Quantile calculator for a given function. More...

#include <JQuantiles.hh>

Inheritance diagram for JTOOLS::JQuantiles:

Public Types
typedef JAbstractCollection < double >	JAbscissa_t

typedef JRange< double, std::less< double > >	range_type

typedef JLANG::JClass< double > ::argument_type	argument_type

typedef JKey_t	key_type

typedef JValue_t	mapped_type

Public Member Functions
	JQuantiles ()
	Default constructor. More...

template<class JFunction1D_t >
	JQuantiles (const JFunction1D_t &f1, const double Q=1.0, const double eps=1.0e-6)
	Constructor. More...

template<class JFunction1D_t >
	JQuantiles (const JAbscissa_t &abscissa, const JFunction1D_t &f1, const double Q=1.0, const double eps=1.0e-6)
	Constructor. More...

template<class JFunction1D_t >
void	set (const JFunction1D_t &f1, const double Q=1.0, const double eps=1.0e-6)
	Set quantiles. More...

template<class JFunction1D_t >
void	set (const JAbscissa_t &abscissa, const JFunction1D_t &f1, const double Q=1.0, const double eps=1.0e-6)
	Set quantiles. More...

double	getX () const
	Get position of maximum. More...

double	getY () const
	Get value of maximum. More...

double	getFWHM () const
	Get Full Width at Half Maximum. More...

double	getIntegral () const
	Get integral of function. More...

const range_type &	getRange () const
	Get range. More...

void	setRange (const range_type &range)
	Set range. More...

void	setRange (argument_type x, argument_type y)
	Set lower and uppper limit. More...

void	setRange (iterator_type __begin, iterator_type __end, result_type value_type::*member)
	Set lower and uppper limit. More...

void	setRange (iterator_type __begin, iterator_type __end, result_type(value_type::*function)() const)
	Set lower and uppper limit. More...

double	getLowerLimit () const
	Get lower limit. More...

double	getUpperLimit () const
	Get upper limit. More...

void	setLowerLimit (argument_type x)
	Set lower limit. More...

void	setUpperLimit (argument_type y)
	Set upper limit. More...

void	fixLowerLimit (argument_type x)
	Fix lower limit. More...

void	fixUpperLimit (argument_type y)
	Fix upper limit. More...

bool	equals (const range_type &range) const
	Equal method. More...

double	getLength () const
	Get length (difference between upper and lower limit). More...

bool	is_valid () const
	Check validity of range. More...

bool	operator() (argument_type x) const
	Test whether value is inside range. More...

double	constrain (argument_type x) const
	Constrain value to range. More...

bool	overlap (const range_type &range) const
	Test overlap with given range. More...

range_type	include (argument_type x)
	Include given value to range. More...

range_type &	join (const range_type &range)
	Join ranges. More...

range_type &	combine (const range_type &range)
	Combine ranges. More...

range_type &	add (argument_type x)
	Add offset. More...

range_type &	add (const range_type &range)
	Add offset. More...

range_type &	sub (argument_type x)
	Subtract offset. More...

range_type &	sub (const range_type &range)
	Subtract offset. More...

range_type &	mul (const double factor)
	Multiply range. More...

JFirst_t &	mul (const JSecond_t &object)
	Multiply with object. More...

range_type &	div (const double factor)
	Divide range. More...

double	getN (const double R) const
	Get expected number of occurances of given rate within this interval. More...

const key_type &	getKey () const

const mapped_type &	getValue () const

mapped_type &	getValue ()

Static Public Member Functions
static double	getMinimum ()
	Get minimum possible value. More...

static double	getMaximum ()
	Get maximum possible value. More...

Public Attributes
std::less< double >	compare
	Function object. More...

JKey_t	first

JValue_t	second

Static Public Attributes
static const JRange< double, std::less< double > >	DEFAULT_RANGE
	Default range. More...

