cDenseAffineMatrixFunction< DataType > Class Template Reference

Container for dense affine matrix functions of one parameter. More...

#include <c_dense_affine_matrix_function.h>

Inheritance diagram for cDenseAffineMatrixFunction< DataType >:

Collaboration diagram for cDenseAffineMatrixFunction< DataType >:

Public Member Functions
	cDenseAffineMatrixFunction (const DataType *A_, const LongIndexType num_rows_, const LongIndexType num_columns_, const FlagType A_is_row_major_, const FlagType A_is_symmetric_)
	Default constructor.
	cDenseAffineMatrixFunction (const DataType *A_, const LongIndexType num_rows_, const LongIndexType num_columns_, const FlagType A_is_row_major_, const FlagType A_is_symmetric_, const DataType *B_, const FlagType B_is_row_major_, const FlagType B_is_symmetric_)
	Constructor.
virtual	~cDenseAffineMatrixFunction ()
	Destructor.
virtual void	set_symmetry (const FlagType symmetric)
	Specify whether the matrices are symmetic or non-symmetric.
virtual void	dot (const DataType *vector, DataType *product)
	Matrix vector product.
virtual void	transpose_dot (const DataType *vector, DataType *product)
	Matrix vector product written in place.
Public Member Functions inherited from cAffineMatrixFunction< DataType >
	cAffineMatrixFunction ()
	Constructor.
virtual	~cAffineMatrixFunction ()
	Virtual destructor.
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.
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 Attributes
cDenseMatrix< DataType >	A
cDenseMatrix< DataType >	B
Protected Attributes inherited from cAffineMatrixFunction< DataType >
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

Additional Inherited Members
Protected Member Functions inherited from cAffineMatrixFunction< DataType >
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.

Detailed Description

template<typename DataType>
class cDenseAffineMatrixFunction< DataType >

Container for dense affine matrix functions of one parameter.

The cDenseAffineMatrixFunction contains two-dimensional dense matrices A and B. This operoator can perofrom matrix-vector product and transposed matrix-vector product.

See also

cAffineMatrixFunction, cCSRMatrixFunction, cCSCMatrixFunction, cDenseMatrix, cuDenseAffineMatrixFunction

Definition at line 45 of file c_dense_affine_matrix_function.h.

Constructor & Destructor Documentation

cDenseAffineMatrixFunction() [1/2]

template<typename DataType >

cDenseAffineMatrixFunction< DataType >::cDenseAffineMatrixFunction	(	const DataType *	A_,
		const LongIndexType	num_rows_,
		const LongIndexType	num_columns_,
		const FlagType	A_is_row_major_,
		const FlagType	A_is_symmetric_
	)

Default constructor.

Matrix B is assumed to be the identity matrix.

Parameters

[in]	A_	1D array that represents a 2D dense array with either C (row) major ordering or Fortran (column) major ordering. The major ordering should de defined by A_is_row_major flag.
[in]	num_rows_	Number of rows of A and B
[in]	num_columns_	Number of columns of A and B
[in]	A_is_row_major_	Boolean, can be 0 or 1 as follows: If A is row major (C ordering where the last index is contiguous) this value should be 1. If A is column major (Fortran ordering where the first index is contiguous), this value should be set to 0.
[in]	A_is_symmetric_	Boolean. If A is symmetric, set this value to 1, otherwise 0.

Definition at line 48 of file c_dense_affine_matrix_function.cpp.

                                       :
 
    // Base class constructor
    cLinearOperatorBase(num_rows_, num_columns_),
 
    // Initializer list
    A(A_, num_rows_, num_columns_, A_is_row_major_, A_is_symmetric_)
{
    // This constructor is called assuming B is identity
    this->B_is_identity = true;
 
    // When B is identity, the eigenvalues of A+tB are known for any t
    this->eigenvalue_relation_known = 1;
}

References cAffineMatrixFunction< DataType >::B_is_identity, and cLinearOperatorBase::eigenvalue_relation_known.

cDenseAffineMatrixFunction() [2/2]

template<typename DataType >

cDenseAffineMatrixFunction< DataType >::cDenseAffineMatrixFunction	(	const DataType *	A_,
		const LongIndexType	num_rows_,
		const LongIndexType	num_columns_,
		const FlagType	A_is_row_major_,
		const FlagType	A_is_symmetric_,
		const DataType *	B_,
		const FlagType	B_is_row_major_,
		const FlagType	B_is_symmetric_
	)

Constructor.

Matrix B is assumed to be the identity matrix.

Parameters

[in]	A_	1D array that represents a 2D dense array with either C (row) major ordering or Fortran (column) major ordering. The major ordering should de defined by A_is_row_major flag.
[in]	num_rows_	Number of rows of A and B
[in]	num_columns_	Number of columns of A and B
[in]	A_is_row_major_	Boolean, can be 0 or 1 as follows: If A is row major (C ordering where the last index is contiguous) this value should be 1. If A is column major (Fortran ordering where the first index is contiguous), this value should be set to 0.
[in]	A_is_symmetric_	Boolean. If A is symmetric, set this value to 1, otherwise 0.
[in]	B_	1D array that represents a 2D dense array with either C (row) major ordering or Fortran (column) major ordering. The major ordering should de defined by A_is_row_major flag.
[in]	B_is_row_major_	Boolean, can be 0 or 1 as follows: If B is row major (C ordering where the last index is contiguous) this value should be 1. If B is column major (Fortran ordering where the first index is contiguous), this value should be set to 0.
[in]	B_is_symmetric_	Boolean. If B is symmetric, set this value to 1, otherwise 0.

Definition at line 109 of file c_dense_affine_matrix_function.cpp.

