# class ROOT::Math::GSLIntegrator: public ROOT::Math::VirtualIntegratorOneDim

```

Class for performing numerical integration of a function in one dimension.
It uses the numerical integration algorithms of GSL, which reimplements the
algorithms used in the QUADPACK, a numerical integration package written in Fortran.

Various types of adaptive and non-adaptive integration are supported. These include
integration over infinite and semi-infinite ranges and singular integrals.

The integration type is selected using the Integration::type enumeration
in the class constructor.
The default type is adaptive integration with singularity
(ADAPTIVESINGULAR or QAGS in the QUADPACK convention) applying a Gauss-Kronrod 21-point integration rule.
In the case of ADAPTIVE type, the integration rule can also be specified via the
Integration::GKRule. The default rule is 31 points.

In the case of integration over infinite and semi-infinite ranges, the type used is always
ADAPTIVESINGULAR applying a transformation from the original interval into (0,1).

The ADAPTIVESINGULAR type is the most sophicticated type. When performances are
important, it is then recommened to use the NONADAPTIVE type in case of smooth functions or
ADAPTIVE with a lower Gauss-Kronrod rule.

For detailed description on GSL integration algorithms see the
<A HREF="http://www.gnu.org/software/gsl/manual/html_node/Numerical-Integration.html">GSL Manual</A>.

@ingroup Integration

```

## Function Members (Methods)

public:
 virtual ~GSLIntegrator() virtual double Error() const ROOT::Math::GSLIntegrator GSLIntegrator(double absTol = 1.E-9, double relTol = 1E-6, size_t size = 1000) ROOT::Math::GSLIntegrator GSLIntegrator(const ROOT::Math::IntegrationOneDim::Type type, double absTol = 1.E-9, double relTol = 1E-6, size_t size = 1000) ROOT::Math::GSLIntegrator GSLIntegrator(const ROOT::Math::IntegrationOneDim::Type type, const ROOT::Math::Integration::GKRule rule, double absTol = 1.E-9, double relTol = 1E-6, size_t size = 1000) ROOT::Math::GSLIntegrator GSLIntegrator(const char* type, int rule, double absTol, double relTol, size_t size) virtual double Integral() double Integral(const ROOT::Math::IGenFunction& f) virtual double Integral(const vector& pts) double Integral(const ROOT::Math::IGenFunction& f, const vector& pts) virtual double Integral(double a, double b) double Integral(ROOT::Math::GSLFuncPointer f, void* p) double Integral(const ROOT::Math::IGenFunction& f, double a, double b) double Integral(ROOT::Math::GSLFuncPointer f, void* p, const vector& pts) double Integral(ROOT::Math::GSLFuncPointer f, void* p, double a, double b) virtual double IntegralCauchy(double a, double b, double c) double IntegralCauchy(const ROOT::Math::IGenFunction& f, double a, double b, double c) virtual double IntegralLow(double b) double IntegralLow(const ROOT::Math::IGenFunction& f, double b) double IntegralLow(ROOT::Math::GSLFuncPointer f, void* p, double b) virtual double IntegralUp(double a) double IntegralUp(const ROOT::Math::IGenFunction& f, double a) double IntegralUp(ROOT::Math::GSLFuncPointer f, void* p, double a) virtual double Result() const virtual void SetAbsTolerance(double absTolerance) virtual void SetFunction(const ROOT::Math::IGenFunction& f, bool copyFunc = false) void SetFunction(ROOT::Math::GSLFuncPointer f, void* p = 0) void SetIntegrationRule(ROOT::Math::Integration::GKRule) virtual void SetRelTolerance(double relTolerance) virtual int Status() const
protected:
 bool CheckFunction()
private:
 ROOT::Math::GSLIntegrator GSLIntegrator(const ROOT::Math::GSLIntegrator&) ROOT::Math::GSLIntegrator& operator=(const ROOT::Math::GSLIntegrator&)

