.P. Flannery, Cambridge University Press.

        xa < xb < xc

        is = +1  ->  There is a minimum, i.e:  f(xb) < min(f(xa),f(xc))
        is = -1  ->  There is a maximum, i.e:  f(xb) > max(f(xa),f(xc))

Parameters

xa
xb
xc
f	function
is	sign (+1 -> minimim, -1 -> maximum)
eps	relative precision

Definition at line 48 of file JQuantiles.hh.

   {
     static const double R = 0.61803399;
     static const double C = 1.0 - R;
 
     double x0 = xa;
     double x3 = xc;
     double x1, x2;
 
     if (fabs(xc-xb) > fabs(xb-xa)) {
       x1 = xb;
       x2 = xb + C*(xc-xb);
     } else {
       x2 = xb;
       x1 = xb - C*(xb-xa);
     }
 
     double f1 = is * get_value(f(x1));
     double f2 = is * get_value(f(x2));
 
     while (fabs(x3-x0) > eps*(fabs(x1)+fabs(x2))) {
 
       if (f2 < f1) {
 
         x0 = x1;
         x1 = x2;
         x2 = R*x2 + C*x3;
 
         f1 = f2;
         f2 = is * get_value(f(x2));
 
       } else {
 
         x3 = x2;
         x2 = x1;
         x1 = R*x1 + C*x0;
 
         f2 = f1;
         f1 = is * get_value(f(x1));
       }
     }
 
     if (f1 < f2)
       return x1;
     else
       return x2;
   }

template<class T , class JComparator_t >

JRange<T, JComparator_t> JTOOLS::operator+	(	const JRange< T, JComparator_t > &	first,
		const JRange< T, JComparator_t > &	second
	)

inline

Add ranges.

The new lower limit is the sum of the two lower limits and
the new upper limit is the sum of the two upper limits.

Parameters

first	first range
second	second range

Returns: range

Definition at line 634 of file JRange.hh.

   {
     return JRange<T, JComparator_t>(first).add(second);
   }

template<class T , class JComparator_t >

JRange<T, JComparator_t> JTOOLS::operator-	(	const JRange< T, JComparator_t > &	first,
		const JRange< T, JComparator_t > &	second
	)

inline

Subtract ranges.

The new lower limit is the difference of the two lower limits and the new upper limit is the difference of the two upper limits.

Parameters

first	first range
second	second range

Returns: range

Definition at line 650 of file JRange.hh.

   {
     return JRange<T, JComparator_t>(first).sub(second);
   }

template<class T , class JComparator_t >

bool JTOOLS::overlap	(	const JRange< T, JComparator_t > &	first,
		const JRange< T, JComparator_t > &	second
	)

inline

Test overlap between ranges.

Parameters

first	first range
second	second range

Returns: true if there is a non-zero overlap; else false

Definition at line 664 of file JRange.hh.

   {
     return first.overlap(second);
   }

template<class T , class JComparator_t >

JRange<T, JComparator_t> JTOOLS::join	(	const JRange< T, JComparator_t > &	first,
		const JRange< T, JComparator_t > &	second
	)

inline

Join ranges.

The new lower limit is the maximim of the two lower limits and
the new upper limit is the minimum of the two upper limits.
This operation results in an equal or smaller range and may result in an unphysical range (i.e. lower limit > upper limit).

Parameters

first	first range
second	second range

Returns: range

Definition at line 682 of file JRange.hh.

   {  
     return JRange<T, JComparator_t>(first).join(second);
   }

template<class T , class JComparator_t >

JRange<T, JComparator_t> JTOOLS::combine	(	const JRange< T, JComparator_t > &	first,
		const JRange< T, JComparator_t > &	second
	)

inline

Combine ranges.

The new lower limit is the minimim of the two lower limits and
the new upper limit is the maximum of the two upper limits.
This operation results in an equal or larger range.

Parameters

first	first range
second	second range

Returns: range

Definition at line 699 of file JRange.hh.

   {  
     return JRange<T, JComparator_t>(first).combine(second);
   }

template<class T >

JRange<T> JTOOLS::make_range	(	T	x,
		T	y
	)

inline

Auxiliary method to create range of values.

Parameters

x	lower limit
y	upper limit

Returns: range

Definition at line 713 of file JRange.hh.

