cAffineMatrixFunction< DataType > Class Template Reference

Base class for affine matrix functions of one parameter. More...

#include <c_affine_matrix_function.h>

Inheritance diagram for cAffineMatrixFunction< DataType >:

Collaboration diagram for cAffineMatrixFunction< DataType >:

Public Member Functions
	cAffineMatrixFunction ()
	Constructor.
virtual	~cAffineMatrixFunction ()
	Virtual destructor.
virtual void	set_symmetry (FlagType symmetric)=0
DataType	get_eigenvalue (const DataType *known_parameters, const DataType known_eigenvalue, const DataType *inquiry_parameters) const
	This function defines an analytic relationship between a given set of parameters and the corresponding eigenvalue of the operator. Namely, given a set of parameters and a known eigenvalue of the operator for that specific set of parameters, this function obtains the eigenvalue of the operator for an other given set of parameters.
Public Member Functions inherited from cLinearOperator< DataType >
	cLinearOperator ()
	Default constructor.
virtual	~cLinearOperator ()
	Destructor.
void	set_parameters (DataType *parameters_)
	Sets the scalar parameter this->parameters. Parameter is initialized to NULL. However, before calling dot or transpose_dot functions, the parameters must be set.
virtual void	dot (const DataType *vector, DataType *product)=0
virtual void	transpose_dot (const DataType *vector, DataType *product)=0
Public Member Functions inherited from cLinearOperatorBase
	cLinearOperatorBase ()
	Default constructor.
	cLinearOperatorBase (const LongIndexType num_rows_, const LongIndexType num_columns_)
	Constructor with setting num_rows and num_columns.
virtual	~cLinearOperatorBase ()
	Destructor.
LongIndexType	get_num_rows () const
	Returns the number of rows of the matrix.
LongIndexType	get_num_columns () const
	Returns the number of columns of the matrix.
IndexType	get_num_parameters () const
	Returns the number of parameters of the linear operator.
FlagType	is_eigenvalue_relation_known () const
	Returns a flag that determines whether a relation between the parameters of the operator and its eigenvalue(s) is known.

Protected Member Functions
void	_add_scaled_vector (const DataType *input_vector, const LongIndexType vector_size, const DataType scale, DataType *output_vector) const
	Performs the operation \( \boldsymbol{c} = \boldsymbol{c} + \alpha \boldsymbol{b} \), where \( \boldsymbol{b} \) is an input vector scaled by \( \alpha \) and \( \boldsymbol{c} \) it the output vector.

Protected Attributes
bool	B_is_identity
Protected Attributes inherited from cLinearOperator< DataType >
DataType *	parameters
Protected Attributes inherited from cLinearOperatorBase
const LongIndexType	num_rows
const LongIndexType	num_columns
FlagType	eigenvalue_relation_known
IndexType	num_parameters

Detailed Description

template<typename DataType>
class cAffineMatrixFunction< DataType >

Base class for affine matrix functions of one parameter.

The cAffineMatrixFunction holds a two two-dimensional dense matrices \( \mathbf{A} \) and \( \mathbf{B} \). The affine matrix function with the parameter \( t \) is defined by:

\[ t \mapsto \mathbf{A} + t \mathbf{B}. \]

This operoator can perofrom matrix-vector product and transposed matrix-vector product.

Note

The prefix c in this class's name (and its derivatves), stands for the cpp code, intrast to the cu prefix, which stands for the cuda code. Most derived classes have a cuda counterpart.

See also

cMatrix, cDenseAffineMatricFunction, cCSRAffineMatrixFunction, cCSCAffineMatrixFunction, cLinearOperator, cuAffineMatrixFunction

Definition at line 55 of file c_affine_matrix_function.h.

Constructor & Destructor Documentation

cAffineMatrixFunction()

template<typename DataType >

cAffineMatrixFunction< DataType >::cAffineMatrixFunction

(

)

Constructor.

Definition at line 29 of file c_affine_matrix_function.cpp.

                                                      :
    B_is_identity(false)
{
    // This class has one parameter that is t in A+tB
    this->num_parameters = 1;
}

References cLinearOperatorBase::num_parameters.

~cAffineMatrixFunction()

template<typename DataType >

cAffineMatrixFunction< DataType >::~cAffineMatrixFunction ( )

virtual

Virtual destructor.

Definition at line 45 of file c_affine_matrix_function.cpp.