Protected Attributes
double	Xmax

double	Ymax

double	fwhm

double	sum

Detailed Description

Quantile calculator for a given function.

It is assumed that the function has a single maximum.

Definition at line 106 of file JQuantiles.hh.

Member Typedef Documentation

typedef JAbstractCollection<double> JTOOLS::JQuantiles::JAbscissa_t

Definition at line 111 of file JQuantiles.hh.

typedef JRange<double , std::less<double > > JTOOLS::JRange< double , std::less<double > >::range_type

inherited

Definition at line 40 of file JRange.hh.

typedef JLANG::JClass<double >::argument_type JTOOLS::JRange< double , std::less<double > >::argument_type

inherited

Definition at line 41 of file JRange.hh.

template<class JKey_t, class JValue_t>

typedef JKey_t JTOOLS::JPair< JKey_t, JValue_t >::key_type

inherited

Definition at line 32 of file JPair.hh.

template<class JKey_t, class JValue_t>

typedef JValue_t JTOOLS::JPair< JKey_t, JValue_t >::mapped_type

inherited

Definition at line 33 of file JPair.hh.

Constructor & Destructor Documentation

JTOOLS::JQuantiles::JQuantiles ( )

inline

Default constructor.

Definition at line 116 of file JQuantiles.hh.

                  :
       Xmax(0.0),
       Ymax(0.0),
       fwhm(0.0),
       sum (0.0)
     {}

template<class JFunction1D_t >

JTOOLS::JQuantiles::JQuantiles	(	const JFunction1D_t &	f1,
		const double	Q = `1.0`,
		const double	eps = `1.0e-6`
	)

inline

Constructor.

Parameters

f1	functional collection
Q	quantile
eps	relative precision

Definition at line 132 of file JQuantiles.hh.

                                                   :
       Xmax(0.0),
       Ymax(0.0),
       fwhm(0.0),
       sum (0.0)
     {
       set(f1, Q, eps);
     }

template<class JFunction1D_t >

JTOOLS::JQuantiles::JQuantiles	(	const JAbscissa_t &	abscissa,
		const JFunction1D_t &	f1,
		const double	Q = `1.0`,
		const double	eps = `1.0e-6`
	)

inline

Constructor.

Parameters

abscissa	abscissa
f1	function
Q	quantile
eps	relative precision

Definition at line 153 of file JQuantiles.hh.

                                                   :
       Xmax(0.0),
       Ymax(0.0),
       fwhm(0.0),
       sum (0.0)
     {
       set(abscissa, f1, Q, eps);
     }

Member Function Documentation

template<class JFunction1D_t >

void JTOOLS::JQuantiles::set	(	const JFunction1D_t &	f1,
		const double	Q = `1.0`,
		const double	eps = `1.0e-6`
	)

inline

Set quantiles.

Parameters

f1	functional collection
Q	quantile
eps	relative precision

Definition at line 174 of file JQuantiles.hh.

     {
       typedef typename JFunction1D_t::const_iterator  const_iterator;
 
       if (f1.empty()) {
         throw JEmptyCollection("JQuantiles() no data.");
       }
 
 
       // maximum
 
       const_iterator p = f1.begin();
 
       for (const_iterator i = f1.begin(); i != f1.end(); ++i) {
         if (i->getY() > p->getY()) {
           p = i;
         }
       }
       
 
       // x at maximum
       
       Xmax = p->getX();
         
       if (p != f1.begin()) {
           
         const double xa = (--p)->getX();
         const double xb = (++p)->getX();
           
         if (++p != f1.end()) {
             
           const double xc = p->getX();
             
           Xmax = search(xa, xb, xc, f1, -1, eps);
         }
       }
         
       Ymax = get_value(f1(Xmax));
 