   {
     return JRange<T>(x,y);
   } 

template<class JResult_t >

JResultEvaluator<JResult_t>::result_type JTOOLS::get_value ( const JResult_t & value )

inline

Helper method to recursively evaluate a to function value.

Parameters

value result

Returns: function value

Definition at line 936 of file JResult.hh.

   { 
     return JResultEvaluator<JResult_t>::get_value(value);
   }

template<class JResult_t >

JResultEvaluator<JResult_t>::result_type JTOOLS::get_derivative ( const JResult_t & value )

inline

Helper method to convert function value to derivative value.

Parameters

value result

Returns: derivative value

Definition at line 949 of file JResult.hh.

   { 
     return JResultEvaluator<JResult_t>::get_derivative(value);
   }

template<class JResult_t >

JResultEvaluator<JResult_t>::result_type JTOOLS::get_integral ( const JResult_t & value )

inline

Helper method to convert function value to partial integral value.

Parameters

value result

Returns: partial integral value

Definition at line 962 of file JResult.hh.

   { 
     return JResultEvaluator<JResult_t>::get_integral(value);
   }

template<class T >

JSet<typename std::iterator_traits<T>::value_type> JTOOLS::make_set	(	T	__begin,
		T	__end
	)

inline

Helper method for JSet.

Parameters

__begin	begin of abscissa values
__end	end of abscissa values

Returns: set

Definition at line 144 of file JSet.hh.

   {
     return JSet<typename std::iterator_traits<T>::value_type>(__begin, __end);
   }

template<class JAbscissa_t >

JSet<JAbscissa_t> JTOOLS::make_set ( const JAbstractCollection< JAbscissa_t > & input )

inline

Helper method for JSet.

Parameters

input abstract collection

Returns: set

Definition at line 157 of file JSet.hh.

   {
     return JSet<JAbscissa_t>(input);
   }

template<class JOrdinate_t >

JSplineBounds<JOrdinate_t> JTOOLS::make_spline_bounds	(	const JOrdinate_t	fpAtXmin,
		const JOrdinate_t	fpAtXmax
	)

inline

Helper method for JSplineBounds.

Parameters

fpAtXmin	1st derivative at minimal abscissa value
fpAtXmax	1st derivative at maximal abscissa value

Returns: spline bounds

Definition at line 150 of file JSpline.hh.

   {
     return JSplineBounds<JOrdinate_t>(fpAtXmin, fpAtXmax);
   }

template<class JElement_t , template< class, class > class JCollection_t, class JResult_t , class JDistance_t >

JElement_t::ordinate_type JTOOLS::integrate	(	const JSplineFunction1D< JElement_t, JCollection_t, JResult_t, JDistance_t > &	input,
		typename JMappable< JElement_t >::map_type &	output
	)

inline

Conversion of data points to integral values.

The integration includes the use of 2nd derivatives of the data points of the input spline interpolating function.

Parameters

input	collection
output	mappable collection

Returns: integral

Definition at line 790 of file JSpline.hh.

   {
     typedef typename JElement_t::ordinate_type                                                             ordinate_type;
     typedef typename JSplineFunction1D<JElement_t, JCollection_t, JResult_t, JDistance_t>::const_iterator  const_iterator;
     
     ordinate_type V(JMATH::zero);
     
     if (input.getSize() > 1) {
       
       output.put(input.begin()->getX(), V);
       
       for (const_iterator j = input.begin(), i = j++; j != input.end(); ++i, ++j) {
         
         const double        dx = input.getDistance(i->getX(), j->getX());
         const ordinate_type y  = i->getY()  +  j->getY();
         const ordinate_type z  = i->getU()  +  j->getU();             
         const ordinate_type v  = dx * 0.50 * y;
         const ordinate_type w  = dx * 0.25 * z*dx*dx/6;
         
         V += v - w;
         
         output.put(j->getX(), V);
       }
     }
     
     return V;
   }

template<class JElement_t , template< class, class > class JCollection_t, class JDistance_t >

JElement_t::ordinate_type JTOOLS::integrate	(	const JSplineFunction1D< JElement_t, JCollection_t, JResultPDF< typename JElement_t::ordinate_type >, JDistance_t > &	input,
		typename JMappable< JElement_t >::map_type &	output
	)

inline

Conversion of data points to integral values.

The integration directly uses the integral values of the input spline interpolating function.

Parameters

input	collection
output	mappable collection

Returns: integral

Definition at line 833 of file JSpline.hh.