## Data Members

private:
 double fAbsTol double fError ROOT::Math::GSLFunctionWrapper* fFunction size_t fMaxIntervals double fRelTol double fResult ROOT::Math::Integration::GKRule fRule size_t fSize int fStatus ROOT::Math::IntegrationOneDim::Type fType ROOT::Math::GSLIntegrationWorkspace* fWorkspace

## Function documentation

GSLIntegrator(double absTol = 1.E-9, double relTol = 1E-6, size_t size = 1000)
``` constructors
Default constructor of GSL Integrator for Adaptive Singular integration

@param absTol desired absolute Error
@param relTol desired relative Error
@param size maximum number of sub-intervals

```
GSLIntegrator(const ROOT::Math::IntegrationOneDim::Type type, double absTol = 1.E-9, double relTol = 1E-6, size_t size = 1000)
``` constructor of GSL Integrator. In the case of Adaptive integration the Gauss-Krond rule of 31 points is used

@param type type of integration. The possible types are defined in the Integration::Type enumeration
@param absTol desired absolute Error
@param relTol desired relative Error
@param size maximum number of sub-intervals

```
GSLIntegrator(const Integration::Type type, const Integration::GKRule rule, double absTol = 1.E-9, double relTol = 1E-6, size_t size = 1000)
```generic constructor for GSL Integrator

@param type type of integration. The possible types are defined in the Integration::Type enumeration
@param rule Gauss-Kronrod rule. It is used only for ADAPTIVE::Integration types. The possible rules are defined in the Integration::GKRule enumeration
@param absTol desired absolute Error
@param relTol desired relative Error
@param size maximum number of sub-intervals

```
GSLIntegrator(const char * type, int rule, double absTol, double relTol, size_t size )
``` constructor of GSL Integrator. In the case of Adaptive integration the Gauss-Krond rule of 31 points is used
This is used by the plug-in manager (need a char * instead of enumerations)

@param type type of integration. The possible types are defined in the Integration::Type enumeration
@param rule Gauss-Kronrod rule (from 1 to 6)
@param absTol desired absolute Error
@param relTol desired relative Error
@param size maximum number of sub-intervals

```
virtual ~GSLIntegrator()
```~GSLIntegrator();
```
GSLIntegrator(const ROOT::Math::GSLIntegrator& )
``` disable copy ctrs
```
GSLIntegrator & operator=(const ROOT::Math::GSLIntegrator& )
void SetFunction(const IGenFunction &f, bool copyFunc = false)
``` template methods for generic functors

method to set the a generic integration function

@param f integration function. The function type must implement the assigment operator, <em>  double  operator() (  double  x ) </em>

```
void SetFunction( GSLFuncPointer f, void * p = 0)
```Set function from a GSL pointer function type

```
double Integral(const IGenFunction & f, double a, double b)
``` methods using IGenFunction

evaluate the Integral of a function f over the defined interval (a,b)
@param f integration function. The function type must implement the mathlib::IGenFunction interface
@param a lower value of the integration interval
@param b upper value of the integration interval

```
double Integral(const IGenFunction & f)
```evaluate the Integral of a function f over the infinite interval (-inf,+inf)
@param f integration function. The function type must implement the mathlib::IGenFunction interface

```
double IntegralCauchy(double a, double b, double c)
```evaluate the Cauchy principal value of the integral of  a previously defined function f over
the defined interval (a,b) with a singularity at c
@param a lower interval value
@param b lower interval value
@param c singular value of f

```
double IntegralCauchy(const ROOT::Math::IGenFunction& f, double a, double b, double c)
```evaluate the Cauchy principal value of the integral of  a function f over the defined interval (a,b)
with a singularity at c
@param f integration function. The function type must implement the mathlib::IGenFunction interface
@param a lower interval value
@param b lower interval value
@param c singular value of f

```
double IntegralUp(const ROOT::Math::IGenFunction& f, double a)
```evaluate the Integral of a function f over the semi-infinite interval (a,+inf)
@param f integration function. The function type must implement the mathlib::IGenFunction interface
@param a lower value of the integration interval

```
double IntegralLow(const ROOT::Math::IGenFunction& f, double b)
```evaluate the Integral of a function f over the over the semi-infinite interval (-inf,b)
@param f integration function. The function type must implement the mathlib::IGenFunction interface
@param b upper value of the integration interval

```
double Integral(const IGenFunction & f, const std::vector<double> & pts )
```evaluate the Integral of a function f with known singular points over the defined Integral (a,b)
@param f integration function. The function type must implement the mathlib::IGenFunction interface
@param pts vector containing both the function singular points and the lower/upper edges of the interval. The vector must have as first element the lower edge of the integration Integral ( \a a) and last element the upper value.