 
       // integral & quantile
 
       if (Q > 0.0 && Q <= 1.0) {
 
         JSplineFunction1D<JSplineElement2D<double, double>, JCollection, double> buffer;
 
         try {
 
           sum = makeCDF(f1, buffer);
 
           setLowerLimit(buffer(0.5 * (1.0 - Q)));
           setUpperLimit(buffer(0.5 * (1.0 + Q)));
         }
         catch(const JException& error) {
           sum = 0.0;
         }
 
       } else {
 
         sum = JTOOLS::getIntegral(f1);
 
         if        (Q >  1.0) {
           setLowerLimit(f1. begin()->getX());
           setUpperLimit(f1.rbegin()->getX());
         } else if (Q <= 0.0) {
           setLowerLimit(Xmax);
           setUpperLimit(Xmax);
         }
       }
 
 
       // FWHM
         
       fwhm = 0.0;
         
       for (double xmin = f1.begin()->getX(), xmax = Xmax, v = 0.5*Ymax; ; ) {
         
         const double x = 0.5 * (xmin + xmax);
         const double y = get_value(f1(x));
         
         if (fabs(y - v) < eps*v || xmax - xmin < eps) {
           fwhm -= x;
           break;
         }
         
         if (y > v)
           xmax = x;
         else
           xmin = x;
       }
       
       for (double xmin = Xmax, xmax = f1.rbegin()->getX(), v = 0.5*Ymax; ; ) {
         
         const double x = 0.5 * (xmin + xmax);
         const double y = get_value(f1(x));
           
         if (fabs(y - v) < eps*v || xmax - xmin < eps) {
           fwhm += x;
           break;
         }
         
         if (y > v)
           xmin = x;
         else
           xmax = x;
       }
     }

template<class JFunction1D_t >

void JTOOLS::JQuantiles::set	(	const JAbscissa_t &	abscissa,
		const JFunction1D_t &	f1,
		const double	Q = `1.0`,
		const double	eps = `1.0e-6`
	)

inline

Set quantiles.

Parameters

abscissa	abscissa
f1	function
Q	quantile
eps	relative precision

Definition at line 294 of file JQuantiles.hh.

     {
       JSplineFunction1D<JSplineElement2D<double, double>, JCollection, double> buffer;
 
       buffer.configure(abscissa, f1);
       buffer.compile();
 
       set(buffer, Q, eps);
     }

double JTOOLS::JQuantiles::getX ( ) const

inline

Get position of maximum.

Returns: x value at maximum

Definition at line 313 of file JQuantiles.hh.

     { 
       return Xmax;
     }

double JTOOLS::JQuantiles::getY ( ) const

inline

Get value of maximum.

Returns: y value at maximum

Definition at line 324 of file JQuantiles.hh.

     {
       return Ymax;
     }

double JTOOLS::JQuantiles::getFWHM ( ) const

inline

Get Full Width at Half Maximum.

Returns: FWHM

Definition at line 335 of file JQuantiles.hh.

     {
       return fwhm;
     }

double JTOOLS::JQuantiles::getIntegral ( ) const

inline

Get integral of function.

Returns: integral

Definition at line 346 of file JQuantiles.hh.

     {
       return sum;
     }

const range_type& JTOOLS::JRange< double , std::less<double > >::getRange ( ) const

inlineinherited

Get range.

Returns: range

Definition at line 109 of file JRange.hh.

     {
       return static_cast<const range_type&>(*this);
     }

void JTOOLS::JRange< double , std::less<double > >::setRange ( const range_type & range )

inlineinherited

Set range.

Parameters

range range

Definition at line 120 of file JRange.hh.

     {
       static_cast<range_type&>(*this) = range;
     }

void JTOOLS::JRange< double , std::less<double > >::setRange	(	argument_type	x,
		argument_type	y
	)

inlineinherited

Set lower and uppper limit.

Parameters

x	lower limit
y	upper limit

Definition at line 132 of file JRange.hh.

     {
       this->first  = x;
       this->second = y;
     }

void JTOOLS::JRange< double , std::less<double > >::setRange	(	iterator_type	__begin,
		iterator_type	__end,
		result_type value_type::*	member
	)

inlineinherited

Set lower and uppper limit.