   {
     typedef typename JElement_t::ordinate_type                                                               ordinate_type;
     typedef JResultPDF<ordinate_type>                                                                        result_type;
     typedef typename JSplineFunction1D<JElement_t, JCollection_t, result_type, JDistance_t>::const_iterator  const_iterator;
     
     if (input.getSize() > 1) {
       
       for (const_iterator i = input.begin(); i != input.end(); ++i) {
         output.put(i->getX(), i->getIntegral());
       }
 
       return input.rbegin()->getIntegral();
     }
     
     return JMATH::zero;
   }

template<class JContainer_t , class JKey_t , class JValue_t >

JContainer_t::ordinate_type JTOOLS::makeCDF	(	const JContainer_t &	input,
		JMappableCollection< JKey_t, JValue_t > &	output,
		const typename JContainer_t::ordinate_type	eps = `JMATH::zero`
	)

inline

Conversion of data points to cumulative probability distribition (CDF).

Note that the data type of the input container should be preserved so that the corresponding method integrate() is used.

Parameters

input	collection
output	mappable collection
eps	minimal step size

Returns: integral value

Definition at line 51 of file JToolsToolkit.hh.

   {
     typedef typename JContainer_t::ordinate_type       ordinate_type;
     typedef typename JContainer_t::abscissa_type       abscissa_type;
     typedef JElement2D<abscissa_type, ordinate_type>   element_type;
     typedef JCollection<element_type>                  buffer_type;
 
 
     if (input.getSize() > 1) {
       
       buffer_type buffer;
 
       const ordinate_type V = integrate(input, buffer);
       
       if (V == ordinate_type(JMATH::zero)) {
         THROW(JDivisionByZero, "Method makeCDF(): integral equals zero.");
       }
       
       output.clear();
       
       typename buffer_type::const_iterator i = buffer.begin();
             
       for ( ; i != buffer.end() && i->getY() <= 0.5 * eps * V; ++i) {}
       
       if (i != buffer.end()) {
         
         // force first point at (0, ymin)
       
         JKey_t   x = 0.0;
         JValue_t y = i->getX();
         
         output.put(x, y);
       
         JKey_t   xmax = x;
         JValue_t ymax = y;
       
         for (++i; i != buffer.end(); ++i) {
           
           x = i->getY() / V;
           y = i->getX();
           
           if (x > xmax) {
           
             ymax = y;
             
             if (x > xmax + eps) {
               
               output.put(x, y);
               
               xmax = x;
             }
           }
         }
         
         // force last point at (1, ymax)
         
         x = 1.0;
         y = ymax;
         
         output.put(x,y);
         
       } else {
         THROW(JDivisionByZero, "Method makeCDF(): no remaining data.");
       }
 
       return V;
 
     } else {
       THROW(JEmptyCollection, "Method makeCDF(): not sufficient input data.");
     }
   }

template<class JContainer_t >

JContainer_t::ordinate_type JTOOLS::getIntegral ( const JContainer_t & input )

inline

Get integral of input data points.

Parameters

input input data

Returns: integral value

Definition at line 133 of file JToolsToolkit.hh.

   { 
     JGarbageCollection<typename JContainer_t::abscissa_type, typename JContainer_t::ordinate_type> garbage;
     
     return integrate(input, garbage);
   }

template<class JFunction_t , template< class, class, class > class JMap_t, class JTail_t >

JFunction_t::ordinate_type JTOOLS::getIntegral ( const JMultiMap< typename JFunction_t::abscissa_type, JFunction_t, JMapList< JMap_t, JTail_t >, typename JFunction_t::distance_type > & input )

inline

Auxiliary method to get integral of input data points.

Parameters

input input data

Returns: integral value

Definition at line 151 of file JToolsToolkit.hh.