```
double Integral(double a, double b)
``` evaluate using cached function

evaluate the Integral over the defined interval (a,b) using the function previously set with GSLIntegrator::SetFunction method
@param a lower value of the integration interval
@param b upper value of the integration interval

```
double Integral( )
```evaluate the Integral over the infinite interval (-inf,+inf) using the function previously set with GSLIntegrator::SetFunction method.

```
double IntegralUp(double a)
```evaluate the Integral of a function f over the semi-infinite interval (a,+inf) using the function previously set with GSLIntegrator::SetFunction method.
@param a lower value of the integration interval

```
double IntegralLow(double b)
```evaluate the Integral of a function f over the over the semi-infinite interval (-inf,b) using the function previously set with GSLIntegrator::SetFunction method.
@param b upper value of the integration interval

```
double Integral( const std::vector<double> & pts)
```evaluate the Integral over the defined interval (a,b) using the function previously set with GSLIntegrator::SetFunction method. The function has known singular points.
@param pts vector containing both the function singular points and the lower/upper edges of the interval. The vector must have as first element the lower edge of the integration Integral ( \a a) and last element the upper value.

```
double Integral(ROOT::Math::GSLFuncPointer f, void* p, double a, double b)
``` evaluate using free function pointer (same GSL signature)

signature for function pointers used by GSL

typedef double ( * GSLFuncPointer ) ( double, void * );

evaluate the Integral of  of a function f over the defined interval (a,b) passing a free function pointer
The integration function must be a free function and have a signature consistent with GSL functions:

<em>double my_function ( double x, void * p ) { ...... } </em>

This method is the most efficient since no internal adapter to GSL function is created.
@param f pointer to the integration function
@param p pointer to the Parameters of the function
@param a lower value of the integration interval
@param b upper value of the integration interval

```
double Integral(GSLFuncPointer f, void * p)
```evaluate the Integral  of a function f over the infinite interval (-inf,+inf) passing a free function pointer

```
double IntegralUp(ROOT::Math::GSLFuncPointer f, void* p, double a)
```evaluate the Integral of a function f over the semi-infinite interval (a,+inf) passing a free function pointer

```
double IntegralLow(ROOT::Math::GSLFuncPointer f, void* p, double b)
```evaluate the Integral of a function f over the over the semi-infinite interval (-inf,b) passing a free function pointer

```
double Integral(GSLFuncPointer f, void * p, const std::vector<double> & pts)
```evaluate the Integral of a function f with knows singular points over the over a defined interval passing a free function pointer

```
double Result()
```return  the Result of the last Integral calculation

```
double Error()
```return the estimate of the absolute Error of the last Integral calculation

```
int Status()
```return the Error Status of the last Integral calculation

```
void SetRelTolerance(double relTolerance)
``` setter for control Parameters  (getters are not needed so far )

set the desired relative Error

```
void SetAbsTolerance(double absTolerance)
```set the desired absolute Error

```
void SetIntegrationRule(ROOT::Math::Integration::GKRule )
```set the integration rule (Gauss-Kronrod rule).
The possible rules are defined in the Integration::GKRule enumeration.
The integration rule can be modified only for ADAPTIVE type integrations

```
bool CheckFunction()
``` internal method to check validity of GSL function pointer
```

Last update: root/mathmore:\$Id: GSLIntegrator.h 21503 2007-12-19 17:34:54Z moneta \$
Copyright (c) 2004 ROOT Foundation, CERN/PH-SFT *

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