Parameters

__begin	begin of data
__end	end of data
member	pointer to data member

Definition at line 147 of file JRange.hh.

     {
       setRange(getMaximum(), getMinimum());
 
       for (iterator_type i = __begin; i != __end; ++i) {
         include((*i).*member);
       }
     }

void JTOOLS::JRange< double , std::less<double > >::setRange	(	iterator_type	__begin,
		iterator_type	__end,
		result_type(value_type::*)() const	function
	)

inlineinherited

Set lower and uppper limit.

Parameters

__begin	begin of data
__end	end of data
function	pointer to member method

Definition at line 165 of file JRange.hh.

     {
       setRange(getMaximum(), getMinimum());
 
       for (iterator_type i = __begin; i != __end; ++i) {
         include(((*i).*function)());
       }
     }

double JTOOLS::JRange< double , std::less<double > >::getLowerLimit ( ) const

inlineinherited

Get lower limit.

Returns: lower limit

Definition at line 180 of file JRange.hh.

     {
       return this->first;
     }

double JTOOLS::JRange< double , std::less<double > >::getUpperLimit ( ) const

inlineinherited

Get upper limit.

Returns: upper limit

Definition at line 191 of file JRange.hh.

     {
       return this->second;
     }

void JTOOLS::JRange< double , std::less<double > >::setLowerLimit ( argument_type x )

inlineinherited

Set lower limit.

Parameters

x	lower limit

Definition at line 202 of file JRange.hh.

     {
       this->first  = x;
     }

void JTOOLS::JRange< double , std::less<double > >::setUpperLimit ( argument_type y )

inlineinherited

Set upper limit.

Parameters

y	upper limit

Definition at line 213 of file JRange.hh.

     {
       this->second = y;
     }

void JTOOLS::JRange< double , std::less<double > >::fixLowerLimit ( argument_type x )

inlineinherited

Fix lower limit.

The range is shifted to the given lower limit.

Parameters

x	lower limit

Definition at line 226 of file JRange.hh.

     {
       this->second += x - this->first;
       this->first   = x;
     }

void JTOOLS::JRange< double , std::less<double > >::fixUpperLimit ( argument_type y )

inlineinherited

Fix upper limit.

The range is shifted to the given upper limit.

Parameters

y	upper limit

Definition at line 240 of file JRange.hh.

     {
       this->first  += y - this->second;
       this->second  = y;
     }

bool JTOOLS::JRange< double , std::less<double > >::equals ( const range_type & range ) const

inlineinherited

Equal method.

Parameters

range range

Returns: true if this module range equal to given module range; else false

Definition at line 253 of file JRange.hh.

     {
       return (!this->compare(this->getLowerLimit(), range.getLowerLimit()) &&
               !this->compare(range.getLowerLimit(), this->getLowerLimit()) &&
               !this->compare(this->getUpperLimit(), range.getUpperLimit()) &&
               !this->compare(range.getUpperLimit(), this->getUpperLimit()));
     }

double JTOOLS::JRange< double , std::less<double > >::getLength ( ) const

inlineinherited

Get length (difference between upper and lower limit).

Returns: length

Definition at line 267 of file JRange.hh.

     {
       return getUpperLimit() - getLowerLimit();
     }

bool JTOOLS::JRange< double , std::less<double > >::is_valid ( ) const

inlineinherited

Check validity of range.

Returns: true if lower limit less than or equal to upper limit; else false

Definition at line 278 of file JRange.hh.

     {
       return !compare(getUpperLimit(), getLowerLimit());
     }

bool JTOOLS::JRange< double , std::less<double > >::operator() ( argument_type x ) const

inlineinherited

Test whether value is inside range.

Parameters

x value

Returns: true if lower limit <= value <= upper limit; else false

Definition at line 290 of file JRange.hh.