   { 
     typedef typename JFunction_t::abscissa_type                                               abscissa_type;
     typedef typename JFunction_t::ordinate_type                                               ordinate_type;
     typedef typename JFunction_t::distance_type                                               distance_type;
     typedef typename JFunctionalMap<JMap_t>::template function_type<abscissa_type,
                                                                     ordinate_type,
                                                                     ordinate_type,
                                                                     distance_type>            buffer_type;
     typedef JMultiMap<abscissa_type, JFunction_t, JMapList<JMap_t, JTail_t>, distance_type>   multimap_type;
     
     static buffer_type buffer;
     
     buffer.configure(input);
     
     typename buffer_type::iterator out = buffer.begin();
     
     for (typename multimap_type::const_iterator in = input.begin(); in != input.end(); ++in, ++out) {
       out->getY() = getIntegral(in->getY());
     }
     
     buffer.compile();
     
     return getIntegral(buffer);
   }

template<class JFunction_t , template< class, class, class > class JMap_t, class JTail_t >

JFunction_t::ordinate_type JTOOLS::getIntegral ( const JMultiFunction< JFunction_t, JMapList< JMap_t, JTail_t >, typename JFunction_t::distance_type > & input )

inline

Get integral of input data points.

Parameters

input input data

Returns: integral value

Definition at line 188 of file JToolsToolkit.hh.

   { 
     typedef typename JFunction_t::abscissa_type                                      abscissa_type;
     typedef typename JFunction_t::ordinate_type                                      ordinate_type;
     typedef typename JFunction_t::distance_type                                      distance_type;
     typedef typename JFunctionalMap<JMap_t>::template function_type<abscissa_type,
                                                                     ordinate_type,
                                                                     ordinate_type,
                                                                     distance_type>   buffer_type;
     typedef JMultiFunction<JFunction_t, JMapList<JMap_t, JTail_t>, distance_type>    multifunction_type;
     
     buffer_type buffer;
     
     for (typename multifunction_type::const_iterator i = input.begin(); i != input.end(); ++i) {      
       buffer.put(i->getX(), getIntegral(i->getY()));
     }
     
     buffer.compile();
     
     return getIntegral(buffer);
   }

template<class T >

void JTOOLS::reset ( T & value )

inline

Reset value.

The value is set to (the equivalent of) zero, see method JMATH::getZero.

Parameters

value value

Definition at line 219 of file JToolsToolkit.hh.

   {
     value = JMATH::getZero<T>();
   }

template<class JElement_t , class JDistance_t >

void JTOOLS::reset ( JCollection< JElement_t, JDistance_t > & collection )

inline

Recursive reset of collection.

Parameters

collection collection

Definition at line 231 of file JToolsToolkit.hh.

   {
     typedef typename JCollection<JElement_t, JDistance_t>::iterator  iterator;
 
     for (iterator i = collection.begin(); i != collection.end(); ++i) {
       reset(i->getY());
     }
   }

template<class T >

void JTOOLS::copy	(	const T &	input,
		T &	output
	)

inline

Copy of input to output.

The output value is set to the input value.

Parameters

input	input
output	output

Definition at line 250 of file JToolsToolkit.hh.

   {
     output = input;
   }

template<class JElement_t , class JDistance_t , class JKey_t , class JValue_t >

void JTOOLS::copy	(	const JCollection< JElement_t, JDistance_t > &	input,
		JMappableCollection< JKey_t, JValue_t > &	output
	)

inline

Recursive copy of input collection to output collection.

Parameters

input	input
output	output

Definition at line 263 of file JToolsToolkit.hh.

   {
     typedef typename JCollection<JElement_t, JDistance_t>::const_iterator  const_iterator;
 
     output.clear();
 
     for (const_iterator i = input.begin(); i != input.end(); ++i) {
       copy(i->getY(), output.get(i->getX()));
     }
   }

template<class T , class JAbscissa_t >

void JTOOLS::configure	(	const T &	value,
		const JAbstractCollection< JAbscissa_t > &	bounds,
		JBool< false >	option
	)

inline

Configuration of value.

This is a fall-back method; it does nothing.

Parameters

value	value
bounds	bounds
option	false

Definition at line 285 of file JToolsToolkit.hh.

286 {}

template<class JElement_t , class JDistance_t >

void JTOOLS::configure	(	JCollection< JElement_t, JDistance_t > &	collection,
		const JAbstractCollection< typename JElement_t::abscissa_type > &	bounds,
		JBool< true >	option = `JBool<true>()`
	)

inline

Recursive configuration of collection.

Parameters

collection	collection
bounds	bounds
option	true

Definition at line 297 of file JToolsToolkit.hh.

   {
     typedef typename JCollection<JElement_t, JDistance_t>::iterator       iterator;
     typedef typename JCollection<JElement_t, JDistance_t>::ordinate_type  ordinate_type;
 
     collection.configure(bounds);
 
     for (iterator i = collection.begin(); i != collection.end(); ++i) {
       configure(i->getY(), bounds, JBool<JAssembler<ordinate_type>::is_collection>());
     }
   }

template<class T >

void JTOOLS::accumulate	(	T &	value,
		JBool< false >	option
	)

inline

Accumulation of value.