{
}

Member Function Documentation

_add_scaled_vector()

template<typename DataType >

void cAffineMatrixFunction< DataType >::_add_scaled_vector ( const DataType *  input_vector, const LongIndexType  vector_size, const DataType  scale, DataType *  output_vector  ) const

protected

Performs the operation \( \boldsymbol{c} = \boldsymbol{c} + \alpha \boldsymbol{b} \), where \( \boldsymbol{b} \) is an input vector scaled by \( \alpha \) and \( \boldsymbol{c} \) it the output vector.

Parameters

[in]	input_vector	The input 1D vector of size vector_size.
[in]	vector_size	The size of both input_vector and output_vector
[in]	scale	The scalar scale at whch the input vector is multiplied by.
[in,out]	output_vector	The output 1D vector of size vector_size. This array will be written in-place.

Definition at line 130 of file c_affine_matrix_function.cpp.

{
    // Subtracting two vectors with minus scale sign, which is adding.
    cVectorOperations<DataType>::subtract_scaled_vector(
            input_vector, vector_size, -scale, output_vector);
}

References cVectorOperations< DataType >::subtract_scaled_vector().

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get_eigenvalue()

template<typename DataType >

DataType cAffineMatrixFunction< DataType >::get_eigenvalue ( const DataType *  known_parameters, const DataType  known_eigenvalue, const DataType *  inquiry_parameters  ) const

virtual

This function defines an analytic relationship between a given set of parameters and the corresponding eigenvalue of the operator. Namely, given a set of parameters and a known eigenvalue of the operator for that specific set of parameters, this function obtains the eigenvalue of the operator for an other given set of parameters.

A relation between eigenvalue(s) and the set of parameters can be made when the matrix \( \mathbf{B} \) is equal to the identity matrix \( \mathbf{I} \), and corresponding linear operator is as follows:

\[ \mathbf{A}(t) = \mathbf{A} + t \mathbf{I} \]

Then, the eigenvalues \( \lambda \) of the operator is

\[ \lambda(\mathbf{A}(t)) = \lambda(\mathbf{A}) + t. \]

Thus, by knowing the eigenvalue \( \lambda_{t_0} \) at the known parameter \( t_0 \), the eigenvalue \( \lambda_{t} \) at the inquiry parameter \( t \) can be obtained.

Parameters

[in]	known_parameters	A set of parameters of the operator where the corresponding eigenvalue of the parameter is known for.
[in]	known_eigenvalue	The known eigenvalue of the operator for the known parameters.
[in]	inquiry_parameters	A set of inquiry parameters of the operator where the corresponding eigenvalue of the operator is sought.

Returns

The eigenvalue of the operator corresponding the inquiry parameters.

Implements cLinearOperator< DataType >.

Definition at line 92 of file c_affine_matrix_function.cpp.

{
    assert((this->eigenvalue_relation_known == 1) && \
            "An eigenvalue relation is not known. This function should be "
            "called only when the matrix B is a scalar multiple of the "
            "identity matrix");
 
    // Shift the eigenvalue by the parameter
    DataType inquiry_eigenvalue = \
        known_eigenvalue - known_parameters[0] + inquiry_parameters[0];
 
    return inquiry_eigenvalue;
}

set_symmetry()

template<typename DataType >

virtual void cAffineMatrixFunction< DataType >::set_symmetry ( FlagType  symmetric )

pure virtual

Implements cLinearOperatorBase.

Implemented in cCSCAffineMatrixFunction< DataType >, cCSRAffineMatrixFunction< DataType >, and cDenseAffineMatrixFunction< DataType >.

Member Data Documentation

B_is_identity

template<typename DataType >

bool cAffineMatrixFunction< DataType >::B_is_identity

protected

Definition at line 81 of file c_affine_matrix_function.h.

Referenced by cCSCAffineMatrixFunction< DataType >::cCSCAffineMatrixFunction(), cCSCAffineMatrixFunction< DataType >::cCSCAffineMatrixFunction(), cCSRAffineMatrixFunction< DataType >::cCSRAffineMatrixFunction(), cCSRAffineMatrixFunction< DataType >::cCSRAffineMatrixFunction(), cDenseAffineMatrixFunction< DataType >::cDenseAffineMatrixFunction(), and cDenseAffineMatrixFunction< DataType >::cDenseAffineMatrixFunction().

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

• /home/runner/work/imate/imate/imate/_c_linear_operator/c_affine_matrix_function.h
• /home/runner/work/imate/imate/imate/_c_linear_operator/c_affine_matrix_function.cpp