     {
       return (!compare(x, getLowerLimit()) && 
               !compare(getUpperLimit(), x));
     }

double JTOOLS::JRange< double , std::less<double > >::constrain ( argument_type x ) const

inlineinherited

Constrain value to range.

This method returns the original value if it is in this range, else lower limit if value < lower limit or upper limit if value > upper limit.

Parameters

x value

Returns: lower limit <= x <= upper limit

Definition at line 305 of file JRange.hh.

     {
       if (compare(x, getLowerLimit())) return getLowerLimit();
       if (compare(getUpperLimit(), x)) return getUpperLimit();
 
       return x;
     }

bool JTOOLS::JRange< double , std::less<double > >::overlap ( const range_type & range ) const

inlineinherited

Test overlap with given range.

The result is equivalent to join(range).is_valid().

Parameters

range range

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

Definition at line 321 of file JRange.hh.

     {  
       return (compare(getLowerLimit(), range.getUpperLimit()) &&
               compare(range.getLowerLimit(), getUpperLimit()));
     }

range_type JTOOLS::JRange< double , std::less<double > >::include ( argument_type x )

inlineinherited

Include given value to range.

The new lower limit is the minimim of the original lower limit and given value and the new upper limit is the maximum of the original upper limit and given value;

Parameters

x value

Returns: range

Definition at line 336 of file JRange.hh.

     {
       if (compare(x, getLowerLimit())) setLowerLimit(x);
       if (compare(getUpperLimit(), x)) setUpperLimit(x);
 
       return *this;
     }

range_type& JTOOLS::JRange< double , std::less<double > >::join ( const range_type & range )

inlineinherited

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

range range

Definition at line 354 of file JRange.hh.

     {  
       if (compare(getLowerLimit(), range.getLowerLimit())) setLowerLimit(range.getLowerLimit());
       if (compare(range.getUpperLimit(), getUpperLimit())) setUpperLimit(range.getUpperLimit());
 
       return *this;      
     }

range_type& JTOOLS::JRange< double , std::less<double > >::combine ( const range_type & range )

inlineinherited

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

range range

Definition at line 371 of file JRange.hh.

     {  
       if (compare(range.getLowerLimit(), getLowerLimit())) setLowerLimit(range.getLowerLimit());
       if (compare(getUpperLimit(), range.getUpperLimit())) setUpperLimit(range.getUpperLimit());
 
       return *this;
     }

range_type& JTOOLS::JRange< double , std::less<double > >::add ( argument_type x )

inlineinherited

Add offset.

Parameters

x offset

Definition at line 385 of file JRange.hh.

     { 
       this->first  += x;
       this->second += x;
 
       return *this;
     }

range_type& JTOOLS::JRange< double , std::less<double > >::add ( const range_type & range )

inlineinherited

Add offset.

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

range offset

Definition at line 415 of file JRange.hh.

     { 
       this->first  += range.getLowerLimit();
       this->second += range.getUpperLimit();
 
       return *this;
     }

range_type& JTOOLS::JRange< double , std::less<double > >::sub ( argument_type x )

inlineinherited

Subtract offset.

Parameters

x offset

Definition at line 399 of file JRange.hh.

     { 
       this->first  -= x;
       this->second -= x;
 
       return *this;
     }

range_type& JTOOLS::JRange< double , std::less<double > >::sub ( const range_type & range )

inlineinherited

Subtract offset.

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

range offset

Definition at line 431 of file JRange.hh.

     { 
       this->first  -= range.getLowerLimit();
       this->second -= range.getUpperLimit();
 
       return *this;
     }

range_type& JTOOLS::JRange< double , std::less<double > >::mul ( const double factor )

inlineinherited

Multiply range.

Parameters

factor factor

Definition at line 445 of file JRange.hh.

     { 
       this->first  *= factor;
       this->second *= factor;
 
       return *this;
     }

template<class JFirst_t, class JSecond_t = JNullType>

JFirst_t& JMATH::JMath< JFirst_t, JSecond_t >::mul ( const JSecond_t & object )

inlineinherited

Multiply with object.