This is a fall-back method; it does nothing.

Parameters

value	value
option	false

Definition at line 321 of file JToolsToolkit.hh.

322 {}

template<class JElement_t , class JDistance_t >

void JTOOLS::accumulate	(	JCollection< JElement_t, JDistance_t > &	collection,
		JBool< true >	option = `JBool<true>()`
	)

inline

Recursive accumulation of collection.

Parameters

collection	collection
option	true

Definition at line 332 of file JToolsToolkit.hh.

   {
     typedef typename JCollection<JElement_t, JDistance_t>::iterator       iterator;
     typedef typename JCollection<JElement_t, JDistance_t>::ordinate_type  ordinate_type;
 
     for (iterator i = collection.begin(); i != collection.end(); ++i) {
       accumulate(i->getY(), JBool<JAssembler<ordinate_type>::is_collection>());
     }
 
     if (collection.getSize() > 1) {
 
       for (iterator j = collection.begin(), i = j++; j != collection.end(); ++i, ++j) {
         j->getY() += i->getY();
       }
 
       reset(collection.begin()->getY());
     }
   }

template<class JHistogram_t , class JHistogramMaplist_t , class JHistogramDistance_t , class JFunction_t , class JFunctionMaplist_t , class JFunctionDistance_t >

void JTOOLS::makePDF	(	const JTransformableMultiHistogram< JHistogram_t, JHistogramMaplist_t, JHistogramDistance_t > &	input,
		JTransformableMultiFunction< JFunction_t, JFunctionMaplist_t, JFunctionDistance_t > &	output
	)

inline

Conversion of multidimensional histogram to multidimensional function.

Parameters

input	multidimensional histogram
output	multidimensional function

Definition at line 287 of file JTransformableMultiFunction.hh.

   {
     output.insert(input);
   }

template<class JObject_t , class JHead_t , class JTail_t , class T >

JObject_t& JTOOLS::for_each	(	JObject_t &	object,
		JType< JTypeList< JHead_t, JTail_t > >	typelist,
		const JTuple< T > &	tuple
	)

For each data type method.

The given object should provide for the function object operator

   template<class T>
   void object()(JType<T> type, tuple);

Parameters

object	object
typelist	type list
tuple	tuple

Returns: object

Definition at line 666 of file JTuple.hh.

   {
     for_each(object, JType<JHead_t>(), tuple);
     for_each(object, JType<JTail_t>(), tuple);
 
     return object;
   }

template<class JObject_t , class JTypelist_t , class T >

JObject_t& JTOOLS::for_each	(	JObject_t &	object,
		JType< JTypelist_t >	type,
		const JTuple< T > &	tuple
	)

For each data type method.

The given object should provide for the function object operator

   template<class T>
   void object()(JType<T> type, tuple);

Parameters

object	object
type	type
tuple	tuple

Returns: object

Definition at line 690 of file JTuple.hh.

   {
     object(type, tuple);
 
     return object;
   }

template<class... Args>

JTuple<typename JTYPELIST<Args...>::typelist> JTOOLS::make_tuple ( const Args &... args )

inline

Helper method for tuple.

Parameters

args values

Returns: tuple

Definition at line 705 of file JTuple.hh.

   {
     return JTuple<typename JTYPELIST<Args...>::typelist>(args...);
   }

template<class JObject_t , class T >

JObject_t& JTOOLS::for_each	(	JObject_t &	object,
		JType< JNullType >	type,
		const JTuple< T > &	tuple
	)

Termination method of for each data type method.

Parameters

object	object
type	null type
tuple	tuple

Returns: object

Definition at line 720 of file JTuple.hh.

   {
     return object;
   }

template<class T >

void JTOOLS::inplace_merge	(	T	__begin,
		const size_t	N,
		const size_t *	delimiter
	)

Merge multiple sorted ranges.

Parameters

__begin	begin of data
N	number of delimiters (equals number of ranges plus one)
delimiter	incremental delimiters

Definition at line 28 of file JMergeSort.cc.

