dg::Simpsons< ContainerType > Struct Template Reference

Time integration based on Simpson's rule. More...

Public Types
using	value_type = get_value_type<ContainerType>
	the value type of the time variable (float or double)
using	container_type = ContainerType
	the type of the vector class in use

Public Member Functions
	Simpsons (unsigned order=3)
	Set integration order without initializing values.
void	set_order (unsigned order)
	Set integration order without initializing values.
unsigned	get_order () const
	Access current integration order.
void	init (value_type t0, const ContainerType &u0)
	Initialize the left-side boundary of the integration.
void	flush ()
	Reset the integral to zero and the last (t,u) pair in the add function as the new left-side.
void	add (value_type t_new, const ContainerType &u_new)
	Add a new (t,u) pair to the time integral.
const ContainerType &	get_integral () const
	Access the current value of the time integral.
std::array< value_type, 2 >	get_boundaries () const
	Access the left and right boundary in time.

Detailed Description

template<class ContainerType>
struct dg::Simpsons< ContainerType >

Time integration based on Simpson's rule.

The intention of this class is to provide a means to continuously integrate a sample of \(( t_i, u_i)\) pairs that become available one after the other (e.g. from the integration of an ODE) and approximate

\[ \int_{t_0}^T u(t) dt \]

Note

The algorithm simply integrates the Lagrange-polynomial through up to three data points. For equidistant Data points this equals either the Trapezoidal (linear) or the Simpson's rule (quadratic)

See also

For an explanation of Simpson's rule: https://en.wikipedia.org/wiki/Simpson%27s_rule

The class works by first calling the init function to set the left-side boundary and then adding values as they become available. Calling the flush member resets the integral to 0 and the right boundary as the new left boundary

        // Construct a list of data points to integrate
        dg::Grid1d g1d( 0, M_PI/2., 3, 20 );
        dg::HVec times = dg::evaluate( dg::cooX1d, g1d);
        dg::HVec values = dg::evaluate( cos, g1d);
 
        dg::Simpsons<double> simpsons;
 
        //Init the left side boundary
        simpsons.init( 0., 1.);
 
        //Now add (time, value) pairs to the integral
        for ( unsigned i=0; i<g1d.size(); i++)
            simpsons.add( times[i], values[i]);
 
        //Add a last point since the dg grid is cell-centered
        simpsons.add( M_PI/2., 0.);
 
        //Ask for the integral
        double integral = simpsons.get_integral();
        INFO( "Error Simpsons is "<<fabs(integral-1.));
        CHECK( fabs( integral - 1.) < 1e-8);
 
        std::array<double,2> boundaries = simpsons.get_boundaries();
        INFO( "Integrated from "<<boundaries[0]<<" (0) to "<<boundaries[1]<<" ("<<M_PI/2.<<")");
        CHECK( boundaries[0] == 0);
        CHECK( boundaries[1] == M_PI/2.);

Template Parameters

ContainerType

Any class for which a specialization of TensorTraits exists and which fulfills the requirements of the there defined data and execution policies derived from AnyVectorTag and AnyPolicyTag. Among others dg::HVec (serial), dg::DVec (cuda / omp), dg::MHVec (mpi + serial) or dg::MDVec (mpi + cuda / omp) std::vector<dg::DVec> (vector of shared device vectors), std::array<double, 4> (array of 4 doubles) or std::map < std::string, dg::DVec> ( a map of named vectors) double (scalar) and other primitive types ... If there are several ContainerTypes in the argument list, then TensorTraits must exist for all of them

See also

See The dg dispatch system for a detailed explanation of our type dispatch system

Member Typedef Documentation

container_type

template<class ContainerType >

using dg::Simpsons< ContainerType >::container_type = ContainerType

the type of the vector class in use

value_type

template<class ContainerType >

using dg::Simpsons< ContainerType >::value_type = get_value_type<ContainerType>

the value type of the time variable (float or double)

Constructor & Destructor Documentation

Simpsons()

template<class ContainerType >

dg::Simpsons< ContainerType >::Simpsons ( unsigned order = 3 )

inline

Set integration order without initializing values.

Parameters

order

number of vectors to use for integration. Choose 2 (linear) or 3 (parabola) integration.

Member Function Documentation

add()

template<class ContainerType >

void dg::Simpsons< ContainerType >::add ( value_type t_new, const ContainerType & u_new )

inline

Add a new (t,u) pair to the time integral.

The times in subsequent calls must strictly increase

Parameters

t_new	time (must be strictly larger than in the previous call)
u_new	value (must have the same size as u0 in the init function)

Attention

the init function must be called before you can add values to the integral

flush()

template<class ContainerType >

void dg::Simpsons< ContainerType >::flush ( )

inline

Reset the integral to zero and the last (t,u) pair in the add function as the new left-side.

get_boundaries()

template<class ContainerType >

std::array< value_type, 2 > dg::Simpsons< ContainerType >::get_boundaries ( ) const

inline

Access the left and right boundary in time.

associated with the current value of the integral

Returns

the current integral boundaries

get_integral()

template<class ContainerType >

const ContainerType & dg::Simpsons< ContainerType >::get_integral ( ) const

inline

Access the current value of the time integral.

Returns

the current integral

get_order()

template<class ContainerType >

unsigned dg::Simpsons< ContainerType >::get_order ( ) const

inline

Access current integration order.

init()

template<class ContainerType >

void dg::Simpsons< ContainerType >::init ( value_type t0, const ContainerType & u0 )

inline

Initialize the left-side boundary of the integration.

Parameters

t0	left-side time
u0	left-side value

Note

The integral itself is initialized to zero

set_order()

template<class ContainerType >

void dg::Simpsons< ContainerType >::set_order ( unsigned order )

inline

Set integration order without initializing values.

Parameters

order

number of vectors to use for integration. Choose 2 (linear) or 3 (parabola) integration.

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

• simpsons.h