                                       :
 
    // Base class constructor
    cLinearOperatorBase(num_rows_, num_columns_),
 
    // Initializer list
    A(A_, num_rows_, num_columns_, A_is_row_major_, A_is_symmetric_),
    B(B_, num_rows_, num_columns_, B_is_row_major_, B_is_symmetric_)
{
    // Matrix B is assumed to be non-zero. Check if it is identity or generic
    if (this->B.is_identity_matrix())
    {
        this->B_is_identity = true;
        this->eigenvalue_relation_known = 1;
    }
}

References cDenseAffineMatrixFunction< DataType >::B, cAffineMatrixFunction< DataType >::B_is_identity, and cLinearOperatorBase::eigenvalue_relation_known.

~cDenseAffineMatrixFunction()

template<typename DataType >

cDenseAffineMatrixFunction< DataType >::~cDenseAffineMatrixFunction ( )

virtual

Destructor.

Definition at line 143 of file c_dense_affine_matrix_function.cpp.

{
}

Member Function Documentation

dot()

template<typename DataType >

void cDenseAffineMatrixFunction< DataType >::dot ( const DataType *  vector, DataType *  product  )

virtual

Matrix vector product.

Performs the matrix vector product \( \boldsymbol{y} = (\mathbf{A} + t \mathbf{B}) \boldsymbol{x} \).

Parameters

[in]	vector	A one-dimensional input vector \( \boldsymbol{x} \) with size the of the number of columns of the matrix \( \mathbf{A} \).
[out]	product	A one-dimensional output vector \( \boldsymbol{y} \) with the size of the number of rows of \( \mathbf{A} \). This vector will be overwritten.

See also

cDenseAffineMatrixFunction::transpose_dot

Implements cLinearOperator< DataType >.

Definition at line 201 of file c_dense_affine_matrix_function.cpp.

{
    // Matrix A times vector
    this->A.dot(vector, product);
    LongIndexType min_vector_size;
 
    // Matrix B times vector to be added to the product
    if (this->B_is_identity)
    {
        // Check parameter is set
        assert((this->parameters != NULL) && "Parameter is not set.");
 
        // Find minimum of the number of rows and columns
        min_vector_size = \
            (this->num_rows < this->num_columns) ? \
            this->num_rows : this->num_columns;
 
        // Adding input vector to product
        this->_add_scaled_vector(vector, min_vector_size,
                                 this->parameters[0], product);
    }
    else
    {
        // Check parameter is set
        assert((this->parameters != NULL) && "Parameter is not set.");
 
        // Adding parameter times B times input vector to the product
        this->B.dot_plus(vector, this->parameters[0], product);
    }
}

set_symmetry()

template<typename DataType >

void cDenseAffineMatrixFunction< DataType >::set_symmetry ( const FlagType  symmetric )

virtual

Specify whether the matrices are symmetic or non-symmetric.

This function overwrites the symmetry status that has been set by the constructor. Note that the symmetry status of both matrices \( \mathbf{A} \) and \( \mathbf{B} \) in the linear operator \( \mathbf{A} + t \mathbf{B} \) will be set together.

Parameters

[in]

symmetric

Boolean. If set to 1, the matrix is assumed to be symmetric. Otherwiese non-symmetric.

Implements cAffineMatrixFunction< DataType >.

Definition at line 165 of file c_dense_affine_matrix_function.cpp.

{
    if (symmetric == 1)
    {
        this->A.set_symmetry(1);
        this->B.set_symmetry(1);
    }
    else
    {
        this->A.set_symmetry(0);
        this->B.set_symmetry(0);
    }
}

References cLinearOperatorBase::set_symmetry().

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transpose_dot()

template<typename DataType >

void cDenseAffineMatrixFunction< DataType >::transpose_dot ( const DataType *  vector, DataType *  product  )

virtual

Matrix vector product written in place.

Performs the matrix vector product \( \boldsymbol{y} = (\mathbf{A} + t \mathbf{B})^{\intercal} \boldsymbol{x} \).

Parameters

[in]	vector	A one-dimensional input vector \( \boldsymbol{x} \) with size the of the number of columns of the matrix \( \mathbf{A} \).
[out]	product	A one-dimensional output vector \( \boldsymbol{y} \) with the size of the number of rows of \( \mathbf{A} \).

See also

cDenseAffineMatrixFunction::dot

Implements cLinearOperator< DataType >.

Definition at line 254 of file c_dense_affine_matrix_function.cpp.

{
    // Matrix A times vector
    this->A.transpose_dot(vector, product);
    LongIndexType min_vector_size;
 
    // Matrix B times vector to be added to the product
    if (this->B_is_identity)
    {
        // Check parameter is set
        assert((this->parameters != NULL) && "Parameter is not set.");
 
        // Find minimum of the number of rows and columns
        min_vector_size = \
            (this->num_rows < this->num_columns) ? \
            this->num_rows : this->num_columns;
 
        // Adding input vector to product
        this->_add_scaled_vector(vector, min_vector_size,
                                 this->parameters[0], product);
    }
    else
    {
        // Check parameter is set
        assert((this->parameters != NULL) && "Parameter is not set.");
 
        // Adding "parameter * B * input vector" to the product
        this->B.transpose_dot_plus(vector, this->parameters[0], product);
    }
}

Member Data Documentation

A

template<typename DataType >

cDenseMatrix<DataType> cDenseAffineMatrixFunction< DataType >::A

protected

Definition at line 82 of file c_dense_affine_matrix_function.h.

B

template<typename DataType >

cDenseMatrix<DataType> cDenseAffineMatrixFunction< DataType >::B

protected

Definition at line 83 of file c_dense_affine_matrix_function.h.

Referenced by 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_dense_affine_matrix_function.h
• /home/runner/work/imate/imate/imate/_c_linear_operator/c_dense_affine_matrix_function.cpp