   {
     switch (N - 1) {
 
     case 0:
     case 1:
       break;
 
     case 2:
 
       std::inplace_merge(__begin + delimiter[0],
                          __begin + delimiter[1],
                          __begin + delimiter[2]);
 
       break;
 
     default:
       
       const size_t n = (N - 1) >> 1;
 
       inplace_merge(__begin, n + 1, delimiter);
       inplace_merge(__begin, N - n, delimiter + n);
 
       std::inplace_merge(__begin + delimiter[ 0 ],
                          __begin + delimiter[ n ],
                          __begin + delimiter[N-1]);
 
       break;
     };
   }

template<class T >

bool JTOOLS::is_sorted	(	T	__begin,
		T	__end
	)

inline

Test whether range is sorted.

Parameters

__begin	begin of data
__end	end of data

Returns: true if sorted; else false

Definition at line 105 of file JMergeSort.cc.

   {
     if (std::distance(__begin, __end) > 1) {
       for (T q = __begin, p = q++; q != __end; ++p, ++q) {
         if (*p > *q) {
           return false;
         }
       }
     }
 
     return true;
   }

Variable Documentation

const double JTOOLS::PI = 3.1415927

static

Constants.

pi

Definition at line 20 of file JConstants.hh.

const double JTOOLS::EULER = 0.577215664901533

static

Euler number.

Definition at line 21 of file JConstants.hh.

const double JTOOLS::C = 0.299792458

static

Speed of light in vacuum [m/ns].

Definition at line 22 of file JConstants.hh.

const double JTOOLS::C_INVERSE = 1.0/C

static

Inverse speed of light in vacuum [ns/m].

Definition at line 23 of file JConstants.hh.

const double JTOOLS::AVOGADRO = 6.0221415e23

static

Avogadro's number [gr^-1].

Definition at line 24 of file JConstants.hh.

const double JTOOLS::H = 4.13566733e-15

static

Planck constant [eV s].

Definition at line 25 of file JConstants.hh.

const double JTOOLS::HBAR = H/(2*PI)

static

Planck constant [eV s].

Definition at line 26 of file JConstants.hh.

const double JTOOLS::HBARC = HBAR*C*1.0e9

static

Planck constant [eV m].

Definition at line 27 of file JConstants.hh.

const double JTOOLS::ALPHA_ELECTRO_MAGNETIC = 1.0/137.036

static

Electro-Magnetic coupling constant.

Definition at line 28 of file JConstants.hh.

const double JTOOLS::THETA_MCS = 13.6e-3

static

Multiple Coulomb scattering constant [GeV].

Definition at line 29 of file JConstants.hh.

const double JTOOLS::DENSITY_SEA_WATER = 1.038

static

Fixed environment values.

Density of sea water [g/cm^3]

Definition at line 34 of file JConstants.hh.

const double JTOOLS::DENSITY_ROCK = 2.65

static

Density of rock [g/cm^3].

Definition at line 35 of file JConstants.hh.

const double JTOOLS::SALINITY_SEA_WATER = 0.035

static

Salinity of sea water.

Definition at line 36 of file JConstants.hh.

const double JTOOLS::INDEX_OF_REFRACTION_WATER = 1.3800851282

static

average index of refraction of water

Definition at line 37 of file JConstants.hh.

const double JTOOLS::X0_WATER_M = 0.36

static

Radiation length pure water [m].

Definition at line 38 of file JConstants.hh.

const double JTOOLS::TAN_THETA_C_WATER = sqrt((INDEX_OF_REFRACTION_WATER - 1.0) * (INDEX_OF_REFRACTION_WATER + 1.0))

static

Derived quantities of optical medium.

Definition at line 43 of file JConstants.hh.

const double JTOOLS::COS_THETA_C_WATER = 1.0 / INDEX_OF_REFRACTION_WATER

static

Definition at line 44 of file JConstants.hh.

const double JTOOLS::SIN_THETA_C_WATER = TAN_THETA_C_WATER * COS_THETA_C_WATER

static

Definition at line 45 of file JConstants.hh.

const double JTOOLS::KAPPA_WATER = 0.96

static

Definition at line 46 of file JConstants.hh.

const double JTOOLS::MASS_PHOTON = 0.0

static

Particle masses.