Parameters

object object

Returns: result object

Definition at line 273 of file JMath.hh.

     {
       return static_cast<JFirst_t&>(*this) = JCalculator<JFirst_t>::calculator.mul(static_cast<const JFirst_t&>(*this), object);
     }

range_type& JTOOLS::JRange< double , std::less<double > >::div ( const double factor )

inlineinherited

Divide range.

Parameters

factor factor

Definition at line 459 of file JRange.hh.

     { 
       this->first  /= factor;
       this->second /= factor;
 
       return *this;
     }

double JTOOLS::JRange< double , std::less<double > >::getN ( const double R ) const

inlineinherited

Get expected number of occurances of given rate within this interval.

Parameters

R rate

Returns: expectation value

Definition at line 474 of file JRange.hh.

     {
       return R * (getUpperLimit() - getLowerLimit());
     }

static double JTOOLS::JRange< double , std::less<double > >::getMinimum ( )

inlinestaticinherited

Get minimum possible value.

Returns: minimum possible value

Definition at line 485 of file JRange.hh.

     { 
       return JMATH::JLimits<T>::min();
     }

static double JTOOLS::JRange< double , std::less<double > >::getMaximum ( )

inlinestaticinherited

Get maximum possible value.

Returns: maximum possible value

Definition at line 496 of file JRange.hh.

     { 
       return JMATH::JLimits<T>::max();
     }

template<class JKey_t, class JValue_t>

const key_type& JTOOLS::JPair< JKey_t, JValue_t >::getKey ( ) const

inlineinherited

Definition at line 123 of file JPair.hh.

123 { return this->first; }

JTOOLS::JPair::first

JKey_t first

Definition: JPair.hh:128

template<class JKey_t, class JValue_t>

const mapped_type& JTOOLS::JPair< JKey_t, JValue_t >::getValue ( ) const

inlineinherited

Definition at line 124 of file JPair.hh.

124 { return this->second; }

JTOOLS::JPair::second

JValue_t second

Definition: JPair.hh:129

template<class JKey_t, class JValue_t>

mapped_type& JTOOLS::JPair< JKey_t, JValue_t >::getValue ( )

inlineinherited

Definition at line 126 of file JPair.hh.

126 { return this->second; }

JTOOLS::JPair::second

JValue_t second

Definition: JPair.hh:129

Member Data Documentation

double JTOOLS::JQuantiles::Xmax

protected

Definition at line 353 of file JQuantiles.hh.

double JTOOLS::JQuantiles::Ymax

protected

Definition at line 354 of file JQuantiles.hh.

double JTOOLS::JQuantiles::fwhm

protected

Definition at line 355 of file JQuantiles.hh.

double JTOOLS::JQuantiles::sum

protected

Definition at line 356 of file JQuantiles.hh.

const JRange<double , std::less<double > > JTOOLS::JRange< double , std::less<double > >::DEFAULT_RANGE

staticinherited

Default range.

This range corresponds to an unphysical range.

Definition at line 506 of file JRange.hh.

std::less<double > JTOOLS::JRange< double , std::less<double > >::compare

inherited

Function object.

Parameters

first	first argument
second	second argument

Returns: true if first < second; else false

Definition at line 516 of file JRange.hh.

template<class JKey_t, class JValue_t>

JKey_t JTOOLS::JPair< JKey_t, JValue_t >::first

inherited

Definition at line 128 of file JPair.hh.

template<class JKey_t, class JValue_t>

JValue_t JTOOLS::JPair< JKey_t, JValue_t >::second

inherited

Definition at line 129 of file JPair.hh.

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

JQuantiles.hh

Public Types

Public Member Functions

Static Public Member Functions

Public Attributes

Static Public Attributes

Protected Attributes

Detailed Description

Member Typedef Documentation

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation