Implements the Up/Down scheme with two dimensions with special operations: i,j. More...

#include <UpDownTwoOpDims.hpp>

Inheritance diagram for sgpp::pde::UpDownTwoOpDims:

Public Member Functions
virtual void	mult (sgpp::base::DataVector &alpha, sgpp::base::DataVector &result)
	starts the Multiplication with the matrix More...

void	multParallelBuildingBlock (sgpp::base::DataVector &alpha, sgpp::base::DataVector &result, size_t operationDimOne, size_t operationDimTwo)
	this functions provides the same functionality as the normal mult routine. More...

	UpDownTwoOpDims (sgpp::base::GridStorage *storage, sgpp::base::DataMatrix &coef)
	Constructor. More...

	UpDownTwoOpDims (sgpp::base::GridStorage *storage)
	Constructor. More...

virtual	~UpDownTwoOpDims ()
	Destructor. More...

Public Member Functions inherited from sgpp::base::OperationMatrix
	OperationMatrix ()
	Constructor. More...

virtual	~OperationMatrix ()
	Destructor. More...

Protected Types
typedef sgpp::base::GridStorage::grid_iterator	grid_iterator

Protected Member Functions
virtual void	down (sgpp::base::DataVector &alpha, sgpp::base::DataVector &result, size_t dim)=0
	Down-step in dimension dim for \((\phi_i(x),\phi_j(x))_{L_2}\). More...

virtual void	downOpDimOne (sgpp::base::DataVector &alpha, sgpp::base::DataVector &result, size_t dim)=0
	1D down if the current dim is equal to i More...

virtual void	downOpDimOneAndOpDimTwo (sgpp::base::DataVector &alpha, sgpp::base::DataVector &result, size_t dim)=0
	1D down, if the current dim is equal to i and j More...

virtual void	downOpDimTwo (sgpp::base::DataVector &alpha, sgpp::base::DataVector &result, size_t dim)=0
	1D down if the current dim is equal to j More...

void	specialOpOne (sgpp::base::DataVector &alpha, sgpp::base::DataVector &result, size_t dim, size_t op_dim_one, size_t op_dim_two)
	All calculations for gradient, parallel version using OpenMP 3. More...

void	specialOpOneAndOpTwo (sgpp::base::DataVector &alpha, sgpp::base::DataVector &result, size_t dim, size_t op_dim_one, size_t op_dim_two)
	if the current dimension is equal to the both special operation dimensions More...

void	specialOpTwo (sgpp::base::DataVector &alpha, sgpp::base::DataVector &result, size_t dim, size_t op_dim_one, size_t op_dim_two)
	All calculations for gradient, Part 2, parallel version using OpenMP 3. More...

virtual void	up (sgpp::base::DataVector &alpha, sgpp::base::DataVector &result, size_t dim)=0
	Up-step in dimension dim for \((\phi_i(x),\phi_j(x))_{L_2}\). More...

void	updown (sgpp::base::DataVector &alpha, sgpp::base::DataVector &result, size_t dim, size_t op_dim_one, size_t op_dim_two)
	Recursive procedure for updown, parallel version using OpenMP 3. More...

virtual void	upOpDimOne (sgpp::base::DataVector &alpha, sgpp::base::DataVector &result, size_t dim)=0
	1D up if the current dim is equal to i More...

virtual void	upOpDimOneAndOpDimTwo (sgpp::base::DataVector &alpha, sgpp::base::DataVector &result, size_t dim)=0
	1D up, if the current dim is equal to i and j More...

virtual void	upOpDimTwo (sgpp::base::DataVector &alpha, sgpp::base::DataVector &result, size_t dim)=0
	1D up if the current dim is equal to j More...

Protected Attributes
const std::vector< size_t >	algoDims
	algorithmic dimensions, operator is applied in this dimensions More...

sgpp::base::DataMatrix *	coefs
	Pointer to the coefficients of this bilinear form. More...

const size_t	numAlgoDims_
	number of algorithmic dimensions More...

sgpp::base::GridStorage *	storage
	Pointer to the grid's storage object. More...

Static Protected Attributes
static const size_t	maxParallelDims_ = TASKS_PARALLEL_UPDOWN
	max number of parallel stages (dimension recursive calls) More...

Detailed Description

Implements the Up/Down scheme with two dimensions with special operations: i,j.

Parallelization with OpenMP 2 / 3 is supported!