Note that the neutrino masses are set to zero.photon mass [GeV]

Definition at line 52 of file JConstants.hh.

const double JTOOLS::MASS_ELECTRON_NEUTRINO = 0.0

static

electron neutrino mass [GeV]

Definition at line 54 of file JConstants.hh.

const double JTOOLS::MASS_MUON_NEUTRINO = 0.0

static

muon neutrino mass [GeV]

Definition at line 55 of file JConstants.hh.

const double JTOOLS::MASS_TAU_NEUTRINO = 0.0

static

tau neutrino mass [GeV]

Definition at line 56 of file JConstants.hh.

const double JTOOLS::MASS_ELECTRON = 0.510998946e-3

static

electron mass [GeV]

Definition at line 58 of file JConstants.hh.

const double JTOOLS::MASS_MUON = 0.1056583745

static

muon mass [GeV]

Definition at line 59 of file JConstants.hh.

const double JTOOLS::MASS_TAU = 1.77682

static

tau mass [GeV]

Definition at line 60 of file JConstants.hh.

const double JTOOLS::MASS_NEUTRAL_PION = 0.1349766

static

pi_0 mass [GeV]

Definition at line 62 of file JConstants.hh.

const double JTOOLS::MASS_CHARGED_PION = 0.13957018

static

pi^+/- mass [GeV]

Definition at line 63 of file JConstants.hh.

const double JTOOLS::MASS_NEUTRAL_KAON = 0.497614

static

K_0 mass [GeV].

Definition at line 64 of file JConstants.hh.

const double JTOOLS::MASS_CHARGED_KAON = 0.493677

static

K^+/- mass [GeV].

Definition at line 65 of file JConstants.hh.

const double JTOOLS::MASS_PROTON = 0.9382720813

static

proton mass [GeV]

Definition at line 67 of file JConstants.hh.

const double JTOOLS::MASS_NEUTRON = 0.9395654133

static

neutron mass [GeV]

Definition at line 68 of file JConstants.hh.

const double JTOOLS::MASS_LAMBDA = 1.115683

static

Lambda mass [GeV].

Definition at line 69 of file JConstants.hh.

const double JTOOLS::MASS_NEUTRAL_SIGMA = 1.192642

static

Sigma_0 mass [GeV].

Definition at line 70 of file JConstants.hh.

const double JTOOLS::MASS_CHARGED_SIGMA = 1.18937

static

Sigma^+/- mass [GeV].

Definition at line 71 of file JConstants.hh.

const double JTOOLS::MASS_NEUTRAL_XI = 1.31486

static

Xi_0 mass [GeV].

Definition at line 72 of file JConstants.hh.

const double JTOOLS::MASS_CHARGED_XI = 1.32171

static

Xi^+/- mass [GeV].

Definition at line 73 of file JConstants.hh.

const double JTOOLS::MASS_CHARGED_OMEGA = 1.67245

static

Omega^+/- mass [GeV].

Definition at line 74 of file JConstants.hh.

const long long int JTOOLS::KILOBYTE = 1024

static

Computing quantities.

Definition at line 79 of file JConstants.hh.

const long long int JTOOLS::MEGABYTE = KILOBYTE*KILOBYTE

static

Number of bytes in a kilobyte.

Definition at line 80 of file JConstants.hh.

const long long int JTOOLS::GIGABYTE = KILOBYTE*KILOBYTE*KILOBYTE

static

Number of bytes in a megabyte.

Definition at line 81 of file JConstants.hh.

const JCompiler JTOOLS::compiler

static

Function object for functional object compilation.

Definition at line 369 of file JFunctional.hh.

const JCumulator JTOOLS::cumulator

static

Function object for functional object compilation.

Definition at line 231 of file JHistogram.hh.

JTOOLS::pX

Definition at line 625 of file JPolint.hh.

const int JTOOLS::n = std::min((int) (N + 1), (int) this->size())

Definition at line 628 of file JPolint.hh.

JTOOLS::j = 0

Definition at line 634 of file JPolint.hh.

result_type JTOOLS::result

mutable

Definition at line 695 of file JPolint.hh.

double JTOOLS::u[N+1]

mutable

Definition at line 706 of file JPolint.hh.

data_type JTOOLS::v[N+1][M+1]

mutable

Definition at line 707 of file JPolint.hh.

data_type JTOOLS::w[N+1][M+1]

mutable

Definition at line 708 of file JPolint.hh.

data_type JTOOLS::r[M+1]

mutable

Definition at line 709 of file JPolint.hh.

Classes

Typedefs

Functions

Variables

Detailed Description

Typedef Documentation

Function Documentation

Variable Documentation