Only symmetric operations are support –> only the "left lower triangular matrix", i <= j, is calculated, please keep that in mind when designing the coefficient vector: the non-diagonal elements must be multiplied by 2 before executing this Up/down scheme!

Member Typedef Documentation

◆ grid_iterator

typedef sgpp::base::GridStorage::grid_iterator sgpp::pde::UpDownTwoOpDims::grid_iterator

protected

Constructor & Destructor Documentation

◆ UpDownTwoOpDims() [1/2]

sgpp::pde::UpDownTwoOpDims::UpDownTwoOpDims	(	sgpp::base::GridStorage *	storage,
		sgpp::base::DataMatrix &	coef
	)

Constructor.

Parameters

storage	the grid's sgpp::base::GridStorage object
coef	vector that contains the constant coefficients of this operation

◆ UpDownTwoOpDims() [2/2]

sgpp::pde::UpDownTwoOpDims::UpDownTwoOpDims ( sgpp::base::GridStorage * storage )

explicit

Constructor.

Parameters

storage the grid's sgpp::base::GridStorage object

◆ ~UpDownTwoOpDims()

sgpp::pde::UpDownTwoOpDims::~UpDownTwoOpDims ( )

virtual

Destructor.

Member Function Documentation

◆ down()

virtual void sgpp::pde::UpDownTwoOpDims::down	(	sgpp::base::DataVector &	alpha,
		sgpp::base::DataVector &	result,
		size_t	dim
	)

protectedpure virtual

Down-step in dimension dim for \((\phi_i(x),\phi_j(x))_{L_2}\).

Applies the down-part of the one-dimensional mass matrix in one dimension. Computes

\[\int_{x=0}^1 \phi_i(x) \sum_{j, l_i\geq l_j} \alpha_j \phi_j(x) dx.\]

Parameters

dim	dimension in which to apply the down-part
alpha	vector of coefficients
result	vector to store the results in

Referenced by updown().

◆ downOpDimOne()

virtual void sgpp::pde::UpDownTwoOpDims::downOpDimOne	(	sgpp::base::DataVector &	alpha,
		sgpp::base::DataVector &	result,
		size_t	dim
	)

protectedpure virtual

1D down if the current dim is equal to i

Parameters

alpha	the coefficients of the gridpoints
result	vector with the result of this operation
dim	the dimension in that down-Gradient is applied

Referenced by specialOpOne().

◆ downOpDimOneAndOpDimTwo()

virtual void sgpp::pde::UpDownTwoOpDims::downOpDimOneAndOpDimTwo	(	sgpp::base::DataVector &	alpha,
		sgpp::base::DataVector &	result,
		size_t	dim
	)

protectedpure virtual

1D down, if the current dim is equal to i and j

Parameters

alpha	the coefficients of the gridpoints
result	vector with the result of this operation
dim	the dimension in that down-Gradient is applied

Referenced by specialOpOneAndOpTwo().

◆ downOpDimTwo()

virtual void sgpp::pde::UpDownTwoOpDims::downOpDimTwo	(	sgpp::base::DataVector &	alpha,
		sgpp::base::DataVector &	result,
		size_t	dim
	)

protectedpure virtual

1D down if the current dim is equal to j

Parameters

alpha	the coefficients of the gridpoints
result	vector with the result of this operation
dim	the dimension in that down-Gradient is applied

Referenced by specialOpTwo().

◆ mult()

void sgpp::pde::UpDownTwoOpDims::mult	(	sgpp::base::DataVector &	alpha,
		sgpp::base::DataVector &	result
	)

virtual

starts the Multiplication with the matrix

Parameters

alpha	DataVector that contains the ansatzfunctions' coefficients
result	DataVector into which the result of the Laplace operation is stored

Implements sgpp::base::OperationMatrix.

References sgpp::base::DataVector::add(), sgpp::base::DataVector::axpy(), coefs, sgpp::base::DataMatrix::get(), sgpp::base::DataVector::getSize(), python.statsfileInfo::i, python.utils.statsfile2gnuplot::j, numAlgoDims_, sgpp::base::DataVector::setAll(), and updown().

◆ multParallelBuildingBlock()

void sgpp::pde::UpDownTwoOpDims::multParallelBuildingBlock	(	sgpp::base::DataVector &	alpha,
		sgpp::base::DataVector &	result,
		size_t	operationDimOne,
		size_t	operationDimTwo
	)

this functions provides the same functionality as the normal mult routine.

However, it doesn't set up an OpenMP task initialization as the mult routine. This method has to be called within a OpenMP task parallelized region.

Using this function is useful in the following case: Assuming the solver of a certain Equation requires several operators in the space discretization (e.g. Black Scholes Equations) this method can be used to parallelize their calculation which might result in a better parallel efficiency on systems with 4 or more cores hence fewer barriers are needed.

For a full calculation of this operator, in mult serval number of up/downs are needed. This number is equal to the square of the number of the grid's dimensions. All different steps can be executed in parallel. Here only one up/Down is executed, identified by its special dimensions.

Attention: A symmetric operator is assumed: This method only start a calculation if operationDimTwo is less or equal operationDimOne

Parameters

alpha	vector of coefficients
result	vector to store the results in
operationDimOne	Dimension in which the first special operator is applied
operationDimTwo	Dimension in which the second special operator is applied

References sgpp::base::DataVector::add(), sgpp::base::DataVector::axpy(), coefs, sgpp::base::DataMatrix::get(), sgpp::base::DataVector::getSize(), numAlgoDims_, sgpp::base::DataVector::setAll(), and updown().

◆ specialOpOne()

void sgpp::pde::UpDownTwoOpDims::specialOpOne	(	sgpp::base::DataVector &	alpha,
		sgpp::base::DataVector &	result,
		size_t	dim,
		size_t	op_dim_one,
		size_t	op_dim_two
	)

protected

All calculations for gradient, parallel version using OpenMP 3.

Parameters

alpha	the coefficients of the grid points
result	the result of the operations
dim	the current dimension in the recursion
op_dim_one	the dimension in which to use the first gradient
op_dim_two	the dimension in which to use the second gradient

References sgpp::base::DataVector::add(), algoDims, downOpDimOne(), sgpp::base::DataVector::getSize(), maxParallelDims_, numAlgoDims_, updown(), and upOpDimOne().

Referenced by updown().

◆ specialOpOneAndOpTwo()

void sgpp::pde::UpDownTwoOpDims::specialOpOneAndOpTwo	(	sgpp::base::DataVector &	alpha,
		sgpp::base::DataVector &	result,
		size_t	dim,
		size_t	op_dim_one,
		size_t	op_dim_two
	)

protected

if the current dimension is equal to the both special operation dimensions

Parameters

alpha	the coefficients of the grid points
result	the result of the operations
dim	the current dimension in the recursion
op_dim_one	the dimension in which to use the first gradient
op_dim_two	the dimension in which to use the second gradient

References sgpp::base::DataVector::add(), algoDims, downOpDimOneAndOpDimTwo(), sgpp::base::DataVector::getSize(), maxParallelDims_, numAlgoDims_, updown(), and upOpDimOneAndOpDimTwo().

Referenced by updown().

◆ specialOpTwo()

void sgpp::pde::UpDownTwoOpDims::specialOpTwo	(	sgpp::base::DataVector &	alpha,
		sgpp::base::DataVector &	result,
		size_t	dim,
		size_t	op_dim_one,
		size_t	op_dim_two
	)

protected

All calculations for gradient, Part 2, parallel version using OpenMP 3.

Parameters

alpha	the coefficients of the grid points
result	the result of the operations
dim	the current dimension in the recursion
op_dim_one	the dimension in which to use the first gradient
op_dim_two	the dimension in which to use the second gradient

References sgpp::base::DataVector::add(), algoDims, downOpDimTwo(), sgpp::base::DataVector::getSize(), maxParallelDims_, numAlgoDims_, updown(), and upOpDimTwo().

Referenced by updown().

◆ up()

virtual void sgpp::pde::UpDownTwoOpDims::up	(	sgpp::base::DataVector &	alpha,
		sgpp::base::DataVector &	result,
		size_t	dim
	)

protectedpure virtual

Up-step in dimension dim for \((\phi_i(x),\phi_j(x))_{L_2}\).

Applies the up-part of the one-dimensional mass matrix in one dimension. Computes

\[\int_{x=0}^1 \phi_i(x) \sum_{j, l_i < l_j} \alpha_j \phi_j(x) dx.\]

Parameters

dim	dimension in which to apply the up-part
alpha	vector of coefficients
result	vector to store the results in

Referenced by updown().

◆ updown()

void sgpp::pde::UpDownTwoOpDims::updown	(	sgpp::base::DataVector &	alpha,
		sgpp::base::DataVector &	result,
		size_t	dim,
		size_t	op_dim_one,
		size_t	op_dim_two
	)

protected

Recursive procedure for updown, parallel version using OpenMP 3.

Parameters

dim	the current dimension
op_dim_one	the dimension in which to use the first gradient
op_dim_two	the dimension in which to use the second gradient
alpha	vector of coefficients
result	vector to store the results in

References sgpp::base::DataVector::add(), algoDims, down(), sgpp::base::DataVector::getSize(), maxParallelDims_, numAlgoDims_, specialOpOne(), specialOpOneAndOpTwo(), specialOpTwo(), and up().

Referenced by mult(), multParallelBuildingBlock(), specialOpOne(), specialOpOneAndOpTwo(), and specialOpTwo().

◆ upOpDimOne()

virtual void sgpp::pde::UpDownTwoOpDims::upOpDimOne	(	sgpp::base::DataVector &	alpha,
		sgpp::base::DataVector &	result,
		size_t	dim
	)

protectedpure virtual

1D up if the current dim is equal to i

Parameters

alpha	the coefficients of the gridpoints
result	vector with the result of this operation
dim	the dimension in that up-Gradient is applied

Referenced by specialOpOne().

◆ upOpDimOneAndOpDimTwo()

virtual void sgpp::pde::UpDownTwoOpDims::upOpDimOneAndOpDimTwo	(	sgpp::base::DataVector &	alpha,
		sgpp::base::DataVector &	result,
		size_t	dim
	)

protectedpure virtual

1D up, if the current dim is equal to i and j

Parameters

alpha	the coefficients of the gridpoints
result	vector with the result of this operation
dim	the dimension in that up-Gradient is applied

Referenced by specialOpOneAndOpTwo().

◆ upOpDimTwo()

virtual void sgpp::pde::UpDownTwoOpDims::upOpDimTwo	(	sgpp::base::DataVector &	alpha,
		sgpp::base::DataVector &	result,
		size_t	dim
	)

protectedpure virtual

1D up if the current dim is equal to j

Parameters

alpha	the coefficients of the gridpoints
result	vector with the result of this operation
dim	the dimension in that up-Gradient is applied

Referenced by specialOpTwo().

Member Data Documentation

◆ algoDims

const std::vector<size_t> sgpp::pde::UpDownTwoOpDims::algoDims

protected

algorithmic dimensions, operator is applied in this dimensions

Referenced by specialOpOne(), specialOpOneAndOpTwo(), specialOpTwo(), and updown().

◆ coefs

sgpp::base::DataMatrix* sgpp::pde::UpDownTwoOpDims::coefs

protected

Pointer to the coefficients of this bilinear form.

Referenced by mult(), and multParallelBuildingBlock().

◆ maxParallelDims_

const size_t sgpp::pde::UpDownTwoOpDims::maxParallelDims_ = TASKS_PARALLEL_UPDOWN

staticprotected

max number of parallel stages (dimension recursive calls)

Referenced by specialOpOne(), specialOpOneAndOpTwo(), specialOpTwo(), and updown().

◆ numAlgoDims_

const size_t sgpp::pde::UpDownTwoOpDims::numAlgoDims_

protected

number of algorithmic dimensions

Referenced by mult(), multParallelBuildingBlock(), specialOpOne(), specialOpOneAndOpTwo(), specialOpTwo(), and updown().

◆ storage

sgpp::base::GridStorage* sgpp::pde::UpDownTwoOpDims::storage

protected

Pointer to the grid's storage object.

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

pde/src/sgpp/pde/algorithm/UpDownTwoOpDims.hpp
pde/src/sgpp/pde/algorithm/UpDownTwoOpDims.cpp

Public Member Functions

Protected Types

Protected Member Functions

Protected Attributes

Static Protected Attributes

Detailed Description

Member Typedef Documentation

◆ grid_iterator

Constructor & Destructor Documentation

◆ UpDownTwoOpDims() [1/2]

◆ UpDownTwoOpDims() [2/2]

◆ ~UpDownTwoOpDims()

Member Function Documentation

◆ down()

◆ downOpDimOne()

◆ downOpDimOneAndOpDimTwo()

◆ downOpDimTwo()

◆ mult()

◆ multParallelBuildingBlock()

◆ specialOpOne()

◆ specialOpOneAndOpTwo()

◆ specialOpTwo()

◆ up()

◆ updown()

◆ upOpDimOne()

◆ upOpDimOneAndOpDimTwo()

◆ upOpDimTwo()

Member Data Documentation

◆ algoDims

◆ coefs

◆ maxParallelDims_

◆ numAlgoDims_

◆ storage